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2601135 | 10.1007/s00026-009-0003-3 | In 1986 S. Sattolo introduced a simple algorithm for uniform random
generation of cyclic permutations on a fixed number of symbols. This algorithm
is very similar to the standard method for generating a random permutation, but
is less well known.
We consider both methods in a unified way, and discuss their relation with
exhaustive generation methods. We analyse several random variables associated
with the algorithms and find their grand probability generating functions,
which gives easy access to moments and limit laws.Comment: 9 page | Random and exhaustive generation of permutations and cycles | random and exhaustive generation of permutations and cycles | sattolo cyclic permutations symbols. generating permutation known. unified exhaustive methods. analyse grand generating moments | non_dup | [] |
55843001 | 10.1007/s00026-010-0056-3 | Let e be one of the following full projective embeddings of a finite dual polar space Delta of rank n >= 2: (i) The Grassmann-embedding of the symplectic dual polar space Delta congruent to DW(2n 1,q); (ii) the Grassmann-embedding of the Hermitian dual polar space Delta congruent to DH(2n-1, q(2)); (iii) the spin-embedding of the orthogonal dual polar space Delta congruent to DQ(2n, q); (iv) the spin-embedding of the orthogonal dual polar space Delta congruent to DQ(-)(2n+ 1, q). Let H-e denote the set of all hyperplanes of Delta arising from the embedding e. We give a method for constructing the hyperplanes of H-e without implementing the embedding e and discuss (possible) applications of the given construction | Direct constructions of hyperplanes of dual polar spaces arising from embeddings | direct constructions of hyperplanes of dual polar spaces arising from embeddings | projective embeddings polar delta grassmann embedding symplectic polar delta congruent grassmann embedding hermitian polar delta congruent embedding orthogonal polar delta congruent embedding orthogonal polar delta congruent hyperplanes delta arising embedding constructing hyperplanes implementing embedding | non_dup | [] |
2581367 | 10.1007/s00026-010-0057-2 | We give an in-depth study of the Tchebyshev transforms of the first and
second kind of a poset, recently discovered by Hetyei. The Tchebyshev transform
(of the first kind) preserves desirable combinatorial properties, including
Eulerianess (due to Hetyei) and EL-shellability. It is also a linear
transformation on flag vectors. When restricted to Eulerian posets, it
corresponds to the Billera, Ehrenborg and Readdy omega map of oriented
matroids. One consequence is that nonnegativity of the cd-index is maintained.
The Tchebyshev transform of the second kind is a Hopf algebra endomorphism on
the space of quasisymmetric functions QSym. It coincides with Stembridge's peak
enumerator for Eulerian posets, but differs for general posets. The complete
spectrum is determined, generalizing work of Billera, Hsiao and van
Willigenburg.
The type B quasisymmetric function of a poset is introduced. Like Ehrenborg's
classical quasisymmetric function of a poset, this map is a comodule morphism
with respect to the quasisymmetric functions QSym.
Similarities among the omega map, Ehrenborg's r-signed Birkhoff transform,
and the Tchebyshev transforms motivate a general study of chain maps. One such
occurrence, the chain map of the second kind, is a Hopf algebra endomorphism on
the quasisymmetric functions QSym and is an instance of Aguiar, Bergeron and
Sottile's result on the terminal object in the category of combinatorial Hopf
algebras. In contrast, the chain map of the first kind is both an algebra map
and a comodule endomorphism on the type B quasisymmetric functions BQSym.Comment: 33 page | The Tchebyshev transforms of the first and second kind | the tchebyshev transforms of the first and second kind | tchebyshev transforms kind poset discovered hetyei. tchebyshev transform kind preserves desirable combinatorial eulerianess hetyei shellability. flag vectors. restricted eulerian posets billera ehrenborg readdy omega oriented matroids. nonnegativity maintained. tchebyshev transform kind hopf endomorphism quasisymmetric qsym. coincides stembridge enumerator eulerian posets differs posets. generalizing billera hsiao willigenburg. quasisymmetric poset introduced. ehrenborg quasisymmetric poset comodule morphism quasisymmetric qsym. similarities omega ehrenborg signed birkhoff transform tchebyshev transforms motivate maps. occurrence kind hopf endomorphism quasisymmetric qsym aguiar bergeron sottile combinatorial hopf algebras. kind comodule endomorphism quasisymmetric | non_dup | [] |
2595124 | 10.1007/s00026-010-0063-4 | In this paper we classify the multiplicity-free skew characters of the
symmetric group. Furthermore we show that the Schubert calculus is equivalent
to that of skew characters in the following sense: If we decompose the product
of two Schubert classes we get the same as if we decompose a skew character and
replace the irreducible characters by Schubert classes of the `inverse'
partitions (Theorem 4.2).Comment: 14 pages, to appear in Annals. Comb. minor changes from v1 to v2 as
suggested by the referees, Example 3.4 inserted so numeration changed in
section | On multiplicity-free skew characters and the Schubert Calculus | on multiplicity-free skew characters and the schubert calculus | classify multiplicity skew characters group. schubert calculus skew characters decompose schubert decompose skew character replace irreducible characters schubert partitions .comment pages annals. comb. minor referees inserted numeration changed | non_dup | [] |
55802444 | 10.1007/s00026-011-0080-y | This is the third paper dealing with the classification of the dense near octagons of order (3, t). Using the partial classification of the valuations of the possible hexes obtained in [12], we are able to show that almost all such near octagons admit a big hex. Combining this with the results in [11], where we classified the dense near octagons of order (3, t) with a big hex, we get an incomplete classification for the dense near octagons of order (3, t): There are 28 known examples and a few open cases. For each open case, we have a rather detailed description of the structure of the near octagons involved | Dense near octagons with four points on each line, III | dense near octagons with four points on each line, iii | dealing dense octagons valuations hexes octagons admit hex. combining classified dense octagons incomplete dense octagons cases. octagons | non_dup | [] |
1964411 | 10.1007/s00026-011-0087-4 | It is well a known and fundamental result that the Jones polynomial can be
expressed as Potts and vertex partition functions of signed plane graphs. Here
we consider constructions of the Jones polynomial as state models of unsigned
graphs and show that the Jones polynomial of any link can be expressed as a
vertex model of an unsigned embedded graph.
In the process of deriving this result, we show that for every diagram of a
link in the 3-sphere there exists a diagram of an alternating link in a
thickened surface (and an alternating virtual link) with the same Kauffman
bracket. We also recover two recent results in the literature relating the
Jones and Bollobas-Riordan polynomials and show they arise from two different
interpretations of the same embedded graph.Comment: Minor corrections. To appear in Annals of Combinatoric | Unsigned state models for the Jones polynomial | unsigned state models for the jones polynomial | jones potts partition signed graphs. constructions jones unsigned jones unsigned embedded graph. deriving sphere alternating thickened alternating virtual kauffman bracket. recover relating jones bollobas riordan polynomials arise interpretations embedded minor corrections. annals combinatoric | non_dup | [] |
77617983 | 10.1007/s00026-011-0119-0 | Let V be a complex vector space with basis {x 1, x 2, . . . , x n } and G be a finite subgroup of GL(V). The tensor algebra T(V) over the complex is isomorphic to the polynomials in the non-commutative variables x 1, x 2, . . . , x n with complex coefficients. We want to give a combinatorial interpretation for the decomposition of T(V) into simple G-modules. In particular, we want to study the graded space of invariants in T(V) with respect to the action of G. We give a general method for decomposing the space T(V) into simple modules in terms of words in a Cayley graph of the group G. To apply the method to a particular group, we require a homomorphism from a subalgebra of the group algebra into the character algebra. In the case of G as the symmetric group, we give an example of this homomorphism from the descent algebra. When G is the dihedral group, we have a realization of the character algebra as a subalgebra of the group algebra. In those two cases, we have an interpretation for the graded dimensions and the number of free generators of the algebras of invariants in terms of those words | Words and Polynomial Invariants of Finite Groups in Non-Commutative Variables | words and polynomial invariants of finite groups in non-commutative variables | subgroup isomorphic polynomials commutative coefficients. want combinatorial decomposition modules. want graded invariants decomposing modules cayley homomorphism subalgebra character algebra. homomorphism descent algebra. dihedral realization character subalgebra algebra. graded generators algebras invariants | non_dup | [] |
2107673 | 10.1007/s00026-012-0144-7 | We provide an explicit formula for the toric $h$-contribution of each cubical
shelling component, and a new combinatorial model to prove Clara Chan's result
on the non-negativity of these contributions. Our model allows for a variant of
the Gessel-Shapiro result on the $g$-polynomial of the cubical lattice, this
variant may be shown by simple inclusion-exclusion. We establish an isomorphism
between our model and Chan's model and provide a reinterpretation in terms of
noncrossing partitions. By discovering another variant of the Gessel-Shapiro
result in the work of Denise and Simion, we find evidence that the toric
$h$-polynomials of cubes are related to the Morgan-Voyce polynomials via
Viennot's combinatorial theory of orthogonal polynomials.Comment: Minor correction | A second look at the toric h-polynomial of a cubical complex | a second look at the toric h-polynomial of a cubical complex | toric cubical shelling combinatorial clara chan negativity contributions. variant gessel shapiro cubical variant inclusion exclusion. establish isomorphism chan reinterpretation noncrossing partitions. discovering variant gessel shapiro denise simion toric polynomials cubes morgan voyce polynomials viennot combinatorial orthogonal minor | non_dup | [] |
2157121 | 10.1007/s00026-012-0172-3 | We give two contructions of sets of masks on cograssmannian permutations that
can be used in Deodhar's formula for Kazhdan-Lusztig basis elements of the
Iwahori-Hecke algebra. The constructions are respectively based on a formula of
Lascoux-Schutzenberger and its geometric interpretation by Zelevinsky. The
first construction relies on a basis of the Hecke algebra constructed from
principal lower order ideals in Bruhat order and a translation of this basis
into sets of masks. The second construction relies on an interpretation of
masks as cells of the Bott-Samelson resolution. These constructions give
distinct answers to a question of Deodhar.Comment: 43 page | Mask formulas for cograssmannian Kazhdan-Lusztig polynomials | mask formulas for cograssmannian kazhdan-lusztig polynomials | contructions masks cograssmannian permutations deodhar kazhdan lusztig iwahori hecke algebra. constructions lascoux schutzenberger geometric zelevinsky. relies hecke principal ideals bruhat translation masks. relies masks bott samelson resolution. constructions answers | non_dup | [] |
2245081 | 10.1007/s00026-013-0207-4 | The competition graph of a digraph $D$ is a (simple undirected) graph which
has the same vertex set as $D$ and has an edge between two distinct vertices
$x$ and $y$ if and only if there exists a vertex $v$ in $D$ such that $(x,v)$
and $(y,v)$ are arcs of $D$. For any graph $G$, $G$ together with sufficiently
many isolated vertices is the competition graph of some acyclic digraph. The
competition number $k(G)$ of a graph $G$ is the smallest number of such
isolated vertices. Computing the competition number of a graph is an NP-hard
problem in general and has been one of the important research problems in the
study of competition graphs. Opsut [1982] showed that the competition number of
a graph $G$ is related to the edge clique cover number $\theta_E(G)$ of the
graph $G$ via $\theta_E(G)-|V(G)|+2 \leq k(G) \leq \theta_E(G)$. We first show
that for any positive integer $m$ satisfying $2 \leq m \leq |V(G)|$, there
exists a graph $G$ with $k(G)=\theta_E(G)-|V(G)|+m$ and characterize a graph
$G$ satisfying $k(G)=\theta_E(G)$. We then focus on what we call
\emph{competitively tight graphs} $G$ which satisfy the lower bound, i.e.,
$k(G)=\theta_E(G)-|V(G)|+2$. We completely characterize the competitively tight
graphs having at most two triangles. In addition, we provide a new upper bound
for the competition number of a graph from which we derive a sufficient
condition and a necessary condition for a graph to be competitively tight.Comment: 10 pages, 2 figure | Competitively tight graphs | competitively tight graphs | competition digraph undirected arcs sufficiently competition acyclic digraph. competition smallest vertices. competition competition graphs. opsut competition clique cover theta theta theta integer satisfying theta characterize satisfying theta call emph competitively tight satisfy i.e. theta characterize competitively tight triangles. competition derive competitively pages | non_dup | [] |
32327907 | 10.1007/s00026-013-0215-4 | The well-known Rogers-Ramanujan identities have been a rich source of mathematical study over the last fifty years. In particular, Gordon’s generalization in the early 1960s led to additional work by Andrews and Bressoud in subsequent years. Unfortunately, these results lacked a certain amount of uniformity in terms of combinatorial interpretation. In this work, we provide a single combinatorial interpretation of the series sides of\ud
these generating function results by using the concept of cluster parities. This unifies the aforementioned results of Andrews and Bressoud and also allows for a strikingly broader family of q–series results to be obtained. We close the paper by proving congruences for a “degenerate case” of Bressoud’s theorem | Variations on a result of Bressoud | variations on a result of bressoud | rogers ramanujan identities mathematical fifty years. gordon’s generalization andrews bressoud years. unfortunately lacked uniformity combinatorial interpretation. combinatorial sides generating parities. unifies aforementioned andrews bressoud strikingly broader q–series obtained. proving congruences “degenerate case” bressoud’s | non_dup | [] |
78058475 | 10.1007/s00026-014-0235-8 | The s-lecture hall polytopes P [subscript s] are a class of integer polytopes defined by Savage and Schuster which are closely related to the lecture hall partitions of Eriksson and Bousquet-Mélou. We define a half-open parallelopiped Par [subscript s] associated with P [subscript s] and give a simple description of its integer points. We use this description to recover earlier results of Savage et al. on the δ-vector (or h*-vector) and to obtain the connections to s-ascents and s-descents, as well as some generalizations of these results.National Science Foundation (U.S.) (Grant DMS-1068625 | The Lecture Hall Parallelepiped | the lecture hall parallelepiped | lecture hall polytopes subscript integer polytopes savage schuster closely lecture hall partitions eriksson bousquet mélou. parallelopiped subscript subscript integer points. recover savage connections ascents descents generalizations results.national foundation u.s. | non_dup | [] |
24770526 | 10.1007/s00026-014-0236-7 | To every labeled poset (P,\omega), one can associate a quasisymmetric
generating function for its (P,\omega)-partitions. We ask: when do two labeled
posets have the same generating function? Since the special case corresponding
to skew Schur function equality is still open, a complete classification of
equality among (P,\omega) generating functions is likely too much to expect.
Instead, we determine necessary conditions and separate sufficient conditions
for two labeled posets to have equal generating functions. We conclude with a
classification of all equalities for labeled posets with small numbers of
linear extensions.Comment: 24 pages, 19 figures. Incorporates minor changes suggested by the
referees. To appear in Annals of Combinatoric | Equality of P-partition generating functions | equality of p-partition generating functions | labeled poset omega associate quasisymmetric generating omega partitions. labeled posets generating skew schur equality equality omega generating expect. labeled posets generating functions. equalities labeled posets pages figures. incorporates minor referees. annals combinatoric | non_dup | [] |
25014741 | 10.1007/s00026-015-0261-1 | Let $\mathcal M$ be a class of matroids closed under minors and isomorphism.
Let $N$ be a matroid in $\mathcal M$ with an exact $k$-separation $(A, B)$. We
say $N$ is a $k$-decomposer for $\mathcal M$ having $(A, B)$ as an inducer, if
every matroid $M\in \mathcal M$ having $N$ as a minor has a $k$-separation $(X,
Y)$ such that, $A\subseteq X$ and $B\subseteq Y$. Seymour [3, 9.1] proved that
a matroid $N$ is a $k$-decomposer for an excluded-minor class, if certain
conditions are met for all 3-connected matroids $M$ in the class, where
$|E(M)-E(N)|\le 2$. We reinterpret Seymour's Theorem in terms of the
connectivity function and give a check-list that is easier to implement because
case-checking is reduced | On Seymour's Decomposition Theorem | on seymour's decomposition theorem | mathcal matroids minors isomorphism. matroid mathcal decomposer mathcal inducer matroid mathcal minor subseteq subseteq seymour proved matroid decomposer excluded minor matroids reinterpret seymour connectivity check easier implement checking | non_dup | [] |
24938804 | 10.1007/s00026-015-0264-y | We define an action of the 0-Hecke algebra of type A on the Stanley-Reisner
ring of the Boolean algebra. By studying this action we obtain a family of
multivariate noncommutative symmetric functions, which specialize to the
noncommutative Hall-Littlewood symmetric functions and their (q,t)-analogues
introduced by Bergeron and Zabrocki, and to a more general family of
noncommutative symmetric functions having parameters associated with paths in
binary trees introduced recently by Lascoux, Novelli, and Thibon. We also
obtain multivariate quasisymmetric function identities, which specialize to
results of Garsia and Gessel on generating functions of multivariate
distributions of permutation statistics.Comment: Added connections with a family of noncommutative symmetric functions
introduced recently by Lascoux, Novelli, and Thibo | 0-Hecke algebra action on the Stanley-Reisner ring of the Boolean
algebra | 0-hecke algebra action on the stanley-reisner ring of the boolean algebra | hecke stanley reisner boolean algebra. studying multivariate noncommutative specialize noncommutative hall littlewood analogues bergeron zabrocki noncommutative paths trees lascoux novelli thibon. multivariate quasisymmetric identities specialize garsia gessel generating multivariate permutation connections noncommutative lascoux novelli thibo | non_dup | [] |
24938282 | 10.1007/s00026-015-0272-y | In this paper we obtain precise asymptotics for certain families of graphs,
namely circulant graphs and degenerating discrete tori. The asymptotics contain
interesting constants from number theory among which some can be interpreted as
corresponding values for continuous limiting objects. We answer one question
formulated in a paper from Atajan, Yong and Inaba in [1] and formulate a
conjecture in relation to the paper from Zhang, Yong and Golin [21]. A crucial
ingredient in the proof is to use the matrix tree theorem and express the
combinatorial laplacian determinant in terms of Bessel functions. A
non-standard Poisson summation formula and limiting properties of theta
functions are then used to evaluate the asymptotics.Comment: 27pages, 3 figure | Asymptotics for the number of spanning trees in circulant graphs and
degenerating d-dimensional discrete tori | asymptotics for the number of spanning trees in circulant graphs and degenerating d-dimensional discrete tori | precise asymptotics families circulant degenerating tori. asymptotics interpreted limiting objects. answer formulated atajan yong inaba formulate conjecture yong golin crucial ingredient express combinatorial laplacian determinant bessel functions. poisson summation limiting theta pages | non_dup | [] |
55895160 | 10.1007/s00026-015-0277-6 | We investigate the combinatorial interplay between automorphisms and opposition in (primarily finite) generalised polygons. We provide restrictions on the fixed element structures of automorphisms of a generalised polygon mapping no chamber to an opposite chamber. Furthermore, we give a complete classification of automorphisms of finite generalised polygons which map at least one point and at least one line to an opposite, but map no chamber to an opposite chamber. Finally, we show that no automorphism of a finite thick generalised polygon maps all chambers to opposite chambers, except possibly in the case of generalised quadrangles with coprime parameters | The combinatorics of automorphisms and opposition in generalised polygons | the combinatorics of automorphisms and opposition in generalised polygons | combinatorial interplay automorphisms opposition primarily generalised polygons. restrictions automorphisms generalised polygon chamber opposite chamber. automorphisms generalised polygons opposite chamber opposite chamber. automorphism thick generalised polygon chambers opposite chambers possibly generalised quadrangles coprime | non_dup | [] |
48320325 | 10.1007/s00026-015-0278-5 | International audienceIn the combinatorics of finite finite Coxeter groups, there is a simple formula giving the number of maximal chains of noncrossing partitions. It is a reinterpre-tation of a result by Deligne which is due to Chapoton, and the goal of this article is to refine the formula. First, we prove a one-parameter generalization, by the considering enumeration of noncrossing chains where we put a weight on some relations. Second, we consider an equivalence relation on noncrossing chains coming from the natural action of the group on set partitions, and we show that each equivalence class has a simple generating function. Using this we recover Postnikov's hook length formula in type A and obtain a variant in type B | Refined Enumeration of Noncrossing Chains and Hook Formulas | refined enumeration of noncrossing chains and hook formulas | audiencein combinatorics coxeter giving maximal chains noncrossing partitions. reinterpre tation deligne chapoton goal refine formula. generalization enumeration noncrossing chains relations. equivalence noncrossing chains coming partitions equivalence generating function. recover postnikov hook variant | non_dup | [] |
25043500 | 10.1007/s00026-015-0280-y | The canonical ring $S_D = \bigoplus_{d \geq 0} H^0(X, \lfloor dD \rfloor)$ of
a divisor D on a curve X is a natural object of study; when D is a Q-divisor,
it has connections to projective embeddings of stacky curves and rings of
modular forms. We study the generators and relations of S_D for the simplest
curve X = P^1. When D contains at most two points, we give a complete
description of S_D; for general D, we give bounds on the generators and
relations. We also show that the generators (for at most five points) and a
Groebner basis of relations between them (for at most four points) depend only
on the coefficients in the divisor D, not its points or the characteristic of
the ground field; we conjecture that the minimal system of relations varies in
a similar way. Although stated in terms of algebraic geometry, our results are
proved by translating to the combinatorics of lattice points in simplices and
cones.Comment: 19 pages, 3 figure | Canonical rings of Q-divisors on P^1 | canonical rings of q-divisors on p^1 | canonical bigoplus lfloor rfloor divisor divisor connections projective embeddings stacky rings modular forms. generators simplest bounds generators relations. generators groebner divisor conjecture varies way. stated algebraic proved translating combinatorics simplices pages | non_dup | [] |
24948089 | 10.1007/s00026-016-0303-3 | The immaculate basis of the non-commutative symmetric functions was recently
introduced by the first and third author to lift certain structures in the
symmetric functions to the dual Hopf algebras of the non-commutative and
quasi-symmetric functions. It was shown that immaculate basis satisfies a
positive, multiplicity free right Pieri rule. It was conjectured that the left
Pieri rule may contain signs but that it would be multiplicity free. Similarly,
it was also conjectured that the dual quasi-symmetric basis would also satisfy
a signed multiplicity free Pieri rule. We prove these two conjectures here.Comment: 14 pages, corrections from v1 and v | The Pieri rule for dual immaculate quasi-symmetric functions | the pieri rule for dual immaculate quasi-symmetric functions | immaculate commutative lift hopf algebras commutative quasi functions. immaculate satisfies multiplicity pieri rule. conjectured pieri signs multiplicity free. conjectured quasi satisfy signed multiplicity pieri rule. conjectures pages | non_dup | [] |
78475806 | 10.1007/s00026-016-0313-1 | We prove an arithmetic removal result for all compact abelian groups, generalizing a finitary removal result of Král’, Serra, and the third author. To this end, we consider infinite measurable hypergraphs that are invariant under certain group actions, and for these hypergraphs we prove a symmetry-preserving removal lemma, which extends a finitary result of the same name by the second author. We deduce our arithmetic removal result by applying this lemma to a specific type of invariant measurable hypergraph. As a direct consequence of our removal result, we obtain the following generalization of Szemerédi’s theorem: for any compact abelian group G, any measurable set A⊆ G with Haar probability μ(A) ≥ α> 0 satisfies ∫G∫G1A(x)1A(x+r)..1A(x+(k-1)r)dμ(x)dμ(r)≥c, where the constant c= c(α, k) > 0 is valid uniformly for all G. This result is shown to hold more generally for any translationinvariant system of r linear equations given by an integer matrix with coprime r× r minors. © 2016, Springer International Publishing | On Linear Configurations in Subsets of Compact Abelian Groups, and Invariant Measurable Hypergraphs | on linear configurations in subsets of compact abelian groups, and invariant measurable hypergraphs | arithmetic removal abelian generalizing finitary removal král’ serra author. infinite measurable hypergraphs hypergraphs preserving removal extends finitary name author. deduce arithmetic removal measurable hypergraph. removal generalization szemerédi’s abelian measurable haar satisfies ∫g∫g valid uniformly hold translationinvariant integer coprime minors. springer publishing | non_dup | [] |
29506513 | 10.1007/s00026-016-0324-y | Phylogenetic networks are rooted acyclic directed graphs in which the leaves
are identified with members of a set X of species. The cluster of a vertex is
the set of leaves that are descendants of the vertex. A network is
"distinct-cluster" if distinct vertices have distinct clusters. This paper
focuses on the set DC(X) of distinct-cluster networks whose leaves are
identified with the members of X. For a fixed X, a metric on DC(X) is defined.
There is a "cluster-preserving" simplification process by which vertices or
certain arcs may be removed without changing the clusters of any remaining
vertices. Many of the resulting networks may be uniquely determined without
regard to the order of the simplifying operations.Comment: This is version 2. A previous version is already on ArXi | Comparing and simplifying distinct-cluster phylogenetic networks | comparing and simplifying distinct-cluster phylogenetic networks | phylogenetic rooted acyclic directed leaves species. leaves descendants vertex. clusters. focuses leaves defined. preserving simplification arcs removed changing vertices. uniquely regard simplifying arxi | non_dup | [] |
29523740 | 10.1007/s00026-016-0330-0 | Consider non-negative lattice paths ending at their maximum height, which
will be called admissible paths. We show that the probability for a lattice
path to be admissible is related to the Chebyshev polynomials of the first or
second kind, depending on whether the lattice path is defined with a reflective
barrier or not. Parameters like the number of admissible paths with given
length or the expected height are analyzed asymptotically. Additionally, we use
a bijection between admissible random walks and special binary sequences to
prove a recent conjecture by Zhao on ballot sequences | Analysis of Bidirectional Ballot Sequences and Random Walks Ending in
their Maximum | analysis of bidirectional ballot sequences and random walks ending in their maximum | paths ending admissible paths. admissible chebyshev polynomials kind reflective barrier not. admissible paths asymptotically. additionally bijection admissible walks conjecture zhao ballot | non_dup | [] |
29531459 | 10.1007/s00026-017-0350-4 | This work enrols the research line of M. Haiman on the Operator Theorem (the
old operator conjecture). This theorem states that the smallest
$\mathfrak{S}_n$-module closed under taking partial derivatives and closed
under the action of polarization operators that contains the Vandermonde
determinant is the space of diagonal harmonics polynomials. We start
generalizing the context of this theorem to the context of polynomials in
$\ell$ sets of $n$ variables $x_{ij}$ with $1\leq i\leq \ell$ et $1\leq j\leq
n$. Given a $\mathfrak{S}_n$-stable family of homogeneous polynomials in the
variables $x_{ij}$ the smallest vector space closed under taking partial
derivatives and closed under the action of polarization operators that contains
$F$ is the polarization module generated by the family $F$. These polarization
modules are all representation of the direct product
$\mathfrak{S}_n\times{GL}_{\ell}(\mathbb{C})$. In order to study the
decomposition into irreducible submodules, we compute the graded Frobenius
characteristic of these modules. For several cases of $\mathfrak{S}_n$-stable
families of homogeneous polynomials in $n$ variables, for every $n\geq 1$, we
show general formulas for this graded characteristic in a global manner,
independent of the value of $\ell$.Comment: This is a full version of the Extended Abstract arXiv:1411.4197
[math.CO | Generalized Polarization Modules | generalized polarization modules | enrols haiman conjecture smallest mathfrak module derivatives vandermonde determinant diagonal harmonics polynomials. generalizing polynomials mathfrak homogeneous polynomials smallest derivatives module modules mathfrak mathbb decomposition irreducible submodules graded frobenius modules. mathfrak families homogeneous polynomials formulas graded manner .comment math.co | non_dup | [] |
42699234 | 10.1007/s00026-018-0392-2 | The fractional stable set polytope ${\rm FRAC}(G)$ of a simple graph $G$ with
$d$ vertices is a rational polytope that is the set of nonnegative vectors
$(x_1,\ldots,x_d)$ satisfying $x_i+x_j\le 1$ for every edge $(i,j)$ of $G$. In
this paper we show that (i) The $\delta$-vector of a lattice polytope $2 {\rm
FRAC}(G)$ is alternatingly increasing; (ii) The Ehrhart ring of ${\rm FRAC}(G)$
is Gorenstein; (iii) The coefficients of the numerator of the Ehrhart series of
${\rm FRAC}(G)$ are symmetric, unimodal and computed by the $\delta$-vector of
$2 {\rm FRAC}(G)$.Comment: 12 pages, V2: some minor revisions, references adde | Ehrhart series of fractional stable set polytopes of finite graphs | ehrhart series of fractional stable set polytopes of finite graphs | fractional polytope frac rational polytope nonnegative ldots satisfying delta polytope frac alternatingly ehrhart frac gorenstein numerator ehrhart frac unimodal delta frac .comment pages minor revisions adde | non_dup | [] |
42682055 | 10.1007/s00026-018-0393-1 | We explore several families of flip-graphs, all related to polygons or
punctured polygons. In particular, we consider the topological flip-graphs of
once-punctured polygons which, in turn, contain all possible geometric
flip-graphs of polygons with a marked point as embedded sub-graphs. Our main
focus is on the geometric properties of these graphs and how they relate to one
another. In particular, we show that the embeddings between them are strongly
convex (or, said otherwise, totally geodesic). We also find bounds on the
diameters of these graphs, sometimes using the strongly convex embeddings.
Finally, we show how these graphs relate to different polytopes, namely type D
associahedra and a family of secondary polytopes which we call pointihedra.Comment: 24 pages, 6 figure | Once punctured disks, non-convex polygons, and pointihedra | once punctured disks, non-convex polygons, and pointihedra | explore families flip polygons punctured polygons. topological flip punctured polygons geometric flip polygons marked embedded graphs. geometric relate another. embeddings convex said totally geodesic bounds diameters sometimes convex embeddings. relate polytopes associahedra polytopes call pages | non_dup | [] |
11754016 | 10.1007/s00027-003-0651-z | Measurements of physical properties have been conducted in Mining Lake 111 (ML111), located in Lusatia, Germany over the time period 1996- 2002. In the deepest area of the ML111, a monimolimnion was observed, that persisted for the years 1996-1999. It disappeared in 2000 and again formed in 2001. The definition of the main physical properties, such as the temperature compensation for electrical conductivity, in acidic mining lakes required a lake specific approach. The relation between conductivity, temperature and density was determined for the acidic ML111. The variation in dissolved substances affected these relationships such that conductivity varied with temperature even in different layers of the water column and the limitations for a lake wide correlation was evident. Variation in the conductivity of the epilimnion could be verified, and agreed with the estimates of evaporation from the lake surface during summer stratification. Calculations, following the gradient flux method, indicated vertical transport coefficients between 10-7 and 10-6m2/s throughout the hypolimnion. The heat budget indicated that heat was transferred into the lake bed or the ground during spring | Physical characteristics of Acidic Mining Lake 111 | physical characteristics of acidic mining lake 111 | mining lake lusatia deepest monimolimnion persisted disappeared compensation electrical conductivity acidic mining lakes lake approach. conductivity acidic dissolved substances conductivity varied limitations lake evident. conductivity epilimnion verified agreed evaporation lake summer stratification. hypolimnion. budget transferred lake spring | non_dup | [] |
36058826 | 10.1007/s00027-008-8060-y | 10 páginas, 6 figuras.-- The final publication is\ud
available at www.springerlink.comFrom September 2005 to May 2006 four\ud
cruises were performed in the Strait of Gibraltar to\ud
study the seasonal variability of carbon dioxide surface\ud
waters and assess the air-sea CO2 fluxes. Continuous\ud
water measurement of fugacity ofCO2 (fCO2),\ud
temperature and salinity was performed along the\ud
longitudinal and latitudinal axes of the Strait. Additionally,\ud
discrete surface water samples were taken to\ud
measure dissolved inorganic carbon (DIC) and oxygen.\ud
The spatial distribution of surface fCO2 showed low variability compared to the seasonal scale, with\ud
fCO2 values ranging from 329 matm in March to 387\ud
matm in September. Seasonal variability of fCO2 was\ud
assessed and discussed in terms of temperature and\ud
biology, and the temperature was the main controlling\ud
factor. The Strait of Gibraltar is CO2 undersaturated\ud
most of the year, except in September, when the\ud
annual average CO2 uptake equals 0.28 mol C m 2\ud
yr 1, if behaves as a discreet sink of CO2 on an annual\ud
scaleThis work has\ud
been supported by the Spanish CICYT under the\ud
contract CTM2005-01364/MAR and by the European\ud
CARBOOCEAN IP (511176 GOCE)Peer reviewe | Seasonal variability of surface fCO2 in the Strait of Gibraltar | seasonal variability of surface fco2 in the strait of gibraltar | páginas figuras. publication september cruises strait gibraltar seasonal dioxide waters fluxes. fugacity ofco salinity longitudinal latitudinal axes strait. additionally dissolved inorganic oxygen. seasonal ranging matm matm september. seasonal controlling factor. strait gibraltar undersaturated september uptake equals behaves discreet sink scalethis spanish cicyt contract carboocean goce peer reviewe | non_dup | [] |
83533678 | 10.1007/s00027-009-9195-1 | The structure and function of alluvial Highly Dynamic River Systems (HDRS) are driven by highly variable hydrological disturbance regimes, and alternate between resistant, metastable states and resilient, transitional states. These are in turn subject to influences of feedback loops within hydrogeomorphic and biological processes. Here we consider how resistance and resilience largely determine HDRS ecosystem trajectories and how these characteristics can be modified by natural and anthropogenic processes. We review the mechanisms by which biodiversity can affect both resistance and resilience and introduce a conceptual framework that incorporates some unique HDRS characteristics. We suggest that resilient and resistant patterns frequently coexist in the active tract of these river systems, and that this coexistance promotes the return of metastable states after major disturbances. In contrast, highly resistant and poorly resilient patterns dominate at their external boundaries. The loss of these natural dynamics resulting from direct and indirect human impacts causes deviations to resistance and resilience patterns and therefore to HDRS trajectory. We propose that understanding the role of interactions between biological and physical processes that control resistance and resilience is crucial for system restoration and management | Implications of biological and physical diversity for resilience and resistance patterns within Highly Dynamic River Systems | implications of biological and physical diversity for resilience and resistance patterns within highly dynamic river systems | alluvial river hdrs hydrological disturbance regimes alternate resistant metastable resilient transitional states. influences loops hydrogeomorphic processes. resilience largely hdrs ecosystem trajectories anthropogenic processes. biodiversity resilience conceptual incorporates hdrs characteristics. resilient resistant frequently coexist tract river coexistance promotes return metastable disturbances. resistant poorly resilient dominate boundaries. indirect impacts deviations resilience hdrs trajectory. propose resilience crucial restoration | non_dup | [] |
29197939 | 10.1007/s00027-010-0131-1 | The factors affecting vertical distributions of chlorophyll fluorescence were examined in four temperate, warm monomictic lakes. Each of the lakes (maximum depth >80 m) was sampled over 2 years at intervals from monthly to seasonal. Profiles were taken of chlorophyll fluorescence (as a proxy for algal biomass), temperature and irradiance, as well as integrated samples from the surface mixed layer for chlorophyll a (chl a) and nutrient concentrations in each lake. Depth profiles of chlorophyll fluorescence were also made along transects of the longest axis of each lake. Chlorophyll fluorescence maxima occurred at depths closely correlated with euphotic depth (r ² = 0.67, P < 0.01), which varied with nutrient status of the lakes. While seasonal thermal density stratification is a prerequisite for the existence of a deep chlorophyll maximum (DCM), our study provides evidence that the depth of light penetration largely dictates the DCM depth during stratification. Reduction in water clarity through eutrophication can cause a shift in phytoplankton distributions from a DCM in spring or summer to a surface chlorophyll maximum within the surface mixed layer when the depth of the euphotic zone (z eu) is consistently shallower than the depth of the surface mixed layer (z SML). Trophic status has a key role in determining vertical distributions of chlorophyll in the four lakes, but does not appear to disrupt the annual cycle of maximum chlorophyll in winter | Vertical distributions of chlorophyll in deep, warm monomictic lakes | vertical distributions of chlorophyll in deep, warm monomictic lakes | affecting chlorophyll fluorescence temperate warm monomictic lakes. lakes sampled intervals monthly seasonal. chlorophyll fluorescence proxy algal biomass irradiance chlorophyll nutrient lake. chlorophyll fluorescence transects longest lake. chlorophyll fluorescence maxima occurred depths closely euphotic varied nutrient lakes. seasonal stratification prerequisite chlorophyll penetration largely dictates stratification. clarity eutrophication phytoplankton spring summer chlorophyll euphotic consistently shallower trophic determining chlorophyll lakes disrupt chlorophyll winter | non_dup | [] |
11900629 | 10.1007/s00027-010-0163-6 | Stable isotope and fatty acid analyses were used to study carbon sources for animals in a submerged plant bed. Epiphytes growing on Potamogeton perfoliatus, sand microflora, and alder leaves were the most important carbon sources. The most abundant macrophyte, P. perfoliatus was unimportant as a food source. Modelling (IsoSource) showed that epiphytes were the most important food source for the most abundant benthic invertebrates, the isopod Asellus aquaticus (annual mean contribution 64%), the amphipod Gammarus pulex (66%), and the gastropod Potamopyrgus antipodarum (83%). The mean annual contributions of sand microflora were, respectively, 21, 19, and 9%; and of alder leaves, 15, 15, and 8% for these three species. The relative importance of carbon sources varied seasonally. The relative contribution of epiphytes was lowest for all three grazer species in July: A. aquaticus 38%, G. pulex 43%, and P. antipodarum 42%. A decline in epiphyte biomass in summer may have caused this switch to less attractive food sources. P. perfoliatus provided habitat and shelter for consumers, but food was mainly supplied indirectly by providing space for attached epiphytes, which are fast-growing and provide a highly nutritious food source | The trophic importance of epiphytic algae in a freshwater macrophyte system (Potamogeton perfoliatus L.): stable isotope and fatty acid analyses | the trophic importance of epiphytic algae in a freshwater macrophyte system (potamogeton perfoliatus l.): stable isotope and fatty acid analyses | isotope fatty submerged bed. epiphytes growing potamogeton perfoliatus sand microflora alder leaves sources. abundant macrophyte perfoliatus unimportant source. isosource epiphytes abundant benthic invertebrates isopod asellus aquaticus amphipod gammarus pulex gastropod potamopyrgus antipodarum sand microflora alder leaves species. varied seasonally. epiphytes grazer aquaticus pulex antipodarum decline epiphyte biomass summer switch attractive sources. perfoliatus habitat shelter consumers supplied indirectly attached epiphytes growing nutritious | non_dup | [] |
143875709 | 10.1007/s00027-011-0209-4 | This study examined the sources and fate of nutrient inputs from two principal tributaries to the eutrophic subtropical Wivenhoe reservoir: an unregulated river and a dammed river with regular releases, during a period of declining reservoir water levels. Nutrient budgets were constructed over a period of 6 years, and combined with short-term data on nutrient concentrations and forms, and d15N stable isotope data. Our study found that over a 6 year period, there was net retention of phosphorus (P) in the reservoir, with 60% of inputs retained. Most of the P input load came from the unregulated river, with an agricultural catchment, during periods of high flow. During one event half of the total TP load from the unregulated river in the study period was delivered in only 12 days. Much of the P was dissolved inorganic P (DIP) and was derived from high P concentrations in soils and sediments. This highlights the importance of appropriate catchment management practices to reduce P losses from terrestrial systems because retention of P in reservoir sediments reduces the availability of this nutrient for agricultural production. In contrast, there was negligible retention of nitrogen (N). The unregulated river was an important source of N derived from N fixation in the river and adjacent soils, while the source from the dammed river was mostly reprocessed N. The high retention of P relative to N is consistent with relatively higher accumulation of P in sediments.Griffith Sciences, Griffith School of EnvironmentFull Tex | Sources and fate of nutrients in a subtropical reservoir | sources and fate of nutrients in a subtropical reservoir | fate nutrient inputs principal tributaries eutrophic subtropical wivenhoe reservoir unregulated river dammed river releases declining reservoir levels. nutrient budgets nutrient isotope data. retention phosphorus reservoir inputs retained. came unregulated river agricultural catchment flow. unregulated river delivered days. dissolved inorganic soils sediments. highlights catchment practices losses terrestrial retention reservoir sediments reduces availability nutrient agricultural production. negligible retention nitrogen unregulated river fixation river adjacent soils dammed river mostly reprocessed retention accumulation sediments.griffith griffith environmentfull | non_dup | [] |
143885980 | 10.1007/s00027-011-0217-4 | Dry river beds are common worldwide and are rapidly increasing in extent due to the effects of water management and prolonged drought periods due to climate change. While attention has been given to the responses of aquatic invertebrates to drying rivers, few studies exist on the terrestrial invertebrates colonizing dry river beds. Dry river beds are physically harsh and they often differ substantially in substrate, topography, microclimate and inundation frequency from adjacent riparian zones. Given these differences, we predicted that dry river beds provide a unique habitat for terrestrial invertebrates, and that their assemblage composition differs from that in adjacent riparian zones. Dry river beds and riparian zones in Australia and Italy were sampled for terrestrial invertebrates with pitfall traps. Sites differed in substrate type, climate and flow regime. Dry river beds contained diverse invertebrate assemblages and their composition was consistently different from adjacent riparian zones, irrespective of substrate, climate or hydrology. Although some taxa were shared between dry river beds and riparian zones, 66 of 320 taxa occurred only in dry river beds. Differences were due to species turnover, rather than shifts in abundance, indicating that dry river bed assemblages are not simply subsets of riparian assemblages. Some spatial patterns in invertebrate assemblages were associated with environmental variables (irrespective of habitat type), but these associations were statistically weak. We suggest that dry river beds are unique habitats in their own right. We discuss potential human stressors and management issues regarding dry river beds and provide recommendations for future research.Griffith Sciences, Griffith School of EnvironmentFull Tex | Terrestrial invertebrates of dry river beds are not simply subsets of riparian assemblages | terrestrial invertebrates of dry river beds are not simply subsets of riparian assemblages | river beds worldwide rapidly prolonged drought change. aquatic invertebrates drying rivers terrestrial invertebrates colonizing river beds. river beds physically harsh substantially topography microclimate inundation adjacent riparian zones. river beds habitat terrestrial invertebrates assemblage differs adjacent riparian zones. river beds riparian zones australia sampled terrestrial invertebrates pitfall traps. differed regime. river beds diverse invertebrate assemblages consistently adjacent riparian zones irrespective hydrology. taxa shared river beds riparian zones taxa occurred river beds. turnover shifts abundance river assemblages subsets riparian assemblages. invertebrate assemblages irrespective habitat associations statistically weak. river beds habitats right. stressors river beds recommendations research.griffith griffith environmentfull | non_dup | [] |
36095702 | 10.1007/s00027-011-0233-4 | [EN] The present area of European wetlands is only a fraction of their area before the start of large-scale human colonization of Europe. Many European wetlands have been exploited and managed for various purposes. Large wetland areas have been drained and reclaimed mainly for agriculture and establishment of human settlements. These threats to European wetlands persist. The main responses of European wetlands to ongoing climate change will vary according to wetland type and geographical location. Sea level rise will probably be the decisive factor affecting coastal wetlands, especially along the Atlantic coast. In the boreal part of Europe, increased temperatures will probably lead to increased annual evapotranspiration and lower organic matter accumulation in soil. The role of vast boreal wetlands as carbon sinks may thus be suppressed. In central and western Europe, the risk of floods may support the political will for ecosystem-unfriendly flood defence measures, which may threaten the hydrology of existing wetlands. Southern Europe will probably suffer most from water shortage, which may strengthen the competition for water resources between agriculture, industry and settlements on the one hand and nature conservancy, including wetland conservation, on the other. © 2011 Springer Basel AG.Work on this paper was supported by the projects NPV 2B06023 and MSM 6007665801 of the Ministry of Education, Youth and Sports of the Czech Republic, 526/09/1545 of the Grant Agency of the Czech Republic and QH 82078 of the Czech National Agency of Agricultural Research. We warmly thank Hana Santruckova for helpful comments on the manuscript, Stepan Husak for providing the information on Coleanthus subtilis, Vaclav Nedbal for techical help with the compilation of the map of European wetlands (Fig. 1), Jakub Brom for providing photographs in Fig. 5, and Ondrej Novak for technical help with the preparation of the manuscriptPeer Reviewe | Actual state of European wetlands and their possible future in the context of global climate change | actual state of european wetlands and their possible future in the context of global climate change | wetlands colonization europe. wetlands exploited managed purposes. wetland drained reclaimed agriculture establishment settlements. threats wetlands persist. wetlands ongoing vary wetland geographical location. probably decisive affecting coastal wetlands atlantic coast. boreal europe probably evapotranspiration accumulation soil. vast boreal wetlands sinks suppressed. europe floods ecosystem unfriendly flood defence threaten hydrology wetlands. southern europe probably suffer shortage strengthen competition agriculture settlements conservancy wetland conservation other. springer basel ag.work projects ministry youth sports czech republic agency czech republic czech agency agricultural research. warmly hana santruckova helpful comments stepan husak coleanthus subtilis vaclav nedbal techical compilation wetlands fig. jakub brom photographs fig. ondrej novak preparation manuscriptpeer reviewe | non_dup | [] |
36071022 | 10.1007/s00027-011-0240-5 | The online version of this article (doi:10.1007/s00027-011-0240-5) contains supplementary material, which is available to authorized users.The aim of this 6 year study was to assess whether freshwater inputs (rainfall and dam discharges) were acting as physical, physiological or trophic forcing factors on phytoplankton pigment concentrations and the dominant mysids of a temperate estuary (Guadalquivir estuary; SW, Spain). The effects of natural and human-controlled freshwater inputs modified the physico-chemical conditions and consequently biological production (bottom up control). Nutrient (nitrogen hypernutrification), suspended particulate matter and allochthonous photosynthetic pigment imports linked to freshwater inputs from adjacent habitats were observed, as well as light-limited autochthonous primary production. Seasonal and/or spatial patterns were shown by all study variables, including mysids. Freshwater management effects on dominant mysids differed depending on the species’ salinity tolerance (physiological forcing) and preferred prey availability (trophic forcing). Moreover, high inorganic matter content had a negative effect on the density of Mesopodopsis slabberi (physical forcing), which led to an increased detritivory/herbivory ratio (Neomysis integer/M. slabberi ratio). In conclusion, freshwater inputs appeared to effect estuarine lower trophic levels via a combination of different forcing mechanisms. Although several general patterns can be derived, the response of the system to freshwater inputs was not always univocal.The study was supported by the Spanish Ministry of Science and Innovation through the projects REN2000-0822 MAR and Consolider-Ingenio 2010 CSD2009-00065, the Environmental and Fishery Agency of Autonomous Andalusia Government ("Consejería de Medio Ambiente" and "Consejería de Agricultura y Pesca: Junta de Andalucía") and an EU Fishery Grant.Peer reviewe | Effects of freshwater inputs on the lower trophic levels of a temperate estuary: physical, physiological or trophic forcing? | effects of freshwater inputs on the lower trophic levels of a temperate estuary: physical, physiological or trophic forcing? | supplementary authorized users.the freshwater inputs rainfall discharges acting physiological trophic forcing phytoplankton pigment mysids temperate estuary guadalquivir estuary spain freshwater inputs physico nutrient nitrogen hypernutrification suspended particulate allochthonous photosynthetic pigment imports freshwater inputs adjacent habitats autochthonous production. seasonal mysids. freshwater mysids differed species’ salinity tolerance physiological forcing preferred prey availability trophic forcing inorganic mesopodopsis slabberi forcing detritivory herbivory neomysis integer slabberi freshwater inputs appeared estuarine trophic forcing mechanisms. freshwater inputs univocal.the spanish ministry innovation projects consolider ingenio fishery agency autonomous andalusia consejería medio ambiente consejería agricultura pesca junta andalucía fishery grant.peer reviewe | non_dup | [] |
19966711 | 10.1007/s00027-011-0245-0 | Inorganic fine sediments are easily carried into streams and rivers from disturbed land. These sediments can affect the stream biota, including detritivorous invertebrates (shredders) and impair ecosystem functions, such as leaf litter decomposition. We hypothesized that fine sediment (kaolin) deposited on leaves would reduce or suppress fungal development, reducing decomposition rates of leaves. Moreover, we predicted that shredders would act as ecosystem engineers by perturbing sediment deposition, reducing its impact on decomposition and fungi. We used a fully crossed experimental design of sediment addition (control, 400 mg L-1) and shredders (none, Gammarus, Potamophylax) in laboratory aquaria. Leaf mass loss, sus- pended solids, microbial respiration, fungal biomass and spore production were measured. Sediment addition had no significant effects on the leaf mass remaining nor on shredders’ consumption rates. However, sediment slightly reduced fungal assemblage richness and the sporulation rate of three fungal species. The presence of shredders sub- stantially increased the resuspension of fine sediments ([300%),resultinginhighersuspendedloads.However,the action of shredders did not have a significant effect on fungal biomass nor on leaf mass loss. Even if shredders did not enhance fungal colonisation, they affected the settle- ment of fine sediment, serving as allogenic engineers. Our study suggests that concentrations of fine sediment of 400 mg L-1 with short exposure times (192 h) can have some effect on leaf decomposition | Fine sediment on leaves : shredder removal of sediment does not enhance fungal colonisation | fine sediment on leaves : shredder removal of sediment does not enhance fungal colonisation | inorganic fine sediments streams rivers disturbed land. sediments stream biota detritivorous invertebrates shredders impair ecosystem leaf litter decomposition. hypothesized fine sediment kaolin deposited leaves suppress fungal reducing decomposition leaves. shredders ecosystem engineers perturbing sediment deposition reducing decomposition fungi. crossed sediment shredders none gammarus potamophylax aquaria. leaf pended solids microbial respiration fungal biomass spore measured. sediment leaf shredders’ rates. sediment fungal assemblage richness sporulation fungal species. shredders stantially resuspension fine sediments resultinginhighersuspendedloads.however shredders fungal biomass leaf loss. shredders enhance fungal colonisation settle fine sediment serving allogenic engineers. fine sediment leaf decomposition | non_dup | [] |
36094557 | 10.1007/s00027-012-0284-1 | 28 páginas, 4 figuras, 3 tablas.[EN]Ecosystem metabolism is an important measure of wetland restoration efficiency, and serves to indicate if the system is capable of processing energetic resources. Despite its value, ecosystem metabolism has rarely been included in monitoring programs. In this study, we aimed to achieve the following objectives: (i) compare net ecosystem production (NEP) rates of constructed vs. natural wetlands; (ii) identify the highest NEP rate habitats; and (iii) define the main environmental factors regulating NEP in different wetland types. Pelagic and benthic NEP rates and physicochemical features were measured in three natural and five constructed wetlands in the middle Ebro River floodplain (NE Spain). Statistical analyses showed pelagic NEP rates peaked in natural wetlands, which produced up to 187.5 mg C m−3 h−1 compared to lower rates in constructed wetlands (up to 46.2 mg C m−3 h−1). Pelagic NEP responded positively to temperature, total dissolved solids, and nutrients. Benthic NEP rates were 3 to 30-fold greater than pelagic in natural (up to 994.9 mg C m−3 h−1) and constructed (up to 1,551.5 mg C m−3 h−1) wetlands, and were heavily influenced by habitat type, with NEP peaking in areas dominated by submerged vegetation and fine organic sediment. Rapid recovery in aquatic communities (i.e. macroinvertebrate diversity) has been previously reported for the studied wetlands; however, our study suggests a slower recovery of functional processes (i.e. pelagic NEP) in constructed habitats. We therefore strongly advocate the inclusion of ecosystem function in the design and evaluation of restoration projects to optimise long-term wetland ecosystem sustainability.This project was funded by the Spanish Ministry of Science and Innovation (National Research Plan CGL2008-\ud
05153-C02-01), the Aragon Government (Research Group E61 on\ud
Ecological Restoration; Applied Research Consolidated Group-GIMACES E02; and B079/09 pre-doctoral grant), the Caja\ud
Inmaculada—Aragon Government (Programa Europa XXI, CB31/11\ud
research mobility grant) and counted with the support of ‘‘APN\ud
Galachos Natural Reserve’’. We thank M. Garcı´a and A. Barcos for\ud
analysing water samples, and P. Sanchez, F. Carranza, L. Miguel and\ud
J. Garcı´a for their field assistance and Write Science Right for English\ud
editing. We are also grateful to two anonymous reviewers whose\ud
comments highly improved the quality of this paper.Peer reviewe | Is net ecosystem production higher in natural relative to constructed wetlands? | is net ecosystem production higher in natural relative to constructed wetlands? | páginas figuras tablas. ecosystem metabolism wetland restoration serves capable energetic resources. ecosystem metabolism rarely programs. aimed objectives ecosystem wetlands habitats regulating wetland types. pelagic benthic physicochemical wetlands ebro river floodplain spain pelagic peaked wetlands wetlands pelagic responded positively dissolved solids nutrients. benthic pelagic wetlands heavily influenced habitat peaking dominated submerged vegetation fine sediment. recovery aquatic communities i.e. macroinvertebrate diversity wetlands slower recovery i.e. pelagic habitats. advocate inclusion ecosystem restoration projects optimise wetland ecosystem sustainability.this funded spanish ministry innovation plan aragon ecological restoration consolidated gimaces doctoral caja inmaculada—aragon programa europa mobility counted ‘‘apn galachos reserve’’. garcı´a barcos analysing sanchez carranza miguel garcı´a field assistance english editing. grateful anonymous reviewers comments paper.peer reviewe | non_dup | [] |
19563680 | 10.1007/s00027-013-0297-4 | Light within the littoral zone affects the productivity and interaction between periphyton and its\ud
macrophyte substrate. The effect of periphyton on macrophyte photosynthesis, seasonal variation\ud
and vertical distribution of periphyton on artificial substrates (plastic strips), and the effect of\ud
periphyton on the light environment was studied in Lake Balaton.\ud
Data showed that an average of 4.1±0.4 mg (dry weight) cm-2 of periphyton had accumulated on\ud
the plastic strips after 8.8±0.4 days. This biomass corresponded to 294±30 μg m-2 chl-a of\ud
epiphytic algae and blocked 92.3±0.8 % of the depth specific radiation.\ud
Seasonal variation and specific vertical distribution of periphyton were observed. The most active\ud
time of periphyton accumulation corresponded to spring up until mid-June. Later in the year, the\ud
amount of periphyton significantly decreased. The optimal conditions for periphyton accumulation\ud
were at 30-40 cm depth.\ud
Most of the light reaching the adaxial leaf surface was attenuated by periphyton, decreasing the\ud
production of Potamogeton perfoliatus by 60-80%. This increased the importance of backscattered\ud
light that corresponded to 10-15% of the macrophyte production.\ud
A smaller part of the periphyton consisted of precipitated inorganic material, while epiphytic\ud
algae, making up the majority of the periphyton, were connected to both benthic (dominantly benthic penales) and pelagic (very close seasonal dynamics of pelagic and epiphytic biomass)\ud
algae. Periphyton affects macrophyte production especially in spring and in the upper water layers\ud
even in a mesotrophic water body. This increases the importance of the light absorbed through the\ud
abaxial side of the leaf and confirm the role of periphyton in transition from clear to turbid water\ud
states | The effect of periphyton on the light environment and production of Potamogeton perfoliatus L. in the mesotrophic basin of Lake Balaton | the effect of periphyton on the light environment and production of potamogeton perfoliatus l. in the mesotrophic basin of lake balaton | littoral affects productivity periphyton macrophyte substrate. periphyton macrophyte photosynthesis seasonal periphyton artificial substrates plastic strips periphyton lake balaton. periphyton accumulated plastic strips days. biomass corresponded epiphytic algae blocked radiation. seasonal periphyton observed. periphyton accumulation corresponded spring june. periphyton decreased. periphyton accumulation depth. reaching adaxial leaf attenuated periphyton decreasing potamogeton perfoliatus backscattered corresponded macrophyte production. periphyton consisted precipitated inorganic epiphytic algae majority periphyton benthic dominantly benthic penales pelagic seasonal pelagic epiphytic biomass algae. periphyton affects macrophyte spring mesotrophic body. absorbed abaxial leaf confirm periphyton turbid | non_dup | [] |
20126467 | 10.1007/s00027-013-0322-7 | Litter decomposition, a fundamental ecosystem
process in woodland streams, is potentially affected by the
predicted increase in water temperature. Here, we assessed
the effects of experimental and seasonal warming on oak
litter decomposition and on the relative contributions of
microbes and invertebrates to this process. Experimental
warming (*3 C) stimulated litter decomposition in the
coldest, but not in the warmest, months. This may be
attributed to (1) higher temperature sensitivity of decomposition
at lower ambient temperature due to temperature
limitation of enzymatic activity, (2) higher relative temperature
increase in winter than in warmer months, (3) existence
of a previous warming period in winter, and (4) stronger
stimulation of the activity of detritivores by warming in
winter due to the prevalence of earlier (smaller) instars than
in warmer months. The low response of litter decomposition
to warming may have been due to the low nutrient availability
in the study stream. The 30-day litter decomposition
was stimulated over the seasonal gradient (monthly mean
temperature: 6–16 C), which may be attributed to a stimulation
of metabolic activities by warming and to changes in
detritivore life history over the seasons. The stimulation of
litter decomposition with temperature suggests that the rate
of CO2 release from freshwaters will increase under global
warming. However, invertebrate-driven litter decomposition
was more responsive to warming than microbial-driven litter
decomposition, suggesting that a larger fraction of litter
carbon may be converted into secondary production and
stored in the system for longer periods.This study was partially financed by the Institute
of Marine Research (IMAR), the European Fund for Economic and
Regional Development (FEDER) through the Program Operational
Factors of Competitiveness (COMPETE), and National Funds
through the Portuguese Foundation of Science and Technology (FCT)
under the project ‘‘Predicting the effect of global warming on stream
ecosystems’’ (PTDC/CLI/67180/2006; FCOMP-01-0124-FEDER-
007112). Financial support granted by the FCT to VF (SFRH/BPD/
34368/2006 and SFRH/BPD/76482/2011, program POPH/FSE) is
gratefully acknowledged | Effect of experimental and seasonal warming on litter decomposition in a temperate stream | effect of experimental and seasonal warming on litter decomposition in a temperate stream | litter decomposition ecosystem woodland streams potentially temperature. seasonal warming litter decomposition microbes invertebrates process. warming stimulated litter decomposition coldest warmest months. attributed decomposition ambient limitation enzymatic winter warmer warming winter stronger stimulation detritivores warming winter prevalence instars warmer months. litter decomposition warming nutrient availability stream. litter decomposition stimulated seasonal monthly attributed stimulation metabolic warming detritivore seasons. stimulation litter decomposition freshwaters warming. invertebrate litter decomposition responsive warming microbial litter decomposition litter converted stored periods.this partially financed marine imar fund feder operational competitiveness compete funds portuguese foundation ‘‘predicting warming stream ecosystems’’ ptdc fcomp feder granted sfrh sfrh poph gratefully acknowledged | non_dup | [] |
36165459 | 10.1007/s00027-014-0355-6 | 14 páginas, 5 figuras, 2 tablas.Among the environmental factors affecting\ud
benthic algae and cyanobacteria in streams, the one often\ud
producing the largest effects is flow intermittency. This\ud
study aimed to characterize the responses of algal assemblages\ud
to flow intermittency in a Mediterranean\ud
intermittent stream during the drying, non-flow (112 days),\ud
and rewetting phases. Algae growing in the epilithic,\ud
epipsammic and hyporheic streambed compartments were\ud
analyzed for pigment composition, and for the existence of\ud
structural changes in cells. Chlorophyll-a concentrations\ud
decreased between 60 to 90 % during the non-flow phase,\ud
indicating low resistance of algal assemblages to desiccation.\ud
In contrast, fast recoveries of Chlorophyll-a when\ud
flow resumed indicated high resilience. Pigment composition\ud
revealed that the epilithic algal assemblage was\ud
considerably different than the epipsammic and hyporheic\ud
ones. These differences were mainly attributed to the\ud
physical conditions prevailing on each streambed compartment\ud
that allowed the growth of different algal\ud
assemblages. During the non-flow phase, the synthesis of\ud
protective carotenoids (i.e. echinenone and scytonemin)\ud
and the occurrence of cell resistance structures (i.e.\ud
enlarged membrane thickness and resistant spores)\ud
enhanced resistance of the epilithic biofilm. The resistance\ud
observed in the epilithic biofilm might also be related to the\ud
tightly adhered growth-form of algae on this substratum.\ud
Main results suggest that algal assemblages in the epilithic\ud
compartment, which were the most exposed to desiccation,\ud
were structurally and functionally better adapted to flow\ud
interruption than those colonizing other streambed compartments,\ud
and that this compartment plays a crucial role in\ud
maintaining ecosystem functions under varying flow\ud
periods.Xisca Timoner was recipient of a PhD\ud
fellowship from the Spanish Ministry of science and technology (AP-\ud
2007-01945), and Teresa Buchaca was partially supported by the\ud
Spanish Government project Invasive fish (427/2011). This research\ud
was funded by the projects SCARCE (CONSOLIDER-INGENIO\ud
CSD2009-00065), and CARBONET (CGL2011-30474-C02-01) of\ud
the Spanish Ministry of Science and Innovation.Peer reviewe | Photosynthetic pigment changes and adaptations in biofilms in response to flow intermittency | photosynthetic pigment changes and adaptations in biofilms in response to flow intermittency | páginas figuras tablas.among affecting benthic algae cyanobacteria streams producing intermittency. aimed characterize algal assemblages intermittency mediterranean intermittent stream drying rewetting phases. algae growing epilithic epipsammic hyporheic streambed compartments pigment cells. chlorophyll algal assemblages desiccation. recoveries chlorophyll resumed resilience. pigment epilithic algal assemblage considerably epipsammic hyporheic ones. attributed prevailing streambed compartment algal assemblages. protective carotenoids i.e. echinenone scytonemin occurrence i.e. enlarged resistant spores epilithic biofilm. epilithic biofilm tightly adhered algae substratum. algal assemblages epilithic compartment exposed desiccation structurally functionally adapted interruption colonizing streambed compartments compartment plays crucial maintaining ecosystem periods.xisca timoner recipient fellowship spanish ministry teresa buchaca partially spanish invasive fish funded projects scarce consolider ingenio carbonet spanish ministry innovation.peer reviewe | non_dup | [] |
80907512 | 10.1007/s00027-014-0370-7 | Invasive species and anthropogenic sources of allochthonous trophic subsidies can have substantial eco-logical
consequences for freshwater ecosystems, including modifying the diet of consumers and altering food web structure. Here,
the diet of an omnivorous cyprinid fish, European barbel Barbus barbus, was assessed in relation to the presence of
invasive signal crayfish Pacifastacus le-niusculus and pelletized fish-meal in four rivers in England. Pellets are often used
in large quantities by river anglers and thus could provide an important trophic subsidy, not only to the fish but also
indirectly via P. leniusculus. Carbon and nitrogen stable isotopes were used to estimate the proportion of diet assimilated
from natural sources and from P. leniusculus and pellets by B. barbus of lengths between 420 and 800 mm. Pellets
generally made a large contribution to the overall biomass of B. barbus (up to 59 % of population diet) and in the two rivers
where they were present, P. leniusculus were also an important resource (up to 30 % of population diet). The proportion
derived from macro-invertebrates (excluding P. leniuscu-lus) was substantially lower. Stable isotope mixing models further
demonstrated considerable intraspecific variability in B. barbus diet within the rivers, with pellets comprising up to 79 % of
the biomass of individual B. barbus in rivers where P. leniusculus was absent. Where present, P. le-niusculus effectively
replaced and thus reduced the contribution of pellets to individual fish diet. Thus, isotopic evidence from three of the four
rivers indicates that B. barbus populations are heavily reliant ([50 %) upon angler-introduced baits that act as an important
allochtho-nous subsidy and will also prey upon invasive P. leniusculus where they are present.http://link.springer.com/journal/272016-01-31hb201 | Angling baits and invasive crayfish as important trophic subsidies for a large cyprinid fish | angling baits and invasive crayfish as important trophic subsidies for a large cyprinid fish | invasive anthropogenic allochthonous trophic subsidies substantial logical consequences freshwater ecosystems modifying diet consumers altering structure. diet omnivorous cyprinid fish barbel barbus barbus invasive crayfish pacifastacus niusculus pelletized fish meal rivers england. pellets quantities river anglers trophic subsidy fish indirectly leniusculus. nitrogen isotopes proportion diet assimilated leniusculus pellets barbus lengths pellets biomass barbus diet rivers leniusculus resource diet proportion macro invertebrates excluding leniuscu substantially lower. isotope considerable intraspecific barbus diet rivers pellets comprising biomass barbus rivers leniusculus absent. niusculus effectively replaced pellets fish diet. isotopic rivers barbus heavily reliant angler baits allochtho nous subsidy prey invasive leniusculus present. | non_dup | [] |
38631768 | 10.1007/s00027-015-0430-7 | Remote sensing (RS) technology offers unparalleled opportunities to explore river systems using RADAR, multispectral, hyperspectral, and LIDAR data. The accuracy reached by these technologies recently has started to satisfy the spatial and spectral resolutions required to properly analyse the hydromorphological character of river systems at multiple scales. Using the River Hierarchical Framework (RHF) as a reference we describe the state-ofthe- art RS technologies that can be implemented to quantify hydromorphological characteristics at each of the spatial scales incorporated in the RHF (i.e. catchment, landscape unit, river segment, river reach, sub-reach - geomorphic and hydraulic units). We also report the results of a survey on RS data availability in EU member states that provides the basis for a discussion on the current potential to derive RHF hydromorphological indicators from high-resolution multispectral images and topographic LiDAR at the national scale across Europe. This paper shows that many of the assessment indicators proposed by the RHF can be already derived by different RS sources and existing methodologies, and that EU countries have sufficient RS data at present to already begin their incorporation into hydromorphology assessment and monitoring, as mandated by WFD, which so far have been insufficiently addressed by the member states due to the demanding efforts it would require. With cooperation and planning, RS data can form a fundamental component of hydromorphological assessment and monitoring in the future to help support the effective and sustainable management of rivers, and this would be done most effectively through the establishment of multi-purpose RS acquisition campaigns and the development of shared and standardized hydromorphological RS databases updated regularly through planned resurveyed campaigns.JRC.H.1-Water Resource | The use of remote sensing to characterise hydromorphological properties of European rivers | the use of remote sensing to characterise hydromorphological properties of european rivers | remote sensing offers unparalleled opportunities explore river radar multispectral hyperspectral lidar data. reached technologies started satisfy resolutions properly analyse hydromorphological character river scales. river hierarchical ofthe technologies implemented quantify hydromorphological incorporated i.e. catchment landscape river segment river geomorphic hydraulic availability member derive hydromorphological indicators multispectral topographic lidar europe. indicators methodologies begin incorporation hydromorphology mandated insufficiently addressed member demanding efforts require. cooperation planning hydromorphological sustainable rivers effectively establishment acquisition campaigns shared standardized hydromorphological databases updated regularly planned resurveyed campaigns.jrc.h. resource | non_dup | [] |
33453936 | 10.1007/s00027-015-0447-y | Accounting for greenhouse gas (GHG) emissions and removals in managed ecosystems has generally focused on direct land-atmosphere fluxes, but in peatlands a significant proportion of total carbon loss occurs via fluvial transport. This study considers the composition of this ‘waterborne carbon’ flux, its potential contribution to GHG emissions, and the extent to which it may change in response to land-management. The work describes, and builds on, a methodology to account for major components of these emissions developed for the 2013 Wetland Supplement of the Intergovernmental Panel on Climate Change. We identify two major components of GHG emissions from waterbodies draining organic soil: i) ‘on site’ emissions of methane (and to a lesser extent CO2) from drainage ditches located within the peatland; and ii) ‘off site’ emissions of CO2 resulting from downstream oxidation of dissolved and particulate organic carbon (DOC and POC) within the aquatic system. Methane emissions from ditches were found to be large in many cases (mean 60 g CH4 m-2 yr-1 based on all reported values), countering the view that methane emissions cease following wetland drainage. Emissions were greatest from ditches in intensive agricultural peatlands, but data were sparse and showed high variability. For DOC, the magnitude of the natural flux varied strongly with latitude, from 5 g C m-2 yr-1 in northern boreal peatlands to 60 g C m-2 yr-1 in tropical peatlands. Available data suggest that DOC fluxes increase by around 60% following drainage, and that this increase may be reversed in the longer-term through re-wetting, although variability between studies was high, especially in relation to re-wetting response. Evidence regarding the fate of DOC is complex and inconclusive, but overall suggests that the majority of DOC exported from peatlands is converted to CO2 through photo- and/or bio-degradation in rivers, standing waters and oceans. The contribution of POC export to GHG emissions is even more uncertain, but we estimate that over half of exported POC may eventually be converted to CO2. Although POC fluxes are normally small, they can become very large when bare peat surfaces are exposed to fluvial erosion. Overall, we estimate that waterborne carbon emissions may contribute about 1 to 4 t CO2-eq ha-1 yr-1 of additional GHG emissions from drained peatlands. For a number of worked examples this represented around 15 to 50% of total GHG emissions | The role of waterborne carbon in the greenhouse gas balance of drained and re-wetted peatlands | the role of waterborne carbon in the greenhouse gas balance of drained and re-wetted peatlands | accounting greenhouse removals managed ecosystems focused atmosphere fluxes peatlands proportion fluvial transport. considers ‘waterborne carbon’ management. describes builds methodology wetland supplement intergovernmental change. waterbodies draining site’ methane lesser drainage ditches peatland ‘off site’ downstream oxidation dissolved particulate aquatic system. methane ditches countering methane cease wetland drainage. greatest ditches intensive agricultural peatlands sparse variability. varied latitude northern boreal peatlands tropical peatlands. fluxes drainage reversed wetting wetting response. fate inconclusive majority exported peatlands converted photo degradation rivers standing waters oceans. export uncertain exported eventually converted fluxes normally bare peat exposed fluvial erosion. waterborne drained peatlands. worked | non_dup | [] |
76969709 | 10.1007/s00027-015-0456-x | In-stream processing of allochthonous dissolved organic carbon (DOC) and particulate organic carbon (POC) in peat-sourced headwaters has been shown to be a significant part of the terrestrial carbon cycle, through photo- and bio-degradation, with both DOC and POC converted to carbon dioxide (CO2). This study reports a series of 70-h, in situ experiments investigating rates of degradation in unfiltered surface water from a headwater stream in the River Tees, North Pennines, UK. Half the samples were exposed to the normal day/night cycle (ambient); half were continuously dark. The study found that the DOC concentration of samples in the ambient treatment declined by 64 % over the 70 h, compared with 6 % decline for the samples kept in the dark. For POC, the loss in the ambient treatment was 13 %. The average initial rate of loss of DOC in the ambient treatment during the first day of the experiment was 3.36 mg C/l/h, and the average rate of photo-induced loss over the whole 70 h was 1.25 mg C/l/h. Scaling up these losses, the estimate of total organic carbon loss from UK rivers to the atmosphere is 9.4 Tg CO2/year which would be 0.94 % of the global estimate of CO2 emissions from streams and rivers from the 2013 IPCC report. Initial rate kinetics in the light were as high as 3rd order, but the study showed that no single rate law could describe the whole diurnal degradation cycle and that separate rate laws were required for night and day processes. The comparison of dark and ambient treatment processes showed no evidence of photo-stimulated bacterial degradation | Sub-daily rates of degradation of fluvial carbon from a peat headwater stream. | sub-daily rates of degradation of fluvial carbon from a peat headwater stream. | stream allochthonous dissolved particulate peat sourced headwaters terrestrial photo degradation converted dioxide situ investigating degradation unfiltered headwater stream river tees pennines exposed night ambient continuously dark. ambient declined decline kept dark. ambient ambient photo losses rivers atmosphere streams rivers ipcc report. kinetics diurnal degradation laws night processes. ambient photo stimulated bacterial degradation | non_dup | [] |
76971337 | 10.1007/s00027-015-0458-8 | Peatlands and other terrestrial ecosystems export large amounts of dissolved organic carbon (DOC) to freshwater ecosystems. In catchments used for supplying drinking water, water treatment works (WTWs) can remove large quantities of this organic matter, and can therefore play a unique modifying role in DOC processing and associated greenhouse gas (GHG) emissions within the fluvial system. During this study we quantified the GHG emissions due to processes associated with carbon (C) removal during water treatment at four contrasting WTWs in the UK. Our results demonstrate that the removal of DOC from raw water supplies via coagulation, leading to the formation of sludge, usually makes it less susceptible to short-term oxidation when compared to DOC remaining in the fluvial system. Although this could be considered a means of reducing CO2 emissions from waterborne carbon, the current practise of land spreading of sludge is unlikely to represent a long-term C sink and therefore water treatment probably only delays the rate at which fluvial C re-enters the atmosphere. Furthermore, we estimate that indirect CO2 missions resulting from electricity use during water treatment, together with the use of chemicals and CO2 degassing from the water during treatment, far outweigh any potential CO2 reductions associated with DOC removal. Thus, the post-treatment handling of sludge has the potential to mitigate, but not to negate, GHG emissions associated with water treatment processes | The greenhouse gas (GHG) emissions associated with aquatic carbon removal during drinking water treatment | the greenhouse gas (ghg) emissions associated with aquatic carbon removal during drinking water treatment | peatlands terrestrial ecosystems export amounts dissolved freshwater ecosystems. catchments supplying drinking wtws remove quantities modifying greenhouse fluvial system. quantified removal contrasting wtws removal supplies coagulation sludge susceptible oxidation fluvial system. reducing waterborne practise spreading sludge unlikely sink probably delays fluvial enters atmosphere. indirect missions electricity chemicals degassing outweigh reductions removal. handling sludge mitigate negate | non_dup | [] |
76971338 | 10.1007/s00027-015-0461-0 | Peatlands export significant amounts of dissolved organic carbon (DOC) to freshwaters, but the quantity of DOC reaching marine environments is typically less than the input to the fluvial system due to processing within the water column. Key removal processes include photo-chemical degradation, and heterotrophic bacterial respiration. In this study we examined these processes using 14C-labelled DOC to quantify the extent of DOC breakdown and to determine its fate following irradiation under controlled laboratory conditions. We examined the influence of microbial processes occurring within the water column, the potential role of stream-bed biofilms, and the possible modifying effects of downstream mixing, as DOC in water from the peatland encounters runoff from upland mineral soils (“Mountain”), nutrient-rich runoff from agricultural soils, and seawater in an estuary. Our results demonstrated conservative mixing of DOC from Peatland and Mountain waters but interactive effects when Peatland water was mixed with Agricultural and Estuary waters and exposed to solar radiation. The mixing of Peatland and Agricultural waters led to net DOC production, suggesting that DOC was only partially degraded by solar radiation and that the products of this might have fuelled autotrophic microbial growth in the samples. The mixing of Peatland water with saline estuary water resulted in net DOC loss following irradiation, suggesting a role for sunlight in enhancing the flocculation of DOC to particulate organic carbon (POC) in saline environments | Transformations in DOC along a source to sea continuum; impacts of photo-degradation, biological processes and mixing | transformations in doc along a source to sea continuum; impacts of photo-degradation, biological processes and mixing | peatlands export amounts dissolved freshwaters quantity reaching marine environments fluvial column. removal photo degradation heterotrophic bacterial respiration. labelled quantify breakdown fate irradiation conditions. microbial occurring stream biofilms modifying downstream peatland encounters runoff upland mineral soils “mountain” nutrient runoff agricultural soils seawater estuary. conservative peatland mountain waters interactive peatland agricultural estuary waters exposed radiation. peatland agricultural waters partially degraded fuelled autotrophic microbial samples. peatland saline estuary resulted irradiation sunlight enhancing flocculation particulate saline environments | non_dup | [] |
33454136 | 10.1007/s00027-016-0470-7 | This special issue brought together a complementary set of\ud
studies describing the range of processes affecting the\ud
cycling and fate of terrigenous organic matter within\ud
aquatic systems. It focuses in particular on headwater\ud
streams, and on peat catchments as major global sources of\ud
freshwater dissolved organic matter and of particulate organic matter in areas of peat erosion. This work is placed within the wider context of processes\ud
occurring in forested and agricultural headwaters, larger\ud
river systems and estuaries, and in a policy context in\ud
relation to national-scale carbon fluxes, the treatment of\ud
organic matter in drinking water supplies and the inclusion\ud
of aquatic carbon in international greenhouse gas\ud
accounting | Controls on the processing and fate of terrestrially-derived organic carbon in aquatic ecosystems: synthesis of special issue | controls on the processing and fate of terrestrially-derived organic carbon in aquatic ecosystems: synthesis of special issue | brought complementary describing affecting cycling fate terrigenous aquatic systems. focuses headwater streams peat catchments freshwater dissolved particulate peat erosion. placed wider occurring forested agricultural headwaters river estuaries fluxes drinking supplies inclusion aquatic greenhouse accounting | non_dup | [] |
43227206 | 10.1007/s00027-016-0491-2 | We report a data-set of monthly vertical profiles obtained from January 2012 to October 2013, from the surface to 70 m depth of nitrous oxide (N2O) and dissolved methane (CH4) in Lake Kivu, a large and deep meromictic tropical lake (East Africa). Vertical variations of N2O were modest, with ranges of 6--9 and 0--16 nmol L−1 in surface and bottom waters, respectively, and occasionally peaks of N2O (up to 58 nmol L−1) were observed at the oxic-anoxic interface. On the contrary, steep vertical gradients of CH4 were observed with values changing several orders of magnitude from surface (19--103 nmol L−1) to 70 m (113,000--520,000 nmol L−1). Seasonal variations of CH4 were caused by annual cycles of mixing and stratification, during the dry and rainy seasons, respectively. This mixing allowed the establishment of a thick oxic layer (maximum 65 m deep), leading to decreased CH4 concentrations (minimum of 8 nmol L−1), presumably due to bacterial CH4 oxidation. During the stratification period, the oxic mixed layer was thinner (minimum 25 m deep), and an increase of CH4 concentrations in surface waters was observed (maximum of 103 nmol L−1), probably due to a lower integrated CH4 oxidation on the water column. Lake Kivu seasonally alternated between a source and a sink for atmospheric N2O, but on an annual scale was a small source of N2O to the atmosphere (on average 0.43 \textmumol m−2 day−1), while it was a small source of CH4 to the atmosphere throughout the year (on average 86 \textmumol m−2 day−1). Vertical and seasonal variations of N2O are discussed in terms of nitrification and denitrification, although from the present data-set it is not possible to unambiguously identify the main drivers of N2O production.Peer reviewe | Nitrous oxide and methane seasonal variability in the epilimnion of a large tropical meromictic lake (Lake Kivu, East-Africa) | nitrous oxide and methane seasonal variability in the epilimnion of a large tropical meromictic lake (lake kivu, east-africa) | monthly october nitrous oxide dissolved methane lake kivu meromictic tropical lake east africa modest ranges nmol waters occasionally nmol oxic anoxic interface. contrary steep gradients changing orders nmol nmol seasonal cycles stratification rainy seasons respectively. establishment thick oxic nmol presumably bacterial oxidation. stratification oxic thinner waters nmol probably oxidation column. lake kivu seasonally alternated sink atmosphere textmumol day− atmosphere textmumol day− seasonal nitrification denitrification unambiguously drivers production.peer reviewe | non_dup | [] |
154933766 | 10.1007/s00027-017-0518-3 | Disruption of longitudinal connectivity is a major concern in most of the world¿s rivers. Approaches based on graph theory have proven to be a suitable tool for analysing functional connectivity. However, previous applications of graph-based connectivity methods to river systems have been oversimplified in that they have treated potential barriers as binary features and rivers as symmetric networks. We here apply a network analytical approach in which (a) upstream and downstream connectivity are considered so that fish passability values across dams are asymmetrical, and (b) it is possible to consider a continuous range of passability values for every dam. We build on previous and widely used connectivity metrics (Probability of Connectivity, PC), which here are generalised and adapted toward that end. We compare the results of our approach with those that would be obtained under the more simplified assumptions of symmetric movement and of barriers as binary features. We want to prove if there are substantial differences between considering or not the asymmetry in river networks. The application of symmetrical and asymmetrical PC highlights major differences between the upstream connectivity versus the downstream connectivity. We provide our methods in a free software package so that they can be used in any other application to riverscapes. We expect to provide a better graph-based approach for the prioritisation of the removal or permeabilization of artificial obstacles as well as for the preservation of target river segments for connectivity conservation and restoration | Longitudinal connectivity loss in a riverine network: accounting for the likelihood of upstream and downstream movement across dams | longitudinal connectivity loss in a riverine network: accounting for the likelihood of upstream and downstream movement across dams | disruption longitudinal connectivity concern world¿s rivers. proven analysing connectivity. connectivity river oversimplified barriers rivers networks. upstream downstream connectivity fish passability dams asymmetrical passability dam. build widely connectivity metrics connectivity generalised adapted toward end. simplified assumptions movement barriers features. want substantial asymmetry river networks. symmetrical asymmetrical highlights upstream connectivity downstream connectivity. package riverscapes. prioritisation removal permeabilization artificial obstacles preservation river segments connectivity conservation restoration | non_dup | [] |
151304404 | 10.1007/s00027-018-0573-4 | The hydrological status of river systems is expected to change due to dam operations and climate change. This will affect the riverine fluxes of sediment and carbon (C). In rivers with strong seasonal and inter-annual variability, quantification and extrapolation of sediment and C fluxes can be a challenge as measurement periods are often too short to cover all hydrological conditions. We studied the dynamics of the Tana River (Kenya) from 2012 to 2014 through daily monitoring of sediment concentrations at three sites (Garissa, Tana River Primate Reserve and Garsen) and daily monitoring of C concentrations in Garissa and Garsen during three distinct seasons. A bootstrap method was applied to calculate the range of sediment and C fluxes as a function of annual discharge by using daily discharge data (1942–2014). Overall, we estimated that on average, sediment and carbon were retained in this 600 km long river section between Garissa to Garsen over the 73 years (i.e., fluxes were higher at the upstream site than downstream): integration over all simulations resulted in an average net retention of sediment (~ 2.9 Mt year− 1), POC (~ 18,000 tC year− 1), DOC (~ 920 tC year− 1) and DIC (~ 1200 tC year− 1). To assess the impact of hydrological variations, we constructed four different hydrological scenarios over the same period. Although there was significant non-linearity and difference between the C species, our estimates generally predicted a net increase of C retention between the upstream and downstream site when the annual discharge would decrease, for example caused by an increase of irrigation with reservoir water. When simulating an increase in the annual discharge, e.g. as a potential effect of climate change, we predicted a decrease in C retention.Peer reviewe | Seasonal and inter-annual variations in carbon fluxes in a tropical river system (Tana River, Kenya) | seasonal and inter-annual variations in carbon fluxes in a tropical river system (tana river, kenya) | hydrological river operations change. riverine fluxes sediment rivers seasonal quantification extrapolation sediment fluxes challenge cover hydrological conditions. tana river kenya sediment garissa tana river primate reserve garsen garissa garsen seasons. bootstrap sediment fluxes discharge discharge sediment retained river garissa garsen i.e. fluxes upstream downstream resulted retention sediment year− year− year− year− hydrological hydrological scenarios period. linearity retention upstream downstream discharge irrigation reservoir water. simulating discharge e.g. retention.peer reviewe | non_dup | [] |
2591814 | 10.1007/s00028-007-0288-9 | This is the second part of a series of four articles on weighted norm
inequalities, off-diagonal estimates and elliptic operators. We consider a
substitute to the notion of pointwise bounds for kernels of operators which
usually is a measure of decay. This substitute is that of off-diagonal
estimates expressed in terms of local and scale invariant $L^p-L^q$ estimates.
We propose a definition in spaces of homogeneous type that is stable under
composition. It is particularly well suited to semigroups. We study the case of
semigroups generated by elliptic operators.Comment: 40 pages. Second of 4 papers. Can be read independentl | Weighted norm inequalities, off-diagonal estimates and elliptic
operators. Part II: Off-diagonal estimates on spaces of homogeneous type | weighted norm inequalities, off-diagonal estimates and elliptic operators. part ii: off-diagonal estimates on spaces of homogeneous type | articles weighted norm inequalities diagonal elliptic operators. substitute notion pointwise bounds kernels decay. substitute diagonal estimates. propose homogeneous composition. suited semigroups. semigroups elliptic pages. papers. read independentl | non_dup | [] |
2601526 | 10.1007/s00028-007-0351-6 | Second order equations of the form $z'' + A_0 z + D z'=0$ in an abstract
Hilbert space are considered. Such equations are often used as a model for
transverse motions of thin beams in the presence of damping. We derive various
properties of the operator matrix $A$ associated with the second order problem
above. We develop sufficient conditions for analyticity of the associated
semigroup and for the existence of a Riesz basis consisting of eigenvectors and
associated vectors of $A$ in the phase space | Analyticity and Riesz basis property of semigroups associated to damped
vibrations | analyticity and riesz basis property of semigroups associated to damped vibrations | hilbert considered. motions beams damping. derive above. analyticity semigroup riesz consisting eigenvectors | non_dup | [] |
2018781 | 10.1007/s00028-009-0022-x | We consider the radial wave equation in similarity coordinates within the
semigroup formalism. It is known that the generator of the semigroup exhibits a
continuum of eigenvalues and embedded in this continuum there exists a discrete
set of eigenvalues with analytic eigenfunctions. Our results show that, for
sufficiently regular data, the long time behaviour of the solution is governed
by the analytic eigenfunctions. The same techniques are applied to the linear
stability problem for the fundamental self--similar solution $\chi_T$ of the
wave equation with a focusing power nonlinearity. Analogous to the free wave
equation, we show that the long time behaviour (in similarity coordinates) of
linear perturbations around $\chi_T$ is governed by analytic mode solutions. In
particular, this yields a rigorous proof for the linear stability of $\chi_T$
with the sharp decay rate for the perturbations.Comment: This new version fixes a problem with an incorrect use of spectral
projections; results remain unchange | Asymptotics and analytic modes for the wave equation in similarity
coordinates | asymptotics and analytic modes for the wave equation in similarity coordinates | similarity semigroup formalism. generator semigroup exhibits continuum eigenvalues embedded continuum eigenvalues analytic eigenfunctions. sufficiently governed analytic eigenfunctions. focusing nonlinearity. analogous similarity perturbations governed analytic solutions. rigorous sharp fixes incorrect projections unchange | non_dup | [] |
53861020 | 10.1007/s00028-011-0115-1 | Given a parabolic cylinder $Q =(0,T)\times\Omega$, where $\Omega\subset \rn$ is a bounded domain, we \ud
prove new properties of solutions of \ud
\[\ud
u_t-\Delta_p u = \mu \quad \text{in $Q$}\ud
\]\ud
with Dirichlet boundary conditions, where $\mu$ is a finite Radon measure in $Q$. We first prove a priori estimates on the $p$-parabolic capacity of level sets of $u$. We then show that diffuse measures (i.e.\@ measures which do not charge sets of zero parabolic $p$-capacity) can be strongly approximated by the measures $\mu_k = (T_k(u))_t-\Delta_p(T_k(u))$, and we introduce a new notion of renormalized solution based on this property. We finally apply our new approach to prove the existence of solutions of \ud
$$\ud
u_t-\Delta_{p} u + h(u)=\mu \quad \text{in $Q$,}\ud
$$\ud
for any function $h$ such that $h(s)s\geq 0$ and for any diffuse measure $\mu$; when $h$ is nondecreasing we also prove uniqueness in the renormalized formulation | Diffuse measures and nonlinear parabolic \ud
equations | diffuse measures and nonlinear parabolic \ud equations | parabolic cylinder omega omega delta quad dirichlet radon priori parabolic diffuse i.e. parabolic approximated delta notion renormalized property. delta quad diffuse nondecreasing uniqueness renormalized formulation | non_dup | [] |
2244711 | 10.1007/s00028-012-0135-5 | Morphogen transport is a biological process, occurring in the tissue of
living organisms, which is a determining step in cell differentiation. We
present rigorous analysis of a simple model of this process, which is a system
coupling parabolic PDE with ODE. We prove existence and uniqueness of solutions
for both stationary and evolution problems. Moreover we show that the solution
converges exponentially to the equilibrium in $C^1\times C^0$ topology. We
prove all results for arbitrary dimension of the domain. Our results improve
significantly previously known results for the same model in the case of one
dimensional domain | Well-posedness and asymptotic behavior of a multidimensional model of
morphogen transport | well-posedness and asymptotic behavior of a multidimensional model of morphogen transport | morphogen occurring living organisms determining differentiation. rigorous parabolic ode. uniqueness stationary problems. converges exponentially topology. domain. | non_dup | [] |
56658041 | 10.1007/s00028-013-0187-1 | This paper is devoted to a semigroup approach to an initial-boundary value problem of linear elastodynamics in the case where the boundary condition is a regularization of the genuine mixed displacement-traction boundary condition. More precisely, it is a smooth linear combination of displacement and traction boundary conditions, but is not equal to the pure traction boundary condition. Some previous results with mixed displacement-traction boundary condition are due to Inoue and Ito. The crucial point in our semigroup approach is to generalize the classical variational approach to the degenerate case, by using the theory of fractional powers of analytic semigroups | A mixed problem of linear elastodynamics | a mixed problem of linear elastodynamics | devoted semigroup elastodynamics regularization genuine displacement traction condition. precisely displacement traction traction condition. displacement traction inoue ito. crucial semigroup generalize variational degenerate fractional powers analytic semigroups | non_dup | [] |
24944003 | 10.1007/s00028-013-0200-8 | We present a formula for the regular part of a sectorial form that represents
a general linear second-order differential expression that may include
lower-order terms. The formula is given in terms of the original coefficients.
It shows that the regular part is again a differential sectorial form and
allows to characterise when also the singular part is sectorial. While this
generalises earlier results on pure second-order differential expressions, it
also shows that lower-order terms truly introduce new behaviour.Comment: 11 page | The regular part of second-order differential sectorial forms with
lower-order terms | the regular part of second-order differential sectorial forms with lower-order terms | sectorial terms. coefficients. sectorial characterise singular sectorial. generalises expressions truly | non_dup | [] |
19212465 | 10.1007/s00028-013-0208-0 | We reveal three surprising properties of cosine families, distinguishing them from semigroups of operators: (1) A single trajectory of a cosine family is either strongly continuous or not measurable. (2) Pointwise convergence of a sequence of equibounded cosine families implies that the convergence is almost uniform for time in the entire real line; in particular, cosine families cannot be perturbed in a singular way. (3) A non-constant trajectory of a bounded cosine family does not have a limit at infinity; in particular, the rich theory of asymptotic behaviour of semigroups does not have a counterpart for cosine families. In addition, we show that equibounded cosine families that converge strongly and almost uniformly in time may fail to converge uniformly.Adam Bobrowski and Wojciech Chojnack | Cosine families and semigroups really differ | cosine families and semigroups really differ | reveal surprising cosine families distinguishing semigroups trajectory cosine measurable. pointwise equibounded cosine families cosine families perturbed singular way. trajectory cosine infinity asymptotic semigroups counterpart cosine families. equibounded cosine families converge uniformly fail converge uniformly.adam bobrowski wojciech chojnack | non_dup | [] |
48199584 | 10.1007/s00028-013-0214-2 | International audienceSystems of Hamilton-Jacobi equations arise naturally when we study the optimal control problems with pathwise deterministic trajectories with random switching. In this work, we are interested in the large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations in the periodic setting. The large time behavior for systems of Hamilton-Jacobi equations have been obtained by Camilli-Loreti-Ley and the author (2012) and Mitake-Tran (2012) under quite strict conditions. In this work, we use a PDE approach to extend the convergence result proved by Barles-Souganidis (2000) in the scalar case. This general result permits us to treat lot of general cases, for instance, systems with nonconvex Hamiltonians and systems with strictly convex Hamiltonians. We also obtain some other convergence results under different assumptions, these results give a clearer view on the large time behavior for systems of Hamilton-Jacobi equations | Some results on the large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations | some results on the large time behavior of weakly coupled systems of first-order hamilton-jacobi equations | audiencesystems hamilton jacobi arise naturally pathwise deterministic trajectories switching. interested weakly hamilton jacobi setting. hamilton jacobi camilli loreti mitake tran strict conditions. extend proved barles souganidis case. permits treat nonconvex hamiltonians strictly convex hamiltonians. assumptions clearer hamilton jacobi | non_dup | [] |
41776283 | 10.1007/s00028-014-0242-6 | The final publication is available at Springer via http://dx.doi.org/10.1007/s00028-014-0242-6.In two recent papers, the authors have studied conditions on the relaxation parameters in order to guarantee the stability or instability of solutions for the Taylor approximations to dual-phase-lag and three-phase-lag heat conduction equations. However, for several limit cases relating to the parameters, the kind of stability was unclear. Here, we analyze these limit cases and clarify whether we can expect exponential or slow decay for the solutions. Moreover, rather general well-posedness results for three-phase-lag models are presented. Finally, the exponential stability expected by spectral analysis is rigorously proved exemplarily.Peer ReviewedPostprint (author’s final draft | Phase-lag heat conduction: decay rates for limit problems and well-posedness | phase-lag heat conduction: decay rates for limit problems and well-posedness | publication springer papers relaxation guarantee instability taylor approximations conduction equations. relating kind unclear. analyze clarify exponential slow solutions. posedness presented. exponential rigorously proved exemplarily.peer reviewedpostprint author’s draft | non_dup | [] |
24982708 | 10.1007/s00028-014-0243-5 | In this paper we study the stability properties of strongly continuous
semigroups generated by block operator matrices. We consider triangular and
full operator matrices whose diagonal operator blocks generate polynomially
stable semigroups. As our main results, we present conditions under which also
the semigroup generated by the operator matrix is polynomially stable. The
theoretic results are applied to deriving conditions for the polynomial
stability of a system consisting of a two-dimensional and a one-dimensional
damped wave equations.Comment: 28 pages, 1 figures, submitte | Polynomial Stability of Semigroups Generated by Operator Matrices | polynomial stability of semigroups generated by operator matrices | semigroups matrices. triangular diagonal blocks polynomially semigroups. semigroup polynomially stable. theoretic deriving consisting damped pages submitte | non_dup | [] |
42641835 | 10.1007/s00028-015-0279-1 | In this paper we study differential operators of the form \begin{align*}
\left[\mathcal{L}_\infty v \right](x) = A\triangle v(x) + \left\langle
Sx,\nabla v(x) \right\rangle - Bv(x), \,x \in \mathbb{R}^d, \,d \geqslant 2,
\end{align*} for matrices $A,B\in\mathbb{C}^{N,N}$, where the eigenvalues of
$A$ have positive real parts. The sum $A\triangle v(x) + \left\langle Sx,
\nabla v(x) \right\rangle$ is known as the Ornstein-Uhlenbeck operator with an
unbounded drift term defined by a skew-symmetric matrix $S\in\mathbb{R}^{d,d}$.
Differential operators such as $\mathcal{L}_{\infty}$ arise as linearizations
at rotating waves in time-dependent reaction diffusion systems. The results of
this paper serve as foundation for proving exponential decay of such waves.
Under the assumption that $A$ and $B$ can be diagonalized simultaneously we
construct a heat kernel matrix $H(x,\xi,t)$ of $\mathcal{L}_{\infty}$ that
solves the evolution equation $v_t=\mathcal{L}_{\infty}v$. In the following we
study the Ornstein-Uhlenbeck semigroup \begin{align*} \left[ T(t)v\right](x) =
\int_{\mathbb{R}^d} H(x,\xi,t) v(\xi) d\xi,\,x \in \mathbb{R}^d,\, t>0,
\end{align*} in exponentially weighted function spaces. This is used to derive
resolvent estimates for $\mathcal{L}_{\infty}$ in exponentially weighted
$L^p$-spaces $L^p_{\theta} (\mathbb{R}^d,\mathbb{C}^N)$, $1\leqslant p<\infty$,
as well as in exponentially weighted $C_{\mathrm{b}}$-spaces
$C_{\mathrm{b},\theta}(\mathbb{R}^d,\mathbb{C}^N)$.Comment: 35 pages, J. Evol. Equ. (published online 2015 | Exponentially weighted resolvent estimates for complex
Ornstein-Uhlenbeck systems | exponentially weighted resolvent estimates for complex ornstein-uhlenbeck systems | begin align mathcal infty triangle langle nabla rangle mathbb geqslant align mathbb eigenvalues parts. triangle langle nabla rangle ornstein uhlenbeck unbounded drift skew mathbb mathcal infty arise linearizations rotating systems. serve foundation proving exponential waves. diagonalized simultaneously kernel mathcal infty solves mathcal infty ornstein uhlenbeck semigroup begin align mathbb mathbb align exponentially weighted spaces. derive resolvent mathcal infty exponentially weighted theta mathbb mathbb leqslant infty exponentially weighted mathrm mathrm theta mathbb mathbb .comment pages evol. equ. | non_dup | [] |
25017616 | 10.1007/s00028-015-0280-8 | Given a linear semi-bounded symmetric operator $S\ge -\omega$, we explicitly
define, and provide their nonlinear resolvents, nonlinear maximal monotone
operators $A_\Theta$ of type $\lambda>\omega$ (i.e. generators of one-parameter
continuous nonlinear semi-groups of contractions of type $\lambda$) which
coincide with the Friedrichs extension of $S$ on a convex set containing
${\mathscr D}(S)$. The extension parameter $\Theta\subset{\mathfrak
h}\times{\mathfrak h}$ ranges over the set of nonlinear maximal monotone
relations on an auxiliary Hilbert space $\mathfrak h$ isomorphic to the
deficiency subspace of $S$. Moreover $A_\Theta+\lambda$ is a sub-potential
operator (i.e. is the sub-differential of a lower semicontinuos convex
function) whenever $\Theta$ is sub-potential. Examples describing Laplacians
with nonlinear singular perturbations supported on null sets and Laplacians
with nonlinear boundary conditions on a bounded set are given.Comment: Revised final version. To appear in Journal of Evolution Equation | Nonlinear Maximal Monotone Extensions of Symmetric Operators | nonlinear maximal monotone extensions of symmetric operators | omega explicitly resolvents maximal monotone theta lambda omega i.e. generators contractions lambda coincide friedrichs convex mathscr theta mathfrak mathfrak ranges maximal monotone auxiliary hilbert mathfrak isomorphic deficiency subspace theta lambda i.e. semicontinuos convex whenever theta potential. describing laplacians singular perturbations laplacians revised version. | non_dup | [] |
29512707 | 10.1007/s00028-015-0302-6 | Well posedness is established for a family of equations modelling particle
populations undergoing delocalised coagulation, advection, inflow and outflow
in a externally specified velocity field. Very general particle types are
allowed while the spatial domain is a bounded region of $d$-dimensional space
for which every point lies on exactly one streamline associated with the
velocity field. The problem is formulated as a semi-linear ODE in the Banach
space of bounded measures on particle position and type space. A local
Lipschitz property is established in total variation norm for the propagators
(generalised semi-groups) associated with the problem and used to construct a
Picard iteration that establishes local existence and global uniqueness for any
initial condition. The unique weak solution is shown further to be a
differentiable or at least bounded variation strong solution under smoothness
assumptions on the parameters of the coagulation interaction. In the case of
one spatial dimension strong differentiability is established even for
coagulation parameters with a particular bounded variation structure in space.
This one dimensional extension establishes the convergence of the simulation
processes studied in [Patterson, Stoch. Anal. Appl. 31, 2013] to a unique and
differentiable limit | Properties of the solutions of delocalised coagulation and inception
problems with outflow boundaries | properties of the solutions of delocalised coagulation and inception problems with outflow boundaries | posedness undergoing delocalised coagulation advection inflow outflow externally specified field. lies streamline field. formulated banach space. lipschitz norm propagators generalised picard iteration establishes uniqueness condition. differentiable smoothness assumptions coagulation interaction. differentiability coagulation space. establishes patterson stoch. anal. appl. differentiable | non_dup | [] |
29537459 | 10.1007/s00028-015-0316-0 | We study a simple one-dimensional coupled wave-heat system and obtain a sharp
estimate for the rate of energy decay of classical solutions. Our approach is
based on the asymptotic theory of $C_0$-semigroups and in particular on a
result due to Borichev and Tomilov (Math. Ann., 2010), which reduces the
problem of estimating the rate of energy decay to finding a growth bound for
the resolvent of the semigroup generator. This technique not only leads to an
optimal result, it is also simpler than the methods used by other authors in
similar situations.Comment: To appear in Journal of Evolution Equation | Optimal energy decay in a one-dimensional coupled wave-heat system | optimal energy decay in a one-dimensional coupled wave-heat system | sharp solutions. asymptotic semigroups borichev tomilov math. ann. reduces estimating resolvent semigroup generator. simpler | non_dup | [] |
47083897 | 10.1007/s00028-016-0321-y | For a given bounded connected domain in $\R^n$ , the issue of computing the observability constant associated to a wave operator, an observation time $T$ and a generic observation subdomain constitutes in general a hard task, even for one-dimensional problems. In this work, we introduce and describe two methods to provide precise (and even sharp in some cases) estimates of observability constants for general one dimensional wave equations: the first one uses a spectral decomposition of the solution of the wave equation whereas the second one is based on a propagation argument along the characteristics. Both methods are extensively described and we then comment on the advantages and drawbacks of each one. The discussion is illustrated by several examples and numerical simulations. As a byproduct, we deduce from the main results estimates of the cost of control (resp. the decay rate of the energy) for several controlled (resp. damped) wave equations | How to estimate observability constants of one-dimensional wave equations? Propagation versus spectral methods | how to estimate observability constants of one-dimensional wave equations? propagation versus spectral methods | observability generic subdomain constitutes problems. precise sharp observability decomposition propagation argument characteristics. extensively comment advantages drawbacks one. illustrated simulations. byproduct deduce resp. resp. damped | non_dup | [] |
54012379 | 10.1007/s00028-016-0325-7 | The paper contains a representation formula for positive solutions of linear degenerate second-order equations of the form of "sum of squares of vector fields plus a drift term" where the vector fields X_j's satisfy the Hörmander condition. It is assumed that X_j's are invariant under left translations of a Lie group and the corresponding paths satisfy a local admissibility criterion. The representation formula is established by an analytic approach based on Choquet theory. As a consequence we obtain Liouville-type theorems and uniqueness results for the positive Cauchy problem | On Liouville-type theorems and the uniqueness of the positive Cauchy problem for a class of hypoelliptic operators | on liouville-type theorems and the uniqueness of the positive cauchy problem for a class of hypoelliptic operators | degenerate squares drift satisfy hörmander condition. translations paths satisfy admissibility criterion. analytic choquet theory. liouville theorems uniqueness cauchy | non_dup | [] |
29561169 | 10.1007/s00028-016-0345-3 | Using analysis for 2-admissible functions in weighted Sobolev spaces and
stochastic calculus for possibly degenerate symmetric elliptic forms, we
construct weak solutions to a wide class of stochastic differential equations
starting from an explicitly specified subset in Euclidean space. The solutions
have typically unbounded and discontinuous drift but may still in some cases
start from all points of $\mathbb{R}^d$ and thus in particular from those where
the drift terms are infinite. As a consequence of our approach we are able to
provide new non-explosion criteria for the unique strong solutions of
\cite{Zh}.Comment: Minor corrections, modified title, reference [19] update | Pointwise weak existence for diffusions associated with degenerate
elliptic forms and 2-admissible weights | pointwise weak existence for diffusions associated with degenerate elliptic forms and 2-admissible weights | admissible weighted sobolev stochastic calculus possibly degenerate elliptic stochastic explicitly specified euclidean space. unbounded discontinuous drift mathbb drift infinite. explosion cite .comment minor title update | non_dup | [] |
42679711 | 10.1007/s00028-016-0347-1 | In this paper we establish optimal solvability results, that is, maximal
regularity theorems, for the Cauchy problem for linear parabolic differential
equations of arbitrary order acting on sections of tensor bundles over
boundaryless complete Riemannian manifolds with bounded geometry. We employ an
anisotropic extension of the Fourier multiplier theorem for arbitrary Besov
spaces introduced in earlier by the author. This allows for a unified treatment
of Sobolev-Slobodeckii and little H\"older spaces. In the flat case we recover
classical results for Petrowskii-parabolic Cauchy problems.Comment: typos have been corrected and additional references have been
include | Cauchy Problems for Parabolic Equations in Sobolev-Slobodeckii and
H\"older Spaces on Uniformly Regular Riemannian Manifolds | cauchy problems for parabolic equations in sobolev-slobodeckii and h\"older spaces on uniformly regular riemannian manifolds | establish solvability maximal regularity theorems cauchy parabolic acting bundles boundaryless riemannian manifolds geometry. employ anisotropic fourier multiplier besov author. unified sobolev slobodeckii older spaces. recover petrowskii parabolic cauchy typos corrected | non_dup | [] |
42655421 | 10.1007/s00028-016-0369-8 | We investigate a partial differential equation model of a cancer cell
population, which is structured with respect to age and telomere length of
cells. We assume a continuous telomere length structure, which is applicable to
the clonal evolution model of cancer cell growth. This model has a non-standard
non-local boundary condition. We establish global existence of solutions and
study their qualitative behaviour. We study the effect of telomere restoration
on cancer cell dynamics. Our results indicate that without telomere
restoration, the cell population extinguishes. With telomere restoration,
exponential growth occurs in the linear model. We further characterise the
specific growth behaviour of the cell population for special cases. We also
study the effects of crowding induced mortality on the qualitative behaviour,
and the existence and stability of steady states of a nonlinear model
incorporating crowding effect. We present examples and extensive numerical
simulations, which illustrate the rich dynamic behaviour of the linear and
nonlinear models.Comment: 36 pages, 12 figure | Mathematical Analysis of a Clonal Evolution Model of Tumour Cell
Proliferation | mathematical analysis of a clonal evolution model of tumour cell proliferation | structured telomere cells. telomere applicable clonal growth. condition. establish qualitative behaviour. telomere restoration dynamics. telomere restoration extinguishes. telomere restoration exponential model. characterise cases. crowding qualitative steady incorporating crowding effect. extensive illustrate pages | non_dup | [] |
52422208 | 10.1007/s00028-017-0415-1 | International audienceThis paper is devoted to studying the null and approximate controllability of two linear coupled parabolic equations posed on a smooth domain Ω of R^N with coupling terms of zero and first orders and one control localized in some arbitrary nonempty open subset ω of the domain Ω. We prove the null controllability under a new sufficient condition and we also provide the first example of a not approximately controllable system in the case where the support of one of the nontrivial first order coupling terms intersects the control domain ω | Positive and negative results on the internal controllability of parabolic equations coupled by zero and first order terms | positive and negative results on the internal controllability of parabolic equations coupled by zero and first order terms | audiencethis devoted studying approximate controllability parabolic posed orders localized nonempty controllability controllable nontrivial intersects | non_dup | [] |
73354813 | 10.1007/s00028-017-0423-1 | In this paper, we consider convex sets $K_r = \{g \ge r\}$ in an infinite
dimensional Hilbert space, where $g$ is suitably related to a reference
Gaussian measure $\mu$ in $H$. We first show how to define a surface measure on
the level sets $\{g = r\}$ that is related to $\mu$. This allows to introduce
an integration-by-parts formula in $H$. This formula can be applied in several
important constructions, as for instance the case where $\mu$ is the law of a
(Gaussian) stochastic process and $H$ is the space of its trajectoriesComment: 22 page | Construction of a surface integral under local Malliavin assumption and
integration by parts formulae | construction of a surface integral under local malliavin assumption and integration by parts formulae | convex infinite hilbert suitably constructions stochastic trajectoriescomment | non_dup | [] |
93945840 | 10.1007/s00028-018-0435-5 | For both localized and periodic initial data, we prove local existence in
classical energy space $H^s, s>\frac{3}{2}$, for a class of dispersive
equations $u_{t}+(n(u))_{x}+Lu_{x}=0$ with nonlinearities of mild regularity.
Our results are valid for symmetric Fourier multiplier operators $L$ whose
symbol is of temperate growth, and $n(\cdot)$ in local Sobolev space
$H^{s+2}_{\mathrm{loc}}(\mathbb{R})$. In particular, the results include
non-smooth and exponentially growing nonlinearities. Our proof is based on a
combination of semi-group methods and a new composition result for Besov
spaces. In particular, we extend a previous result for Nemytskii operators on
Besov spaces on $\mathbb{R}$ to the periodic setting by using the
difference-derivative characterization of Besov spaces | Classical well-posedness in dispersive equations with nonlinearities of
mild regularity, and a composition theorem in Besov spaces | classical well-posedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in besov spaces | localized frac dispersive nonlinearities mild regularity. valid fourier multiplier symbol temperate cdot sobolev mathrm mathbb exponentially growing nonlinearities. besov spaces. extend nemytskii besov mathbb besov | non_dup | [] |
141534763 | 10.1007/s00028-018-0459-x | We study growth rates for strongly continuous semigroups. We prove that a
growth rate for the resolvent on imaginary lines implies a corresponding growth
rate for the semigroup if either the underlying space is a Hilbert space, or
the semigroup is asymptotically analytic, or if the semigroup is positive and
the underlying space is an $L^{p}$-space or a space of continuous functions. We
also prove variations of the main results on fractional domains; these are
valid on more general Banach spaces. In the second part of the article we apply
our main theorem to prove optimality in a classical example by Renardy of a
perturbed wave equation which exhibits unusual spectral behavior.Comment: 20 pages. To appear in Journal of Evolution Equation | Sharp growth rates for semigroups using resolvent bounds | sharp growth rates for semigroups using resolvent bounds | semigroups. resolvent imaginary semigroup hilbert semigroup asymptotically analytic semigroup functions. fractional valid banach spaces. optimality renardy perturbed exhibits unusual pages. | non_dup | [] |
2567608 | 10.1007/s00029-004-0350-1 | Let $G_M$ be one of the complex Lie groups $O_M$ and $Sp_M$. The irreducible
finite-dimensional representations of the group $G_M$ are labeled by partitions
$\mu$ satisfying certain extra conditions. Let $U$ be the representation of
$G_M$ corresponding to $\mu$. Regard the direct product $G_N\times G_M$ as a
subgroup of $G_{N+M}$. Let $V$ be the irreducible representation of $G_{N+M}$
corresponding to a partition $\lambda$. Consider the vector space
$W=Hom_{G_M}(U,V)$. It comes with a natural action of the group $G_N$. Let $n$
be sum of parts of $\lambda$ less the sum of parts of $\mu$. For any choice of
a standard Young tableau of skew shape $\lambda/\mu$, we realize $W$ as a
subspace in the tensor product of $n$ copies of the defining $N$-dimensional
representation of $G_N$. This subspace is determined as the image of a certain
linear operator $F(M)$ in the tensor product, given by an explicit formula.
When M=0 and $W=V$ is an irreducible representation of $G_N$, we recover the
classical realization of $V$ as a subspace in the space of all traceless
tensors. Then the operator F(0) can be regarded as the analogue for $G_N$ of
the Young symmetrizer, corresponding to the chosen standard tableau of shape
$\lambda$. Even in the special case M=0, our formula for the operator $F(M)$ is
new. Our results are applications of representation theory of the twisted
Yangian, corresponding to $G_N$. In particular, $F(M)$ is an intertwining
operator between two representations of the twisted Yangian in the $n$-fold
tensor product.Comment: 60 pages; final version, Section 0 adde | Representations of twisted Yangians associated with skew Young diagrams | representations of twisted yangians associated with skew young diagrams | irreducible representations labeled partitions satisfying extra conditions. regard subgroup irreducible partition lambda comes lambda tableau skew lambda realize subspace copies defining subspace formula. irreducible recover realization subspace traceless tensors. regarded analogue symmetrizer tableau lambda new. twisted yangian intertwining representations twisted yangian pages adde | non_dup | [] |
19637819 | 10.1007/s00029-004-0362-x | Dette er forfatternes aksepterte versjon.We find d − 2 relative differential invariants for a d-web, d ≥ 4, on a
two-dimensional manifold and prove that their vanishing is necessary and
sufficient for a d-web to be linearizable. If one writes the above invariants
in terms of web functions f(x, y) and g4(x, y), ..., gd(x, y), then necessary
and sufficient conditions for the linearizabilty of a d-web are two PDEs of
the fourth order with respect to f and g4, and d − 4 PDEs of the second
order with respect to f and g4, ..., gd. For d = 4, this result confirms
Blaschke’s conjecture on the nature of conditions for the linearizabilty
of a 4-web. We also give Mathematica codes for testing 4- and d-webs
(d > 4) for linearizability and examples of their usage | Linearizability of d-webs, d ≥ 4, on
two-dimensional manifolds | linearizability of d-webs, d ≥ 4, on two-dimensional manifolds | dette forfatternes aksepterte versjon.we invariants manifold vanishing linearizable. writes invariants linearizabilty pdes fourth pdes confirms blaschke’s conjecture linearizabilty web. mathematica codes webs linearizability usage | non_dup | [] |
2578519 | 10.1007/s00029-005-0004-y | We introduce a notion of integration on the category of proper birational
maps to a given variety $X$, with value in an associated Chow group.
Applications include new birational invariants; comparison results for Chern
classes and numbers of nonsingular birational varieties; `stringy' Chern
classes of singular varieties; and a zeta function specializing to the
topological zeta function.
In its simplest manifestation, the integral gives a new expression for
Chern-Schwartz-MacPherson classes of possibly singular varieties, placing them
into a context in which a `change-of-variable' formula holds. v2: References
added, and overly optimistic claims concerning non log-terminal singularities
expunged.Comment: 42 pages, LaTeX, 2 figure | Modification systems and integration in their Chow groups | modification systems and integration in their chow groups | notion proper birational chow group. birational invariants chern nonsingular birational varieties stringy chern singular varieties zeta specializing topological zeta function. simplest manifestation chern schwartz macpherson possibly singular varieties placing holds. overly optimistic claims concerning singularities pages latex | non_dup | [] |
1939181 | 10.1007/s00029-007-0040-x | We investigate the degree of the polar transformations associated to a
certain class of multi-valued homogeneous functions. In particular we prove
that the degree of the pre-image of generic linear spaces by a polar
transformation associated to a homogeneous polynomial $F$ is determined by the
zero locus of $F$. For zero dimensional-dimensional linear spaces this was
conjecture by Dolgachev and proved by Dimca-Papadima using topological
arguments. Our methods are algebro-geometric and rely on the study of the Gauss
map of naturally associated logarithmic foliations | On the degree of Polar Transformations -- An approach through
Logarithmic Foliations | on the degree of polar transformations -- an approach through logarithmic foliations | polar transformations valued homogeneous functions. generic polar homogeneous locus conjecture dolgachev proved dimca papadima topological arguments. algebro geometric rely gauss naturally logarithmic foliations | non_dup | [] |
2557804 | 10.1007/s00029-007-0046-4 | We consider the heat equation $u_t=Lu$ where $L$ is a second-order difference
operator in a discrete variable $n$. The fundamental solution has an expansion
in terms of the Bessel functions of imaginary argument. The coefficients
$\alpha_k(n,m)$ in this expansion are analogs of Hadamard's coefficients for
the (continuous) Schrodinger operator.
We derive an explicit formula for $\alpha_k$ in terms of the wave and the
adjoint wave functions of the Toda lattice hierarchy. As a first application of
this result, we prove that the values of these coefficients on the diagonals
$n=m$ and $n=m+1$ define a hierarchy of differential-difference equations which
is equivalent to the Toda lattice hierarchy. Using this fact and the
correspondence between commutative rings of difference operators and algebraic
curves we show that the fundamental solution can be summed up, giving a finite
formula involving only two Bessel functions with polynomial coefficients in the
time variable $t$, if and only if the operator $L$ belongs to the family of
bispectral operators constructed in [18].Comment: corrected typo | Heat kernel expansions on the integers and the Toda lattice hierarchy | heat kernel expansions on the integers and the toda lattice hierarchy | bessel imaginary argument. alpha analogs hadamard schrodinger operator. derive alpha adjoint toda hierarchy. diagonals hierarchy toda hierarchy. correspondence commutative rings algebraic summed giving involving bessel belongs bispectral .comment corrected typo | non_dup | [] |
28938563 | 10.1007/s00029-008-0053-0 | Let \(G\) be a reductive group. The geometric Satake equivalence realized the category of representations of the Langlands dual group \(\check G\) in terms of spherical perverse sheaves (or D-modules) on the affine Grassmannian \(Gr_G=G((t))/G[[t]]\) of the original group G. In the present paper we perform a first step in realizing the category of representations of the quantum group corresponding to \(\check G\) in terms of the geometry of \(Gr_G\). The idea of the construction belongs to Jacob Lurie.Mathematic | Twisted Whittaker Model and Factorizable Sheaves | twisted whittaker model and factorizable sheaves | reductive group. geometric satake equivalence realized representations langlands check spherical perverse sheaves modules affine grassmannian realizing representations check belongs jacob lurie.mathematic | non_dup | [] |
1962540 | 10.1007/s00029-008-0058-8 | We classify certain non-linear Lie conformal algebras with three generators,
which can be viewed as deformations of the current Lie conformal algebra of
sl_2. In doing so we discover an interesting 1-parameter family of non-linear
Lie conformal algebras R_{-1}^d and the corresponding freely generated vertex
algebras V_{-1}^d, which includes for d=1 the affine vertex algebra of sl_2 at
the critical level k=-2. We construct free-field realizations of the algebras
V_{-1}^d extending the Wakimoto realization of the affine vertex algebra of
sl_2 at the critical level, and we compute their Zhu algebras.Comment: 36 pages, v2 minor change | Non-linear Lie conformal algebras with three generators | non-linear lie conformal algebras with three generators | classify conformal algebras generators viewed deformations conformal discover conformal algebras freely algebras affine realizations algebras extending wakimoto realization affine pages minor | non_dup | [] |
2017287 | 10.1007/s00029-008-0067-7 | We introduce several associative algebras and series of vector spaces
associated to these algebras. Using lattice vertex operators, we obtain
dimension and character formulae for these spaces. In particular, we a series
of representations of symmetric groups which turn out to be isomorphic to
parking function modules. We also construct series of vector spaces whose
dimensions are Catalan numbers and Fuss--Catalan numbers respectively.
Conjecturally, these spaces are related to spaces of global sections of vector
bundles on (zero fibres of) Hilbert schemes and representations of rational
Cherednik algebras.Comment: 17 pages, 1 figure, proofs are made more detailed. To appear in
Selecta Mathematic | Parking functions and vertex operators | parking functions and vertex operators | associative algebras algebras. character formulae spaces. representations isomorphic parking modules. catalan fuss catalan respectively. conjecturally bundles fibres hilbert schemes representations rational cherednik pages proofs detailed. selecta mathematic | non_dup | [] |
2017614 | 10.1007/s00029-009-0015-1 | We define complexes of vector bundles on products of moduli spaces of framed
rank r torsion-free sheaves on the complex projective plane. The top
non-vanishing Chern classes of the cohomology of these complexes yield actions
of the r-colored Heisenberg and Clifford algebras on the equivariant cohomology
of the moduli spaces. In this way we obtain a geometric realization of the
boson-fermion correspondence and related vertex operators.Comment: 36 pages; v2: Definition of geometric Heisenberg operators modified;
v3: Minor typos correcte | Vertex operators and the geometry of moduli spaces of framed
torsion-free sheaves | vertex operators and the geometry of moduli spaces of framed torsion-free sheaves | complexes bundles moduli framed torsion sheaves projective plane. vanishing chern cohomology complexes colored heisenberg clifford algebras equivariant cohomology moduli spaces. geometric realization boson fermion correspondence pages geometric heisenberg minor typos correcte | non_dup | [] |
9590436 | 10.1007/s00029-009-0507-z | Parabolic induction and restriction functors play an important role in the
representation theory of finite and affine Hecke algebras. This makes it desirable
to generalize them to the setting of double affine Hecke algebras, or
Cherednik algebras. However, a naive attempt to do so fails: the definition
of parabolic induction and restriction functors for finite and affine Hecke
algebras uses the fact that the Hecke algebra attached to a parabolic subgroup
can be embedded into the Hecke algebra attached to the whole group,
which is not the case in the double affine setting | Parabolic induction and restriction functors for rational Cherednik algebras | parabolic induction and restriction functors for rational cherednik algebras | parabolic restriction functors affine hecke algebras. desirable generalize affine hecke algebras cherednik algebras. naive attempt fails parabolic restriction functors affine hecke algebras hecke attached parabolic subgroup embedded hecke attached affine | non_dup | [] |
2133489 | 10.1007/s00029-011-0060-4 | We develop a mathematical framework for the computation of open orbifold
Gromov-Witten invariants of [C^3/Z_n], and provide extensive checks with
predictions from open string mirror symmetry. To this aim we set up a
computation of open string invariants in the spirit of Katz-Liu, defining them
by localization. The orbifold is viewed as an open chart of a global quotient
of the resolved conifold, and the Lagrangian as the fixed locus of an
appropriate anti-holomorphic involution. We consider two main applications of
the formalism. After warming up with the simpler example of [C^3/Z_3], where we
verify physical predictions of Bouchard, Klemm, Marino and Pasquetti, the main
object of our study is the richer case of [C^3/Z_4], where two different
choices are allowed for the Lagrangian. For one choice, we make numerical
checks to confirm the B-model predictions; for the other, we prove a mirror
theorem for orbifold disc invariants, match a large number of annulus
invariants, and give mirror symmetry predictions for open string invariants of
genus \leq 2.Comment: 44 pages + appendices; v2: exposition improved, misprints corrected,
version to appear on Selecta Mathematica; v3: last minute mistake found and
fixed for the symmetric brane setup of [C^3/Z_4]; in pres | Open orbifold Gromov-Witten invariants of [C^3/Z_n]: localization and
mirror symmetry | open orbifold gromov-witten invariants of [c^3/z_n]: localization and mirror symmetry | mathematical orbifold gromov witten invariants extensive checks mirror symmetry. invariants spirit katz defining localization. orbifold viewed chart quotient resolved conifold lagrangian locus holomorphic involution. formalism. warming simpler verify bouchard klemm marino pasquetti richer choices lagrangian. checks confirm mirror orbifold disc invariants match annulus invariants mirror invariants genus pages appendices exposition misprints corrected selecta mathematica minute mistake brane setup pres | non_dup | [] |
37976881 | 10.1007/s00029-011-0061-3 | It is proved that all wild z-automorphisms including the well-known Nagata automorphism (all wild z-coordinates including the Nagata coordinates, respectively) of the polynomial algebra F[x, y, z] over an arbitrary field F cannot be lifted to a z-automorphism (z-coordinate, respectively) of the free associative algebra 〈x, y, z〉. The proof is based on the following two new results, which have their own interests: degree estimate of Q *F F〈x 1, ..., x n〉 and tameness of the automorphism group Aut q(Q * F F〈x, y〉). The structure of the group of all z-automorphisms of the free associative algebra F〈x, y〉 over an arbitrary field F is also determined. © 2011 Springer Basel AG.postprin | On the lifting of the Nagata automorphism | on the lifting of the nagata automorphism | proved automorphisms nagata automorphism nagata lifted automorphism coordinate associative interests tameness automorphism automorphisms associative determined. springer basel ag.postprin | non_dup | [] |
28938532 | 10.1007/s00029-011-0065-z | We extend the theory of chiral and factorization algebras, developed for
curves by Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004), to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and factorization structures, in a sense analogous to Quillen’s homotopy theory of differential graded Lie algebras. We prove the equivalence of higher-dimensional chiral and factorization algebras by embedding factorization algebras into a larger category of chiral commutative coalgebras, then realizing this interrelation as a chiral form of Koszul duality. We apply these techniques to rederive some fundamental results of Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004) on chiral enveloping algebras of \(\star\)-Lie algebras.Mathematic | Chiral Koszul Duality | chiral koszul duality | extend chiral factorization algebras beilinson drinfeld mathematical colloquium publications mathematical providence varieties. entails homotopy chiral factorization analogous quillen’s homotopy graded algebras. equivalence chiral factorization algebras embedding factorization algebras chiral commutative coalgebras realizing interrelation chiral koszul duality. rederive beilinson drinfeld mathematical colloquium publications mathematical providence chiral enveloping algebras algebras.mathematic | non_dup | [] |
2187404 | 10.1007/s00029-012-0099-x | We show that the quantum coordinate ring of the unipotent subgroup N(w) of a
symmetric Kac-Moody group G associated with a Weyl group element w has the
structure of a quantum cluster algebra. This quantum cluster structure arises
naturally from a subcategory C_w of the module category of the corresponding
preprojective algebra. An important ingredient of the proof is a system of
quantum determinantal identities which can be viewed as a q-analogue of a
T-system. In case G is a simple algebraic group of type A, D, E, we deduce from
these results that the quantum coordinate ring of an open cell of a partial
flag variety attached to G also has a cluster structure.Comment: v2: minor corrections. v3: references updated, final version to
appear in Selecta Mathematic | Cluster structures on quantum coordinate rings | cluster structures on quantum coordinate rings | coordinate unipotent subgroup moody weyl algebra. arises naturally subcategory module preprojective algebra. ingredient determinantal identities viewed analogue system. algebraic deduce coordinate flag attached minor corrections. updated selecta mathematic | non_dup | [] |
24764993 | 10.1007/s00029-013-0119-5 | Let V be a symplectic vector space of dimension 2n. Given a partition \lambda
with at most n parts, there is an associated irreducible representation
S_{[\lambda]}(V) of Sp(V). This representation admits a resolution by a natural
complex L^\lambda, which we call the Littlewood complex, whose terms are
restrictions of representations of GL(V). When \lambda has more than n parts,
the representation S_{[\lambda]}(V) is not defined, but the Littlewood complex
L^\lambda still makes sense. The purpose of this paper is to compute its
homology. We find that either L^\lambda is acyclic or that it has a unique
non-zero homology group, which forms an irreducible representation of Sp(V).
The non-zero homology group, if it exists, can be computed by a rule
reminiscent of that occurring in the Borel-Weil-Bott theorem. This result can
be interpreted as the computation of the "derived specialization" of
irreducible representations of Sp(\infty), and as such categorifies earlier
results of Koike-Terada on universal character rings. We prove analogous
results for orthogonal and general linear groups. Along the way, we will see
two topics from commutative algebra: the minimal free resolutions of
determinantal ideals and Koszul homology.Comment: 32 pages; v2: corrected minor typos and changed theorem/equation
numberin | Homology of Littlewood complexes | homology of littlewood complexes | symplectic partition lambda irreducible lambda admits lambda call littlewood restrictions representations lambda lambda littlewood lambda sense. homology. lambda acyclic homology irreducible homology reminiscent occurring borel weil bott theorem. interpreted specialization irreducible representations infty categorifies koike terada universal character rings. analogous orthogonal groups. topics commutative resolutions determinantal ideals koszul pages corrected minor typos changed numberin | non_dup | [] |
5231273 | 10.1007/s00029-013-0123-9 | We work in the category of locally definable groups in an o-minimal expansion
of a field. Eleftheriou and Peterzil conjectured that every definably generated
abelian connected group G in this category is a cover of a definable group. We
prove that this is the case under a natural convexity assumption inspired by
the same authors, which in fact gives a necessary and sufficient condition. The
proof is based on the study of the zero-dimensional compatible subgroups of G.
Given a locally definable connected group G (not necessarily definably
generated), we prove that the n-torsion subgroup of G is finite and that every
zero-dimensional compatible subgroup of G has finite rank. Under a convexity
hypothesis we show that every zero-dimensional compatible subgroup of G is
finitely generated.Comment: Final version. 17 pages. To appear in Selecta Mathematic | Discrete subgroups of locally definable groups | discrete subgroups of locally definable groups | locally definable field. eleftheriou peterzil conjectured definably abelian cover definable group. convexity inspired condition. compatible subgroups locally definable necessarily definably torsion subgroup compatible subgroup rank. convexity compatible subgroup finitely version. pages. selecta mathematic | non_dup | [] |
48237032 | 10.1007/s00029-013-0130-x | 39 pagesInternational audienceLet $\mathcal V$ be a discrete valuation ring of mixed characteristic with perfect residue field. Let $X$ be a geometrically connected smooth proper curve over $\mathcal V$. We introduce the notion of constructible convergent $\nabla$-module on the analytification $X_{K}^{\mathrm{an}}$ of the generic fibre of $X$. A constructible module is an $\mathcal O_{X_{K}^{\mathrm{an}}}$-module which is not necessarily coherent, but becomes coherent on a stratification by locally closed subsets of the special fiber $X_{k}$ of $X$. The notions of connection, of (over-) convergence and of Frobenius structure carry over to this situation. We describe a specialization functor from the category of constructible convergent $\nabla$-modules to the category of $\mathcal D^\dagger_{\hat X \mathbf Q}$-modules. We show that if $X$ is endowed with a lifting of the absolute Frobenius of $X$, then specialization induces an equivalence between constructible $F$-$\nabla$-modules and perverse holonomic $F$-$\mathcal D^\dagger_{\hat X \mathbf Q}$-modules | Constructible nabla-modules on curves | constructible nabla-modules on curves | pagesinternational audiencelet mathcal valuation perfect residue field. geometrically proper mathcal notion constructible convergent nabla module analytification mathrm generic fibre constructible module mathcal mathrm module necessarily coherent coherent stratification locally subsets fiber notions connection frobenius carry situation. specialization functor constructible convergent nabla modules mathcal dagger mathbf modules. endowed lifting frobenius specialization induces equivalence constructible nabla modules perverse holonomic mathcal dagger mathbf modules | non_dup | [] |
17029487 | 10.1007/s00029-013-0131-9 | In this article, we introduce the category of noncommutative Artin motives as well as the category of noncommutative mixed Artin motives. In the pure world, we start by proving that the classical category AM(k)[subscript Q] AM ( k ) Q of Artin motives (over a base field k) can be characterized as the largest category inside Chow motives which fully embeds into noncommutative Chow motives. Making use of a refined bridge between pure motives and noncommutative pure motives, we then show that the image of this full embedding, which we call the category NAM(k)[subscript Q] NAM ( k ) Q of noncommutative Artin motives, is invariant under the different equivalence relations and modification of the symmetry isomorphism constraints. As an application, we recover the absolute Galois group Gal(k−/k) Gal ( k ¯ / k ) from the Tannakian formalism applied to NAM(k)[subscript Q] NAM ( k ) Q . Then, we develop the base-change formalism in the world of noncommutative pure motives. As an application, we obtain new tools for the study of motivic decompositions and Schur/Kimura finiteness. Making use of this theory of base-change, we then construct a short exact sequence relating Gal(k−/k) Gal ( k ¯ / k ) with the noncommutative motivic Galois groups of k and k− k ¯ . Finally, we describe a precise relationship between this short exact sequence and the one constructed by Deligne–Milne. In the mixed world, we introduce the triangulated category NMAM(k)[subscript Q] NMAM ( k ) Q of noncommutative mixed Artin motives and construct a faithful functor from the classical category MAM(k)[subscript Q] MAM ( k ) Q of mixed Artin motives to it. When k is a finite field, this functor is an equivalence. On the other hand, when k is of characteristic zero NMAM(k)[subscript Q] NMAM ( k ) Q is much richer than MAM(k)[subscript Q] MAM ( k ) Q since its higher Ext-groups encode all the (rationalized) higher algebraic K K -theory of finite étale k-schemes. In the appendix, we establish a general result about short exact sequences of Galois groups which is of independent interest. As an application, we obtain a new proof of Deligne–Milne’s short exact sequence.17 Jul 2012 Original ManuscriptNEC Corporation Fund for Research in Computers and Communications (Award-2742738 | Noncommutative Artin motives | noncommutative artin motives | noncommutative artin motives noncommutative artin motives. proving subscript artin motives chow motives embeds noncommutative chow motives. refined bridge motives noncommutative motives embedding call subscript noncommutative artin motives equivalence modification isomorphism constraints. recover galois tannakian formalism subscript formalism noncommutative motives. motivic decompositions schur kimura finiteness. relating noncommutative motivic galois precise deligne–milne. triangulated nmam subscript nmam noncommutative artin motives faithful functor subscript artin motives functor equivalence. nmam subscript nmam richer subscript encode rationalized algebraic étale schemes. establish galois interest. deligne–milne’s sequence. manuscriptnec corporation fund computers communications award | non_dup | [] |
9260533 | 10.1007/s00029-013-0132-8 | In the present paper we generalize the construction of the nil Hecke ring of
Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology
theory of Levine-Morel and Panin-Smirnov, e.g. to Chow groups, Grothendieck's
K_0, connective K-theory, elliptic cohomology, and algebraic cobordism. The
resulting object, which we call a formal (affine) Demazure algebra, is
parameterized by a one-dimensional commutative formal group law and has the
following important property: specialization to the additive and multiplicative
periodic formal group laws yields completions of the nil Hecke and the 0-Hecke
rings respectively. We also introduce a deformed version of the formal (affine)
Demazure algebra, which we call a formal (affine) Hecke algebra. We show that
the specialization of the formal (affine) Hecke algebra to the additive and
multiplicative periodic formal group laws gives completions of the degenerate
(affine) Hecke algebra and the usual (affine) Hecke algebra respectively. We
show that all formal affine Demazure algebras (and all formal affine Hecke
algebras) become isomorphic over certain coefficient rings, proving an analogue
of a result of Lusztig.Comment: 28 pages. v2: Some results strengthened and references added. v3:
Minor corrections, section numbering changed to match published version. v4:
Sign errors in Proposition 6.8(d) corrected. This version incorporates an
erratum to the published versio | Formal Hecke algebras and algebraic oriented cohomology theories | formal hecke algebras and algebraic oriented cohomology theories | generalize hecke kostant kumar algebraic oriented cohomology levine morel panin smirnov e.g. chow grothendieck connective elliptic cohomology algebraic cobordism. call formal affine demazure parameterized commutative formal specialization additive multiplicative formal laws completions hecke hecke rings respectively. deformed formal affine demazure call formal affine hecke algebra. specialization formal affine hecke additive multiplicative formal laws completions degenerate affine hecke usual affine hecke respectively. formal affine demazure algebras formal affine hecke algebras isomorphic rings proving analogue pages. strengthened added. minor numbering changed match version. corrected. incorporates erratum versio | non_dup | [] |
24955255 | 10.1007/s00029-014-0177-3 | The aim of the present paper is to introduce a generalized quantum cluster
character, which assigns to each object V of a finitary Abelian category C over
a finite field FF_q and any sequence ii of simple objects in C the element
X_{V,ii} of the corresponding algebra P_{C,ii} of q-polynomials. We prove that
if C was hereditary, then the assignments V-> X_{V,ii} define algebra
homomorphisms from the (dual) Hall-Ringel algebra of C to the P_{C,ii}, which
generalize the well-known Feigin homomorphisms from the upper half of a quantum
group to q-polynomial algebras.
If C is the representation category of an acyclic valued quiver (Q,d) and
ii=(ii_0,ii_0), where ii_0 is a repetition-free source-adapted sequence, then
we prove that the ii-character X_{V,ii} equals the quantum cluster character
X_V introduced earlier by the second author in [29] and [30]. Using this
identification, we deduce a quantum cluster structure on the quantum unipotent
cell corresponding to the square of a Coxeter element. As a corollary, we prove
a conjecture from the joint paper [5] of the first author with A. Zelevinsky
for such quantum unipotent cells. As a byproduct, we construct the quantum
twist and prove that it preserves the triangular basis introduced by A.
Zelevinsky and the first author in [6].Comment: AMS LaTeX, 46 pages, a reference added, to appear in Selecta
Mathematic | Quantum cluster characters of Hall algebras | quantum cluster characters of hall algebras | character assigns finitary abelian polynomials. hereditary assignments homomorphisms hall ringel generalize feigin homomorphisms algebras. acyclic valued quiver repetition adapted character equals character deduce unipotent coxeter element. corollary conjecture zelevinsky unipotent cells. byproduct twist preserves triangular zelevinsky .comment latex pages selecta mathematic | non_dup | [] |
5254841 | 10.1007/s00029-015-0188-8 | We prove that the quivers with potentials associated to triangulations of
surfaces with marked points, and possibly empty boundary, are non-degenerate,
provided the underlying surface with marked points is not a closed sphere with
exactly 5 punctures. This is done by explicitly defining the QPs that
correspond to tagged triangulations and proving that whenever two tagged
triangulations are related by a flip, their associated QPs are related by the
corresponding QP-mutation. As a byproduct, for (arbitrarily punctured) surfaces
with non-empty boundary we obtain a proof of the non-degeneracy of the
associated QPs which is independent from the one given by the author in the
first paper of the series.
The main tool used to prove the aforementioned compatibility between flips
and QP-mutations is what we have called \emph{Popping Theorem}, which, roughly
speaking, says that an apparent lack of symmetry in the potentials arising from
ideal triangulations with self-folded triangles can be fixed by a suitable
right-equivalence.Comment: v5: Final version. Published by Selecta Mathematica (New Series).
Published version contains a few minor redaction errors. E.g., "related by a
flip" and "related by a QP-mutation" were incorrectly replaced by "related to
a flip" and "related to a QP-mutation" therein. Changes following suggestions
by the referee. 36 pages, 21 figures. Dedicated to the memory of Professor
Andrei Zelevinsk | Quivers with potentials associated to triangulated surfaces, part IV:
Removing boundary assumptions | quivers with potentials associated to triangulated surfaces, part iv: removing boundary assumptions | quivers potentials triangulations marked possibly empty degenerate marked sphere punctures. explicitly defining tagged triangulations proving whenever tagged triangulations flip mutation. byproduct arbitrarily punctured empty degeneracy series. aforementioned compatibility flips emph popping roughly speaking says apparent potentials arising ideal triangulations folded triangles version. selecta mathematica minor redaction errors. e.g. flip mutation incorrectly replaced flip mutation therein. suggestions referee. pages figures. dedicated professor andrei zelevinsk | non_dup | [] |
29505910 | 10.1007/s00029-015-0205-y | In recent years, researchers have discovered various large algebraic
structures that have surprising finiteness properties, such as FI-modules and
Delta-modules. In this paper, we add another example to the growing list: we
show that certain degree two twisted commutative algebras are noetherian. This
example appears to have some fundamental differences from previous examples,
and is therefore especially interesting. Reflective of this, our proof
introduces new methods for establishing noetherianity that are likely to be
applicable in other situations. The algebras considered in this paper are
closely related to the stable representation theory of classical groups, which
is one source of motivation for their study.Comment: 21 pages; v2: small corrections and added Example 1. | Noetherianity of some degree two twisted commutative algebras | noetherianity of some degree two twisted commutative algebras | researchers discovered algebraic surprising finiteness modules delta modules. growing twisted commutative algebras noetherian. interesting. reflective introduces establishing noetherianity applicable situations. algebras closely motivation pages | non_dup | [] |
25026269 | 10.1007/s00029-015-0206-x | We define an invariant of contact 3-manifolds with convex boundary using
Kronheimer and Mrowka's sutured instanton Floer homology theory. To the best of
our knowledge, this is the first invariant of contact manifolds -- with or
without boundary -- defined in the instanton Floer setting. We prove that our
invariant vanishes for overtwisted contact structures and is nonzero for
contact manifolds with boundary which embed into Stein fillable contact
manifolds. Moreover, we propose a strategy by which our contact invariant might
be used to relate the fundamental group of a closed contact 3-manifold to
properties of its Stein fillings. Our construction is inspired by a
reformulation of a similar invariant in the monopole Floer setting defined by
the authors in [1].Comment: 32 pages, 7 figures; this paper was originally part of
arXiv:1403.193 | Instanton Floer homology and contact structures | instanton floer homology and contact structures | manifolds convex kronheimer mrowka sutured instanton floer homology theory. manifolds instanton floer setting. vanishes overtwisted nonzero manifolds embed stein fillable manifolds. propose relate manifold stein fillings. inspired reformulation monopole floer .comment pages originally | non_dup | [] |
42484282 | 10.1007/s00029-015-0213-y | The final publication is available at Springer via http://dx.doi.org/10.1007/s00029-015-0213-y.Gaudin Hamiltonians form families of r-dimensional abelian Lie subalgebras of the holonomy Lie algebra of the arrangement of reflection hyperplanes of a Coxeter group of rank r. We consider the set of principal Gaudin subalgebras, which is the closure in the appropriate Grassmannian of the set of spans of Gaudin Hamiltonians. We show that principal Gaudin subalgebras form a smooth projective variety isomorphic to the De Concini–Procesi compactification of the projectivized complement of the arrangement of reflection hyperplanes | Gaudin subalgebras and wonderful models | gaudin subalgebras and wonderful models | publication springer y.gaudin hamiltonians families abelian subalgebras holonomy arrangement reflection hyperplanes coxeter principal gaudin subalgebras closure grassmannian spans gaudin hamiltonians. principal gaudin subalgebras projective isomorphic concini–procesi compactification projectivized complement arrangement reflection hyperplanes | non_dup | [] |
25044741 | 10.1007/s00029-015-0221-y | We generalize the standard combinatorial techniques of toric geometry to the
study of log Calabi-Yau surfaces. The character and cocharacter lattices are
replaced by certain integral linear manifolds described by Gross, Hacking, and
Keel, and monomials on toric varieties are replaced with the canonical theta
functions which GHK defined using ideas from mirror symmetry. We describe the
tropicalizations of theta functions and use them to generalize the dual pairing
between the character and cocharacter lattices. We use this to describe
generalizations of dual cones, Newton and polar polytopes, Minkowski sums, and
finite Fourier series expansions. We hope that these techniques will generalize
to higher-rank cluster varieties.Comment: 40 pages, 2 figures. The final publication is available at Springer
via http://dx.doi.org/10.1007/s00029-015-0221-y, Selecta Math. (2016 | Tropical Theta Functions and Log Calabi-Yau Surfaces | tropical theta functions and log calabi-yau surfaces | generalize combinatorial toric calabi surfaces. character cocharacter lattices replaced manifolds gross hacking keel monomials toric varieties replaced canonical theta ideas mirror symmetry. tropicalizations theta generalize pairing character cocharacter lattices. generalizations cones newton polar polytopes minkowski sums fourier expansions. hope generalize pages figures. publication springer selecta math. | non_dup | [] |
25036801 | 10.1007/s00029-015-0222-x | The convolution powers of a perverse sheaf on an abelian variety define an
interesting family of branched local systems whose geometry is still poorly
understood. We show that the generating series for their generic rank is a
rational function of a very simple shape and that a similar result holds for
the symmetric convolution powers. We also give formulae for other Schur
functors in terms of characteristic classes on the dual abelian variety, and as
an example we discuss the case of Prym-Tjurin varieties.Comment: Some typos removed, references update | Characteristic classes and Hilbert-Poincar\'e series for perverse
sheaves on abelian varieties | characteristic classes and hilbert-poincar\'e series for perverse sheaves on abelian varieties | convolution powers perverse sheaf abelian branched poorly understood. generating generic rational convolution powers. formulae schur functors abelian prym tjurin typos removed update | non_dup | [] |