共查询到20条相似文献,搜索用时 15 毫秒
1.
Julianna S. Tymoczko 《Selecta Mathematica, New Series》2007,13(2):353-367
Regular nilpotent Hessenberg varieties form a family of subvarieties of the flag variety arising in the study of quantum cohomology,
geometric representation theory, and numerical analysis. In this paper we construct a paving by affines of regular nilpotent
Hessenberg varieties for all classical types, generalizing results of De Concini–Lusztig–Procesi and Kostant. This paving
is in fact the intersection of a particular Bruhat decomposition with the Hessenberg variety. The nonempty cells of the paving
and their dimensions are identified by combinatorial conditions on roots. We use the paving to prove these Hessenberg varieties
have no odd-dimensional homology.
相似文献
2.
We prove convergence for the basic LR algorithm on a real unreduced tridiagonal matrix with a one-point spectrum—the Jordan
form is one big Jordan block. First we develop properties of eigenvector matrices. We also show how to deal with the singular
case. 相似文献
3.
Heike Siebert 《Mathematics in Computer Science》2009,2(3):421-442
In the well-known discrete modeling framework developed by R. Thomas, the structure of a biological regulatory network is
captured in an interaction graph, which, together with a set of Boolean parameters, gives rise to a state transition graph
describing all possible dynamical behaviors. For complex networks the analysis of the dynamics becomes more and more difficult,
and efficient methods to carry out the analysis are needed. In this paper, we focus on identifying subnetworks of the system
that govern the behavior of the system as a whole. We present methods to derive trajectories and attractors of the network
from the dynamics suitable subnetworks display in isolation. In addition, we use these ideas to link the existence of certain
structural motifs, namely circuits, in the interaction graph to the character and number of attractors in the state transition
graph, generalizing and refining results presented in [10]. Lastly, we show for a specific class of networks that all possible
asymptotic behaviors of networks in that class can be derived from the dynamics of easily identifiable subnetworks.
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4.
5.
6.
Joseph Lehec 《Archiv der Mathematik》2009,92(4):366-376
The Yao-Yao partition theorem states that for any probability measure μ on having a density which is continuous and bounded away from 0, it is possible to partition into 2n regions of equal measure for μ in such a way that every affine hyperplane of avoids at least one of the regions. We give a constructive proof of this result and extend it to slightly more general measures.
Received: 21 August 2008 相似文献
7.
Math search is a new area of research with many enabling technologies but also many challenges. Some of the enabling technologies
include XML, XPath, XQuery, and MathML. Some of the challenges involve enabling search systems to recognize mathematical symbols
and structures. Several math search projects have made considerable progress in meeting those challenges. One of the remaining
challenges is the creation and implementation of a math query language that enables the general users to express their information
needs intuitively yet precisely. This paper will present such a language and detail its features. The new math query language
offers an alternative way to describe mathematical expressions that is more consistent and less ambiguous than conventional
mathematical notation. In addition, the language goes beyond the Boolean and proximity query syntax found in standard text
search systems. It defines a powerful set of wildcards that are deemed important for math search. These wildcards provide
for more precise structural search and multi-levels of abstractions. Three new sets of wildcards and their implementation
details will also be discussed.
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8.
Ilwoo Cho 《Complex Analysis and Operator Theory》2007,1(3):367-398
We identify two noncommutative structures naturally associated with countable directed graphs. They are formulated in the
language of operators on Hilbert spaces. If G is a countable directed graphs with its vertex set V(G) and its edge set E(G), then we associate partial isometries to the edges in E(G) and projections to the vertices in V(G). We construct a corresponding von Neumann algebra
as a groupoid crossed product algebra
of an arbitrary fixed von Neumann algebra M and the graph groupoid
induced by G, via a graph-representation (or a groupoid action) α. Graph groupoids are well-determined (categorial) groupoids. The graph
groupoid
of G has its binary operation, called admissibility. This
has concrete local parts
, for all e ∈ E(G). We characterize
of
, induced by the local parts
of
, for all e ∈ E(G). We then characterize all amalgamated free blocks
of
. They are chracterized by well-known von Neumann algebras: the classical group crossed product algebras
, and certain subalgebras
(M) of operator-valued matricial algebra
. This shows that graph von Neumann algebras identify the key properties of graph groupoids.
Received: December 20, 2006. Revised: March 07, 2007. Accepted: March 13, 2007. 相似文献
9.
Sever S. Dragomir 《Archiv der Mathematik》2008,90(5):450-460
Refinements of the generalised trapezoid and Ostrowski inequalities for functions of bounded variation are given. Applications
for the trapezoid and mid-point inequalities are also provided.
Received: 19 May 2008 相似文献
10.
N. M. Ivochkina 《Journal of Fixed Point Theory and Applications》2008,4(1):47-56
We adapt to degenerate m-Hessian evolution equations the notion of m-approximate solutions introduced by N. Trudinger for m-Hessian elliptic equations, and we present close to necessary and sufficient conditions guaranteeing the existence and uniqueness
of such solutions for the first initial boundary value problem.
Dedicated to Professor Felix Browder 相似文献
11.
We prove that the so-called Smoluchowski-Kramers approximation holds for a class of partial differential equations perturbed
by a non-Gaussian noisy term. Namely, we show that the solution of the one-dimensional semi-linear stochastic damped wave
equations
, u(0) = u0, ut (0) = v0, endowed with Dirichlet boundary conditions, converges as the parameter μ goes to zero to the solution of the semi-linear
stochastic heat equation
, u(0) = u0, endowed with Dirichlet boundary conditions.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献
12.
We present the development of the Lucid language from the Original Lucid of the mid-1970s to the TransLucid of today. Each
successive version of the language has been a generalisation of previous languages, but with a further understanding of the
problems at hand.
The Original Lucid (1976), originally designed for purposes of formal verification, was used to formalise the iteration in
while-loop programs. The pLucid language (1982) was used to describe dataflow networks. Indexical Lucid (1987) was introduced for
intensional programming, in which the semantics of a variable was understood as a function from a universe of possible worlds
to ordinary values. With TransLucid, and the use of contexts as firstclass values, programming can be understood in a Cartesian
framework.
相似文献
13.
Niamh O’Sullivan 《Archiv der Mathematik》2007,88(1):1-11
In this paper we prove that rational indecomposability is a genus property for finitely generated torsion-free nilpotent groups
of class 2. We use this result to determine the genus of finitely generated torsion-free nilpotent groups of class 2 which
decompose as a direct product of rationally indecomposable groups.
Received: 3 November 2005 相似文献
14.
Gerd Faltings 《Milan Journal of Mathematics》2008,76(1):93-123
We show that formal groups can be used to simplify the construction of Néron models. Also we give a new proof of the stable
reduction theorem for abelian varieties.
Received: September 2007 相似文献
15.
Bodo Dittmar 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(3):565-568
For a simply connected and normalized domain D in the plane it was proven by Pólya and Schiffer in 1954 for the fixed membrane eigenvalues
for any n, where λj(0) are the fixed membrane eigenvalues of the unit disk. The purpose of this paper is to prove an analog inequality for the free
membrane eigenvalues.
相似文献
16.
Piotr Jucha 《Archiv der Mathematik》2008,90(6):559-571
We discuss the properties of the Wu pseudometric and present counterexamples for its upper semicontinuity that answers the
question posed by Jarnicki and Pflug. We also give formulae for the Wu pseudometric in elementary Reinhardt domains.
Received: 12 September 2007 相似文献
17.
In the recent paper [Adv. Applied Math., 38 (2007), 210–226] it is proved that the special matchings of permutations generate
a Coxeter group. In this paper we generalize this result to a class of Coxeter groups which includes many Weyl and affine
Weyl groups. Our proofs are simpler, and shorter, than those in [loc. cit.]
All authors are partially supported by EU grant HPRN-CT-2001-00272.
Received: 30 October 2006 相似文献
18.
Bertrand Toën 《Selecta Mathematica, New Series》2006,12(1):39-134
The purpose of this work is to introduce a notion of affine stacks, which is a homotopy version of the notion of affine schemes, and to give several applications in the context of algebraic
topology and algebraic geometry.
As a first application we show how affine stacks can be used in order to give a new point of view (and new proofs) on rational
and p-adic homotopy theory. This gives a first solution to A. Grothendieck’s schematization problem described in [18].
We also use affine stacks in order to introduce a notion of schematic homotopy types. We show that schematic homotopy types give a second solution to the schematization problem, which also allows us to go beyond
rational and p-adic homotopy theory for spaces with arbitrary fundamental groups. The notion of schematic homotopy types is also used in
order to construct various homotopy types of algebraic varieties corresponding to various co-homology theories (Betti, de
Rham, l-adic, ...), extending the well known constructions of the various fundamental groups.
Finally, just as algebraic stacks are obtained by gluing affine schemes we define
$$ \infty $$-geometric stacks as a certain gluing of affine stacks. Examples of
$$ \infty $$-geometric stacks in the context of algebraic topology (moduli spaces of dga structures up to quasi-isomorphisms)
and Hodge theory (non-abelian periods) are given. 相似文献
19.
The Generalized Minimal Residual method (GMRES) is often used to solve a nonsymmetric linear system Ax = b. But its convergence analysis is a rather difficult task in general. A commonly used approach is to diagonalize A = XΛ X
−1 and then separate the study of GMRES convergence behavior into optimizing the condition number of X and a polynomial minimization problem over A’s spectrum. This artificial separation could greatly overestimate GMRES residuals and likely yields error bounds that are
too far from the actual ones. On the other hand, considering the effects of both A’s spectrum and the conditioning of X at the same time poses a difficult challenge, perhaps impossible to deal with in general but only possible for certain particular
linear systems. This paper will do so for a (nonsymmetric) tridiagonal Toeplitz system. Sharp error bounds on and sometimes
exact expressions for residuals are obtained. These expressions and/or bounds are in terms of the three parameters that define
A and Chebyshev polynomials of the first kind. 相似文献
20.
Marcello Felisatti 《Mediterranean Journal of Mathematics》2008,5(4):493-499
In this article we give a construction of Max Karoubi’s multiplicative K-theory as the K-theory of an appropriate functor
between two categories. We use this construction to explain why the two definitions of relative multiplicative K-theory for
a compact pair of manifolds we give in the article agree.
Part of this work has been done while I was holding an EEC postdoctoral position funded by the network ‘Algebraic K-theory,
linear algebraic groups and related structures’ at University College Dublin. I would like to thank Professor David Lewis
for inviting me to Dublin. During the later stages of the work, I was supported by EPSERC grant GR/S08046/01. 相似文献