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1.
Richard Ehrenborg 《Journal of Combinatorial Theory, Series A》2007,114(2):339-359
We give a complete classification of the factorial functions of Eulerian binomial posets. The factorial function B(n) either coincides with n!, the factorial function of the infinite Boolean algebra, or 2n−1, the factorial function of the infinite butterfly poset. We also classify the factorial functions for Eulerian Sheffer posets. An Eulerian Sheffer poset with binomial factorial function B(n)=n! has Sheffer factorial function D(n) identical to that of the infinite Boolean algebra, the infinite Boolean algebra with two new coatoms inserted, or the infinite cubical poset. Moreover, we are able to classify the Sheffer factorial functions of Eulerian Sheffer posets with binomial factorial function B(n)=2n−1 as the doubling of an upside-down tree with ranks 1 and 2 modified. When we impose the further condition that a given Eulerian binomial or Eulerian Sheffer poset is a lattice, this forces the poset to be the infinite Boolean algebra BX or the infinite cubical lattice . We also include several poset constructions that have the same factorial functions as the infinite cubical poset, demonstrating that classifying Eulerian Sheffer posets is a difficult problem. 相似文献
2.
Norbert Ortner 《Journal of Mathematical Analysis and Applications》2004,297(2):353-383
Our main task is a presentation of J. Horváth's results concerning
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- singular and hypersingular integral operators,
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- the analytic continuation of distribution-valued meromorphic functions, and
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- a general definition of the convolution of distributions.
3.
Luoshan Xu 《Topology and its Applications》2006,153(11):1886-1894
In this paper, posets which may not be dcpos are considered. The concept of embedded bases for posets is introduced. Characterizations of continuity of posets in terms of embedded bases and Scott topology are given. The main results are:
- (1)
- A poset is continuous iff it is an embedded basis for a dcpo up to an isomorphism;
- (2)
- A poset is continuous iff its Scott topology is completely distributive;
- (3)
- A topological T0 space is a continuous poset equipped with the Scott topology in the specialization order iff its topology is completely distributive and coarser than or equal to the Scott topology;
- (4)
- A topological T1 space is a discrete space iff its topology is completely distributive.
4.
M. Prasolov 《Journal of Combinatorial Theory, Series A》2011,118(3):920-937
This paper is on tilings of polygons by rectangles. A celebrated physical interpretation of such tilings by R.L. Brooks, C.A.B. Smith, A.H. Stone and W.T. Tutte uses direct-current circuits. The new approach of this paper is an application of alternating-current circuits. The following results are obtained:
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- a necessary condition for a rectangle to be tilable by rectangles of given shapes;
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- a criterion for a rectangle to be tilable by rectangles similar to it but not all homothetic to it;
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- a criterion for a “generic” polygon to be tilable by squares.
5.
We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered:
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- we improve the Ray-Chaudhuri-Wilson bound of the size of uniform intersecting families of subsets;
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- we refine the bound of Delsarte-Goethals-Seidel on the maximum size of spherical sets with few distances;
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- we prove a new bound on codes with few distances in the Hamming space, improving an earlier result of Delsarte.
6.
Müge Ta?kin 《Journal of Combinatorial Theory, Series A》2006,113(6):1092-1119
Let SYTn be the set of all standard Young tableaux with n cells. After recalling the definitions of four partial orders, the weak, KL, geometric and chain orders on SYTn and some of their crucial properties, we prove three main results:
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- Intervals in any of these four orders essentially describe the product in a Hopf algebra of tableaux defined by Poirier and Reutenauer.
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- The map sending a tableau to its descent set induces a homotopy equivalence of the proper parts of all of these orders on tableaux with that of the Boolean algebra 2[n−1]. In particular, the Möbius function of these orders on tableaux is (−1)n−3.
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- For two of the four orders, one can define a more general order on skew tableaux having fixed inner boundary, and similarly analyze their homotopy type and Möbius function.
7.
Let T be the class of Banach spaces E for which every weakly continuous mapping from an α-favorable space to E is norm continuous at the points of a dense subset. We show that:
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- T contains all weakly Lindelöf Banach spaces;
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- l∞∉T, which brings clarity to a concern expressed by Haydon ([R. Haydon, Baire trees, bad norms and the Namioka property, Mathematika 42 (1995) 30-42], pp. 30-31) about the need of additional set-theoretical assumptions for this conclusion. Also, (l∞/c0)∉T.
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- T is stable under weak homeomorphisms;
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- E∈T iff every quasi-continuous mapping from a complete metric space to (E,weak) is densely norm continuous;
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- E∈T iff every quasi-continuous mapping from a complete metric space to (E,weak) is weakly continuous at some point.
8.
Bert Zwart 《Operations Research Letters》2005,33(5):544-550
This article reviews the following books:
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- S. Asmussen, Applied Probability and Queues, second ed., Springer, Berlin, 2003, ISBN 0-387-00211-1, xii+438pp., EUR 85.55.
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- H. Chen, D. Yao, Fundamentals of Queueing Networks, Springer, Berlin, 2003, ISBN 0-387-95166-0, xviii+405pp., EUR 74,95.
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- W. Whitt, Stochastic-Process Limits, Springer, Berlin, 2002, ISBN 0-387-95358-2, xxiv+602pp., EUR 106,95.
9.
George JanelidzeManuela Sobral 《Journal of Pure and Applied Algebra》2002,174(3):303-309
It is known that every effective (global-) descent morphism of topological spaces is an effective étale-descent morphism. On the other hand, in the predecessor of this paper we gave examples of:
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- a descent morphism that is not an effective étale-descent morphism;
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- an effective étale-descent morphism that is not a descent morphism.
10.
A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms for
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- nonderogatory complex matrices up to unitary similarity, and
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- pairs of complex matrices up to similarity, in which one matrix has distinct eigenvalues.
11.
Alberto Caprara 《Discrete Applied Mathematics》2006,154(5):738-753
The train timetabling problem (TTP) aims at determining an optimal timetable for a set of trains which does not violate track capacities and satisfies some operational constraints.In this paper, we describe the design of a train timetabling system that takes into account several additional constraints that arise in real-world applications. In particular, we address the following issues:
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- Manual block signaling for managing a train on a track segment between two consecutive stations.
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- Station capacities, i.e., maximum number of trains that can be present in a station at the same time.
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- Prescribed timetable for a subset of the trains, which is imposed when some of the trains are already scheduled on the railway line and additional trains are to be inserted.
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- Maintenance operations that keep a track segment occupied for a given period.
12.
It is well known that the signature operator on a manifold defines a K-homology class which is an orientation after inverting 2. Here we address the following puzzle: What is this class localized at 2, and what special properties does it have? Our answers include the following:
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- the K-homology class ΔM of the signature operator is a bordism invariant;
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- the reduction mod 8 of the K-homology class of the signature operator is an oriented homotopy invariant;
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- the reduction mod 16 of the K-homology class of the signature operator is not an oriented homotopy invariant.
13.
Douglas Farenick Vyacheslav Futorny Tatiana G. Gerasimova Vladimir V. Sergeichuk Nadya Shvai 《Linear algebra and its applications》2011,435(6):1356-1369
Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A=[aij] and B=[bij] be upper triangular n×n matrices that
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- are not similar to direct sums of square matrices of smaller sizes, or
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- are in general position and have the same main diagonal.
14.
The aim of this paper is to extend some arithmetic results on elliptic modular forms to the case of Hilbert modular forms. Among these results let us mention:
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- control of the image of Galois representations modulo p,
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- Hida's congruence criterion outside an explicit set of primes,
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- freeness of the integral cohomology of a Hilbert modular variety over certain local components of the Hecke algebra and Gorenstein property of these local algebras.
15.
Andrei C?ld?raru 《Advances in Mathematics》2005,194(1):34-66
We continue the study of the Hochschild structure of a smooth space that we began in our previous paper, examining implications of the Hochschild-Kostant-Rosenberg theorem. The main contributions of the present paper are:
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- we introduce a generalization of the usual notions of Mukai vector and Mukai pairing on differential forms that applies to arbitrary manifolds;
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- we give a proof of the fact that the natural Chern character map K0(X)→HH0(X) becomes, after the HKR isomorphism, the usual one ; and
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- we present a conjecture that relates the Hochschild and harmonic structures of a smooth space, similar in spirit to the Tsygan formality conjecture.
16.
《Journal of Mathematical Analysis and Applications》2004,296(2):393-402
In 1989 A.N. Sharkovsky asked the question which of the properties characterizing continuous maps of the interval with zero topological entropy remain equivalent for triangular maps of the square. The problem is difficult and only partial results are known. However, in the case of triangular maps with nondecreasing fibres there are only few gaps in a classification (given by Z. Ko?an) of a set of 24 of these conditions. In the present paper we remove these gaps by giving an example of a triangular map in the square with the following properties:
- (1)
- all fibre maps are nondecreasing,
- (2)
- all recurrent points of the map are uniformly recurrent, and
- (3)
- the restriction of the map to the set of recurrent points has an uncountable scrambled set (and so is Li-Yorke chaotic).
17.
Gabriel Padilla 《Topology and its Applications》2007,154(15):2764-2770
A classical result says that a free action of the circle S1 on a topological space X is geometrically classified by the orbit space B and by a cohomological class e∈H2(B,Z), the Euler class. When the action is not free we have a difficult open question:
- (Π)
- “Is the space X determined by the orbit space B and the Euler class?”
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- the intersection cohomology of X,
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- the real homotopy type of X.
18.
Sensitivity of a shallow-water model to parameters 总被引:1,自引:0,他引:1
Eugene Kazantsev 《Nonlinear Analysis: Real World Applications》2012,13(3):1416-1428
An adjoint based technique is applied to a shallow water model in order to estimate the influence of the model’s parameters on the solution. Among parameters, the bottom topography, initial conditions, boundary conditions on rigid boundaries, viscosity coefficients, Coriolis parameter and the amplitude of the wind stress tension are considered. Their influence is analyzed from three points of view:
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- flexibility of the model with respect to a parameter that is related to the lowest value of the cost function that can be obtained in the data assimilation experiment that controls this parameter;
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- possibility to improve the model by the parameter’s control, i.e., whether the solution with the optimal parameter remains close to observations after the end of control;
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- sensitivity of the model solution to the parameter in a classical sense. That implies the analysis of the sensitivity estimates and their comparison with each other and with the local Lyapunov exponents that characterize the sensitivity of the model to initial conditions.
19.
A.V. Karasev 《Topology and its Applications》2006,153(10):1609-1613
In this note we introduce the concept of a quasi-finite complex. Next, we show that for a given countable simplicial complex L the following conditions are equivalent:
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- L is quasi-finite.
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- There exists a [L]-invertible mapping of a metrizable compactum X with e-dimX?[L] onto the Hilbert cube.Finally, we construct an example of a quasi-finite complex L such that its extension type [L] does not contain a finitely dominated complex.
20.
For a space X, X2 denotes the collection of all non-empty closed sets of X with the Vietoris topology, and K(X) denotes the collection of all non-empty compact sets of X with the subspace topology of X2. The following are known:
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- ω2 is not normal, where ω denotes the discrete space of countably infinite cardinality.
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- For every non-zero ordinal γ with the usual order topology, K(γ) is normal iff whenever cf γ is uncountable.
- (1)
- ω2 is strongly zero-dimensional.
- (2)
- K(γ) is strongly zero-dimensional, for every non-zero ordinal γ.