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1.
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:
- •
- we introduce a generalization of the usual notions of Mukai vector and Mukai pairing on differential forms that applies to arbitrary manifolds;
- •
- 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
- •
- we present a conjecture that relates the Hochschild and harmonic structures of a smooth space, similar in spirit to the Tsygan formality conjecture.
2.
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?”
- •
- the intersection cohomology of X,
- •
- the real homotopy type of X.
3.
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;
- •
- 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.
- •
- 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;
- •
- E∈T iff every quasi-continuous mapping from a complete metric space to (E,weak) is weakly continuous at some point.
4.
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:
- •
- ω2 is not normal, where ω denotes the discrete space of countably infinite cardinality.
- •
- 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.
5.
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
- •
- singular and hypersingular integral operators,
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- the analytic continuation of distribution-valued meromorphic functions, and
- •
- a general definition of the convolution of distributions.
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:
- •
- Intervals in any of these four orders essentially describe the product in a Hopf algebra of tableaux defined by Poirier and Reutenauer.
- •
- 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.
- •
- 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.
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.
- •
- W. Whitt, Stochastic-Process Limits, Springer, Berlin, 2002, ISBN 0-387-95358-2, xxiv+602pp., EUR 106,95.
8.
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:
- •
- 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.
9.
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.
10.
11.
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:
- •
- control of the image of Galois representations modulo p,
- •
- Hida's congruence criterion outside an explicit set of primes,
- •
- 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.
12.
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.
13.
Let H be a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. An operator A in L(H) is said to be a Cowen-Douglas operator if there exist Ω, a connected open subset of complex plane C, and n, a positive integer, such that
- (a)
- (b)
- for z in Ω;
- (c)
- ; and
- (d)
- for z in Ω.
14.
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.
15.
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:
- •
- a descent morphism that is not an effective étale-descent morphism;
- •
- an effective étale-descent morphism that is not a descent morphism.
16.
Hoda Bidkhori 《Journal of Combinatorial Theory, Series A》2012,119(3):765-787
In this paper we study finite Eulerian posets which are binomial, Sheffer or triangular. These important classes of posets are related to the theory of generating functions and to geometry. The results of this paper are organized as follows:
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- We completely determine the structure of Eulerian binomial posets and, as a conclusion, we are able to classify factorial functions of Eulerian binomial posets.
- •
- We give an almost complete classification of factorial functions of Eulerian Sheffer posets by dividing the original question into several cases.
- •
- In most cases above, we completely determine the structure of Eulerian Sheffer posets, a result stronger than just classifying factorial functions of these Eulerian Sheffer posets.
17.
The two main results are:
- A.
- If a Banach space X is complementably universal for all subspaces of c0 which have the bounded approximation property, then X∗ is non-separable (and hence X does not embed into c0).
- B.
- There is no separable Banach space X such that every compact operator (between Banach spaces) factors through X.
18.
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
- •
- are not similar to direct sums of square matrices of smaller sizes, or
- •
- are in general position and have the same main diagonal.
19.
Anton Baranov 《Journal of Functional Analysis》2011,261(12):3437-3456
We consider three topics connected with coinvariant subspaces of the backward shift operator in Hardy spaces Hp:
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- properties of truncated Toeplitz operators;
- -
- Carleson-type embedding theorems for the coinvariant subspaces;
- -
- factorizations of pseudocontinuable functions from H1.
20.
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.