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1.
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.
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.
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.
4.
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.
5.
6.
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.
7.
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.
8.
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.
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.
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.
11.
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.
12.
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.
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- We give an almost complete classification of factorial functions of Eulerian Sheffer posets by dividing the original question into several cases.
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- 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.
13.
Peter M. Gruber 《Advances in Mathematics》2004,186(2):456-497
Minimum sums of moments or, equivalently, distortion of optimum quantizers play an important role in several branches of mathematics. Fejes Tóth's inequality for sums of moments in the plane and Zador's asymptotic formula for minimum distortion in Euclidean d-space are the first precise pertinent results in dimension d?2. In this article these results are generalized in the form of asymptotic formulae for minimum sums of moments, resp. distortion of optimum quantizers on Riemannian d-manifolds and normed d-spaces. In addition, we provide geometric and analytic information on the structure of optimum configurations. Our results are then used to obtain information on
- (i)
- the minimum distortion of high-resolution vector quantization and optimum quantizers,
- (ii)
- the error of best approximation of probability measures by discrete measures and support sets of best approximating discrete measures,
- (iii)
- the minimum error of numerical integration formulae for classes of Hölder continuous functions and optimum sets of nodes,
- (iv)
- best volume approximation of convex bodies by circumscribed convex polytopes and the form of best approximating polytopes, and
- (v)
- the minimum isoperimetric quotient of convex polytopes in Minkowski spaces and the form of the minimizing polytopes.
14.
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;
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- Carleson-type embedding theorems for the coinvariant subspaces;
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- factorizations of pseudocontinuable functions from H1.
15.
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.
16.
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.
17.
Roger A. Horn 《Linear algebra and its applications》2008,428(1):193-223
Canonical matrices are given for
- (i)
- bilinear forms over an algebraically closed or real closed field;
- (ii)
- sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and
- (iii)
- sesquilinear forms over a field F of characteristic different from 2 with involution (possibly, the identity) up to classification of Hermitian forms over finite extensions of F; the canonical matrices are based on any given set of canonical matrices for similarity over F.
18.
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.
19.
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.