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1.
There are two methods of reduction of positive definite quadratic forms due to Voronoi. One of these methods is based on the perfect forms and the other on the type of Voronoi polyhedra associated with the form. It was conjectured by Voronoi that these two methods are strongly connected. 相似文献
2.
Paulette Farjot 《Linear algebra and its applications》1976,15(3):189-196
In this paper we study n × n Hermitian semidefinite positive matrices which are infinitely divisible in a sense that we define in Sec. 1. We establish (Theorem 2.2) a stability property for the rank of the “Hadamard power matrices” of such a matrix. 相似文献
3.
V. E. Bening 《Journal of Mathematical Sciences》2000,99(4):1403-1407
In this paper, we consider asymptotic expansions and the rate of convergence for the distribution function of asymptotically
efficient U-statistics under alternatives in the one-sample problem. Section 1 is an introduction. Section 2 contains the
theorem concerning the rate of convergence for U-statistics; in Sec. 3, we formulate sets of sufficient conditions under which
Edgeworth-type asymptotic expansions for U-statistics under alternatives will be constructed (see Theorem 2). Finally, these
theorems are proved in Sec. 4.
Supported by the Russian Foundation for Basic Research (grant No. 96-01-01919).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part II. 相似文献
4.
Victor K. Wei 《Journal of Graph Theory》1988,12(4):571-587
We derive three equivalent conditions on a perfect graph concerning the optimal solution of a convex programming problem, the length-width inequality, and the simultaneous vertex covering by cliques and anticliques. By combining proof techniques including Lagrangian dual, Dilworth's Theorem, and Kuhn-Tucker Theorem, we establish a strong connection between the three topics. This provides new insights into the structure of perfect graphs. The famous Lubell-Yamamoto-Meschalkin (LYM) Property or Sperner Property for partially ordered sets is a specialization of our results to a subclass of perfect graphs. 相似文献
5.
We study percolation in the following random environment: let Z be a Poisson process of constant intensity on ℝ2, and form the Voronoi tessellation of ℝ2 with respect to Z. Colour each Voronoi cell black with probability p, independently of the other cells. We show that the critical probability is 1/2. More precisely, if p>1/2 then the union of the black cells contains an infinite component with probability 1, while if p<1/2 then the distribution of the size of the component of black cells containing a given point decays exponentially. These
results are analogous to Kesten's results for bond percolation in ℤ2.
The result corresponding to Harris' Theorem for bond percolation in ℤ2 is known: Zvavitch noted that one of the many proofs of this result can easily be adapted to the random Voronoi setting.
For Kesten's results, none of the existing proofs seems to adapt. The methods used here also give a new and very simple proof
of Kesten's Theorem for ℤ2; we hope they will be applicable in other contexts as well.
Research supported in part by NSF grant ITR 0225610 and DARPA grant F33615-01-C-1900
Research partially undertaken during a visit to the Forschungsinstitut für Mathematik, ETH Zürich, Switzerland 相似文献
6.
We compare two rational polyhedral admissible decompositions of the cone of positive definite quadratic forms: the perfect cone decomposition and the 2nd Voronoi decomposition. We determine which cones belong to both the decompositions, thus providing a positive answer to a conjecture of Alexeev and Brunyate (Invent. Math. doi:10.1007/s00222-011-0347-2, 2011). As an application, we compare the two associated toroidal compactifications of the moduli space of principal polarized abelian varieties: the perfect cone compactification and the 2nd Voronoi compactification. 相似文献
7.
D. S. Kataev 《Journal of Mathematical Sciences》2002,110(6):3091-3110
We study cubic metaplectic Eisenstein series connected with the Jacobi maximal parabolic subgroup of a symplectic group. We use the so-called ``sl(2)-triples' technique in order to evaluate the Fourier coefficients of these series. In Secs. 1 and 2, we introduce the necessary notation and study the group
and its subgroups in detail. In Sec. 3, we prove the main result of the present paper (Theorem 1). Section 4 is devoted to the study of the Dirichlet series appearing in Theorem 1. Bibliography: 5 titles. 相似文献
9.
Rice's Theorem says that every nontrivia semantic property of programs is undecidable. In this spirit we show the following: Every nontrivia absolute (gap, relative) counting property of circuits is UP‐hard with respect to polynomial‐time Turing reductions. For generators [31] we show a perfect analogue of Rice's Theorem. 相似文献
10.
Recently, it was shown by Bollobás and Riordan 4 that the critical probability for random Voronoi percolation in the plane is 1/2. As a by‐product of the method, a short proof of the Harris–Kesten Theorem was given by Bollobás and Riordan 5 . The aim of this paper is to show that the techniques used in these papers can be applied to many other planar percolation models, both to obtain short proofs of known results and to prove new ones. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006 相似文献
11.
This paper extends the notion of diagonal sums of a square matrix to “weighted diagonal sums”. Using simple probabilistic arguments, most of the results of Wang [5] concerning the maximum and minimum diagonal sums of doubly stochastic matrices are extended to maximum and minimum weighted diagonal sums of stochastic matrices (Sec. 3). Two stronger versions of one of Wang's conjectures are also proven (Theorems 4.1 and 5.1), of which the latter easily generalizes to the case of non-negative matrices (Theorem 5.2). The paper ends with a few open questions and counter-examples. 相似文献
12.
Georgi D. Dimov 《Applied Categorical Structures》2009,17(5):501-516
Generalizing Duality Theorem of H. de Vries, we define a category which is dually equivalent to the category of locally compact
Hausdorff spaces and perfect maps. 相似文献
13.
<正> 1955年A.Grothendieck在建立核空间理论的同时,作为例子也具体给出了一类特殊的完备空间——gestufen空间具有核性的充要条件,十年之后,A.Pietsch和作者的一篇未发表的工作各自独立地得到了一般完备空间的核性条件,从此核完备空间的研究就展开了,如可参看[7—9]. 本文是继续探讨这方面的问题,共分四个部分:首先,为完整起见,在§1我们将重新叙述和证明完备空间为核的条件(我们原先的证明就与Pietsch不同);其次,在§2中我 相似文献
14.
《Journal of Computational and Applied Mathematics》2002,146(2):253-275
We obtain semi-closed forms for the optimal quantizers of some families of one-dimensional probability distributions. They yield the first examples of non-log-concave distributions for which uniqueness holds. We give two types of applications of these results. One is a fast computation of numerical approximations of one-dimensional optimal quantizers and their use in a multidimensional framework. The other is some asymptotics of the standard empirical measures associated to the optimal quantizers in terms of distribution function, Laplace transform and characteristic function. Moreover, we obtain the rate of convergence in the Bucklew & Wise Theorem and finally the asymptotic size of the Voronoi tessels. 相似文献
15.
Mathematical Programming - Even and odd pairs are important tools in the study of perfect graphs and were instrumental in the proof of the Strong Perfect Graph Theorem. We suggest that such pairs... 相似文献
16.
George Ciprian Modoi 《代数通讯》2013,41(3):995-1011
We say that a projective class in a triangulated category with coproducts is perfect if the corresponding ideal is closed under coproducts of maps. We study perfect projective classes and the associated phantom and cellular towers. Given a perfect generating projective class, we show that every object is isomorphic to the homotopy colimit of a cellular tower associated to that object. Using this result and the Neeman's Freyd-style representability theorem, we give a new proof of Brown Representability Theorem. 相似文献
17.
关于矩阵二次型极值的若干结果 总被引:1,自引:0,他引:1
本文出于统计研究的需要,系统地讨论了Rayleigh-Ritz定理在矩阵形式下的推广,给出了若干新结果,完善了现有文献中这方面的研究。 相似文献
18.
19.
Dharmanand Baboolal 《Czechoslovak Mathematical Journal》2011,61(3):845-861
Perfect compactifications of frames are introduced. It is shown that the Stone-Čech compactification is an example of such
a compactification. We also introduce rim-compact frames and for such frames we define its Freudenthal compactification, another
example of a perfect compactification. The remainder of a rim-compact frame in its Freudenthal compactification is shown to
be zero-dimensional. It is shown that with the assumption of the Boolean Ultrafilter Theorem the Freudenthal compactification
for spaces, as well as the Freudenthal-Morita Theorem for spaces, can be obtained from our frame constructions. 相似文献
20.
Krzysztof Pawaowski 《K-Theory》1998,13(1):41-55
The paper presents a procedure for constructing smooth actions of finite perfect groups on spheres with fixed point sets having certain prescribed properties (Theorem A); in particular, having any prescribed configuration of Chern and Pontryagin numbers (Corollary C). The main ingredients used are equivariant thickening and equivariant surgery. 相似文献