A class of special p-groups

Starting by the multiplication table of a finite group G, for each odd prime p a special p-group P of exponent p is constructed. Some connections between the structures of G and P, concerning subgroups and automorphisms, are given. When p does not divide the order of G, for every normal subgroup of G a direct decomposition of P is done. Besides, the order of the derived subgroup of G is proved to be connected with the existence of some abelian subgroups of maximal order in P. Finally, the elements of P with large centralizers are characterized in terms of algebraic properties of the multiplication table of G. Dedicated to Herman Heineken on the occasion of his 60th birthday Work supported by M.U.R.S.T. and G.N.S.A.G.A-C.N.R. of Italy.     

Every T-space is equivalent to a T-space of continuous functions

A T-space U of degree k is a (k + 1)-dimensional vector space over (the real line) of real-valued functions defined on a linearly ordered set, satisfying the condition: for every nonzero u ε U, Z(u), the number of distinct zeros of u and ^-(u), the number of alternations in sign of u(t) with increasing t, each do not exceed k. It is demonstrated that given a T-space U of degree k > 0 on an arbitrary linearly ordered set T, there is a subset T′ of the real line and a nonsingular linear map L:U→ C(T′), the set of continuous functions on T′, such that the following hold: L(U) is a T-space of degree k; for u ε U, Z(u) = Z(L(u)), S^−(u) = S^−(L(u); and for some order-preserving bijection Θ:T → T′, u(t) = O if and only if L(u)(Θ(t) = 0. It is also shown that a T-space on a subset T can be extended to a T-space on the closure of T in ]inf T, sup T], provided that there are no “interval gaps” in T. Examples show that, in general, a T-space cannot be extended across an “interval gap” in its domain, and cannot be extended to both the infimum and supremum of its domain. Conditions for a T-space to be Markov, and to admit an adjoined function are derived.     

Restricted T-Universal Functions

We prove the existence of a function which is holomorphic exactly in the unit disk and has universal translates with respect to a prescribed closed set E∂ and satisfies C^∞(∂ \E). If Q is a subsequence of ₀ with upper density d(Q)=1 then the function can be constructed such that in addition

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Property T and strong property T for unital*-homomorphisms

We introduce and study property T and strong property T for unital*-homomorphisms between two unital C^*-algebras.We also consider the relations between property T and invariant subspaces for some canonical unital^-representations.As a corollary,we show that when G is a discrete group,G is finite if and only if G is amenable and the inclusion map i:Cr^*(G)→B(l^2(G))has property T.We also give some new equivalent forms of property T for countable discrete groups and strong property T for unital C^*-algebras.     

A special class of set covering problems

A class of set covering problems is being introduced. This class is obtained from reformulation of a well-known combinatorial problem of Erdös on the hypercube. An algorithmic method of solution to the problem is proposed. Max-flow algorithms are the main ingredients of our method.The computational results which will be presented here, improves the best existing bound related to the combinatorial problem. This, at the same time, provides a good approximate solution to the corresponding set covering problem of more than a thousand variables and constraints.Moreover, we show that our special class of problems can be recognized from the class of all set covering problems, by a polynomial algorithm with O (MN) complexity, where M and N are numbers of constraints and variables of a given instant, respectively.This research is supported by EPSCOR-NSF of Puerto Rico and by FIPI, the institutional grant of University of Puerto Rico.     

A special class of extended multicriteria location problems

This paper is devoted to the study of extended multicriteria location problems, which are obtained from a given planar single-facility multicriteria location problem with respect to the maximum norm by adding new cost functions. By means of an appropriate decomposition approach, we develop an implementable algorithm for generating an efficient solution of such extended problems.     

半粘合诱导的t-结构

本文研究了对于给定的一个三角范畴的上（下）粘合（C'',C,C"）,如何由C的一个t-结构诱导C''和C"的t-结构的问题.利用左（右）t-正合函子的概念,给出了由C的一个t-结构可诱导出C''和C"的t-结构的充分条件.将粘合的一些相关结果推广到了上（下）粘合的情形.     

A special class of nilmanifolds admitting an Anosov diffeomorphism

A nilmanifold admits an Anosov diffeomorphism if and only if its fundamental group (which is finitely generated, torsion-free and nilpotent) supports an automorphism having no eigenvalues of absolute value one. Here we concentrate on nilpotency class 2 and fundamental groups whose commutator subgroup is of maximal torsion-free rank. We prove that the corresponding nilmanifold admits an Anosov diffeomorphism if and only if the torsion-free rank of the abelianization of its fundamental group is greater than or equal to 3.

     

A special class of Williamson matrices and difference sets

A construction is given of a very special class of Hadamard matrices. This yields Hadamard matrices of the Williamson kind and difference sets of order 4 · 3^2m.     

辫子T-范畴的构造

本文首先引入了一类新的范畴_AYD_G^H, 这个范畴是一簇范畴{_AYD^H(α,β)}_(α,β)∈G的非交并, 获得了范畴{_AYD^H(α,β)}_(α,β)∈G是一个辫子T-范畴当且仅当(A,H,Q)是一个G-偶结构, 推广了2005年Panaite和Staic的主要结论. 最后, 当H是有限维时, 构造了一个拟三角T-余代数{A#H^*(α,β)}_(α,β)∈G, 它的表示范畴与{_AYD^H(α,β)}_(α,β)∈G是同构的.     

A scenario for torus T destruction via a global bifurcation

We show a scenario of a two-frequency torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T² with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-II intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws.     

A class of new special solution of nonlinear diffusion equation

One of the most interesting problems of nonlinear differential equations is the construction of partial solutions. A new method is presented in this paper to seek special solutions of nonlinear diffusion equations. This method is based on seeking suitable function to satisfy Bernolli equation. Many new special solutions are obtained.