THE CAPACITY DENSITY AND THE HAUSDORFF DIMENSION OF FRACTAL SETS

ＴＨＥＣＡＰＡＣＩＴＹＤＥＮＳＩＴＹＡＮＤＴＨＥＨＡＵＳＤＯＲＦＦＤＩＭＥＮＳＩＯＮＯＦＦＲＡＣＴＡＬＳＥＴＳ￥ＸｕＹｏｕ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ２００４３３，Ｓｈａｎｇｈａｉ，...     

ON NECESSARY AND SUFFICIENT CONDITIONS FOR DUALS OF WAVELET FRAMES

（张泽银）（王建忠）ＯＮＮＥＣＥＳＳＡＲＹＡＮＤＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＳＦＯＲＤＵＡＬＳＯＦＷＡＶＥＬＥＴＦＲＡＭＥＳ￥ＺｈａｎｇＺｅｙｉｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＨｕｂａｉＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈａｎ４３００６２，Ｃｈｉｎａ...     

对流扩散问题的流线扩散有限元分析

对流扩散问题的流线扩散有限元分析孙澈，张阳，魏强（南开大学）ＴＨＥＳＴＲＥＡＭＬＩＮＥ－ＤＩＦＦＵＳＩＯＮＦ．Ｅ．ＡＮＡＬＹＳＩＳＦＯＲＣＯＮＶＥＣＴＩＯＮＤＩＦＦＵＳＩＯＮＰＲＯＢＬＥＭＳ￥ＳｕｎＣｈｅ；ＺｈａｎｇＹａｎｇ；ＷｅｉＱｉａｎｇ（Ｎａｎ...     

有限域上的仿射辛空间及其应用

本文中，首先给出了有限域Ｆｑ上的２ｖ维仿射辛空间ＡＳＧ（２ｖ，Ｆｑ）和２ｖ次仿射辛群ＡＳｐ２ｖ（Ｆｑ）的概念，然后讨论ＡＳｐ２ｖ（Ｆｑ）作用在ＡＳＧ（２ｖ，Ｆｑ）上的可迁性及一些相关的计数定理，最后给出应用仿射辛空间构作结合方案和认证码的例子。     

OSCILLATIONS OF ALL UNBOUNDED SOLUTIONS OF LINEAR DELAY DIFFERENTIAL SYSTEMS

ＯＳＣＩＬＬＡＴＩＯＮＳＯＦＡＬＬＵＮＢＯＵＮＤＥＤＳＯＬＵＴＩＯＮＳＯＦＬＩＮＥＡＲＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＳ苏醒湖南财经学院，邮编：４１００７９ＯＳＣＩＬＬＡＴＩＯＮＳＯＦＡＬＬＵＮＢＯＵＮＤＥＤＳＯＬＵＴＩＯＮＳＯＦＬＩＮ...     

EXISTENCE OF FORECAST AND DECISION HORIZONS FOR OPTIMAL CONTROL PROBLEMS OF NONLINEAR SYSTEMS

ＥＸＩＳＴＥＮＣＥＯＦＦＯＲＥＣＡＳＴＡＮＤＤＥＣＩＳＩＯＮＨＯＲＩＺＯＮＳＦＯＲＯＰＴＩＭＡＬＣＯＮＴＲＯＬＰＲＯＢＬＥＭＳＯＦＮＯＮＬＩＮＥＡＲＳＹＳＴＥＭＳ￥ＺｈａｎｇＣｈｅｎｇｙｕｎ（张成云）（ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，复旦大学，邮编：...     

ASSESSMENT OF LOCAL INFLUENCE FOR GENERALIZED CORRELATION COEFFICIENTS

ＡＳＳＥＳＳＭＥＮＴＯＦＬＯＣＡＬＩＮＦＬＵＥＮＣＥＦＯＲＧＥＮＥＲＡＬＩＺＥＤＣＯＲＲＥＬＡＴＩＯＮＣＯＥＦＦＩＣＩＥＮＴＳ（陈建宝，陈涛）￥ＣｈｅｎＪｉａｎｂａｏＣｈｅｎＴａｏ（Ｄｅｐｔ．ｏｆＳｔａｔｉｓｔｉｃｓ，ＹｕｎｎａｎＵｎｉｖ，Ｋｕｎｍｉ...     

EXCESSIVE FUNCTIONS OF A CLASS OF SUPERPROCESSES

ＥＸＣＥＳＳＩＶＥＦＵＮＣＴＩＯＮＳＯＦＡＣＬＡＳＳＯＦＳＵＰＥＲＰＲＯＣＥＳＳＥＳＺｈａｏＸｕｅｌｅｉ（赵学雷）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｔｏｕＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｔｏｕ５１５０６３，Ｃｈｉｎａ）Ａｂｓｔｒａ...     

适用于确定FMS周期的实用迭代法

本文研究了ＦＭＳ系统周期性，给出了一种简便、实用的确定ＦＭＳ周期的迭代法．     

一类奇摄动非线性反应扩散积分微分方程组

一类奇摄动非线性反应扩散积分微分方程组莫嘉琪，许玉兴（安徽师范大学数学系，芜湖２４１０００）ＡＣＬＡＳＳＯＦＳＩＮＧＵＬＡＲＬＹＰＥＲＴＵＲＢＥＤＮＯＮＬＩＮＥＡＲＲＥＡＣＴＩＯＮＤＩＦＦＵＳＩＯＮＩＮＴＥＧＲＡＬ－ＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥ...     

Macroscopic dimension and essential manifolds

M. Gromov asked whether the macroscopic dimension of rationally essential n-dimensional manifolds equals n. We show that the answer depends only on the corresponding group homology class and give an affirmative answer for certain classes. In particular, the answer is positive for manifolds with amenable fundamental groups.     

Rigid actions of amenable groups

Given a countable discrete amenable group G, does there exist a free action of G on a Lebesgue probability space which is both rigid and weakly mixing? The answer to this question is positive if G is abelian. An affirmative answer is given in this paper, in the case that G is solvable or residually finite. For a locally finite group, the question is reduced to an algebraic one. It is exemplified how the algebraic question can be positively resolved for some groups, whereas for others the algebraic viewpoint suggests the answer may be negative.     

On a problem posed by Murray and Tent

In this short note, we give a positive answer to a problem posed by Murray and Tent (J. Algebra 398:318–328, 2014).     

Almost sure convergence of the multiple ergodic average for certain weakly mixing systems

The family of pairwise independently determined(PID) systems, i.e., those for which the independent joining is the only self joining with independent 2-marginals, is a class of systems for which the long standing open question by Rokhlin, of whether mixing implies mixing of all orders, has a positive answer. We show that in the class of weakly mixing PID one finds a positive answer for another long-standing open problem, whether the multiple ergodic averages 1/N N-1∑n=0 f_1(T~nx)···f_d(T~(dnx)),N→∞,almost surely converge.     

Completeness of weak perturbations of self-adjoint operators

One solves the following problem of M. V. Keldysh: let H be a completely continuous self-adjoint operator acting in a separable Hubert space ?, being a weak perturbation (i.e., the operator S is completely continuous and I+S is invertible); is it true that the operator T will be complete together with H (i.e., the family of its root vectors complete in ?)? The answer is negative. One describes H alloperators, forwhich the answer is positive (for any S): these are those totally positive completely continuous operators H for which where v(t) is the number of eigenvalues of H larger than .     

Simplexes in a normed space

Is it true that any set of n + 1 points in Rⁿ can be isometrically embedded into any n-dimensional real normed apace? For n ≥ 3, the answer to this question is unknown to the author of this paper. For n = 2, it is clear that the answer is positive. For n = 3, the problem is reduced to the case where four points lie in a plane. A certain reduction is assigned for arbitrary n.     

Singularities of positive supersolutions in elliptic PDEs

We present several extensions of the Brezis–Lions Lemma on removable singularities. We also give a positive answer to a question raised by H. Brezis and M. Marcus about an inverse maximum principle for the Laplacian.     

On the maximal length of two sequences of integers in arithmetic progressions with the same prime divisors

In this paper we consider an analogue of the problem of Erds and Woods for arithmetic progressions. A positive answer follows from theabc conjecture. Partial results are obtained unconditionally.     

Hyperreflexivity of finite-dimensional subspaces

We show that each reflexive finite-dimensional subspace of operators is hyperreflexive. This gives a positive answer to a problem of Kraus and Larson. We also show that each n-dimensional subspace of Hilbert space operators is -hyperreflexive.     

Shape preserving representations and optimality of the Bernstein basis

This paper gives an affirmative answer to a conjecture given in [10]: the Bernstein basis has optimal shape preserving properties among all normalized totally positive bases for the space of polynomials of degree less than or equal ton over a compact interval. There is also a simple test to recognize normalized totally positive bases (which have good shape preserving properties), and the corresponding corner cutting algorithm to generate the Bézier polygon is also included. Among other properties, it is also proved that the Wronskian matrix of a totally positive basis on an interval [a, ) is also totally positive.Both authors were partially supported by DGICYT PS90-0121.