R~n上的一类广义Poisson括号

利用任意一个n阶反对称矩阵,我们在欧氏空间P~n上定义一个广义Poisson括号,并讨论了相关的性质     

基于输入-输出数据的重心法模糊系统及其泛逼近性

研究基于输入-输出数据的重心法模糊系统及其泛逼近性.首先,将一组单输入-单榆出数据转换成模糊推理规则,通过选择适当的模糊蕴涵算子生成模糊关系,再利用这种模糊关系求出二雄随机变量的联合概率密度函数.当将模糊蕴涵分别取为Larsen蕴涵和Mamdani蕴涵时,分别得到了两种具体的概率密度函数(称之为Larsen分布和Mamdani分布).其次,利用这两种概率分布.分别求出了对应的两种回归函数,指出这种回归函数实际上是模糊控制中的重心法模糊系统.我们分别给出了这种模糊系统具有泛逼近性的充分条件.从而进一步揭示了模糊系统的概率论意义.     

First Order Differential Operators in Real Dimension Eight

In this article some generalizations to eight dimensional real algebras of the notion of Cauchy-Fueter regularity are introduced, by defining suitable operators. Some properties of the nullsolutions of those operators such as removability of compact singularities are studied and the analogue of the Cauchy formula is provided. Special attention is devoted to the case of regularity in the Clifford algebra on three units.     

On an inverse problem of entropy othimization and related questions

In a fundamental paper Arov and Krein studied entropy minimization problems over a set of matrix-valued Schur functions which arises from a fractional linear transformation the generating matrix-valued function of which is a j_pq -inner function.Our paper handles the corresponding inverse problem: If a p x q Schur function f is given, then the problem is to determine all j_pq -inner functions for which f turns out to be the associatedentropy-minimal function     

A generalized steepest descent method for continuously subdifferentiable functions

A class of methods for unconstrained minimization of quasidifferentiable, especially subdifferentiable functions is described, which includes well-known algorithms as special cases. Moreover, it is shown that an algorithm previously published fails to converge to an e-inf-stationary point in general. Some preliminary numerical results are reported on.     

闭模糊拟阵模糊圈的极值问题

本文主要方法是通过基本序列、导出拟阵序列和模糊集分解定理,将模糊圈的研究转化为对圈子集套和数组的研究。在闭模糊拟阵中,我们得出三个结论:以同一集合为支撑集的模糊圈的最大模糊圈总是存在;以同一子集串为圈子集套的模糊圈的最大模糊圈不一定存在。但是,找到了存在最大模糊圈的充要条件;以同一集合为支撑集的模糊圈的最小模糊圈,以同一子集串为圈子集套的模糊圈的最小模糊圈都是不存在的。但它们的最小模糊势是存在的,而且找出了计算最小模糊势的公式。我们构造了两个算法:一是构造支撑集最大模糊圈算法。通过这个算法可构造出支撑集最大模糊圈,同时计算出其最大模糊势;二是判断和构造圈子集套最大模糊圈算法。通过这个算法首先判断最大模糊圈是否存在,如果存在就可以找出圈子集套最大模糊圈同时计算出最大模糊势。     

On Optimization Properties of Functions, with a Concave Minorant

We give a definition of the class of functions with a concave minorant and compare these functions with other classes of functions often used in global optimization, e.g. weakly convex functions, d.c. functions, Lipschitzian functions, continuous and lower semicontinuous functions. It is shown that the class of functions with a concave minorant is closed under operations mainly used in optimization and how a concave minorant can be constructed for a given function.     

Liley模型的模拟EEG信号的非线性预测和分析

分析Liley模型的模拟脑电(Electroencephalogram,EEG)信号的非线性预测和径向基函数(Radial Basis Functions,RBF)神经网络预测,利用相图分析和非线性正交预测(Nonlinear Cross-Prediction,NLCP)方法研究模拟EEG信号.结果发现:①RBF神经网络预测的效果要好于非线性预测;②NLCP方法对含有强周期分量的高维系统具有较好的适用性;③支持了EEG中存在混沌运动的观点.     

Electronic properties of a molecular system with Platinum

The electronic properties are studied using a finite homogeneous molecule called Trans-platinum-linked oligo(tetraethenylethenes). This system is composed of individual molecules such as benzene rings, platinum, Phosphore and Sulfur. The mechanism for the study of the electron transport through this system is based on placing the molecule between metal contacts to control the current through the molecular system.We study this molecule based on the tight-binding approach for the calculation of the transport properties using the Landauer-Büttiker formalism and the Fischer-Lee relationship, based on a semi-analytic Green's function method within a real-space renormalization approach. Our results show a significant agreement with experimental measurements.     

Is it a function? Generalizing from single- to multivariable settings

Generalizing is a hallmark of mathematical thinking. The term ‘generalization’ is used to mean both the process of generalizing and the product of that process. This paper reports on five calculus students’ generalizing activity and what they generalized about multivariable functions. The study makes two contributions. The first is a fine-grained, actor-oriented characterization of the ways undergraduates generalized. This adds to knowledge in two areas: the use of the actor-oriented perspective and generalization in advanced mathematics. The second contribution is the products of students’ generalizing: what they generalized about what it means for a multivariable relation to represent a function). This adds to the literature about student reasoning regarding multivariable topics by characterizing the powerful ways of reasoning students possess pre-instruction.