一种平移三角函数图像的简易方法

关于三角函数图像经平移与另一个函数图像重合的问题.本文给出一种简便而又不易出错的判断方法——函数最值判断法方法先求出第一个三角函数的最大值(或最小值)点A的坐标.然后再求出第二个函数在点A左右两侧(距A最近)的最大值(或最小值)点C、B的坐标.那么平移的距离为线段     

浅谈一类最值题的解法

解决两个点或多个点变化的最大最小值问题,首先可以让某个点固定,找出另一个点变化的规律,得出一个函数式,研究这个函数的单调性,再让固定的点运动,从而得出最值,这就是我们常说的"动静互换"思想.     

浅谈一类最值题的解法

解决两个点或多个点变化的最大最小值问题，首先可以让某个点固定，找出另一个点变化的规律，得出一个函数式，研究这个函数的单调性，再让固定的点运动，从而得出最值，这就是我们常说的“动静互换”思想．     

谈谈关于多元函数极值的一个错误认识

分析了数学分析教材中关于最小二乘法处理过程中的一个常见错误，说明了多元函数的惟一极值点不一定是最小值点     

关于Hamilton-Jacobi方程解的正则性和全局结构的注记

该文考虑高维Hamilton-Jacobi方程的柯西问题.作者证明了从任一初始点出发的特征线永不碰到奇异点集合的充分必要条件是初始函数在该点取到最小值.在此基础上,证明了奇异点集合的道路连通分支和初始函数不取最小值的点集合的道路连通分支之间存在一一对应,而且解的梯度的间断一旦产生就不会消失.特别指出,该文的结果不需要"初始函数梯度在无穷远趋近于零"这一限制条件,而文献[12]中重要的命题2.7和主要结果之一的定理3.3是在这一条件下得到的.     

导数应用

一、复习要求：会从几何直观了解可导函数的单调性与其导数的关系;掌握函数极值的定义,了解可导函数的极值点的必要条件与充分条件（导数在极值点两侧异号）,会求一些实际问题（一般指单峰函数）的最大值和最小值．     

关于Hamilton-Jacobi方程解的正则性和全局结构的注记——纪念李国平院士吴新谋教授诞辰100周年

该文考虑高维Hamilton-Jacobi方程的柯西问题. 作者证明了从任一初始点出发的特征线永不碰到奇异点集合的充分必要条件是初始函数在该点取到最小值.在此基础上,证明了奇异点集合的道路连通分支和初始函数不取最小值的点集合的道路连通分支之间存在一一对应, 而且解的梯度的间断一旦产生就不会消失. 特别指出, 该文的结果不需要“初始函数的梯度在无穷远趋近于零”这一限制条件, 而文献[12]中重要的命题2.7和主要结果之一的定理3.3是在这一条件下得到的.     

P*(κ)阵线性互补问题一种新的宽邻域预估-校正内点算法

基于邻近度量函数的最小值,对P*(κ)阵线性互补问题提出了一种新的宽邻域预估-校正算法,在较一般的条件下,证明了算法的迭代复杂性为O(κ+1)23n log(x0ε)Ts0.算法既可视为Miao的P*(κ)阵线性互补问题Mizuno-Todd-Ye预估-校正内点算法的一种变形,也可以视为最近Zhao提出的线性规划基于邻近度量函数最小值的宽邻域内点算法的推广.     

多元函数极值的求法及其应用

在实际问题中,往往会遇到多元函数的最大值、最小值问题.多元函数的最大值、最小值问题与极大值、极小值有密切联系.求多元函数极值,一般可以利用偏导数来解决.与一元函数相类似,可以利用函数的极值来求函数的最大值和最小值.但是由于自变量个数的增加,应特别注意概念中的一些变化和计算复杂性.这里主要讨论二元函数,对于二元以上的函数极值可以类似加以解决.     

函数的逼近及其在下半连续函数可微性中的应用

通过函数的下卷积函数列的逼近方法,在变分原理中从扰动最小值点集的“大小”入手,研究了下半连续函数的可微性。     

Superconvergence of the Composite Rectangle Rule for Computing Hypersingular Integral on Interval

The generalized middle rectangle rule for the computation of certain hypersingular integrals is discussed. A generalized middle rectangle rule with the density function approximated and the singular kernel analysis calculated is presented and the asymptotic expansion of error functional is obtained. When the special function in the error functional equals to zero, the superconvergence point is obtained and the superconvergence phenomenon which is one order higher than the general case is presented. At last, numerical examples are given to confirm the theoretical results.     

Nondifferentiability of an objective function at its point of minimum for most minimax problems

In this paper we study a class of minimax problems where . We show that the subclass of all problems for which there exists a point of minimum such that and is small. The paper is dedicated to the memory of Alexander M. Rubinov.     

ω-Limit Set of a Tree Map

1 IntroductionA tree is any spece whidi is uniquely arcwise connected and homeomorphic to the unionof finitely many copies of the unit interval, that is, a graPh (see [1]) contains no cycles.The dynamics of a tree maP have been studied intensively in recent years (see, fOr instance,[2Al1). The interest in studying maPs on such a one--dimensional space is due to the faCtthat for maPs on manifolds with an invariant foiation of codimension one, the correspondingquotient maP tuxns out to be def…     

The cover-index of infinite graphs

We show that the cover-index of an infinite graph can be expressed in terms of colouring properties of its finite subgraphs when the minimum degree of the graph is finite. We prove that every simple graph with infinite minimum degree contains a tree which is regular of degree and use this to prove that every graph with minimum degree can be decomposed into mutually edge-disjoint spanning subgraphs without ioslated vertices. In particular, the cover-index of a graph equals the minimum degree, when this is infinite.     

Point Code Minimum Steiner Triple Systems

The point code of a Steiner triple system uniquely determines the system when the number of vectors whose weight equals the replication number agrees with the number of points. The existence of a Steiner triple system with this minimum point code property is established for all v 1,3 (mod 6) with v 15.     

On the Efficiency of a Global Non-differentiable Optimization Algorithm Based on the Method of Optimal Set Partitioning

The examined algorithm for global optimization of the multiextremal non-differentiable function is based on the following idea: the problem of determination of the global minimum point of the function f(x) on the set (f(x) has a finite number of local minima in this domain) is reduced to the problem of finding all local minima and their attraction spheres with a consequent choice of the global minimum point among them. This reduction is made by application of the optimal set partitioning method. The proposed algorithm is evaluated on a set of well-known one-dimensional, two-dimensional and three-dimensional test functions. Recommendations for choosing the algorithm parameters are given.     

On an extremal property of the Poiseuille flow between two coaxial cylinders

Some extremal property is established of the axial stationary flow of a Newtonian fluid between two concentric cylinders. It is shown that the ratio of the flow rate through the cross-section of an eccentric gap to the pressure drop (along the axis) reaches its minimum when the eccentricity equals zero; i.e., the minimum of the ratio is realized for the Poiseuille flow.     

A Min–Max Property of Chordal Bipartite Graphs with Applications

We show that if G is a bipartite graph with no induced cycles on exactly 6 vertices, then the minimum number of chain subgraphs of G needed to cover E(G) equals the chromatic number of the complement of the square of line graph of G. Using this, we establish that for a chordal bipartite graph G, the minimum number of chain subgraphs of G needed to cover E(G) equals the size of a largest induced matching in G, and also that a minimum chain subgraph cover can be computed in polynomial time. The problems of computing a minimum chain cover and a largest induced matching are NP-hard for general bipartite graphs. Finally, we show that our results can be used to efficiently compute a minimum chain subgraph cover when the input is an interval bigraph.     

一类循环码的极小距离

循环码的极小距离大于或等于BCH界。本文考虑的是极小距离等于BCH界的特殊情形。利用一类自反循环码的事实。证明了使循环码的极小距离等于其BCH界的两个充分条件；并指出极小距离等于任意给定值，维数任意大的循环码可以构造。     

THE SUM OF DEFICIENCIES OF ENTIRE FUNCTION ON C~n

This paper proves that: Let / be an entire function of finite order λon Cn. Then(1) , where k(X) is a nonnegative constant depending only on A;(2) If (a, f) = 1, then A is a positive integer and equals the lower order of /.