一个有关函数单调性命题的推广

对文[1]给出的一个函数单调性的判别命题进行推广,得出两个无穷小量之比的单调性的判别命题1,2.利用结果可简便判别两个无穷小量之比的单调性及证明不等式     

一类数列单调性判别的常用三法

由于数列是特殊的函数,故数列既有函数的共性。又有数列的个性,因此数列单调性的判别方法有共性法（比差、比商法）和个性法（两头夹）,同时应用单调性时,也要因“题”制宜．为说明问题特举例说明如下．     

交错级数收敛性判别法

研究交错级数收敛性判别法.通过计算级数通项的极限和单调性得到三个判据,并对其中两个结论给出形式简化的推论,最后举例说明所提判别法的应用.     

单调函数判别法的推广

将单调函数的判别法由在开区间内有有限个导数为零,推广到开区间内有可数(列)个导数为零的情形,从而扩大了判别法的应用范围     

利用非可导性条件判别函数的凸性

本文先给出凸函数两个常用定义,并对连续函数证明其等价性.然后给出函数凸性的一些几何判别法和积分判别法.最后给出一个有用的微分判别法.     

一个有关函数单调性的命题

给出了一个关于函数单调性的判别命题     

方向导数的应用

本文将一元函数的高阶导数对应为多元函数的高阶导数，用方向导数表达泰勒公式，使之与一元函数的泰勒公式有统，的形式。又引入方向单调性、方向极值等概念，使多元函数的极值判别法基于一元函数极值判别法，此法不但直观又解法了判别式Δ＝０时的不确定性。限于篇幅只讨论二元函数。     

数列的几乎单调性

讨论了数列的几乎单调概念,利用数列的几乎单调性,得到了相应条件下的莱布尼茨判别法、阿贝尔判别法和狄利克雷判别法．     

论导数的“功绩”

导数的出现,为传统函数问题的求解开辟了新的途径,下面就导数在函数问题中的应用举例分析.一、颠覆了函数单调性传统的判别方法函数单调性的判定传统的方法是利用定义,但遇见较复杂的函数,符号的判断确实异常的烦琐,导数的引入为函数单调性的判断,提供了程序     

对正项级数敛散性判别方法的研究

利用函数的泰勒展开及极限的运算性质,借助已知敛散性的级数■和■,推出了判别正项级数敛散性的两个方法,并在此基础上得到了通项递减的正项级数敛散性的两个判别法.文中的结论强于双比值判别法.     

单调函数在具有可选服务的M/M/1排队模型研究中的应用

运用函数的导数与单调性之间的关系证明具有可选服务的M/M/1排队模型的主算子的豫解集研究中出现的三个不等式.由此推出,在虚轴上除了零外其它所有点都属于该模型的主算子的豫解集.     

Global exponential stability in Lagrange sense for recurrent neural networks with both time-varying delays and general activation functions via LMI approach

In this paper, we study the global exponential stability in a Lagrange sense for recurrent neural networks with both time-varying delays and general activation functions. Based on assuming that the activation functions are neither bounded nor monotonous or differentiable, several algebraic criterions in linear matrix inequality form for the global exponential stability in a Lagrange sense of the neural networks are obtained by virtue of Lyapunov functions and Halanay delay differential inequality. Meanwhile, the estimations of the globally exponentially attractive sets are given out. The results derived here are more general than that of the existing reference. Finally, two examples are given and analyzed to demonstrate our results.     

求解超声速无粘绕流的杂交型有限元格式

本文从一维双曲型标量方程出发,以一个普通二阶有限元格式及由其单边对角化导出的一阶单调型格式为基础,构造出一种具有单调性的杂交型有限元格式.为了向二维Euler方程组情形推广,所采用的开关函数是基于流场梯度的局部函数,并专门考虑了相邻单元的影响.二维情形的算例表明新格式可以明显抑制激波附近的振荡.     

两参数齐次独立增量过程在原点的局部性质

Ａｄｌｅｒ曾经给出了两参数独立增量过程的特征函数的一般形式．本文对齐次情形给出了更具体的表达式，引进了累积量的概念．在此基础上，研究了比值Ｘ（ｓ，ｔ）／ｓｔ在原点的分布，单调过程在原点的局部性质以及任意过程在原点的局部增长．由此得到了Ｂｒｏｗｎ单和不包含高斯分量的过程在原点的局部增长．     

Mills' ratio: Monotonicity patterns and functional inequalities

In this paper we study the monotonicity properties of some functions involving the Mills' ratio of the standard normal law. From these we deduce some new functional inequalities involving the Mills' ratio, and we show that the Mills' ratio is strictly completely monotonic. At the end of this paper we present some Turán-type inequalities for Mills' ratio.     

Numerical scheme with convergence for a generalized time‐fractional Telegraph‐type equation

In this work, we design and analyze a numerical scheme for solving the generalized time‐fractional Telegraph‐type equation (GTFTTE) which is defined using the generalized time fractional derivative (GTFD) proposed recently by Agrawal. The GTFD involves the scale and the weight functions, and reduces to the traditional Caputo derivative for a particular choice of the weight and the scale functions. The scale and the weight functions play an important role in describing the behavior of real‐life physical systems and thus we study the solution behavior of the GTFTTE by varying the weight and the scale functions in the GTFD. We investigate the solution profile of the GTFTTE under some of these choices. We also provide the stability and the convergence analysis of the proposed numerical scheme for the GTFTTE. We consider two test examples to perform numerical simulations.     

Composite time-consistent multi-period risk measure and its application in optimal portfolio selection

Through the composition of two real-valued functions, we propose a new class of multi-period risk measure which is time consistent. The new multi-period risk measure is monotonous and convex when the two real-valued functions satisfy monotonicity and convexity. Based on this generic framework, we construct a specific class of time-consistent multi-period risk measure by considering the lower partial moment between the realized wealth and the target wealth at individual periods. With the new multi-period risk measure as the objective function, we formulate a multi-period portfolio selection model by considering transaction costs at individual investment periods. Furthermore, this stochastic programming model is transformed into a deterministic programming problem using the scenario tree technology. Finally, we show through empirical tests and comparisons the rationality, practicality and efficiency of our new multi-period risk measure and the corresponding portfolio selection model.     

再论求导数零点的二次收敛迭代法

一维搜索是最优化理论数值计算的一个基本问题,它可归结为求定义在开凸区域Ｄ上的可微函数 ｆ的导数零点．若用 Ｎｅｗｔｏｎ法求导数零点,则涉及到二阶导数的计算．若用带导数的三次插值法则需要开平方的计算［１］．为了克服上述问题,本文作者之一在 １９７９年［２］首次提出了下述具有二阶收敛速度的迭代法：通常,我们称迭代法（０．１）为基于信息集（ｆ（ｘｎ）,ｆ’（ｘｎ）,ｆ（ｘｎ－１）,ｆ’（ｘｎ－１）｝的迭代法,而δ（ｆｘｙ）是基于信息集｛ｆ（ｘ）,ｆ＇（ｘ）,ｆ（ｙ）,Ｆ＇（ｙ））｝的三次插值多项式在ｘ处…     

The construction of operational matrix of fractional derivatives using B-spline functions

Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. Here we construct the operational matrix of fractional derivative of order α in the Caputo sense using the linear B-spline functions. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus we can solve directly the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the new technique presented in the current paper.     

The generalized Cauchy problem with data on two surfaces for a quasilinear analytic system

We consider the generalized Cauchy problem with data on two surfaces for a second-order quasilinear analytic system. The distinction of the generalized Cauchy problem from the traditional statement of the Cauchy problem is that the initial conditions for different unknown functions are given on different surfaces: for each unknown function we pose its own initial condition on its own coordinate axis. Earlier, the generalized Cauchy problem was considered in the works of C. Riquier, N. M. Gyunter, S. L. Sobolev, N. A. Lednev, V. M. Teshukov, and S. P. Bautin. In this article we construct a solution to the generalized Cauchy problem in the case when the system of partial differential equations additionally contains the values of the derivatives of the unknown functions (in particular outer derivatives) given on the coordinate axes. The last circumstance is a principal distinction of the problem in the present article from the generalized Cauchy problems studied earlier.