一个含参量广义积分的计算

广义积分，包括含参量的广义积分的计算，其计算方法较多，这些方法在一般大学数学教科书如《数学分析》、《复交函数》中均有所见。本文则是从一个线性微分方程的解出发来计算一个含参量的广义积分分。其中ｎ为自然数，ｘ≥０。本文推广了［１］（Ｐ．２８４）的结果。     

傅里叶变换中一个含参变量广义积分的计算

本文利用含参变量广义积分计算中常用的求导和变量替换等技巧等给出了傅里叶变换中一个重要的含参变量广义积分的计算方法.     

几类含参变量积分的极限的证明

根据命题的条件分类归纳,找出几种含参变积量积分的极限的分析证明方法.     

含参变量函数积分求导的推广

对含参变量函数的积分求导进行推广,得到了二重积分形式下的含参变量函数的积分求导公式以及在三维空间下的推广形式,并分析了其物理意义.     

一类含参变量积分的常差分方程计算方法

首次利用常差分方程方法计算了一类形如∫0πa+co bs cnoxs xdx(n∈N,a,b∈R)的含非负整数参数n与实数a,b的积分,且得到了完整的积分公式.     

评广义积分定义

本文论证了有关各书中存在着四种互不等价的广义积分的定义,分析了各种定义方式的优缺点,指出了某些教材中存在的问题,通过对照比较,归纳出一种较好的定义方式供有关书籍编者参考.     

含参量无穷限反常积分的一致收敛性

借助两个具体的含参量无穷限反常积分的一致收敛性问题,分析一致收敛性的一些几何直观特征,希望有助于读者加深理解与认识.     

Fuzzy区间值函数的含参量积分及一致收敛性

在一元实函数无穷积分定义的基础上,定义了含参量Fuzzy区间值函数的正常积分和无穷积分,给出了含参量无穷积分一致收敛的定义和判定定理.     

一族特殊类型的广义积分的计算

本文利用特殊的广义积分的计算方法和计算结果，解决了一批繁琐的广义积分的计算题。     

广义函数Denjoy积分的收敛性问题

本文讨论广义函数De njoy积分的收敛性问题.首先给出了广义Denjoy可积函数空间中强收敛、弱收敛、弱~*收敛和广义函数Denjoy积分收敛的关系;证明拟一致收敛是广义函数Denjoy积分收敛的一个充分必要条件;最后指出了Denjoy可积广义函数列弱~*收敛与强收敛等价当且仅当原函数等度连续.     

On Differentiation with Respect to Parameter of a Hypergeometric Function of a Special Type

We propose an effective construction of Padé approximation for the hypergeometric function of special type and its derivative with respect to parameter and this parameter is included both in numerator and denominator of the general term of the corresponding series. The aforementioned construction has been realized by means of a modification of the method that was applied earlier in simpler situations. Thus obtained approximation is made use of afterwards to establish the lower estimates of the numerical linear forms in the values of the functions under consideration. One could obtain similar estimates by the known in the theory of transcendental numbers Siegel’s method, however the estimates obtained by this method would be of less exactness.

     

Stochastic Integrals with Respect to Consistent Random Measures

We consider integrals of random mappings with respect to consistent random measures in C([0; 1]).     

第一类曲线积分的计算方法

介绍了计算第一类曲线积分的五种方法,给出相应的求解思路,并辅以典型例题,旨在使学生对第一类曲线积分的计算有更深的理解和掌握.     

广义分数积分的复合与Gauss超几何函数积分的估计

In this paper, composition formulas for generalized fractional integral oper-ators involving Gauss hypergeometric function are applied to evaluating of de finite integrals involving two Gauss hypergeometric functions.     

Optimal Bounds for Integrals with Respect to Copulas and Applications

We consider the integration of two-dimensional, piecewise constant functions with respect to copulas. By drawing a connection to linear assignment problems, we can give optimal upper and lower bounds for such integrals and construct the copulas for which these bounds are attained. Furthermore, we show how our approach can be extended in order to approximate extremal values in very general situations. Finally, we apply our approximation technique to problems in financial mathematics and uniform distribution theory, such as the model-independent pricing of first-to-default swaps.     

Set-Valued Stochastic Integrals and Equations with Respect to Two-Parameter Martingales

This article is concerned with notions of set-valued stochastic integrals driven by two-parameter martingales and increasing processes. We investigate their main properties and we consider next multivalued stochastic integral equations in the plane. We establish the existence and uniqueness of solutions to such equations as well as their additional properties.     

Besov Regularity of Stochastic Integrals with Respect to the Fractional Brownian Motion with Parameter H > 1/2

Let {B _t ,t[0,1]} be a fractional Brownian motion with Hurst parameter H > 1/2. Using the techniques of the Malliavin calculus we show that the trajectories of the indefinite divergence integral ^t ₀ u _s B _s belong to the Besov space _p,q for all , provided the integrand u belongs to the space . Moreover, if u is bounded and belongs to for some even integer p2 and for some large enough, then the trajectories of the indefinite divergence integral ^t ₀ u _s B _s belong to the Besov space _p, ^H .     

Generalized Connected Functions with Respect to Cones

In this paper, generalized connected functions with respect to cones such as quasi cone-connected, pseudo cone-connected, strongly pseudo cone-connected, and strictly pseudo cone-connected functions are introduced; necessary and sufficient optimality conditions are obtained for a weak minimum, a minimum, and a strong minimum of a vector-valued minimization problem. A Mond–Weir type dual is associated, and weak and strong duality results are established.     

Wiener Integrals with Respect to the Hermite Process and a Non-Central Limit Theorem

Abstract

We introduce Wiener integrals with respect to the Hermite process and we prove a non-central limit theorem in which this integral appears as limit. As an example, we study a generalization of the fractional Ornstein–Uhlenbeck process.     

Some Properties of Functional Integrals with Respect to the Bogoliubov Measure

We consider problems related to integration with respect to the Bogoliubov measure in the space of continuous functions and calculate some functional integrals with respect to this measure. Approximate formulas that are exact for functional polynomials of a given degree and also some formulas that are exact for integrable functionals belonging to a broader class are constructed. An inequality for traces is proved, and an upper estimate is derived for the Gibbs equilibrium mean square of the coordinate operator in the case of a one-dimensional nonlinear oscillator with a positive symmetric interaction.