反常积分敛散性的两个新的判别法

根据反常积分的比较判别法,给出了反常积分的两个新的对数判别法.     

一种反常积分与正项级数收敛的判别法

介绍一种判别无穷限反常积分与正项级数敛散性的判别法。     

浅析广义积分中的 Cauchy 判别法

Cauchy判别法的核心和难点是选择合适的p积分作为比较对象.当被积函数的结构较复杂或抽象时,更难确定合适的p积分.鉴于此,文章提出了Cauchy试验法,旨在快速准确地找到合适的p积分,进而判断原积分的敛散性.     

反常积分敛散性的对数判别法

给出一个判别无穷限反常积分敛散性的对数判别法,并通过实例说明其应用．     

反常积分敛散性的根值判别法

由于积分与级数在理论上是统一的,因此有关正项级数的根式判别法可被推广以判别无穷限积分和瑕积分的敛散性.设f(x)是[a,+∞)上的非负函数,li mx→+∞xf(x)=ρ,则当ρ1时,反常积分∫a+∞f(x)dx收敛,而当ρ1时,反常积分∫a+∞f(x)dx发散;设f(x)是(a,b]上的非负函数,a为瑕点,xli→ma+(f(x))x-a=ρ,则当ρ1时,反常积分∫abf(x)dx收敛,而当ρ1时,反常积分∫baf(x)dx发散.     

关于级数敛散性的积分判别法的一个新证明及其推广

给出了现行的数学分析 ,微积分与高等数学的教材中的数值级数敛散性的积分判别法的一个新证明 ,获得了这个判别法的一个推广 ,由此得到一批渐近公式与命题     

正项级数敛散性的一个判别法

基于正项级数的比较判别法和p-级数的敛散性,给出一个与D’Alembert判别法和Cauchy判别法平行的判别正项级数敛散性的方法.并通过实例对所给判别法的可行性进行检验,发现它是已有方法的一个有效补充.     

两种反常积分敛散性的判别方法

介绍了两种判别反常积分敛散性的判别方法.     

正函数广义积分收敛性的一个判别法

研究正函数广义积分的敛散性．利用二重积分的性质．从被积函数自身的性态出发．当自变量x充分大时,通过讨论∫β（x＋σ）^β（x＋σ＋1）f（y）dy与f（x）的比值（其中β≥1,σ∈R为固定常数）,可建立一个收敛判别法．并可平行给出相应正项级数审敛法。此法是对DAlembert审敛法和双比值审敛法的推广．     

p-达朗贝尔判别法及其应用

对正项级数的达朗贝尔判别法作了推广,提出并证明了p-达朗贝尔判别法,扩大了其使用范围.进一步利用数列和子列的收敛关系,证明了其与柯西判别法之间的关系.最后通过例子对p-达朗贝尔判别法进行了验证.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Bases of the identities of products of certain varieties of groups

The following theorem is proved: The product of any variety of two-step solvable groups and a variety having a finite basis of identity relations has a finite basis of identity relations.Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 137–144, January, 1969.     

Birational aspects of the geometry of Varieties of Sums of Powers

Varieties of Sums of Powers describe the additive decompositions of a homogeneous polynomial into powers of linear forms. The study of these varieties dates back to Sylvester and Hilbert, but only few of them, for special degrees and number of variables, are concretely identified. In this paper we aim to understand a general birational behavior of VSP. To do this we birationally embed these varieties into Grassmannians and prove the rational connectedness of many VSP in arbitrary degrees and number of variables.