Laplace transform of generalized functions of slow growth

We present certain special sections of the theory of functions of several variables and of the theory of generalized functions, which are the basic mathematical tools for certain directions in modern quantum field theory. In passing we study the properties of certain special algebras of analytic functions. A considerable part of the results in the article are due to the author.     

On automorphisms of biproducts

We study certain subgroups of the full group of Hopf algebra automorphisms of a biproduct. In the process, interesting subgroups of certain permutation groups come into play.     

THEORY OF SINGULAR POINTS OF ORDINARY DIFFERENTIAL EQUATIONS IN COMPLEX DOMAIN

In this paper, the topological of integral surfaces near certain of Lyapunov type singularpoints and certain type of nodes of ordinary differential equations in complex domain are studied.We introduce Briot-Bouquet transformation, in order to study the topological structure of integralsurfaces near higher order singular points. At last we give an estimate of the makimum numberof isolated limit integral surfaces passing through certain type of higher order singular points.     

Arithmetic Properties of Solutions of Certain Functional Equations in Several Variables

We consider the linear independence of the values of solutions of certain functional equations in several variables. As an application we obtain a quantitative refinement of a certain result of Bézivin.     

On the role of supercompact and extendible cardinals in logic

It is proved that the existence of supercompact cardinal is equivalent to a certain Skolem-Löwenheim Theorem for second order logic, whereas the existence of extendible cardinal is equivalent to a certain compactness theorem for that logic. It is also proved that a certain axiom schema related to model theory implies the existence of many extendible cardinals.     

Solvability of matrix equations in rings of quasi-diagonal matrices and similarity of matrix polynomials

A certain standard form is found for a complex matrix with respect to equivalent transformations by quasi-diagonal matrices. The solvability of certain matrix equations in the rings of quasi-diagonal matrices is examined using this standard form.     

Existence of open loop Nash equilibria in certain types of nonlinear differential games

This paper yields sufficient conditions for existence of open loop Nash equilibria in certain types of nonlinear differential games satisfying certain monotonicity and/or convexity conditions.     

某些级数的无理性

本文证明了某些与二阶线性递推数列有关的无穷级数的和的无理性．特别，推广了某些与Ｆｉｂｏｎａｃｃｉ和Ｌｕｃａｓ数列有关的无理性结果     

Low degree cohomologies of congruence groups

We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups.     

Arithmetical properties of finite graphs and polynomials

A study is made of asymptotic arithmetical properties of the isomorphism classes of certain types of finite graphs, and of certain polynomials over Galois fields.     

F分布密度曲线之变化

该文较深入地分析了特殊函数的某些性质,利用这些性质分析了F分布中不同参数所对应的密度曲线之间的位置关系.此外还讨论了密度曲线的某些渐近性质并建立了一些有关的方程.作为结论的应用及验证,作者给出了一些有代表性的例子.该文的分析方法还可用来讨论其它一些分布的密度曲线的某些性质.     

Extensions of Levin's transformations to vector sequences

Levin's transformations are extended to vector sequences. Convergence theorems for certain linear and certain logarithmic vector sequences are proved. Numerical examples are also given.     

某些无穷乘积的代数无关性(Ⅱ)

本文证明了某些具有代数系数的无穷乘积和幂级数定义的函数在某些代数数和超越数上值的代数无关性.     

On singular points of quasilinear differential and differential-algebraic equations

We show how certain singularities of quasilinear differential and differential-algberaic equations can be resolved by taking the solutions to be integral manifolds of certain distributions rather than curves with specific parametrization.     

On the enumeration of certain sets of planted plane trees

Using the definition of planted plane trees given by D. A. Klarner (“A correspondence between sets of trees,” Indag. Math.31 (1969), 292–296) the number of nonisomorphic classes of certain sets of these trees is enumerated by obtaining a one-to-one correspondence between these classes and certain sets of nondecreasing vectors with integral components. A one-to-one correspondence between sets of (r + 1)-ary sequences and a certain set of planted plane trees is also established, which permits enumeration of this set. Finally, a natural generalization of Klarner's one-to-one correspondence between the above sets of trees and certain sets of edge-chromatic trees is obtained.     

On Certain Subcovers of the Hermitian Curve

We present a simple construction that gives explicit equations for certain subcovers of the Hermitian curve. We show that maximal curves with a certain type of defining equations are covered by the Hermitian curve.     

Colorings of k-balanced matrices and integer decomposition property of related polyhedra

We show that a class of polyhedra, arising from certain 0,1 matrices introduced by Truemper and Chandrasekaran, has the integer decomposition property. This is accomplished by proving certain coloring properties of these matrices.     

Factorizations of certain q-series identities of Ramanujan and others

B. Yuttanan has shown that certain identities of Ramanujan and of Horie and Kanou can be factorized, that is, obtained by multiplying together certain pairs of identities. We give alternative, simpler factorizations of the same identities, and more.     

On the embeddability of certain infinitely divisible probability measures on Lie groups

We describe certain sufficient conditions for an infinitely divisible probability measure on a Lie group to be embeddable in a continuous one-parameter semigroup of probability measures. A major class of Lie groups involved in the analysis consists of central extensions of almost algebraic groups by compactly generated abelian groups without vector part. This enables us in particular to conclude the embeddability of all infinitely divisible probability measures on certain connected Lie groups, including the so called Walnut group. The embeddability is concluded also under certain other conditions. Our methods are based on a detailed study of actions of certain nilpotent groups on special spaces of probability measures and on Fourier analysis along the fibering of the extension.     

Positive definite solutions of some matrix equations

In this paper we investigate some existence questions of positive semi-definite solutions for certain classes of matrix equations known as the generalized Lyapunov equations. We present sufficient and necessary conditions for certain equations and only sufficient for others.