Construction and regularity of transition functions on polish spaces under measurability conditions

This paper concerns the construction and regularity of a transition (probability) function of a non-homogeneous continuous-time Markov process with given transition rates and a general state space. Motivating from a lot of restriction in applications of a transition function with continuous (in t≥0) and conservative transition rates q(t, x, Λ), we consider the case that q(t,x,Λ) are only required to satisfy a mild measurability (in t≥0) condition, which is a generalization of the continuity condition. Under the measurability condition we construct a transition function with the given transition rates, provide a necessary and sufficient condition for it to be regular, and further obtain some interesting additional results.     

Λ-模的σ-子模的标准表示式

Let A be a commutative ring with unit element, and let M be a Λ-module and σ∈Hom_Λ (M, M). Then a non-empty subset N of M is called a σ-submodule of the Λ-module M, if (1) a-b∈N for all a, bg∈N, and (2) λσ(α)∈N and x-σ(x)∈N for all λ∈Λ, α∈N, x∈M. Let N be a σ-submodule of M. N is said to be a primary σ-submodule of the Λ-module M, if (1) N≠M, and (2) whenever λ∈Λ, x∈M and λσ(x) ∈N, then either x∈N or λ^kσ(M)?N for some positive integer h. This paper is intended to show (1) that if M satisfies maximal condition of σ-submodule, and K is a σ-submodule of M, then K is a finite intersection of primary σ-submodules, and (2) that the uniqueness on the normal expression of σ-submodule of the Λ-module. Also, some results of fractional module have been obtained.     

A New Class of Complementarity Function and the Boundedness of Its Merit Function for Symmetric Cone Complementarity Problem

In this paper, we introduce a new class of two-parametric penalized function, which includes the penalized minimum function and the penalized Fischer-Burmeister flmc- tion over symmetric cone complementarity problems. We propose that this class of function is a class of complementarity functions（C-function）. Moreover, its merit function has bounded level set under a weak condition.     

The growth of H-harmonic functions on the Heisenberg group

We discuss the relationship between the frequency and the growth of H-harmonic functions on the Heisenberg group.Precisely,we prove that an H-harmonic function must be a polynomial if its frequency is globally bounded.Moreover,we show that a class of H-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.     

Admissibilities of linear estimator in a class of linear models with a multivariate t error variable

This paper discusses admissibilities of estimators in a class of linear models,which include the following common models:the univariate and multivariate linear models,the growth curve model,the extended growth curve model,the seemingly unrelated regression equations,the variance components model,and so on.It is proved that admissible estimators of functions of the regression coefficient β in the class of linear models with multivariate t error terms,called as Model II,are also ones in the case that error terms have multivariate normal distribution under a strictly convex loss function or a matrix loss function.It is also proved under Model II that the usual estimators of β are admissible for p 2 with a quadratic loss function,and are admissible for any p with a matrix loss function,where p is the dimension of β.     

Novel Kernel Function With a Hyperbolic Barrier Term to Primal-dual Interior Point Algorithm for SDP Problems

In this paper, we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP). This add a new type of functions to the class of eligible kernel functions. We prove that the interior-point algorithm based on the new kernel function meets O(n^3/4 logε/n)iterations as the worst case complexity bound for the large-update method. This coincides with the complexity bound obtained by the first kernel function with a trigonometri...     

无约束全局优化的一个可调参数的填充函数

A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded and closed domain. This function has two adjustable parameters. We will discuss the properties of the proposed filled function. Conditions on this function and on the values of parameters are given so that the constructed function has the desired properties of traditional filled function.     

ON THE DIFFERENTIAL AND DIFFERENCE INDEPENDENCE OFΓANDζ

In this paper,we study the algebraic differential and the difference independence between the Riemann zeta function and the Euler gamma function.It is proved that the Riemann zeta function and the Euler gamma function cannot satisfy a class of nontrivial algebraic differential equations and algebraic difference equations.     

Random attractors of stochastic non-newtonian fluids

The present paper investigates the asymptotic behavior of solutions for stochastic non-Newtonian fluids in a two-dimensional domain. Firstly, we prove the existence of random attractors ΛH(ω) in H; Secondly, we prove the existence of random attractors ΛV (ω) in V . Then we verify regularity of the random attractors by showing that ΛH(ω) = ΛV (ω), which implies the smoothing effect of the fluids in the sense that solution becomes eventually more regular than the initial data.     

EXISTENCE OF GENERALIZED SOLUTIONS TO A HYPERBOLIC MODEL OF COMBUSTION

In this paper we obtain the existence of the generalized solutions to the Cauchy problem for a model of combustion provided that the function f is of nonconvexity and initial values lie in the bounded, measurable class.     

Some Theorems of Analytic Functions

1 Introduction We denote that: σ—the class of functions ω(z)=A_1z+A_2z~2+…regular in the unit disk such that sum from n=1 to ∞ (n|A_n|~2<∞);K_c— the class of close-to-convex function f(z),that is, if f(z)=α_1z+α_2z~2+…there exists a starlike function g(z) =b_1z+b_2z~2+…such that     

Three Problems on Trigonometric Sums

Let Λ ? R~n be a uniformly discrete set and let C_Λ be the vector space consisting of all mean periodic functions whose spectrum is simple and contained in Λ. If Λ is a gentle set then for every f ∈ C_Λ we have f(x) = O(ω_Λ(x)) as |x| →∞ and ω_Λ(x) can be estimated(Theorem 4.1). This line of research was proposed by Jean-Pierre Kahane in 1957.     

ADMISSIBILITY IN THE GENERAL GROWTH CURVE MODEL WITH RESPECT TO RESTRICTED PARAMETER SETS UNDER MATRIX LOSS FUNCTION

In this paper, we study the issue of admissibility in the growth curve model with respect to restricted parameter sets under matrix loss function. We obtain some neces- sary and sufficient conditions that the linear estimators of KBL are admissible in the class of homogeneous linear estimators and in the class of non-homogeneous linear estimators under the growth curve model with respect to restricted parameter sets, respectively.     

MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRDINGER SYSTEMS

We study the multiplicity of positive solutions and their limiting behavior as ε tends to zero for a class of coupled nonlinear Schrdinger system in RN . We relate the number of positive solutions to the topology of the set of minimum points of the least energy function for ε suffciently small. Also, we verify that these solutions concentrate at a global minimum point of the least energy function.     

The structure on invariant measures of <Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript> generic diffeomorphisms

Let Λ be an isolated non-trivial transitive set of a C 1 generic diffeomorphism f ∈ Diff (M ). We show that the space of invariant measures supported on Λ coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in Λ (which implies that the set of irregular+ points is also residual in Λ). As an application, we show that the non-uniform hyperbolicity of irregular+ points in Λ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in Λ) determines the uniform hyperbolicity of Λ.     

THE FEKETE-SZEG? INEQUALITY AND SUCCESSIVE COEFFICIENTS DIFFERENCE FOR A SUBCLASS OF CLOSE-TO-STARLIKE MAPPINGS IN COMPLEX BANACH SPACES

Let C be the familiar class of normalized close-to-convex functions in the unit disk.In [17],Koepf demonstrated that,as to a function ■ in the class C,■By applying this inequality,it can be proven that ‖a₃|-|a₂‖≤ 1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.     

On a Problem of Approximation by Linear Means

is valid, where ω(f,δ) is the modulus of continuity of f. Furthermore they asked that: (1.3) If Theorem A can be extended to matrix summability? Later, P. D. Kathal, A. S. B. Holland and B. N. Sahney partially answered this problem. They proved the following Theorem B If {Λ_(n,k)} is monotonic non-increasing for all 0≤k≤n and Λ_(n,k)≥0 (0≤k≤n),Λ_(n,k)=0 (k>n), then we have     

Polar functions and intersections of the random string processes

Let {us(x) : s ≥ 0 , x ∈R} be a random string taking values in Rd . The main goal of this paper is to discuss the characteristics of the polar functions of {u s(x) : s ≥ 0 , x∈R} . The relationship between a class of continuous functions satisfying the H¨older condition and a class of polar-functions of {us (x) : s ≥ 0 , x ∈R} is presented. The Hausdorff and packing dimensions of the set that the string intersects a given non-polar continuous function are determined. The upper and lower bounds are obtained for the probability that the string intersects a given function in terms of respectively Hausdorff measure and capacity.     

Shannon-type sampling for multivariate non-bandlimited signals

In this paper, starting from a function analytic in a neighborhood of the unit disk and based on Bessel functions, we construct a family of generalized multivariate sinc functions, which are radial and named radial Bessel-sinc (RBS) functions being time-frequency atoms with nonlinear phase. We obtain a recursive formula for the RBS functions in R d with d being odd. Based on the RBS function, a corresponding sampling theorem for a class of non-bandlimited signals is established. We investigate a class of radial functions and prove that each of these functions can be extended to become a monogenic function between two parallel planes, where the monogencity is taken to be of the Clifford analysis sense.