In this paper, we studied n-parameter d-dimension radom walk marked by RW~d_n. Its various multiparameter Maxkov properties、Single-point and wide-past transition functions were discussed. A weak law of large numers of RW~1_n (B~1(p, q)) was obtained.

In this paper, we consider a one-dimensional Nosé—Hoover system: $\dot{q}=p^{2m+1},$ $\dot{p}=-q^{2n+1}-\frac{\xi}{Q} p,$ $\dot{\xi}=p^{2m+2}-\beta^{-1},$ where $p, q, \xi\in \mathbb{R}$ are one-dimensional variables, $m,n\geq 0$ are integers and $Q, \beta$ are parameters. For $Q$ large enough, by using the averaging method we prove the existence of a linearly stable periodic solution. In addition, based on Moser's twist theorem we give a proof for the existence of invariant tori surrounding the periodic orbit for large $Q$.

在较为理想的条件下,本文获得了L-统计量的Bootstrap逼近速度.同时作为补充命题,我们给出了一个L-统计量方差估计的几乎处处收敛性。

In this paper, the method of vector measure is used to study the characteristics of dentable operator class and Radon-Nikodym operator class in Banach space. The results obtained are used to research into the structure of Banach space, giving out some new characteristics for Radon-Nikodym property of Banach space.

An abstract ring which is isomorphic to the ring of all linear transformations of a vector space has been studied by wolfson. In this paper we follow his work and obtain a main theorem. Before formulating we first introduce the following.Definition: Let M be a (F, R)-module, i.e. M is a left F, right R-module, and let M' be a (K, R)-module, where F, K, R are rings. We say that M and M' are (ψ, I)isomorphic if there exists a mapping S satisfying the following conditions:(i) S is an isomorphism of (M, +) onto (M', +).(ii) There exists an isomorphism ψ of F onto K such that for all x ∈M, r ∈R we hav.e (fx)S = f~ψ(xS), (fxr)S = f~ψ(xS)r.Theorem: Let R be an abstract ring. Then R is isomorphic to the ring of linear transformations of a left vector space A over a division ring F if and only if the following conditions are satisfied:(i) R has a socle with and every non-zero ideal of R contains.(ii) Suppose that S_1⊕S_2,S_1 are minimal left ideals Of R, then(iii) R has an identity.Moreover, if R satisfies the above three conditions then every minimal right ideal A'= eR of R can be expressed as a left vector space over the division ring K and R is also the complete ring of K-linear transformations of A'. Furthermore there exists a (ψ, I)-isomorphism of A as (F, R)-module onto A' as (K, R)-module, and the rank of A is equal to that of Thus the left vector space of R except semi-linear transformation is uniquely determined by the soele.

<正> 关于 C~2中有界域的分类,从1907年 Poincaré 首先指出超球和多圆柱互不解析等价到现在,只有很少的结果.Thullen 在1931年对 Reinhardt 域,加上条件:最大自同构群的维数大于任一点迷向子群的维数,给出它们的分类.后来 Cartan H.在1932年,在 Thullen 条件丁给出圆型域的分类.在1935年,Cartan H.在其父的文章中,给出了齐性有界域的分类,它们自然满足 Thullen 条件.作者之一在1963年,在 Thullen 条件下给出了正(m,p)圆型域的分类.

<正> 设是复数域C上的Banach空间.我们以记的对偶空间,记上所有有界线性算子的Banach代数.若S是拓扑空间的子集,S记S的闭包;S~o记S的内域;S~c记S的余集.若S,以S记S在S中的零化子;并若S S记S在中的前零化子.

On the basis of fundamental Nevanlinna theory the problem of normality of meromorphic functions that share three finite complex values with their k-th derivatives (k is any positive integer)is discussed and some examples are provided to show the result is sharp.

本文讨论了 Yamato 定理及 Doss-Yamato 定理的逆,所得结果进一步说明了有关 lie 代数的幂零条件在随机微分方程强解表示中的必要性.另外,本文还应用[3]中的分解定理给出了 Doss-Yamato 定理的简捷证明,并讨论了在可解 lie 代数条件下随机微分方程的强解形式.

Let S and T be quasisimilar operators. By introducing the concepts of the RT-class operator, the -R-class operator and the RR-class operator, this paper gives some sufficient and necessary conditions under which each component of σre(5) intersects σre(T), and gives some sufficient conditions under which each component of σre(S) intersets some subsets of σ3(T), and also gives some sufficient and necessary conditions under which an operator is an RT-class operator and an RR-class operator respectively.

In this paper, we prove that a

In this paper, we discuss a simple food web model consisting of one predator and two competing prey populations in an un-stirred chemostat with a single nutrient input. The necessary and sufficient conditions for the existence of coexistence states are established, and the main tools used here are Dancer fixed point index and the degree theory.

In this paper, we investigate some closed mappings properties on sn-metri- zable spaces by using the characterizations of sn-metrizable spaces and the relations among sn-metrizable spaces, g-metrizable spaces and metrizable spaces. We prove that the closed image of a sn-metrizable space is sn-metrizable if it is sn-first countable. By this result, we prove that the finite-to-one closed mappings and the open-closed mappings preserve sn-metrizable spaces, and give a counterexample to show that the perfect mappings do not preserve, sn-metrizable spaces. In addition, we prove that sn-metrizable spaces satisfy the perfect inverse image Cδ-diagonal theorem.

In this paper, we extend the Kolmogorov-type inequality to the case of pairwise NQD random sequences. Moreover, we study the convergence properties of pairwise NQD random sequences. As a result, we extend Baum and Katz complete convergence, the three series theorem, Marcinkiewicz strong law of large number to the case pairwise NQD of random sequences.

 

In this paper, a class of Dirichlet boundary problem of p-Laplacian operators is studied. The problem involves non-odd symmetric critical nonlinearity. Existence of infinitely many solutions of this problem is obtained with improved Compactness- Concentration principle.

Let {X, Xi : i ≥ 1} be a sequence of iid random variables which belongs to the domain of attraction of a nondegenerate stable distribution and let Sn = ∑i=1n Xi. A result on the precise asymptotics of Sn for wide range weighted functions and boundary functions is obtained. The results of precise asymptotics of partial sums for strictly stationary NA sequence are obtained. The results in Wang etc. are improved and extended. Many important results from the literatures are obtained easily as corollaries.

In this paper, some best proximity point theorems for generalized weakly contractive mappings which satisfy certain conditions by using three control functions in partially ordered Menger PM-spaces are obtained, and sufficient conditions to guarantee the uniqueness of the best proximity points are also given. Moreover, some corollaries are derived as consequences of the main results.

<正> 1.INTRODUCTION.Let g be an extremal arc with conjugateend points for the integral(?)In case n=1,the question whether or not g actually minimizes Ⅰrelative to arcs joining the ends of g has been discussed by Kneser(~1),Osgood(~2), Lindeberg(~3),and others by studying the shape of the en-velope of the extremals passing through an end point of g.In thecase n=2,Hahn(~4) has reduced the problem to that of an ordinaryminimum of a function of two variables by using a family of brokenextremals joining the ends of g.The method of Hahn is generaland can be extended in several directions as has been recently doneby Morse(~5)

 

Let g be a general affine Lie algebra associated with a Lie algebra g equipped with a symmetric invariant bilinear form <,>. It is known that for every complex number l, we have a canonical vertex algebra Vg(l,o), and if (g, <, >) satisfies certain conditions, Vg(l,o) is a vertex operator algebra. In this paper, we consider g to be a finite-dimensional solvable Lie algebra equipped with a nondegenerate symmetric invariant bilinear form, and we show that Vg(l,o) contains a Virsoro-vector ω so that (Vg(l,0), Yv, 1,ω) is a vertex operator algebra.

Generalized estimating equations method as a powerful method for estimating parameters, is wildly used in many fields, such as biostatistics, econometrics and medical insurance, and so on. For longitudinal data, We should take account into within-subject correlation structure in order to improve efficiency of a estimator. It is often useful to suppose that there is a parametric assumption within-subject correlation in longitudinal data analysis. But unreasonable assumptions made on within-subject correlation structure can result in inefficient estimation for parameters or even result in misspecification. For the generalized estimating equations with longitudinal data, we propose the extended GMM methods and extended EL methods and construct the large sample properties for our estimators. One of the proposed EL methods which is called block empirical likelihood is robust because of avoiding any assumptions on withinsubject correlation structure. We also provide two simulation examples to illustrate the finite properties for our estimators.  

We give the fundamental solution of the Tricomi operator Tu=y(u_(x_1x_1)+u_(x_2x_2))+u_(yy)=0.(Ⅰ) It has stronger singularity than Tu=yu_(xx)+u_(yy)=0.We indicate that it is necessary to introduce the principal part of Cauchy integral to define the fundamental solution in the theory of distribution.

We use the elementary method and the properties of the floor function to study the infinite sums derived from the reciprocals of the cubic of the Fibonacci numbers, and give a new and interesting identity involving the reciprocals of this sums.

In this paper, we compute, by using cone theory, the topological degree of a class of completely continuous fields where the condition on the lower boundedness of nonlinear operators is sharply weakened. Therefore our results substantially improve and generalize the existing ones in the literature. Finally we use our abstract results to establish the existence of nontrivial solutions for superlinear Hammerstein integral equations.

In this paper, we first prove a fundamental inequality of the theory of meromorphic function; as one of its applications, we then study the value distribution problem which is closely related to a theorem of Hayman and prove that if f is a transcendental meromorphic function all of whose zeros have multiplicities at least κ, then the function of the form ff(κ) assumes every finite nonzero value infinitely often, except for at most three positive integers k with 2≤κ≤4.

This paper deals with a representative glycolysis model in biochemical reaction. We study the non-existence of non-constant positive steady-state solutions by using a priori estimates. A necessary condition for the existence of non-constant positive steady-state solutions is obtained. On the basis of Turing instability of constant steady-state solutions, the degree theory is combined with a priori estimates to give a sufficient condition for the existence of non-constant positive steady-state solutions.  

We establish the global well-posedness and analyticity of mild solution to the generalized three-dimensional incompressible Navier–Stokes equations for rotating fluids if the initial data are in Fourier–Herz spaces ?_q^1-2α (R³) under appropriate conditions for α and q. As corollaries, we also give the corresponding conclusions of the generalized Navier–Stokes equation.

In this paper,we study the convergence of solutions of a class of delay differ- ential equations.These equations have important practical applications and generalize those on which Bernfeld and Haddock conjectured that each solution of the equations tends.to a constant.We first give an example to point out the errors in several existing works on the convergence of solutions of the equations as well as their generalizations. Then we confirm the Bernfeld-Haddock conjecture under weaker conditions.Our re- sult corrects and improves the existing ones.An appendix by Professor Tongren Ding is also given to correct the mistakes in one of his works.

Without the periodity and symmetricity, we present new results on the existence of infinitely solutions for some nonlinear superlinear Schrödinger equation in the entire space without Ambrosetti-Rabinowitz growth condition. Also, we get the existence of infinitely many large energy solutions for some superlinear Schrödinger- Maxwell equations.

We obtain a Stone type theorem under the frame of Hilbert C^*-module, such that the classical Stone theorem is our special case.

We give the definition of a kind of new operator-convex-power condensing operator for the need of applied questions and generalize the definition of condensing operator. The fixed point theorem of this kind of new operator is proved. This generalizes the famous Schauder fixed point theorem and Sadovskii fixed point theorem. As applications, the existence of global mild solutions and positive mild solutions of initial value problem for a class of semilinear evolution equations with noncompact semigroup in Banach spaces is obtained.

Let F be a family of meromorphic functions defined in a domain D, let ψ ( 0) be a holomorphic function in D, and k be a positive integer. If, for every f ∈ F, f ≠ 0, f^(k) ≠ 0 and all zeros of f^(k)(z) - ψ(z) have multiplicities at least (k + 2)/k, then F is normal in D.  

 

This paper deals with a class of boundary value problems of ordinary differential equations of second order which have singular right hand term. We will show that there are no solutions when the singularity of f(t,x) with respect to t is greater than a certain value, and solutions exist while the singularity is less than the value. The singularity with respect to u at u = 0 is not restricted.

 

In this paper, the ill-posed Cauchy problem for two-dimensional Helmholtz equation with mixed boundary is investigated. To obtain stable numerical solution, a mollification regularization method with the de la Vallée Poussin operator is proposed. Error estimate between the exact solution and its approximation is given under the proper choice of a priori parameter. A numerical experiment shows that our procedure is effective and stable with respect to perturbations of noise in the data.

The structure of the ideal J*,k 2k+2k-1 of the unoriented cobordism ring MO* is determined in this paper.

本文讨论一类多项式形式的函数迭代方程,作者给出了这种方程的C~2类解的存在性,唯一性以及稳定性条件,并且指出了文[2]所给例子中的一处疏漏,给出了新的例子.

Let E be a real Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Let D be a nonempty bounded closed convex subset of E and T : D → D be an asymptotically nonexpansive mapping. It is shown that under some suitable conditions, the sequence {xn} defined by the modified Reich-Takahashi iteration method (1.2) converges strongly to a fixed point of T, where x0 is any given point in D, and {αn}, {β} are real sequences in [0,1] with some restrictions.