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, 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.

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.

In this paper, we prove that a

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.

 

<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)

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.  

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.

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.

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.

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 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.  

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.

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.  

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.

 

 

This paper is concerned with the Cotlar’s inequality for the maximal commutators of the m-linear Calderón-Zygmund operator with non-smooth kernels and the weighted norm inequalities for the commutators and the maximal commutators of multilinear singular integrals are established.  

In this paper, some remarkable properties of regular semigroups with a regular ^*-transversal are given. A construction method of a regular semigroup with a quasi-ideal regular ^*-transversal is obtained. Furthermore, congruences on this class of semigroups are also considered by applying our structure theorem.  

The main purpose of this paper is to deal with the uniqueness problem for meromorphic functions on annuli. We obtain two general uniqueness theorems of meromorphic functions sharing sets from which an analog of Nevanlinna’s famous five-value theorem is proposed.  

The metric derivative of the fuzzy-number-valued functions and the representation of the total variation for the fuzzy-number-valued function which is of bounded variation are defined and discussed. It is proved that the fuzzy absolutely continuous functions are metrically differentiable almost everywhere, and the integration of its metric derivative equals to the total variation of the primitive. Finally, the representation of the total variation for the fuzzy-number-valued functions which is of bounded variation is given.  

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.

We study the invariant subspaces of the operator M_z on the Sobolev disk algebra R(D).First,we study the multiplication operator M_z restricted to the invariant subspace.Then we show that M_z restricted to one invariant subspace is unitarily equivalent to M_z restricted to another invariant subspace if and only if the two invariant subspaces are equal.We also characterize the invariant subspaces with common zeros on the boundary of the disk.

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.

In this paper, it is shown that two admissible meromorphic functions in the unit disc must be identical, provided that they share five small functions CM or five values IM in one angular domain.

 

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.

In this paper, the automorphism group of a generalized extraspecial p-group G is determined again, where p is a prime number. Assume that |G| = p^2n+m and |ζG| = p^m, where n ≥ 1 and m ≥ 2. Let Aut_cG be the normal subgroup of AutG consisting of all elements of AutG which act trivially on ζG. Then
(i) If p is odd, then AutG = 〈θ〉  Aut_cG, where θ is of order (p - 1)p^m-1; If p = 2, then AutG = 〈θ₁, θ₂〉 Aut_cG, where 〈θ₁, θ₂〉 = 〈θ₁〉 × 〈θ₂〉 Z_2^m-2 × Z₂.
(ii) If the exponent of G is equal to p^m, then Aut_cG/InnG Sp(2n, p).
(iii) If the exponent of G is equal to p^m+1, then Aut_cG/InnG K Sp(2n - 2, p), where K is an extraspecial p-group of order p^2n-1 (If p is odd) or an elementary abelian 2-group of order 2^2n-1. In particular, Aut_cG/InnG Zp when n = 1. 

In this paper, AS property is introduced, and a problem in [1] is discussed. First, the paper shows that the Scott topology on a distributive complete lattice L has a basis of open filters if and only if L is a KS. frame for some ordinal number a, i.e., KS frame. By the result, one can judge whether the Scott topology and the Scott open filter topology on a distributive complete lattice are coincide. Then some KS frames are constructed in the paper, which are not continuous.

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

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.

Let Tr₁(n,Z) be the group of all n×n (upper) unitriangular matrices over the integral ring. Let k_ij (1 ≤ #em/em# < j ≤ n) be given positive integers and
Then G is a subgroup of Tr₁(n,Z) if and only if k_ij divides d_ij⁽²⁾, where d_ij⁽²⁾ denotes the greatest common divisor of all k_irk_rj (1 ≤ #em/em# < r < j ≤ n). Moreover, when G is a subgroup of Tr₁(n,Z), both the upper central series and the lower central series of G coincide if and only if k_ij = d_ij^(r), (1 ≤ r ≤ j-i), where d_ij^(r) (2 ≤ r ≤ j-i) denotes the greatest common divisor of all k_ilk_ll2 · · · k_lrj (1 ≤ #em/em# < l₁ < l₂ < · · · < l_r < j ≤ n) and d_ij⁽¹⁾ = k_ij if j - i = 1.-1-1₁₁