图的无号Laplace矩阵的最大特征值

The signless Laplacian matrix of a graph is the sum of its diagonal matrix of vertex degrees and its adjacency matrix. Li and Feng gave some basic results on the largest eigenvalue and characteristic polynomial of adjacency matrix of a graph in 1979. In this paper, we translate these results into the signless Laplacian matrix of a graph and obtain the similar results.     

Gromov Hyperbolicity of Riemann Surfaces

We study the hyperbolicity in the Gromov sense of Riemann surfaces. We deduce the hyperbolicity of a surface from the hyperbolicity of its ＂building block components＂. We also prove the equivalence between the hyperbolicity of a Riemann surface and the hyperbolicity of some graph associated with it. These results clarify how the decomposition of a Riemann surface into Y-pieces and funnels affects the hyperbolicity of the surface. The results simplify the topology of the surface and allow us to obtain global results from local information.     

关于亚纯函数微分多项式的值分布

Let f(z) be a meromorphic function andΨbe the differential polynomial of f which satisfies the condition of N(r, f) N (r, 1/f) = S(r, f). We obtain several results about the zero point of theΨand those results extend and improve the results of Yang and Yi in this paper.     

Convergence of the q Analogue of Szász-Beta-Stancu Operators

In the present paper, we propose the q analogue of Sz a′sz-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergence and weighted approximation properties of the q operators. Voronovskaja type theorem is also obtained.Our results generalize and supplement some convergence results of the q-Sz a′sz-Beta operators, thus they improve the existing results.     

EXISTENCE OF SOLUTIONS OF A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS IN L^2-SPACES

By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta (1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L^2 (Ω) are studied. The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen‘s previous papers. Especially,some new techniques are used in this paper.     

THE L_p-SATURATION RESULTS WEIGHTED SIMULTANEOUS APPROXIMATION BY THE METHOD OF BERNSTEIN-DURRMEYER OPERATORS

The aim of the present paper is to prove new equivalence results and L_p-stauration results onweighted simultaneous approximation by the method of Bernstein-Durrmeyer operators (includ-ing results in [7]). One of the main tools and crucial estimates managing the converse results isgiven by a direct modified Vornorskaja theorem which uses the third order weighted modulus ofsmoothness.     

NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH DELAY

In this paper, by making use of the integral method and some results of the functional differential equations, oscillatory properties of the solutions of certain parabolic partial differential equations with multi-delays are investigated and a series of necessary and sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by the delay and hence reveal the varied difference between these equations and those without delay.     

关于结构KKT方程组的扰动分析

We discuss the perturbation analysis for the structured KKT systems. The methods and results of forward perturbation analysis all differ from the recent works of Gulliksson and other authors. The optimal backward perturbation results can not be deduced by the corresponding results of Sun about the KKT systems.     

EXPONENTIALLY BOUNDED C-SEMIGROUP AND INTEGRATED SEMIGROUP WITH NONDENSELY DEFINED GENERATORS I: APPROXIMATION:

In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.     

Results About Parabolic-Like Mappings

In this paper we present the most important definitions and results of the theory of parabolic-like mappings, and we will give an example. The proofs of the results can be found in [2,4] and [3].     

FURTHER INVESTIGATION INTO APPROXIMATION OF A COMMON SOLUTION OF FIXED POINT PROBLEMS AND SPLIT FEASIBILITY PROBLEMS

The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ? of the split feasibility problem and the set F(T)of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of puniformly convex Banach spaces which are also uniformly smooth.By combining Mann's iterative method and the Halpern's approximation method,we propose an iterative algorithm for finding an element of the set F(T) ∩ ?;moreover,we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method.Our results extend and complement many known related results in the literature.     

DECAY OF POSITIVE WAVES OF HYPERBOLIC BALANCE LAWS Dedicated to Professor Constantine M. Dafermos on the occasion of his 70th birthday

Historically,decay rates have been used to provide quantitative and qualitative information on the solutions to hyperbolic conservation laws.Quantitative results include the establishment of convergence rates for approximating procedures and numerical schemes.Qualitative results include the establishment of results on uniqueness and regularity as well as the ability to visualize the waves and their evolution in time.This work presents two decay estimates on the positive waves for systems of hyperbolic and genuinely nonlinear balance laws satisfying a dissipative mechanism.The result is obtained by employing the continuity of Glimm-type functionals and the method of generalized characteristics [7,17,24].     

GENERALIZED FRACTIONAL CALCULUS OF THE ALEPH-FUNCTION INVOLVING A GENERAL CLASS OF POLYNOMIALS

The object of this article is to study and develop the generalized fractional calculus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of ■-function, Appell functionF3 and a general class of polynomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus.On account of the general nature of the Saigo-Maeda operators, ■-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notablyH-function,I-function, Mittag-Leffler function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.     

Tail behavior of supremum of a random walk when Cramér’s condition fails

We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and O-subexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.     

增生映射的扰动理论对与广义(p,q)-Laplace算子相关的非线性椭圆系的应用

Using perturbation results on the sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we present some abstract results for the existence of the solutions of nonlinear Neumann elliptic systems which is related to the so-called generalized （p, q）-Laplacian in this paper. The systems discussed in this paper and the method used extend and complement some of the previous work.     

Continuity of the optimal value function and optimal solutions of parametric mixed-integer quadratic programs

To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.     

A note on Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces

In the present paper, we obtain three independent results on the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces. That is, we are going to obtain the characterization of local means, the boundedness of pseudo-differential operators and the characterization of the Hardy-Morrey spaces. By using the maximal estimate and the molecular decomposition, we shall integrate and extend the known results on these spaces.     

g-Besselian frames in Hilbert spaces

In this paper, we introduce the concept of a g-Besselian frame in a Hilbert space and discuss the relations between a g-Besselian frame and a Besselian frame. We also give some characterizations of g-Besselian frames. In the end of this paper, we discuss the stability of g-Besselian frames. Our results show that the relations and the characterizations between a g-Besselian frame and a Besselian frame are different from the corresponding results of g-frames and frames.     

Strong uniqueness of best approximations in spaces of bounded linear operators

The present paper is concerned with problems of the strong uniqueness of thebest approximation and the characterization of a uniqueness element in operator spaces.Some results on the strong uniqueness of the best approximation operator from RS-setsare proved and the uniqueness element of a sun in the compact operator space from c_0to c_0 is characterized by the strict Kolmogorov's condition. Some recent results due toLewicki and others are extended and improved.     

Multiplication formulas for Kubert functions

The aim of this paper is two folds. First, we shall prove a general reduction theorem to the Spannenintegral of products of （generalized） Kubert functions. Second, we apply the special case of Carlitz＇s theorem to the elaboration of earlier results on the mean values of the product of Dirichlet L-functions at integer arguments. Carlitz＇s theorem is a generalization of a classical result of Nielsen in 1923. Regarding the reduction theorem, we shall unify both the results of Carlitz （for sums） and Mordell （for integrals）, both of which are generalizations of preceding results by Frasnel, Landau, Mikolas, and Romanoff et al. These not only generalize earlier results but also cover some recent results. For example, Beck＇s lamma is the same as Carlitz＇s result, while some results of Maier may be deduced from those of Romanoff. To this end, we shall consider the Stiletjes integral which incorporates both sums and integrals. Now, we have an expansion of the sum of products of Bernoulli polynomials that we may apply it to elaborate on the results of afore-mentioned papers and can supplement them by related results.