ON OPPENHEIM＇S INEQUALITY

We prove several inequalies for symmetric postive semidefinite, general M-matrices and inverse Mmatrices which are generalization of the classical Oppenheim‘s Inequality for symmetric positive semidefinite matrices.     

Becker-Stark不等式与Ste(c)kin不等式

若Becker-Stark不等式成立,则Steckin不等式一定成立．使用微分法或幂级数法可证明Steckin不等式．     

一般对称型的F-Sobolev不等式

Some sufficient conditions for the F-Sobolev inequality for symmetric forms are presented in terms of new Cheeger‘s constants. Meanwhile, an estimate of the F-Sobolev constants is obtained.     

SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN＇S INEQUALITY

A submanifold in a complex space form is called slant it it has constant Wirtinger angles. B, Y, Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP^2 and CH^2. So it seems that the slant immersion has some interesting properties. The authors have great interest to consider slant immersions satisfying some additional conditions, such as unfull first normal bundles or Chen‘s equality holding. They prove that there do not exist n-dimensional Kaehlerian slant immersion sin CP^n and CH^n with unfull first normal bundles. Next, it is seen that every Kaehlerian slant submanifold satisfying an equality of Chen is minimal which is similar to that of Lagrangian immersions. But in contrast, it is shown that a large class of slant immersions do not exist thoroughly. Finally, they give an application of Chen‘s inequality to general slant immersions in a complex projective space, which generalizes a result of Chen.     

The global existence of solutions for two classes of chemotaxis models

This paper is concerned with the global existence and uniform boundedness of solutions for two classes of chemotaxis models in two or three dimensional spaces. Firstly, by using detailed energy estimates, special interpolation relation and uniform Gronwall inequality, we prove the global existence of uniformly bounded solutions for a class of chemotaztic systems with linear chemotactic-sensitivity terms and logistic reaction terms. Secondly, by applying detailed analytic semigroup estimates and special iteration techniques, we obtain the global existence of uniformly bounded solutions for a class of chemotactic systems with nonlinear chemotacticsensitivity terms, which extends the global existence results of [6] to other general cases.     

Hlder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets

In this paper we establish sharp H ¨older estimates of harmonic functions on a class of connected post critically finite(p.c.f.) self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some well-known examples, such as the Sierpinski gasket, the unit interval, the level 3 Sierpinski gasket, the hexagasket,the 3-dimensional Sierpinski gasket, and the Vicsek set are also considered.     

基于增广Lagrange函数的RQP方法

Recursive quadratic programming is a family of techniques developd by Bartholomew-Biggs and other authors for solving nonlinear programming problems.This paperdescribes a new method for constrained optimization which obtains its search di-rections from a quadratic programming subproblem based on the well-known aug-mented Lagrangian function.It avoids the penalty parameter to tend to infinity.We employ the Fletcher‘s exact penalty function as a merit function and the use of an approximate directional derivative of the function that avoids the need toevaluate the second order derivatives of the problem functions.We prove that thealgorithm possesses global and superlinear convergence properties.At the sametime, numerical results are reported.     

不等式的一个改进及其应用

A new improvement of Hilbert＇s inequality for double series can be established by means of a strengthened Cauchy＇s inequality. As application, a quite sharp result on Fejer-Riesz＇s inequality is obtained.     

Characterization of $(c)$-Riordan Arrays, Gegenbauer-Humbert-Type Polynomial Sequences, and $(c)$-Bell Polynomials

Here presented are the definitions of(c)-Riordan arrays and(c)-Bell polynomials which are extensions of the classical Riordan arrays and Bell polynomials.The characterization of(c)-Riordan arrays by means of the A-and Z-sequences is given,which corresponds to a horizontal construction of a(c)-Riordan array rather than its definition approach through column generating functions.There exists a one-to-one correspondence between GegenbauerHumbert-type polynomial sequences and the set of(c)-Riordan arrays,which generates the sequence characterization of Gegenbauer-Humbert-type polynomial sequences.The sequence characterization is applied to construct readily a(c)-Riordan array.In addition,subgrouping of(c)-Riordan arrays by using the characterizations is discussed.The(c)-Bell polynomials and its identities by means of convolution families are also studied.Finally,the characterization of(c)-Riordan arrays in terms of the convolution families and(c)-Bell polynomials is presented.     

REFINEMENTS OF THE FAN－TODD‘S INEQUALITIES

51. IntroductionIn recent years, refinements or interpolations have played an important role on severaltypes of inequalities with new results deduced as a consequence. Please refer to the papers[2, 8, 9, 12], etc. The aim of this paper is to furnish refinements of the Cauchy's and Bessel'sinequalties as shown in Section 2, and also refinements of the Fan-Todd's inequality and theFan-Todd's determinantal inequality in Sections 3 and 4, with an improved condition forequality derived.First of…     

关于Ste(c)kin不等式的上界

利用R．Redheffer不等式和微分法给出了Steckin不等式的上界,核实了它的下界。     

ON INVERSES AND ALGEBRAIC LOOPS OF CO-H-SPACES

In this paper we study the properties of homotopy inverses of comultiplications and Mgebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old ones by using a group action. We are primarily interested in the algebraic loops which have inversive, power-associative and Moufang properties for some comultiplications.     

离散型Carlson's不等式的一些推广及改进

In this paper, we consider Carlson type inequalities and discuss their possible improvement. First, we obtain two different types of generalizations of discrete Carlson's inequality by using the Hlder inequality and the method of real analysis, then we combine the obtained results with a summation formula of infinite series and some Mathieu type inequalities to establish some improvements of discrete Carlson's inequality and some Carlson type inequalities which are equivalent to the Mathieu type inequalities. Finally, we prove an integral inequality that enables us to deduce an improvement of the Nagy-Hardy-Carlson inequality.     

LOWER BOUNDS FOR SUP＋INF AND SUP＊INF AND AN EXTENSION OF CHEN-LIN RESULT IN DIMENSION 3

We give two results about Harnack type inequalities. First, on Riemannian surfaces, we have an estimate of type sup ＋ inf. The second result concern the solutions of prescribed scalar curvature equation on the unit ball of Rn with Dirichlet condition. Next, we give an inequality of type （supK ^u）^2s-1 × infπu ≤ c for positive solutions of △u = V u^5 on Ω belong toR^3, where K is a compact set of Ω and V is s-Holderian, s ∈] - 1/2, 1]. For the case s = 1/2 and Ω = S3, we prove that, if minΩ u 〉 m 〉 0 （for some particular constant m 〉 0）, and the H¨olderian constant A of V tends to 0 （in certain meaning）, we have the uniform boundedness of the supremum of the solutions of the previous equation on any compact set of Ω.     

ISOMORPHISMS OF CIRCULANT DIGRAPHS OF DEGREE 3

Abstract. In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine the isomorphic classes of circulant digraphs of degree 3. In psrticular, we characterize those circulant digraphs of degree 3 which don‘‘t satisfy JkdAm‘‘s conjectttre.     

线性等式约束下奇异线性模型参数的条件BLU估计

考虑带线性等式约束的奇异线性模型对任一条伯可估函数Ｃ’β，本文给出了它的所有条件ＢＬＵ估计，并建立了Ｃ‘（Ｘ’Ｘ）＋Ｘ‘ｙ为Ｃ’β的条件ＢＬＵ估计的一个充分条件。最后研究了带线性等式约束的多元线性模型参数阵的条件ＢＬＵ估计。     

On an Extension and a Refinement of Van der Corput＇s Inequality

By introducing a parameterα,we give an extension of Van der Corput's inequal- ity.Also a new strengthened version of it is considered.     

关于环Z[√c]的商环的注记

讨论了一类环的商环元素的个数，并推广了交[1,2]的结果。     

MATRIX NORM VERSIONS OF THE KANTOROVICH INEQUALITY AND ITS APPLICATIONS

In this paper we discuss the generalizations of the Kantorovich inequality and obtain some generalized Kantorovich inequalities in the sense of matrix norm. We further illustrate how to use these inequalities to determine the lower bound of relative efficiency of the parameter estimate in linear model.     

ON CRITICAL SINGULAR QUASILINEAR ELLIPTIC PROBLEM WHEN n = p

This article deals with the problem where n = p. The authors prove that a Hardy inequality and the constant (p/p-1)p is optimal. They also prove the existence of a nontrivial solution of the above mentioned problem by using the Mountain Pass Lemma.