LOOMIS-WHITNEY'S INEQUALITY ABOUT MIXED BODY

In this article,the authors establish two theorems for mixed body,which are the generalizations of the well-known Loomis-Whitney's inequality.     

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.     

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.     

ON KORN‘S INEQUALITY

This paper is devoted to give a new proof of Korn's inequality in LT - norm (1 < γ < ∞).     

SOME INEQUALITIES ABOUT DUAL MIXED VOLUMES OF STAR BODIES

The authors establish some inequalities about the dual mixed volumes of star bodies in R^n. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symmetric functions of positive reals.     

GENERALIZED ROSENTHAL＇S INEQUALITY FOR BANACH-SPACE-VALUED MARTINGALES

A generalized Rosenthal＇s inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and characterizes the p-uniform smoothness and q-uniform convexity of the underlying Banach space. As an application of this inequality, the strong law of large numbers for Banach-space-valued martingales is also given.     

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.     

AN IMPROVED HARDY＇S INEQUALITY

In this paper we shall extend Hardy’s inequality associated with Fourier trans-form to the strip n(2?p)≤σ相似文献   

Inequalities for polars of mixed projection bodies

In 1993 Lutwak established some analogs of the Brunn-Minkowsi inequality and the Aleksandrov-Fenchel inequality for mixed projection bodies. In this paper, following Lutwak, we give their polars forms. Further, as applications of our methods, we give a generalization of Pythagorean inequality for mixed volumes.     

On Mulholland's inequality

H.P. Mulholland has presented a sufficient condition for a generalization of the Minkowski inequality and another such condition was given by R.M. Tardiff. We show that Mulholland's condition implies Tardiff's, but that the converse is false.

     

混合幂为2,3,a和b的丢番图不等式

运用Davenport-Heilbronn方法证明了如果η是实数,λ1,μ1,μ2,μ3,μ4,θ1,θ2是非零实数,并且不同一符号,且至少一个λ1/μi(i=1,2,3,4)是无理教,假设(i)a=3,3≤b≤11,或者(ii)a=4,4≤b≤5,那么对某些σ=σ(a,b)>0,混合幂为2,3,a和b的丢番图不等式有无穷多正整数解x1,...,x7.     

On the L p -dual mixed volumes

We establish the cyclic inequality for i-th L p-dual mixed volume and Lp-dual Urysohn inequality between p-mean width and Lp-dual quermassintegral. Moreover, the dual isoperimetric inequality for Lp-dual mixed volume is proved, which is an extension of the classical dual isoperimetric inequality.     

A global Carleman inequality and exact controllability of parabolic equations with mixed boundary conditions

This paper establishes a global Carleman inequality of parabolic equations with mixed boundary conditions and an estimate of the solution. Further, we prove exact controllability of the equation by controls acting on an arbitrarily given subdomain or subboundary.     

Extension of Simons' inequality

We prove the following extended version of Simons' inequality and present its applications. Let be a set and be a subset of . Let be a subset of a Hausdorff topological vector space which is invariant under infinite convex combinations. Let be a bounded function such that the functions are convex for all and whenever 0$">, and Let be a sequence in . Assume that, for every , there exists satisfying . Then

If , then the set in the above inequality can be replaced by .

     

关于p-凸函数的Hadamard型不等式

对于P-凸函数在给定连续区间上的算术平均问题,通过P-凸函数理论将其转化为定积分问题,利用定积分的定义计算和定积分运算,建立了P-凸函数的Hadamard 型不等式,给出了证明和发现不等式的实例.     

A mixed Hölder and Minkowski inequality

Hölder's inequality states that for any with . In the same situation we prove the following stronger chains of inequalities, where :

A similar result holds for complex valued functions with Re substituting for . We obtain these inequalities from some stronger (though slightly more involved) ones.