The monotonicity of the ratio between generalized logarithmic means

A monotonicity result for the ratio between two generalized logarithmic means is established. As an application, an inequality of Alzer for negative powers is extended to all real numbers.     

Kantorovich不等式的推广及其在统计中的应用

本文推广了Ｋａｎｔｏｒｏｖｉｃｈ不等式，并把所得结果应用到最小二乘估计的精度和效率，以及广义相关系数中。     

A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions

In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported. Project supported by the National Natural Science Foundation (No. 10261001), Guangxi Science Foundation (Nos. 0236001, 064001), and Guangxi University Key Program for Science and Technology Research (No. 2005ZD02) of China.     

Inequalities for vertex distances of two simplices

We establish in this paper some inequalities for vertex distances of two simplices, and give some applications thereof.     

$\bar \partial $‐energy integral and uniqueness of harmonic maps

In this paper, we introduce a new energy functional, ‐energy functional, instead of the total energy functional to investigate the uniqueness of harmonic maps with respect to any given metric on the unit disk. Even in the setting that the Hopf differentials of harmonic maps are not integrable, certain uniqueness theorems of harmonic maps are obtained, which improve a result due to Markovi? and Mateljevi? in 1999. Moreover, a generalized energy‐minimizing property of harmonic maps is discussed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inequalities for the weighted mean of -convex functions

In this paper, the inequalities for the weighted mean of -convex functions are established. As applications, inequalities between the two-parameter mean of an -convex function and extended mean values are given.

     

Solving nonlinear inequalities in a finite number of iterations

This paper describes a modified Newton algorithm for solving a finite system of inequalities in a finite number of iterations.This research was supported by NSF Grant No. ENG-73-08214-AO1, by NSF-RANN Grant No. ENV-76-04264, and by the United Kingdom Science Research Council.     

Asymptotic inequality of the market system

Do the rich get richer under the market system? We give models supporting such an idea on the basis of: (1) the utility function of the rich person increases at a slower rate and so he bargains for more, and (2) the poor person discounts the future at a higher rate than the rich person.     

An iterative scheme for variational inequalities

In this paper we introduce and study a general iterative scheme for the numerical solution of finite dimensional variational inequalities. This iterative scheme not only contains, as special cases the projection, linear approximation and relaxation methods but also induces new algorithms. Then, we show that under appropriate assumptions the proposed iterative scheme converges by establishing contraction estimates involving a sequence of norms in Eⁿ induced by symmetric positive definite matrices G_m. Thus, in contrast to the above mentioned methods, this technique allows the possibility of adjusting the norm at each step of the algorithm. This flexibility will generally yield convergence under weaker assumptions.