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</svg> in the L&#xf6;wner partial ordering to be feasible, respectively. The findings of this paper widely extend the known results in the literature.

Yirong Yao

The Optimization on Ranks and Inertias of a Quadratic Hermitian Matrix Function and Its Applications

The Optimal Variational Method (OVM) is introduced and applied for calculating approximate periodic solutions of &#x201c;truly nonlinear oscillators&#x201d;. The main advantage of this procedure consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary. This approach does not depend upon any small or large parameters. A very good agreement was found between approximate and numerical solution, which proves that OVM is very efficient and accurate.

Vasile Marinca

Nicolae Heri&#x15f;anu

Optimal Variational Method for Truly Nonlinear Oscillators

We give some refinements of generalized Acz&#xe9;l's inequality and Bellman's inequality proposed by Tian. As applications, some refinements of integral type of generalized Acz&#xe9;l's inequality and Bellman's inequality are given.

Jing-Feng Tian

Shu-Yan Wang

Refinements of Generalized Acz&#xe9;l's Inequality and Bellman's Inequality and Their Applications

We provide a supplementation of the results on the canonical forms for scalar fourth-order ordinary differential equations (ODEs) which admit four-dimensional Lie algebras obtained recently. Together with these new canonical forms, a complete list of scalar fourth-order ODEs that admit four-dimensional Lie algebras is available.

A. Fatima

Muhammad Ayub

F. M. Mahomed

A Note on Four-Dimensional Symmetry Algebras and Fourth-Order Ordinary Differential Equations

Interval censored (IC) failure time data are often observed in medical follow-up studies and clinical trials where subjects can only be followed periodically, and the failure time can only be known to lie in an interval. In this paper, we propose a weighted Wilcoxon-type rank test for the problem of comparing two IC samples. Under a very general sampling technique developed by Fay (1999), the mean and variance of the test statistics under the null hypothesis can be derived. Through simulation studies, we find that the performance of the proposed test is better than that of the two existing Wilcoxon-type rank tests proposed by Mantel (1967) and R. Peto and J. Peto (1972). The proposed test is illustrated by means of an example involving patients in AIDS cohort studies.

Ching-fu Shen

Jin-long Huang

Chin-san Lee

Weighted Wilcoxon-Type Rank Test for Interval Censored Data

Wei-Qi Deng

Peng Bai

An Implicit Iteration Process for Common Fixed Points of Two Infinite Families of Asymptotically Nonexpansive Mappings in Banach Spaces

We investigate a level-set-type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable approximate solutions of the inverse problem, we propose a Tikhonov-type regularization approach coupled with a level-set framework. We prove the existence of generalized minimizers for the Tikhonov functional. Moreover, we prove convergence and stability for regularized solutions with respect to the noise level, characterizing the level-set approach as a regularization method for inverse problems. We also show the applicability of the proposed level-set method in some interesting inverse problems arising in elliptic PDE models.

A. De Cezaro

On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients

A new bandwidth allocation model is studied in this paper. In this model, a system, such as a communication network, is composed of a finite number of users, and they compete for limited bandwidth resources. Each user adopts the decision that maximizes his or her own benefit characterized by the utility function. The decision space of each user is subject to constraints. In
addition, some users form a group, and their joint decision space is also subject to constraints. Under the assumption that each user&#x2019;s utility function satisfies some continuity and concavity conditions, the existence, uniqueness, and fairness, in some appropriate sense, of the Nash equilibrium point in the allocation game are proved. An algorithm yielding a sequence converging to the equilibrium point is proposed. Finally, a numerical example with detailed analysis is provided to illustrate the effectiveness of our work.

Shun-Pin Hsu

Shun-Liang Hsu

Alan Shenghan Tsai

A Game-Theoretic Analysis of Bandwidth Allocation under a User-Grouping Constraint

Derivatives of eigenvectors with respect to structural parameters play an important role in structural design, identification, and optimization. Particularly, calculation of eigenvector sensitivity is considered when the eigenvalues are repeated. A relaxation factor embedded in the combined approximations (CA) method makes it effective to the structural response at various modified designs. The proposed method is feasible after overcoming the defection of irreversibility of the characteristic matrix. Numerical examples show that it is easy to implement the computational procedure, and the method presented in this paper is efficient for the general linear vibration damped systems with repeated frequencies.

Shijia Zhao

Tao Xu

Guikai Guo

Wei Zhang

Dongkai Liu

Efficient Procedures of Sensitivity Analysis for Structural Vibration Systems with Repeated Frequencies

The concept of soft sets introduced by Molodtsov is a general mathematical tool for dealing with uncertainty. Just as the conventional set-theoretic operations of intersection, union, complement, and difference, some corresponding operations on soft sets have been proposed. Unfortunately, such operations cannot keep all classical set-theoretic laws true for soft sets. In this paper, we redefine the intersection, complement, and difference of soft sets and investigate the algebraic properties of these operations along with a known union operation. We find that the new operation system on soft sets inherits all basic properties of operations on classical sets, which justifies our definitions.

Ping Zhu

Qiaoyan Wen

Operations on Soft Sets Revisited

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<p><em>Journal of Applied Mathematics</em> publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.</p>


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<p>Chief Editor, Professor Theodore E. Simos, is based at Ulyanovsk State Technical University, Russia. His main research interest is the numerical analysis of differential equations.</p>


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Journal of Applied Mathematics - Table of contents 2013

title

Journal of Applied Mathematics publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.

Journal of Applied Mathematics