On the generalized Hyers-Ulam stability of multi-quadratic mappings

A mapping f:Vⁿ?W, where V is a commutative group, W is a linear space, and n≥2 is an integer, is called multi-quadratic if it is quadratic in each variable. In this paper, we prove the generalized Hyers-Ulam stability of multi-quadratic mappings in Banach spaces and complete non-Archimedean spaces.     

Hybrid algorithm for generalized mixed equilibrium problems and variational inequality problems and fixed point problems

In this paper, we introduce a new iterative algorithm by hybrid method for finding a common element of the set of solutions of finite general mixed equilibrium problems and the set of solutions of a general variational inequality problem for finite inverse strongly monotone mappings and the set of common fixed points of infinite family of strictly pseudocontractive mappings in a real Hilbert space. Then we prove strong convergence of the scheme to a common element of the three above described sets. Our result improves and extends the corresponding results announced by many others.     

Existence and uniqueness of strictly nondecreasing and positive solution for a fractional three-point boundary value problem

In this paper, we consider the following nonlinear fractional three-point boundary value problem

     

Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability

Data reduction is a key technique in the study of fixed parameter algorithms. In the AI literature, pruning techniques based on simple and efficient-to-implement reduction rules also play a crucial role in the success of many industrial-strength solvers. Understanding the effectiveness and the applicability of data reduction as a technique for designing heuristics for intractable problems has been one of the main motivations in studying the phase transition of randomly-generated instances of NP-complete problems.In this paper, we take the initiative to study the power of data reductions in the context of random instances of a generic intractable parameterized problem, the weighted d-CNF satisfiability problem. We propose a non-trivial random model for the problem and study the probabilistic behavior of the random instances from the model. We design an algorithm based on data reduction and other algorithmic techniques and prove that the algorithm solves the random instances with high probability and in fixed-parameter polynomial time O(dknm) where n is the number of variables, m is the number of clauses, and k is the fixed parameter. We establish the exact threshold of the phase transition of the solution probability and show that in some region of the problem space, unsatisfiable random instances of the problem have parametric resolution proof of fixed-parameter polynomial size. Also discussed is a more general random model and the generalization of the results to the model.     

第三代移动通信系统中的信道分配技术

移动通信系统发展至今信道分配技术一直都是热门话题,一个好的信道分配算法可以在特定的服务等级下(包括链路质量,新呼叫阻塞概率,切换失败概率)产生很高的频谱利用率。本文注重结合第三代移动通信系统对现有的信道分配技术进行综述并分析其优劣。     

A parametric bootstrap approach for ANOVA with unequal variances: Fixed and random models

This article is about testing the equality of several normal means when the variances are unknown and arbitrary, i.e., the set up of the one-way ANOVA. Even though several tests are available in the literature, none of them perform well in terms of Type I error probability under various sample size and parameter combinations. In fact, Type I errors can be highly inflated for some of the commonly used tests; a serious issue that appears to have been overlooked. We propose a parametric bootstrap (PB) approach and compare it with three existing location-scale invariant tests—the Welch test, the James test and the generalized F (GF) test. The Type I error rates and powers of the tests are evaluated using Monte Carlo simulation. Our studies show that the PB test is the best among the four tests with respect to Type I error rates. The PB test performs very satisfactorily even for small samples while the Welch test and the GF test exhibit poor Type I error properties when the sample sizes are small and/or the number of means to be compared is moderate to large. The James test performs better than the Welch test and the GF test. It is also noted that the same tests can be used to test the significance of the random effect variance component in a one-way random model under unequal error variances. Such models are widely used to analyze data from inter-laboratory studies. The methods are illustrated using some examples.     

一个二阶非线性中立时滞微分方程的正解

研究了一个二阶非线性中立时滞微分方程,给出了关于此方程正解存在的一些充分条件,其优点在于省略了对任意的a〉0,aQ1（t）-Q2（t）都是最终非负的限制条件。最后通过数值例子说明研究结果的优越性。     

基于不动点理论的改进遗传算法及其应用

针对遗传算法的遗传效率问题,引入不动点理论的“剖分—标号—剖分”思想,通过寻找全标单纯形来对最优解进行定位,对全标单纯形再次剖分,寻找其内部的全标单纯形,使最优解得范围进一步缩小。遗传算法按相对适应度大小随机选取全标单纯形内的点作为初始化群体,极大地提高了遗传算法的效率。将遗传变异区间化,锁定在全标单纯形内或附近单纯形,使得最优解的精确度也得到极大地提高。     

Effect of fungal damage on seed composition and quality of soybeans

Fungal damage caused by pathogens such asFusarium, Cercospora, andPhomopsis can have a devastating impact on physical quality and farm price of soybeans. In some price-discount schedules, soybeans may be rejected with as low as 5% fungal damage. Although the severity of this problem varies throughout the United States, millions of bushels of fungus-damaged soybeans may be destroyed annually due to a lack of markets. The effect of fungal damage on seed composition was evaluated to assess potential utility of highly damaged soybeans. Graded samples of the cv. Centennial soybean were dried to 10% moisture and blended on a proportional weight basis to derive a series of treatments from 0 to 80% fungal damage. A positive correlation was found between fungal damage and both protein and oil concentrations. This condition was attributed to loss of residual seed mass. As a result, the protein concentration of defatted meal increased from ca. 54 to 66% over the range of 0 to 80% fungal damage. Mycotoxin contamination appeared to be insignificant in these high-protein meals. Fixed colors in bleached, alkali refined oils were intensified by heat treatment prior to extraction. No significant differences, however, were noted in total polar lipid content, phospholipid, or tocopherol composition among treatments of up to 20% fungal damage. Oils from treatments of more than 40% fungal damage were more severely oxidized and could not be degummed effectively. These data suggest that fungus-damaged soybeans may be blended with high-quality soybeans to alleviate the chemical symptoms associated with unacceptable product quality. Thus, through various blend ratios, processors may consider using fungus-damaged soybeans to gain economic advantage, especially when high-quality soybeans have lower protein concentration.     

Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization

The particle swarm optimization (PSO) is a relatively new generation of combinatorial metaheuristic algorithms which is based on a metaphor of social interaction, namely bird flocking or fish schooling. Although the algorithm has shown some important advances by providing high speed of convergence in specific problems it has also been reported that the algorithm has a tendency to get stuck in a near optimal solution and may find it difficult to improve solution accuracy by fine tuning. The present paper proposes a new variation of PSO model where we propose a new method of introducing nonlinear variation of inertia weight along with a particle's old velocity to improve the speed of convergence as well as fine tune the search in the multidimensional space. The paper also presents a new method of determining and setting a complete set of free parameters for any given problem, saving the user from a tedious trial and error based approach to determine them for each specific problem. The performance of the proposed PSO model, along with the fixed set of free parameters, is amply demonstrated by applying it for several benchmark problems and comparing it with several competing popular PSO and non-PSO combinatorial metaheuristic algorithms.