Perturbed recurrence relations II the general case

In this paper, we give some new explicit relations between two families of polynomials defined by recurrence relations of all order. These relations allow us to analyze, even in the Sobolev case, how some properties of a family of orthogonal polynomials are affected when the coefficients of the recurrence relation and the order are perturbed. In a paper we have already given a method which allows us to study the polynomials defined by a three-term recurrence relation. Also here some generalizations are given.     

A fuzzy goal programming method with imprecise goal hierarchy

Two most widely used approaches to treating goals of different importance in goal programming (GP) are: (1) weighted GP, where importance of goals is modelled using weights, and (2) preemptive priority GP, where a goal hierarchy is specified implying infinite trade-offs among goals placed in different levels of importance. These approaches may be too restrictive in modelling of real life decision making problems. In this paper, a novel fuzzy goal programming method is proposed, where the hierarchical levels of the goals are imprecisely defined. The imprecise importance relations among the goals are modelled using fuzzy relations. An additive achievement function is defined, which takes into consideration both achievement degrees of the goals and degrees of satisfaction of the fuzzy importance relations. Examples are given to illustrate the proposed method.     

若干中点迭代法的收敛性

The King-Werner iteration xn 1= xn -F‘(1/2(xn yn))^-1 F(xn);yn 1=xn 1-F‘(1/2(xn yn))^-1F(xn 1) which is used for solving the operator eqution in Banach space F(x) = 0 requires the inverse of the opterator‘s derivative.Now in this paper a deformation King-Werner method without use of inverse is presented and the convergence of this method is proved with the skill of the majoring function. In addition, for the existed convergent theorem the convergent condtions are amended. The corresponding convergence theorem holds also with the amended conditions and its error bounds is obtained. At last a midpoint method of order 1 √2 : yn=xn-F‘(xn)^-1F(xn);xn 1=xn-F‘(xn yn/2)^-1F(xn) which is studied by D.Chen and I.K.Argros is convergent withby milder conditions by recurence relations.     

Monoid Valuations and Value Ordered Supervaluations

We complement two papers on supertropical valuation theory ([11 Izhakian , Z. , Knebusch , M. , Rowen , L. ( 2011 ). Supertropical semirings and supervaluations . J. Pure and Applied Alg. 215 ( 10 ): 2431 – 2463 . Preprint at arXiv:1003.1101 .[Crossref], [Web of Science ®] , [Google Scholar]], [12 Izhakian , Z. , Knebusch , M. , Rowen , L. ( 2013 ). Dominance and transmissions in supertropical valuation theory . Commun. Algebra 41 ( 7 ): 2736 – 2782 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]) by providing natural examples of m-valuations (= monoid valuations), and afterwards of supervaluations and transmissions between them. These supervaluations have values in totally ordered supertropical semirings, and the transmissions discussed respect the orderings. We develop the basics of the theory of such semirings and transmissions.     

On sofic actions and equivalence relations

The notion of sofic equivalence relation was introduced by Gabor Elek and Gabor Lippner. Their technics employ some graph theory. Here we define this notion in a more operator algebraic context, starting from Connes? Embedding Problem, and prove the equivalence of these two definitions. We introduce a notion of sofic action for an arbitrary group and prove that an amalgamated product of sofic actions over amenable groups is again sofic. We also prove that an amalgamated product of sofic groups over an amenable subgroup is again sofic.     

周期性磁谐振材料本构参数的理论分析

将薄的磁谐振介质板等效为面磁流, 利用周期性边界条件, 给出了面磁流的指数形式. 通过计算无穷个面磁流在不同空间位置上产生的总电场和总磁场, 推导出了周期性磁谐振人工材料的色散关系和布洛赫阻抗, 进而获取了布洛赫本构参数的理论计算公式. 由于考虑了磁谐振人工材料中的电反谐振对布洛赫介电常数和磁导率的影响, 所以基于仿真实验的布洛赫本构参数的提取值和布洛赫本构参数理论预测值之间的误差很小, 这说明本文推导的布洛赫本构参数的理论计算公式在描述周期性磁谐振材料的电磁特性方面是十分有效的. 这些理论公式将在解释磁谐振现象、设计和优化周期性磁谐振材料等方面提供重要的理论依据. 关键词： 周期性结构 磁谐振 布洛赫本构参数 面磁流     

Dispersion relations and the spin polarizabilities of the nucleon

A forward dispersion calculation is implemented for the spin polarizabilities γ₁,,γ₄ of the proton and the neutron. These polarizabilities are related to the spin structure of the nucleon at low energies and are structure-constants of the Compton scattering amplitude at . In the absence of a direct experimental measurement of these quantities, a dispersion calculation serves the purpose of constraining the model building, and of comparing with recent calculations in heavy baryon chiral perturbation theory.     

Directed polymers in a random environment: Some results on fluctuations

We consider a polymer model on ℤ ₊ ^d where to each edgee is associated a random variable v(e). A polymer configuration is represented by a directed pathr and has a weight exp[-β ∑ _e ∈r ν(e)], withβ=1/T the inverse temperature. We extend some rigorous results that have been obtained for the ground state of this model to finite temperatures. In particular we obtain some upper and lower bounds on sample-to-sample free energy fluctuations, and also rigorous scaling inequalities between the exponents describing free energy fluctuations and transversal displacements of polymer configurations     

Evidence for a second,local contact condition for a planar electric double layer containing size and valency asymmetric ions

A generalised form of a local contact condition for the charge profile in a primitive model planar double layer [Bhuiyan, Outhwaite, and Henderson, Mol. Phys. 107, 343 (2009)] at low electrode charge is examined for completely asymmetric, binary electrolytes. The cation and anion sizes are taken to be different from each other with the valencies being 2⁺:1^? or 1⁺:2^?, while the electrode surface charge density is varied from being negative through zero to being positive. Monte Carlo simulation data obtained for such double layer systems at varying ionic radius ratios and electrolyte concentrations suggest the generalised contact relation to be valid at low charge on the electrode.