On the constructive characterization of threshold functions

In this paper, the structure of the set of threshold functions and complexity problems are considered. The notion of the signature of a threshold function is defined. It is shown that if a threshold function essentially depends on all of its variables, then the signature of this function is unique. The set of threshold functions is partitioned into classes with equal signatures. A theorem characterizing this partition is proved. The importance of the class of monotone threshold functions is emphasized. The complexity of transferring one threshold function specified by a linear form into another is examined. It is shown that in the worst case this transfer would take exponential time. The structure of the set of linear forms specifying the same threshold function is also examined. It is proved that for any threshold function this set of linear forms has a unique basis in terms of the operation of addition of linear forms. It is also shown that this basis is countable.     

Confluent Form of the Multistep ɛ‐Algorithm,and the Relevant Integrable System

In this paper, the confluent form of the multistep ? ‐algorithm is proposed. The molecule solution of this system is derived by using determinantal identities. A new continuous prediction algorithm based on this confluent form is constructed. It also shows that this algorithm is a special case of the extended Lotka–Volterra system.     

Application of multilevel analysis in animal sciences

Multilevel modeling is considerably useful way to analyze hierarchical data sets. The main purpose of this paper is to apply multilevel analysis in animal science and also show that this modeling technique is appropriate to analyze this kind of data. Thus multilevel modeling technique is used to analyze the milk yield data which has hierarchical structures, sires nested within cows. As a result of the analysis done in this paper, it is obvious that multilevel modeling is needed to use for analyzing this data. This illustrates that it is a convenient way to use multilevel analysis for the data which obtained from animals when the data have hierarchies.     

Global convergence of BFGS and PRP methods under a modified weak Wolfe–Powell line search

The BFGS method is one of the most effective quasi-Newton algorithms for optimization problems. However, its global convergence for general functions is still open. In this paper, under a new line search technique, this problem is solved, and it is shown that other methods in the Broyden class also possess this property. Moreover, the global convergence of the PRP method is established in the case of this new line search. Numerical results are reported to show that the new line search technique is competitive to that of the normal line search.     

Limit boundary conditions for finite volume approximations of some physical problems

In the industrial context, finite volume schemes are used to compute an approximation of the solution of a system of equations set on a certain domain. When this domain is bounded, some numerical boundary conditions have to be implemented in order to complete the computation of the finite volume scheme. This is a tricky step in the elaboration of the scheme, which is still not mastered. In fact, at a closer sight, it appears that there is a deep interaction between the understanding of the physical phenomena at the boundary of the domain and the implementation of the numerical boundary conditions. Unfortunately, this link is not always completely intelligible and a reason for this lack of clarity is the fact that, whereas the continuous equation satisfied by the limit of the numerical solution is known, the boundary conditions satisfied by this very limit are not well-understood. The purpose of this paper is to clarify this point in three industrial situations of one-dimensional two-phase flows.     

求解多孔介质中可压缩混溶驱动问题的一类满足极大值原理的数值方法

多孔介质中可压缩混溶驱动问题是用非线性抛物型方程组来描述的．用Ｐｏｔｅｍｐａ格式求其数值解．证明了构造的求解方法满足极大值原理，从而可以保证饱和度的数值解在［０，１］范围内这一物理特性，同时还得到了解的收敛性．     

A parallel algorithm to solve the stable marriage problem

In this paper a parallel algorithm to solve the stable marriage problem is given. The worst case performance of this algorithm is stated. A theoretical analysis shows that the probability of the occurrence of this worst case is extremely small. For instance, if there are sixteen men and sixteen women involved, then the probability that the worst case occurs is only 10^–45. Possible future research is also discussed in this paper.     

Fiber Buckling in a Viscoelastic Matrix

Within the framework of the three-dimensional linearized theory of stability, an approach for investigating fiber buckling in the structure of unidirectional fibrous viscoelastic composites is developed. For simplicity, a small fiber concentration is considered, and the buckling problem for a single elastic fiber in an infinite viscoelastic matrix is investigated. In this case, it is assumed that the fiber has an insignificant initial periodical imperfection, and the growth of this imperfection with time is studied. The state where this imperfection starts to grow indefinitely is taken as a fiber-buckling criterion, and the critical time is determined from this criterion.     

参激白噪声作用下蔡电路的脉冲控制

考察了参激白噪声和脉冲信号联合作用下蔡电路的渐近P阶矩稳定性问题,得到该随机脉冲系统的比较系统,从而可由该确定性比较系统的稳定性得到原随机脉冲系统的渐近P阶矩稳定性.并从理论上得到能使该随机脉冲系统渐近P阶矩稳定的参数取值范围,即在稳定区域内取值的参数组合能够用脉冲方法对该随机蔡电路实现混沌控制.最后用数值仿真验证了理论结果的正确性.     

22号初等元胞自动机的极限语言复杂性

§1Introduction Thetaskofthispaperistosolvetheproblemproposedin[1],i.e.,toexplorethe complexityoflimitset,orequivalently,limitlanguageoftheelementarycellularautomaton ofrule22bythetoolsofformallanguagetheory.Cellularautomata(abbreviatedasCA),asmathematicalmodelsforcomplexnatural systemscontaininglargenumbersofsimpleidenticalcomponentswithlocalinteractions,havebeenwidelyusedinphysical,biological,chemicalandcomputationalsystems[2].Despitetheirsimpleconstruction,someCAcandisplayveryrichandcompl…     

有势场逆问题的边界元法

本文给出了位势方程逆问题的一种最小二乘边界元解法。控制方程为Ｌａｐｌａｃｅ方程，但一部分边界上未给出任何边值，而只在某些内点上给出了势函值。这一问题在数学上属不适定问题，但在一定条件下存在唯一解。本文同时给出了一种估计解的可靠性的方法。数值试验表明，这类逆问题采用边界元法是非常有效的。     

连续型指数差分布

本文提出了一个连续型随机变量的概率分布:指数差分布。讨论了该分布的极值、拐点、数学期望和方差,推导了参数的矩估计公式,探讨了该分布与指数分布的关系,给出了该分布在药代动力学中的应用。     

非齐次Toda晶格的对称,精确解和可积性

研究非齐次Toda晶格，即一类非齐次非线性微分差分方程的对称与可积性。给出了这一类方程的Lie点对称，条件对称和精确解。给出这类方程与Toda晶格之间的可逆点变换，从而表明这一类方程是可积的。     

Classical Risk Model with Threshold Dividend Strategy

In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.     

A Hilbert-Schmidt integral operator and the Weil distribution

In this paper, a positive operator is given. It is shown that the product of this positive operator and the convolution operator is a trace class Hilbert-Schmidt integral operator and has nonnegative eigenvalues. A formula is given for the trace of this product operator. It seems that this product operator is the closest trace class integral operator which has nonnegative eigenvalues and is related to the Weil distribution in the context of Connes’ program for the Riemann hypothesis. A relation is given between the trace of the product operator and the Weil distribution.

     

离散型指数差分布

本文提出了一个离散型概率分布:指数差分布,推导了该分布的最可能成功次数、数学期望和方差,探讨了该分布与几何分布的关系,给出了该分布在马尔可夫链模型中的应用。     

Fuzzy optimal control problem with non-linear functional

In this paper, we introduce a new space of fuzzy numbers equipped with a scalar product defined in this space. The notion of a derivative of a fuzzy function in this space is defined. By employing these notions, an optimal control problem with non-linear functional is formulated and an optimality condition is obtained in the form of maximum principle. Using this result, the numerical algorithm is offered for the solution of such problems.     

An application of the Vandermonde determinant

Eigenvalue is an important concept in Linear Algebra. It is well known that the eigenvectors corresponding to different eigenvalues of a square matrix are linear independent. In most of the existing textbooks, this result is proven using mathematical induction. In this note, a new proof using Vandermonde determinant is given. It is shown that this method is much simpler.     

利用远场模式的不完全数据反演声波阻尼系数

1.引言 对声波反散射理论的研究,已经有大量的研究[1.5].[7]利用散射波的远场模式反演边界条件中的阻尼系数.但是在实际问题中,要在物体的一周测量到远场模式的值是不现实的.因此,利用远场模式的不完全数据来进行反演有明显的物理和实际意义.一些文献将此类问题称为声波反散射理论的“limited aperture problem”.本文利用远场模式的不完全数据,反演边界条件中的声波阻尼系数.     

Converging algorithm for a class of BMI applied on state-dependent stabilization of switched systems

In this paper, a design of a stabilizing state-dependent switching law is presented. First, it is based on a new reformulation of this control problem into a class of BMI (Bilinear Matrix Inequality) problem. The originality of this reformulation is that it will be used, in a second part, by an algorithm dedicated to solve this class of BMI without loss of generality. The construction of this algorithm is then specified, and the proof of its convergence is given for the two-subsystem case. The last part of the work consists in presenting the problem for a polytopic switching system, and how the previous algorithm can be extended. The proposed scheme is illustrated by an academical example.