A Fast High Order Iterative Solver for the Electromagnetic Scattering by Open Cavities Filled with the Inhomogeneous Media

The scattering of the open cavity filled with the inhomogeneous media is studied. The problem is discretized with a fourth order finite difference scheme and the immersed interface method, resulting in a linear system of equations with the high order accurate solutions in the whole computational domain. To solve the system of equations, we design an efficient iterative solver, which is based on the fast Fourier transformation, and provides an ideal preconditioner for Krylov subspace method. Numerical experiments demonstrate the capability of the proposed fast high order iterative solver.     

基于最小偏差和优势度的区间数互补判断矩阵排序法

针对决策信息以区间数互补判断矩阵形式给出的多目标决策问题。首先,给出相对优势度的概念和区间数加性一致性互补判断矩阵的判定定理。其次,建立一个目标规划模型,通过求解该模型得到区间数互补判断矩阵的权重向量,并利用各权重向量的总体相对优势度对方案进行排序,提出了基于最小偏差和优势度的区间数互补判断矩阵排序法。方法的核心是对数值型互补判断矩阵排序方法的拓展。最后,通过实例说明方法的可行性和有效性。     

A New Loop Algebra and Its Corresponding Multi-component Integrable Hierarchy

A type of new loop algebra $\tilde{G}_M$ is constructed by making use of the concept of cycled numbers. As its application, an isospectral problem is designed and a new multi-component integrable hierarchy with multi-potential functions is worked out, which can be reduced to the famous KN hierarchy.     

Massive and massless neutrinos on unbalanced seesaws

The observation of neutrino oscillations requires new physics beyond the standard model (SM).A SM-like gauge theory with p lepton families can be extended by introducing q heavy right-handed Majorana neutrinos but preserving its SU(2)L x U(1)y gauge symmetry.The overall neutrino mass matrix M turns out to be a symmetric (p+q) x (p+q) matrix.Given p＞q,the rank of M is in general equal to 2q,corresponding to 2q non-zero mass eigenvalues.The existence of (p-q) massless left-handed Majorana neutrinos is an exact consequence of the model,independent of the usual approximation made in deriving the Type-I seesaw relation between the effective p x p light Majorana neutrino mass matrix M,and the q x q heavy Majorana neutrino mass matrix MR.In other words,the numbers of massive left- and right-handed neutrinos are fairly matched.A good example to illustrate this "seesaw fair play rule"is the minimal seesaw model with p ＝ 3 and q ＝ 2,in which one masslese neutrino sits on the unbalanced seesaw.     

Intuitionistic notions of boundedness in ℕ

We consider notions of boundedness of subsets of the natural numbers ? that occur when doing mathematics in the context of intuitionistic logic. We obtain a new characterization of the notion of a pseudobounded subset and we formulate the closely related notion of a detachably finite subset. We establish metric equivalents for a subset of ? to be detachably finite and to satisfy the ascending chain condition. Following Ishihara, we spell out the relationship between detachable finiteness and sequential continuity. Most of the results do not require countable choice. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree

In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a homogeneous tree.     

Application of possibility theory to investment decisions

Carlson and Fuller (2001, Fuzzy Sets and Systems, 122, 315–326) introduced the concept of possibilistic mean, variance and covariance of fuzzy numbers. In this paper, we extend some of these results to a nonlinear type of fuzzy numbers called adaptive fuzzy numbers (see Bodjanova (2005, Information Science, 172, 73–89) for detail). We then discuss the application of these results to decision making problems in which the parameters may involve uncertainty and vagueness. As an application, we develop expression for fuzzy net present value (FNPV) of future cash flows involving adaptive fuzzy numbers by using their possibilistic moments. An illustrative numerical example is given to illustrate the results.     

Joint Distribution of Rises and Falls

The marginal distributions of the number of rises and the number of falls have been used successfully in various areas of statistics, especially in non-parametric statistical inference. Carlitz (1972, Duke Math. J. 39, 268–269) showed that the generating function of the joint distribution for the numbers of rises and falls satisfies certain complex combinatorial equations, and pointed out that he had been unable to derive the explicit formula for the joint distribution from these equations. After more than two decades, this latter problem remains unsolved. In this article, the joint distribution is obtained via the probabilistic method of finite Markov chain imbedding for random permutations. A numerical example is provided to illustrate the theoretical results and the corresponding computational procedures.     

Recent radioactive ion beam program at RIKEN and related topics

Recent experimental programs at RIKEN concerning RI beams are reviewed. RIKEN has the ring cyclotron (RRC) with high intense heavy-ion beams and large acceptance fragment separator, RIPS. The complex can provide high intense RI-beams. By using the high intense RI-beams, a variety of experiments have been done. Recently, nuclear structure for unstable nuclei has been paid much attention. In special, disappearance and appearance of magic numbers are discussed experimentally and theoretically. Thus, in this review, related experiments concerning disappearance and appearance of magic numbers are described. Finally, future project in RIKEN, RI-beam factory. is introduced briefly.     

On the Space bvp（F） of Sequences of p-bounded Variation of Fuzzy Numbers

Recently, the space bvp of real or complex numbers consisting of all sequences whose differences are in the space lp has been studied by Basar, Altay [Ukrainian Math. J. 55（1）（2003）, 136-147], where 1 ≤ p ≤ ∞. The main purpose of the present paper is to introduce the space bvp（F） of sequences of p-bounded variation of fuzzy numbers. Moreover, it is proved that the space bvp（F） includes the space lp（F） and also shown that the spaces bvp（F） and lp（F） axe isomorphic for 1 ≤ p ≤∞. Furthermore, some inclusion relations have been given.