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 theory of the shear-induced isotropic-to-nematic phase transition of side chain liquid-crystalline polymers

The shear-induced isotropic-to-nematic phase transition of side chain liquid-crystalline polymers is studied theoretically. A modification of the previous models of main-chain liquid crystals to the case of side chain liquid-crystalline polymers is proposed. Orientational and rheological properties of the model are studied in plane-shear flow. Predictions of the present model agree qualitatively with experimental results (Pujolle-Robic, Noirez in Nature 409:167, 2001).     

《数书九章》大衍类算题中的数论命题

《数书九章》是我国著名数学家南宋秦九韶撰写(公元1247年)。青年时他“侍亲中都(临安,今杭州市)因得访习于太史(国家天文历法官员)”。《数书九章》有“大衍总数术”以处理天文历法问题,系统论述同余式解法,这在我国历史上是第一次,在世界数学史上也是创举。 本文用整数论知识来检验《数书九章》中有关解同余式算题(大衍类)题文、术文、草文以及清代学者所作注文的得失,使对我国传统数学在这一领域内的工作有,较系统的认识。     

Liouville numbers, Rajchman measures, and small Cantor sets

We show that the set of Liouville numbers carries a positive measure whose Fourier transform vanishes at infinity. The proof is based on a new construction of a Cantor set of Hausdorff dimension zero supporting such a measure.

     

Milnor invariants for spatial graphs

Link-homotopy has been an active area of research for knot theorists since its introduction by Milnor in the 1950s. We introduce a new equivalence relation on spatial graphs called component-homotopy, which reduces to link-homotopy in the classical case. Unlike previous attempts at generalizing link-homotopy to spatial graphs, our new relation allows analogues of some standard link-homotopy results and invariants.In particular we can define a type of Milnor group for a spatial graph under component-homotopy, and this group determines whether or not the spatial graph is splittable. More surprisingly, we will also show that whether the spatial graph is splittable up to component-homotopy depends only on the link-homotopy class of the links contained within it. Numerical invariants of the relation will also be produced.     

A characterization of quadrics by intersection numbers

This work is inspired by a paper of Hertel and Pott on maximum non-linear functions (Hertel and Pott, A characterization of a class of maximum non-linear functions. Preprint, 2006). Geometrically, these functions correspond with quasi-quadrics; objects introduced in De Clerck et al. (Australas J Combin 22:151–166, 2000). Hertel and Pott obtain a characterization of some binary quasi-quadrics in affine spaces by their intersection numbers with hyperplanes and spaces of codimension 2. We obtain a similar characterization for quadrics in projective spaces by intersection numbers with low-dimensional spaces. Ferri and Tallini (Rend Mat Appl 11(1): 15–21, 1991) characterized the non-singular quadric Q(4,q) by its intersection numbers with planes and solids. We prove a corollary of this theorem for Q(4,q) and then extend this corollary to all quadrics in PG(n,q),n ≥ 4. The only exceptions occur for q even, where we can have an oval or an ovoid as intersection with our point set in the non-singular part.      

Applications of an Explicit Formula for the Generalized Euler Numbers

The authors establish an explicit formula for the generalized Euler NumbersE2n^（x）, and obtain some identities and congruences involving the higher＇order Euler numbers, Stirling numbers, the central factorial numbers and the values of the Riemann zeta-function.     

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.     

Convergence of series of dependent φ-subgaussian random variables

The almost sure convergence of weighted sums of φ-subgaussian m-acceptable random variables is investigated. As corollaries, the main results are applied to the case of negatively dependent and m-dependent subgaussian random variables. Finally, an application to random Fourier series is presented.     

Convex fuzzy mapping with differentiability and its application in fuzzy optimization

The concepts of differentiability, convexity, generalized convexity and minimization of a fuzzy mapping are known in the literature. The purpose of this present paper is to extend and generalize these concepts to fuzzy mappings of several variables using Buckley–Feuring approach for fuzzy differentiation and derive Karush–Kuhn–Tucker condition for the constrained fuzzy minimization problem.