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.     

Convex fuzzy random variables

A theory of fuzzy random variables is developed that applies to situations involving both randomness and fuzziness. The use of membership functions that are quasi-concave play an important role in the theory. The expectation of a fuzzy random variable is a fuzzy variable (fuzzy set). The usual linearity properties of probabilistic expectation carry over to fuzzy random variables. A special case of a fuzzy Law of Large Number is proven.     

Pion mass dependence of the nucleon mass in the chiral quark soliton model

The dependence of the nucleon mass on the mass of the pion is studied in the framework of the chiral quark-soliton model. A remarkable agreement is observed with lattice data from recent full dynamical simulations. The possibility and limitations to use the results from the chiral quark soliton model as a guideline for the chiral extrapolation of lattice data are discussed.     

蒙特卡罗模拟中相关变量随机数序列的产生方法

蒙特卡罗模拟有时需要对多维相关随机变量进行模拟抽样．本文介绍基于Choesky因子线性变换一非线性变换产生具有指定边缘分布和相关系数的多维相关随机变量抽样序列的一般方法,给出一种简单易行的高效数值实现途径和一些模拟结果．模拟结果表明,该方法产生的各随机变量抽样序列间具有预期要求的相关性,并能通过指定边缘分布Kolmogorov—Smimov非参数假设检验．对该方法应用中的一些限制问题进行了讨论．     

Butler groups with a single τ-adic relation

It is proved that a τ-adic relation characterizing a Butler group is piecewise rational. Translated fromMatematicheskie Zametki, Vol. 60, No. 6, pp. 882–887, December, 1996.     

A strong limit theorem for generalized Cantor-like random sequences

ＡＳＴＲＯＮＧＬＩＭＩＴＴＨＥＯＲＥＭＦＯＲＧＥＮＥＲＡＬＩＺＥＤＣＡＮＴＯＲ－ＬＩＫＥ　ＲＡＮＤＯＭ　ＳＥＱＵＥＮＣＥＳＬＩＵＷＥＮ（刘文）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＰｈｙｓｉｃｓ,ＨｅｂｅｉＵｎｉｖｅｒｓｉｔｙｏｆＴｅ...     

Complete solutions of a family of quartic Thue and index form equations

Continuing the recent work of the second author, we prove that the diophantine equation

for has exactly 12 solutions except when , when it has 16 solutions. If denotes one of the zeros of , then for we also find all with .

     

Aurifeuillian factorizations and the period of the Bell numbers modulo a prime

We show that the minimum period modulo of the Bell exponential integers is for all primes and several larger . Our proof of this result requires the prime factorization of these periods. For some primes the factoring is aided by an algebraic formula called an Aurifeuillian factorization. We explain how the coefficients of the factors in these formulas may be computed.

     

近红外光谱预测汽油辛烷值和辛烷值仪的研制

本文报道了用近红外光谱预测汽油马达法辛烷值,研究法辛烷值和抗爆指数的方法。用多重线性回归和偏最小二乘法回归建立辛烷值的预测模型。基于此模型,首次研制成功光学多道近红外辛烷值仪。     

非平面图的色数算法

本文对非平面无向简单图的点着色问题进行分析研究后,提出了一个点色数算法.该算法不仅给出了非平面图求点色数的方法,同时也解决了着色方法.并且对算法所涉及的有关性质定理给出了证明.