Zeros of the Jones Polynomial for Torus Knots and 2-bridge Knots

We study zeros of the Jones polynomial and their distributions for torus knots and 2-bridge knots. We prove that e(2m+1)πi/2and e(2m+1)πi/4(m is a positive integer)can not be the zeros of Jones polynomial for torus knots T p,q by the knowledge of the trigonometric function. We elicit the normal form of Jones polynomials of the 2-bridge knot C(-2, 2, · · ·,(-1)r2) by the recursive form and discuss the distribution of their zeros.     

Conductors and newforms for U(1,1)

Let F be a non-Archimedean local field whose residue characteristic is odd. In this paper we develop a theory of newforms forU (1, 1)(F), building on previous work onSL ₂(F). This theory is analogous to the results of Casselman forGL ₂(F) and Jacquet, Piatetski-Shapiro, and Shalika forGL _n(F). To a representation π ofU(1, 1)(F), we attach an integer c(π) called the conductor of π, which depends only on theL-packet π containing π. A newform is a vector in π which is essentially fixed by a congruence subgroup of level c(π). We show that our newforms are always test vectors for some standard Whittaker functionals, and, in doing so, we give various explicit formulae for newforms.     

Knots with the Lens Space Surgery

In this paper we construct an infinite family of hyperbolic (1, 1)–knots with two parameters, and show that some of them admit exceptional Dehn surgery such as lens space surgery, Seifert surgery, and toroidal surgery. Furthermore, we give simple examples of hyperbolic (1, 1)–knots which admit two toroidal surgeries at distance four such that both toroidal surgeries do not create Klein bottles.     

Invariant measures for general(ized) induced transformations

We show that the general(ized) induced transformation derived from an ergodic measure preserving transformation by means of an inducing time has an invariant measure canonically related to that of the original system iff a suitable induced version of is integrable. Moreover, we prove an Abramov-type entropy formula.

     

关于“GM(1,1)模型的适用范围”一文的一个注记

本文扩展了刘思峰和邓聚龙的一个命题的适用范围 ,最后给出了一个相应新命题     

Q过程的不变分布(I)

设E为一可数集,Q=（qij;i,j∈E）为E×E上的矩阵,满足qij≥0（i≠j）,     

Unknotting number and number of Reidemeister moves needed for unlinking

Using unknotting number, we introduce a link diagram invariant of type given in Hass and Nowik (2008) [4], which changes at most by 2 under a Reidemeister move. We show that a certain infinite sequence of diagrams of the trivial two-component link need quadratic number of Reidemeister moves for being splitted with respect to the number of crossings.     

U(1) Invariant Membranes and Singularities

A formulation of U(1)-symmetric classical membrane motions (preserving one rotational symmetry) is given, and reductions to systems of ODE’s, as well as some ideas concerning singularities and integrability. Submitted: June 27, 2008., Accepted: July 14, 2008.     

优化白化方程的GM(1,1)模型

通过对GM(1,1)模型的原始形式的分析,得到与之等价的差分方程,然后把差分方程连续化得到微分方程,并定义为GM(1,1)模型的白化方程,最后通过实例验证了新模型的有效性.     

Nonlinear evolution equations with (1,1)-supersymmetric time

A generalization of the Cauchy-Kowalewsky theorem is obtained for nonlinear evolution equations with (1,1)-supersymmetric time. This theorem ensures the existence and uniqueness of a solution for a large class of superanalytic functions. A generalization of Cartan's technique to the supersymmetric case is also obtained, and by means of it the problem of integrating a system of partial differential equations is transformed into the problem of finding a sequence of integral supermanifolds of lower dimension by means of a succession of integrations based on the Cauchy-Kowalewsky theorem. Evolution equations with (1, 1) time are important for applications to supersymmetric quantum mechanics and field theory, namely, square roots of the Schrödinger and heat-conduction equations. We consider nonlinear generalizations of such equations.Moscow Institute of Electronic Technology; University of Genoa. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 2, pp. 238–246, November, 1993.     

变参数非等间距GM(1,1)模型及应用

在对非等间距序列建模时,考虑到序列本身的特点,结合GM(1,1)模型的建模过程,提出了一种对非等间距序列建立变参数GM(1,1)模型的方法,并将其应用于具体实例进行分析,计算结果表明本文提出的方法具有较高的精度,从而为解决非等间距序列的拟合及预测问题提供了一种比较好的思路.     

Poincaré Series of the Weyl Groups of the Elliptic Root Systems A 1 (1,1), A 1 (1,1)* and A 2 (1,1)

We calculate the Poincaré series of the elliptic Weyl group W(A ₂ ^(1,1)), which is the Weyl group of the elliptic root system of type A ₂ ^(1,1). The generators and relations of W(A ₂ ^(1,1)) have been already given by K. Saito and the author.     

GM(1,1)模型灰色作用量的优化

通过把GM(1,1)模型中的灰色作用量b改进为动态的b_1+b_2k,从而构建了对灰色作用量优化的GM(1,1)模型.通过实例的验证以及与GM(1,1)模型对比,发现优化的GM(1,1)模型的模拟精度和预测精度均较高.     

一类GM(1,1)模型白化方程的优化

利用灰色模型的指数特性,对一类灰作用量优化的GM(1,1)模型,通过积分构建合适的背景值,并把白化方程中灰作用量b_1+b_2t改进为(b_1+0.5b_2)+b_2t,同时采用灰色系统理论的新信息原理,进而得到优化的GM(1,1)灰色模型.实例计算表明改进模型具有良好的模拟预测精度,特别对于指数序列模拟和预测精度几乎达到100%,对指数序列来讲是一种比较优秀的拟合和预测模型.     

Knots and the Bracket Calculus

In this paper, we introduce a way of encoding links (long links). This ways leads to a combinatorial representation of links by words in a given finite alphabet. We prove that the link semigroup is isomorphic to some algebraically defined semigroup with a simple system of relations. Thus, knot theory is represented as a bracket calculus: the link recognition problem is reduced to a recognition problem in this semigroup.     

Locally (-1,1) Rings

If M is a finitely-generated module over a commutative noetherian ring, then it is well-known that the ideal-theoretic assassin and the ideal-theoretic support of M satisfy the following two conditions: (CD supp(M) and ass(M) have the same minimal elements ; (C2) supp(M) has only finitely-many minimal elements. The purpose of this note is to consider a sufficient condition on a noncommutative ring, generalizing the commutative case, for analogous results to hold for the torsion-theoretic assassin and the torsion-theore-tic support of suitable left R-modules M. Since the order in the lattice of torsion theories over the category R-mod of left R-modules is the reverse of the order in the lattice of left ideals of R, we would expect to substitute “maximal” for “minimal” in the above conditions. Also, noetherianness should be replaced by its torsion-theoretic counterpart, semi-noetherianness.     

GM(1,1)模型适用域讨论及模型的改进

在已有灰色系统理论的基础上,讨论了GM(1,1)模型的适用域,明确界定了GM(1,1)模型的有效区域和禁区,并提出了GM(1,1)模型的一种改进形式——离散灰色预测DGM(1,1)模型.通过对我国经济增长的实证分析说明了该模型的有效性和可靠性.研究结果表明,提出的DGM(1,1)模型可作为灰色预测的一种精确模型,因此,为我国经济增长预测提供了一种新的方法,对当前我国经济的理性增长具有重要的指导意义.     

带遗忘因子的递推GM(1,1)预测模型

针对有新信息逐步引入的灰色预测模型,为区分新旧数据对模型的贡献度,提出一种带遗忘因子的递推灰色预测模型.通过在目标函数中增加遗忘因子,实现新旧建模数据的动态加权,达到逐步遗忘旧信息的目的.给出了灰色预测模型参数的递推估计算法,将新获信息实时加入,以提升模型预测精度.网络流量的递推GM(1,1)预测模型建立及数值仿真,验证了改进算法的有效性.