Symbolic Computation of Newton Sum Rules for the Zeros of Polynomial Eigenfunctions of Linear Differential Operators

A symbolic algorithm based on the generalized Lucas polynomials of first kind is used in order to compute the Newton sum rules for the zeros of polynomial eigenfunctions of linear differential operators with polynomial coefficients.     

Quantum Monodromy and Bohr–Sommerfeld Rules

This article is based on a talk given in Dijon for the 2000 summer school Topological and Geometrical Methods: Applications to Dynamical Systems. The standard definitions of the monodromy invariant for completely integrable classical systems are reviewed, and the link to the quantum monodromy observed in the joint spectrum of commuting operators is explained. The mathematical treatment relies on a modern and attractive version of the Bohr–Sommerfeld quantisation rules.     

Local Rules and Fitness Landscapes: A Catastrophe Model

This paper examines the imposition of local rules in five mail delivery centres of Australia Post. Local rules are patterns of behaviour used by subunits of an organization to optimise their payoff. These local rules may ultimately benefit the total organization. Fitness landscapes are used to examine the emergence of local rules in this workplace. This research examined the relationship between the time taken to sort the mail and the volume of this mail. Work rates show a clear catastrophe shift; that is, work rates suddenly drop when the volume of mail exceeds a certain level, as Postal Delivery Officers apply local rules to maximise gains inherent in the pay structures. Such behaviour is close to that predicted by Kauffman (1995) in computer simulations of lattices and may be indicative of the application of local rules in organizations. The implications of the use of local rules are that behaviour in social systems may be dictated by systemic and emergent processes which are outside immediate management control. A further implication is that organizations may be structured to a significant extent by such local rules.     

The Ghirlanda-Guerra Identities

If the variance of a Gaussian spin-glass Hamiltonian grows like the volume the model fulfills the Ghirlanda-Guerra identities in terms of the normalized Hamiltonian covariance.     

应用具有手征流关联函数的光锥求和规则计算B(Bc)→Dlν过程的形状因子

在QCD光锥求和规则(LCSR)框架内应用具有手征流关联函数计算B(B_c)→Dlν衰变过程的弱形状因子. 所获得的形状因子的表达式仅依赖于D介子的主导级分布振幅(DA). 应用了三类D介子的分布振幅计算了形状因子F_B→D(0)和F_Bc→D(0). 在速度迁移1.142=0附近算符乘积展开(OPE)得以有效的情况下所计算的形状因子行为在误差范围内与B(B_c)→Dlν过程实验数据相一致. 在大反冲区域1.35B→D(0)是与微扰QCD(pQCD)结果相一致的. 所以本文的计算在联接格点QCD, 重夸克对称性和pQCD之间起桥梁作用，有助于进一步对B(B_c)→Dlν跃迁过程的理解. 计算 使用了在端点具有指数压低的分布振幅行为, 对F_Bc→D(0)的预言与其他方法获得的结果是可比的, 有利于具有库仑修正的三点求和规则(3PSR)方法所得的结果.     

The <Emphasis Type="Italic">q</Emphasis>-Analogues of Squeezed States and Some Properties

In this paper we shall introduce two q-analogues of the squeezed states in terms of the technique of integration within an ordered product of operators and the properties of the inverses of q-deformed annihilation and creation operators, and some nonclassical properties of the states are examined. Furthermore, we obtain some new completeness relations composed of the bra and ket which are not mutually Hermitian conjugate. PACS numbers: 03.65.-w; 45.50.Ct. Work supported by the National Natural Science Foundation of China under Grant 10574060 and the Natural Science Foundation of Shandong Province of China under Grant Y2004A09.     

Modified Gauss rules for approximate calculation of some strongly singular integrals

The approach we follow consists in transforming the numerical evaluation of hyper-singular integrals into the calculation of a nearly singular integral whose mass is distributed according to a positive parameter ε. To evaluate the latter we apply a Gauss quadrature formula associated with a nearly singular weight function. It is estimated the error in terms of ε. Some numerical results are presented.     

World-line approach to the Bern-Kosower formalism in two-loop Yang-Mills theory

Based on the world-line formalism with a sewing method, we derive the Yang-Mills effective action in a form useful to generate the Bern-Kosower-type master formulae for gluon scattering amplitudes at the two-loop level. It is shown that four-gluon (φ⁴ type sewing) contributions can be encapsulated in the action with three-gluon (φ³ type) vertices only, the total action thus becoming a simple expression. We then derive a general formula for a two-loop Euler-Heisenberg type action in a pseudo-abelian su(2) also studied.     

On the convergence of Filon quadrature

We analyze the convergence behavior of Filon-type quadrature rules by making explicit the dependence on both k, the parameter that controls the oscillatory behavior of the integrand, and n, the number of function evaluations. We provide explicit conditions on the domain of analyticity of the integrand to ensure convergence for n→∞.