陈玡仰
广义相对论,聚合体的统计力学,关联电子系统,随机矩阵理论和正交多项式等
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- 姓名:陈玡仰
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博士生导师
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学科领域:
应用数学
- 研究兴趣:广义相对论,聚合体的统计力学,关联电子系统,随机矩阵理论和正交多项式等
陈玡仰教授,新加坡国籍。1987年获得美国麻省大学(University of Massachusetts)博士学位。国际权威刊物Journal of Physics A: Mathematical and General的指导编委(Member of Advisory Board)。陈玡仰教授先后在卡文迪什实验室(Cavendish Laboratory)和德国卡尔斯鲁厄大学(Karlsruhe University)做博士后研究,1992年至2005年在英国帝国理工学院工作,2005年11月到南开大学工作。陈玡仰教授是国际知名的应用数学和数学物理学家,主要研究领域为广义相对论,聚合体的统计力学,关联电子系统,随机矩阵理论和正交多项式等。先后在国际一流学术刊物上发表论文50余篇。近十年陈玡仰教授的主要研究方向是随机矩阵理论以及与其有密切联系的正交多项式。他与美国著名数学家M. E. H. Ismail教授合作得到了关于正交多项式的一个重要的一般微分公式,并用来计算多项式的渐进,还得到了多项式最大和最小零点的渐进。此后的关于最大零点的渐进方面的工作都建立在这一工作的基础上。他与Ismail教授合作的文章中的一个定理被称为“Berg-Chen-Ismail定理”,美国加州理工学院著名数学家Barry Simon在他的著作Orthogonal Polynomials on the Unit Circle Part I & II中将此定理称为“漂亮的结果(beautiful result)”。
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【期刊论文】Orthogonal polynomials with discontinuous weights
陈玡仰, Yang Chen and Gunnar Pruessner
J. Phys. A: Math. Gen. 38 (2005) L191-L198,-0001,():
-1年11月30日
In this letter we present a brief description of a ladder operator formalism applied to orthogonal polynomials with discontinuous weights. The two coefficient functions, An(z) and Bn(z), appearing in the ladder operators satisfy the two fundamental compatibility conditions previously derived for smooth weights. If the weight is a product of an absolutely continuous reference weight w0 and a standard jump function, then An(z) and Bn(z) have apparent simple poles at these jumps. We exemplify the approach by takingw0 to be the Hermite weight. For this simpler case we derive, without using the compatibility conditions, a pair of difference equations satisfied by the diagonal and offdiagonal recurrence coefficients for a fixed location of the jump. We also derive a pair of Toda evolution equations for the recurrence coefficients which, when combined with the difference equations, yields a particular Painleve IV.
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【期刊论文】A Riemann-Hilbert Approach to the Akhiezer Polynomials
陈玡仰, Yang Cheny†††, Alexander R Its*
,-0001,():
-1年11月30日
In this paper, we study those polynomials, orthogonal with respect to a particular weight, over the unionin of disjoint intervals, first introduced by N.I. Akhiezer, via a reformulation as a matrix factorization or Riemann-Hilbert problem. This approach complements the method proposed in a proevious paper, that involves the construciton of a certain meromorphic function on a hyperelliptic Riemann surface. The method de scribed here is based on the general Riemann-Hilert scheme of the theory of integrable systems and will enable us to derive, in a versy strightforward way, the relevant system of Fuchsian differential equations for the polynomials and the associated system of the Schlesinger deformation equations for certain quantaties involing the corresponding recurrence coffcients. Both of these equations wre obtained earlier by A. Magnus. In our aproach, however, we are able to go beyond Magnus's results by actualy solving the equatins in terms of the Riemann Θ-funcitons. We also show that the related Hankel determinant can be nterpreted as the relevantτ-function.
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【期刊论文】Toeplitz determinants from compatibility conditions
陈玡仰, Estelle L. Basor∗, Yang Chen
,-0001,():
-1年11月30日
In this paper we show, how a straightforward and natural application of a pair of fundamental identities valid for polynomials orthogonal over the unit circle, can be used to calculate the determinant of the finite Toeplitz matrix, △n=det(wj−k)n−1 j,k=0:=det(∫|z|=1 w(z) zj−k+1 dz 2πi n−1 j,k=0, with the Fisher-Hartwig symbol, w(z)=C(1− z) +iβ(1− 1/z)−iβ, |z|=1, α> −1/2, ∈ R. Here C is the normalisation constant chosen so that w0=12π. We use the same approach to compute a difference equation for expressions related to the determinants of the symbol w(z)=et (z+1/z), a symbol important in the study of random permutations. Finally, we study the analogous equations for the symbol w(z)=etz MПα=1 (z-aα/z), gα.
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【期刊论文】Generalizations of Chebyshev polynomials and Polynomial
陈玡仰, Yang Chen†, James Griffin†† and Mourad E H Ismail†††
,-0001,():
-1年11月30日
In this paper we show how polynomial mappings of degree K from a union of disjoint intervals onto [−1, 1] generate a countable number of special cases of generalizations of Chebyshev polynomials. We also derive a new expression for these generalized Chebyshev polynomials for any genus g, from which the coefficients of xn can be found explicitly in terms of the branch points and the recurrence coefficients. We find that this representation is useful for specializing to polynomial mapping cases for small K where we will have explicit expressions for the recurrence coefficients in terms of the branch points. We study in detail certain special cases of the polynomials for small degree mappings and prove a theorem concerning the location of the zeroes of the polynomials. We also derive an explicit expression for the discriminant for the genus 1 case of our Chebyshev polynomials that is valid for any configuration of the branch point.
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【期刊论文】Smallest eigenvalues of Hankel matrices for exponential weights
陈玡仰, Y. Chen a and D.S. Lubinsky b, *
J. Math. Anal. Appl. 293 (2004) 476-495,-0001,():
-1年11月30日
We obtain the rate of decay of the smallest eigenvalue of the Hankel matrices (∫tj+kW2(t) dt)n j,k=0 for a general class of even exponential weights W2=exp(−2Q) on an interval I. More precise asymptotics for more special weights have been obtained by many authors.
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陈玡仰, J Luo and P Huang
Journal of the Operational Research Society (2002) 53, 1150-115,-0001,():
-1年11月30日
EOQ under date-terms supplier credit: a comment on a paper by Carlson and Rousseau.
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【期刊论文】A NOTE ON "lNVENTORY MODELS WITH COST CHANGES"
陈玡仰, JIANWEN LUO and PEIQING HUANG
,-0001,():
-1年11月30日
This note is concerned with the inventory models with finite horizn and cost changes. We presented more specific on the optimal inventory policy than those in previous papers and showed that some of the resuts in Lev and Weiss' (1990) paper are not necessarily optimal.
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陈玡仰, Luo Jianwen, Lu Shijie
高校应用数学学报A辑2001, 16(1):119~124,-0001,():
-1年11月30日
本文对概率约束规划问题的稳定性进秆了探讨得出了当随机向量序列{(k)分布收敛于(w)时,相应于(k)(w)的概率约束规划问题的最优值收敛于原问题的最优值,这个结果为设计逼近算法和改进逼近解提供了一个理论基础。
概率约束规划, 最优值函教, 分布收敛性
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陈玡仰, LUO Jian-wen
中国管理科学,2004,12,482~487,-0001,():
-1年11月30日
对供应链库存进行有效控制是提高核心企业乃至整个供应链绩效的一条主要途径,也是在与其他供应链竞争中赢得优势的重要保证。本文研究了在供应商提供定时信用支付条件下的库存作控制模型。并由启发式逼近算法得到了最优订购策略,这突破了以往始终用数量折扣作为激励机制来研究供应链成员企业间合作的研究框架,为进一步研究供应链的整合问题提供了新的思路。
供应链, 库存控制, 信用, 协调
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陈玡仰, LUO Jian-wen, HUANG Pei-qing
中国管理科学,2001,9(3):20~29,-0001,():
-1年11月30日
本文研究了定期信用支付条件下的多阶段货价变动型存贮问题,得到了最优订购策略并设计了算法以说明模型的使用。
定期信用支付, 机台投资收益, 多阶段库存模型
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