Maximal σ‐polynomials of connected 3‐chromatic graphs

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if c_i(G) ≤ c_i(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where c_i(G) denotes the number of i‐color partitions of G. In this paper the first ? n/2 ? levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003     

A Turán type inequality for rational functions with prescribed poles

Summary By employing a novel idea and simple techniques, we substantially generalize the Turán type inequality for rational functions with real zeros and prescribed poles established by Min [5] to include L^pspaces for 1≤p≤∞<span style='font-size:10.0pt'>while loosing the restriction ρ > 2 at the same time.     

SINGLE MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES AND COMPRESSION COSTS （PART I：EQUAL TIMES AND COSTS）

Most papers in scheduling research have treated individual job processing times as fixed parameters. However, in many practical situations, a manager may control processing time by realloeating resources. In this paper, authors consider a machine scheduling problemwith controllable processing times. In the first part of this paper, a special case where the pro-cessing times and compression costs are uniform among jobs is discussed. Theoretical results are derived that aid in developing an O（n^2) algorithm to slove the problem optimally. In the second part of this paper, authors generalize the discussion to general case, An effective heuristic to the genera/ problem will be presented.     

Estimates for the Rapid Decay of Concentration Functions of n-Fold Convolutions

We estimate the concentration functions of n-fold convolutions of one-dimensional probability measures. The Kolmogorov–Rogozin inequality implies that for nondegenerate distributions these functions decrease at least as O(n ^–1/2). On the other hand, Esseen⁽³⁾ has shown that this rate is o(n ^–1/2) iff the distribution has an infinite second moment. This statement was sharpened by Morozova.⁽⁹⁾ Theorem 1 of this paper provides an improvement of Morozova's result. Moreover, we present more general estimates which imply the rates o(n ^–1/2).     

A DIRECT METHOD FOR THE UNIT CIRCLE PROBLEM

The unit circle problem is the problem of finding the number of eigenvalues of a non-Hermitian matrix inside and outside the unit circle . To reduce the cost of computing eigenvalues for the problem, a direct method, which is analogous to that given in [5], is proposed in this paper.     

Rational approximation in the complex plane using a τ-method and computer algebra

Numerous versions of the Lanczos τ-methods have been extensively used to produce polynomial approximations for functions verifying a linear differential equation with polynomial coefficients. In the case of an initial-value problem, an adapted τ-method based on Chebyshev series and the use of symbolic computation lead to a rational approximation of the solution on a region of the complex plane. Numerical examples show that the simplicity of the method does not prevent a high accuracy of results. This revised version was published online in June 2006 with corrections to the Cover Date.     

γ辐射引发淀粉目由基衰减的动力学研究

用ESR方法研究了红薯淀粉在γ射线预辐照下,产生的淀粉自由基特性及其室温下的自由基衰减动力学反应。结果表明在室温条件下,淀粉自由基的相对浓度随辐射剂量的增大而增加。自由基相对浓度的室温衰减用二级反应动力学处理,求得了衰减速率常数和淀粉自由基反应的半衰期。     

Contributions of Spin–Lattice Relaxation to the Echo Decay of Planar Cu in High-Temperature Superconductors

Measurement ofT_2G, the Gaussian component of the spin-echo envelope of planar Cu nuclei in high-temperature superconductors, gives important information about the real part of the Cu electron spin susceptibility. In the traditional picture of the planar Cu echo decay, the internuclear coupling is assumed to remain static with respect to spin–lattice relaxation and mutual exchange fluctuations. In some circumstances, however, this assumption breaks down. We calculate the internuclear corrections arising from spin–lattice relaxation to the conventional theory ofT_2Gand show thatT_2Gcan be easily corrected for these effects. We argue that mutual exchanges due to the perpendicular indirect couplings are suppressed in these materials. For YBa₂Cu₄O₈, we find a correction on the order of 10% inT_2Gand using the corrected values we find that the isotope ratio⁶³T_2G/⁶⁵T_2Gagrees with theory.     

随机参数Duffing系统中的随机混沌及其延迟反馈控制

研究了谐和激励下含有界随机参数Duffing系统(简称随机Duffing系统)中的随机混沌及其延迟反馈控制问题.借助Gegenbauer多项式逼近理论，将随机Duffing系统转化为与其等效的确定性非线性系统.这样，随机Duffing系统在谐和激励下的混沌响应及其控制问题就可借等效的确定性非线性系统来研究.分析阐明了随机混沌的主要特点，并采用Wolf算法计算等效确定性非线性系统的最大Lyapunov指数，以判别随机Duffing系统的动力学行为.数值计算表明，恰当选取不同的反馈强度和延迟时间，可分别达到抑制或诱发系统混沌的目的，说明延迟反馈技术对随机混沌控制也是十分有效的. 关键词： 随机Duffing系统 延迟反馈控制 随机混沌 Gegenbauer多项式