试解读数学史上的李约瑟之谜

《周易》使中国古代数学取得杰出成就，同时又阻碍了中国近代数学的发展。这种阻碍作用主要来源于“天人合一”的哲学观；自然与政治同归；固步自封的保守性；经世致用的功利思想和述而不作的研究方法。     

Strong edge colorings of uniform graphs

For a graph G=(V(G),E(G)), a strong edge coloring of G is an edge coloring in which every color class is an induced matching. The strong chromatic index of G, χ_s(G), is the smallest number of colors in a strong edge coloring of G. The strong chromatic index of the random graph G(n,p) was considered in Discrete Math. 281 (2004) 129, Austral. J. Combin. 10 (1994) 97, Austral. J. Combin. 18 (1998) 219 and Combin. Probab. Comput. 11 (1) (2002) 103. In this paper, we consider χ_s(G) for a related class of graphs G known as uniform or ε-regular graphs. In particular, we prove that for 0<ε?d<1, all (d,ε)-regular bipartite graphs G=(U∪V,E) with |U|=|V|?n₀(d,ε) satisfy χ_s(G)?ζ(ε)Δ(G)², where ζ(ε)→0 as ε→0 (this order of magnitude is easily seen to be best possible). Our main tool in proving this statement is a powerful packing result of Pippenger and Spencer (Combin. Theory Ser. A 51(1) (1989) 24).     

一阶导数条件下带参数的修正型Euler-Halley迭代族的收敛性

本文研究了Banach空间中非线性算子方程的带参数的修正型Euler-Halley迭代族的收敛性问题.在算子的一阶导数满足Lipschitz条件下建立了修正型Euler-Halley迭代族的半局部二阶收敛性.     

利用V型三能级原子与相干态光场Raman相互作用传送未知奇偶相干态

描述了简并V型三能级原子与单模相干态光场的Raman相互作用，获得了处于激发态单态的原子与相干态光场相互作用的结果。利用探测原子与光场的相互作用将原子和探测光场制备成最大纠缠态，并将原子注入待测任一奇偶相干叠加态，通过原子与待测腔模构成的Bell基矢演化，对原子进行选择性探测，获得奇偶相干叠加态与原子相互作用后可能的量子状态，然后对待测腔场与原子进行联合探测，接着对所测奇偶相干态腔场的量子状态实施么正变换，就将探测腔场制备到待测腔场的初始量子态上，从而实现未知奇偶相干态的隐形传送。     

Unified approach to some geometric results in variational analysis

Based on a study of a minimization problem, we present the following results applicable to possibly nonconvex sets in a Banach space: an approximate projection result, an extended extremal principle, a nonconvex separation theorem, a generalized Bishop-Phelps theorem and a separable point result. The classical result of Dieudonné (on separation of two convex sets in a finite-dimensional space) is also extended to a nonconvex setting.     

Evidential reasoning based preference programming for multiple attribute decision analysis under uncertainty

Multiple attribute decision analysis (MADA) problems having both quantitative and qualitative attributes under uncertainty can be modelled and analysed using the evidential reasoning (ER) approach. Several types of uncertainty such as ignorance and fuzziness can be consistently modelled in the ER framework. In this paper, both interval weight assignments and interval belief degrees are considered, which could be incurred in many decision situations such as group decision making. Based on the existing ER algorithm, several pairs of preference programming models are constructed to support global sensitivity analysis based on the interval values and to generate the upper and lower bounds of the combined belief degrees for distributed assessment and also the expected values for ranking of alternatives. A post-optimisation procedure is developed to identify non-dominated solutions, examine the robustness of the partial ranking orders generated, and provide guidance for the elicitation of additional information for generating more desirable assessment results. A car evaluation problem is examined to show the implementation process of the proposed approach.     

具有热储备可修复平行系统本征值问题

针对具有热储备可修复平行系统模型,得出了一个本征值对应一个本征元的结论并证了除0本征值外还存在另外非零实本征值.     

Harnack's inequality for a nonlinear eigenvalue problem on metric spaces

We prove Harnack's inequality for first eigenfunctions of the p-Laplacian in metric measure spaces. The proof is based on the famous Moser iteration method, which has the advantage that it only requires a weak (1,p)-Poincaré inequality. As a by-product we obtain the continuity and the fact that first eigenfunctions do not change signs in bounded domains.     

A Sturm–Liouville problem depending rationally on the eigenvalue parameter

We consider the Sturm–Liouville problem (1.1) and (1.2) with a potential depending rationally on the eigenvalue parameter. With these equations a λ ‐linear eigenvalue problem is associated in such a way that L₂‐solutions of (1.1), (1.2) correspond to eigenvectors of a linear operator. If the functions q and u are real and satisfy some additional conditions, the corresponding linear operator is a definitizable self‐adjoint operator in some Krein space. Moreover we consider the problem (1.1) and (1.3) on the positive half‐axis. Here we use results on the absense of positive eigenvalues for Sturm–Liouville operators to exclude critical points of the associated definitizable operator. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the first passage times of reflected O-U processes with two-sided barriers

In this article, we give the Laplace transform of the first passage times of reflected Ornstein-Uhlenbeck process with two-sided barriers. AMS Subject Classifications 60H10 · 60G40 · 90B05 Supported by NSF of China.