A New Family of Cyclic Difference Sets with Singer Parameters in Characteristic Three

We construct a new family of cyclic difference sets with parameters ((3 ^d – 1)/2, (3 ^{d – 1} – 1)/2, (3 ^{d – 2} – 1)/2) for each odd d. The difference sets are constructed with certain maps that form Jacobi sums. These new difference sets are similar to Maschietti's hyperoval difference sets, of the Segre type, in characteristic two. We conclude by calculating the 3-ranks of the new difference sets.     

大焦深成像系统仿真实验研究

如何增大非相干光学成像系统的焦深是应用光学研究领域的热点问题.本文对采用高次非球面光学掩模板与图像处理相结合增大成像光学系统焦深的新方法进行了深入分析,建立了大焦深成像系统仿真实验模型,并进行了大焦深成像系统仿真实验.实验结果证明了该方法在维持原相对孔径的同时使光学系统在较大的离焦范围内有好的成像质量.实际应用中还要综合考虑模板参量、信噪比等关键因素.     

离焦散斑技术研究Kirchhoff板在动载作用期的弯曲

本文使用动态离焦散斑技术,测试板的动态弯曲获得成功。并推导了Kirchhoff板动态变形的有关分析,提出了由最大斜率确定材料常数的思想。显然,这是同离焦散斑方法所测数据直接相关的处理手法。     

Fermionic solution of the Andrews-Baxter-Forrester model. II. Proof of Melzer's polynomial identities

We compute the one-dimensional configuration sums of the ABF model using the fermionic technique introduced in part I of this paper. Combined with the results of Andrews, Baxter, and Forrester, we prove polynomial identities for finitizations of the Virasoro characters as conjectured by Melzer. In the thermodynamic limit these identities reproduce Rogers-Ramanujan-type identities for the unitary minimal Virasoro characters conjectured by the Stony Brook group. We also present a list of additional Virasoro character identities which follow from our proof of Melzer's identities and application of Bailey's lemma.Dedicated to the memory of Piet Kasteleyn.     

Real Brauer characters

In this paper, we determine the structure of finite groups with a small number of real-valued irreducible Brauer characters.     

基于RST-QFD-Bayes的新型装甲装备通用质量特性评价指标体系构建研究

针对新型装甲装备通用质量特性评价指标体系难以确定的问题,在明确评价指标体系构建原则的基础上,结合新型装甲装备特点,确定了通用质量特性初始评价指标及指标筛选要求,运用QFD将新型装甲装备通用质量特性需求映射为评价指标筛选要求,采用粗糙集理论(Rough Set Theory,RST)确定了指标筛选重要度,考虑到关联度的不确定性及多个专家估计值的平均值和估计值的波动程度,将贝叶斯理论引入关系矩阵的确定中,用区间数确定了关联度,进行了评价指标筛选,构建了新型装甲装备通用质量特性评价指标体系,为新型装甲装备通用质量特性评价奠定了基础。     

Syntheses, Crystal Structures and Magnetism of Two New Coordination Polymers [Ni（bix）2Cl2]n and [Co（bix）Cl2]n

The self-assembly reactions of MIICl2 (M = Ni, Co) with the flexible bix ligand [bix = 1,4-bis(imidazole-1-ylmethyl)benzene] yielded a 2D network [NiII(bix)2Cl2]n 1 and a 1D chain [CoII(bix)Cl2]n 2. Their crystal structures have been determined by X-ray single-crystal diffraction analysis. Complex 1 characters a two-dimensional grid-type structure and crystallizes in monoclinic, space group P21/c with a = 7.7231(7), b = 12.7787(9), c = 13.9374(13) , β = 105.419(4)o, C28H28Cl2N8Ni, Mr = 606.19, Ζ = 2, V = 1326.0(2) 3, Dc = 1.518 g/cm3, μ = 0.969 mm-1, F(000) = 628, R = 0.0429 and wR = 0.0783 for 2503 observed reflections (I > 2σ(I)). Compound 2 is a one-dimensional chain and crystallizes in orthorhombic, space group Pbca with a = 11.3696(6), b = 10.2128(6), c = 14.4943(9) , C14H14Cl2CoN4, Mr = 368.12, Z = 4, V = 1683.01(17) 3, Dc = 1.453 g/cm3, μ = 1.334 mm-1, F(000) = 748, R = 0.0317 and wR = 0.0800 for 1778 observed reflections (I > 2σ(I)). Magnetic properties of the title complexes were also investigated.     

Schur indices of perfect groups

It has been noticed by many authors that the Schur indices of the irreducible characters of many quasi-simple finite groups are at most . A conjecture has emerged that the Schur indices of all irreducible characters of all quasi-simple finite groups are at most . We prove that this conjecture cannot be extended to the set of all finite perfect groups. Indeed, we prove that, given any positive integer , there exist irreducible characters of finite perfect groups of chief length which have Schur index .

     

<Emphasis Type="Italic">p</Emphasis>-Nuclearity in a New Perspective

In this Letter we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists’ sense vanishes for any p> 1. Our discussion of these issues suggests a new perspective, in terms of ε-entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.Mathematics Subject Classification (2000): 81T05, 47B10, 47L25.