There Exists a Simple Non Trivial t-design with an Arbitrarily Large Automorphism Group for Every t

In 1987, Teirlinckproved that if t and are two integers such that v t(mod(t + 1)!^(2t+1) and v t + 1 >0, then there exists a t - (v, t + 1, (t + 1)!^(2t+1)) design. We prove that if there exists a (t+1)-(v,k,)design and a t-(v-1,k-2, (k-t-1)/(v-k+1))design with t 2, then there exists a t-(v+1,k, (v-t+1)(v-t)/ (v-k+1)(k-t))design. Using this recursive construction, we prove that forany pair (t,n) of integers (t 2and n 0), there exists a simple non trivial t-(v,k,) design having an automorphism groupisomorphic to ⁿ ₂.     

光信息科学与技术专业的建设

就光信息科学与技术专业建设的专业定位、课程设置、学生毕业后的去向等问题发表了个人的看法。介绍了在这方面的一些做法,提供了有关数据,可供同类专业的建设参考。     

Developmental validation of the Yfiler Platinum PCR Amplification Kit for forensic genetic caseworks and databases

Y chromosome kits are successfully applied in cases where human biological material exists. With the development of genotyping ability, more Y chromosomal markers are needed for finer identification of male individuals and lineages. In this study, a developmental validation of a newly emerged Y chromosome kit that combines two different kinds of markers: 38 Y-STRs and 3 Y-indels are conducted. The results show that this kit has high sensitivity when there is a small amount of DNA (125 pg), more than one male (minor:major = 1:7), or a mixture of males and females (male:female = 125pg:1875pg), inhibited substances (800 μM hematin and more than 1600 ng/μL humic acid). The kit exhibits high precision level with a standard deviation of allele size no more than 0.14 nt. Locus DYS481 shows the largest stutter rate, with three stutters per true allele. Population samples are well identified (MP of 0.001106), and mutations can be observed in father–son pairs (46 mutations in 70 pairs, 10 in locus DYS627). Out of all the population samples, 13.2% belong to haplogroup M117-O2a2b1a1, with their ethnic group being Han Chinese. The results show that this kit can improve the performance of identifying male individuals, obtaining more unique haplotypes (increasing from 894 to 918 of 1000 male samples) and higher discrimination capacity (increasing from 0.942 to 0.955) in this study compared to previous widely used Yfiler Plus kit. Besides, it gives information about their paternal lineages in forensic genetic casework and genealogical database construction.     

一种计算工作时间参数新方法

为了编制和优化施工进度计划,计算构成施工项目的各项工作最早开始时间、最迟开始时间、最早完成时间、最迟完成时间、总时差和自由时差等时间参数十分重要.提出了一种计算工作时间参数新方法.该方法以工作完成时间为决策变量,通过建立和求解线性规划模型来得到各种工作时间参数.其建模思路清晰,不需绘制网络图,能用通用办公软件EXCEL求解.模拟计算表明,用该方法与用标准网络计划技术计算出的工作时间参数完全一致.     

Self-Affine Sets and Graph-Directed Systems

   Abstract. A self-affine set in R ⁿ is a compact set T with A(T)= ∪ _{d∈ D} (T+d) where A is an expanding n× n matrix with integer entries and D ={d ₁ , d ₂ ,···, d _N } ⊂ Z ⁿ is an N -digit set. For the case N = | det(A)| the set T has been studied in great detail in the context of self-affine tiles. Our main interest in this paper is to consider the case N > | det(A)| , but the theorems and proofs apply to all the N . The self-affine sets arise naturally in fractal geometry and, moreover, they are the support of the scaling functions in wavelet theory. The main difficulty in studying such sets is that the pieces T+d, d∈ D, overlap and it is harder to trace the iteration. For this we construct a new graph-directed system to determine whether such a set T will have a nonvoid interior, and to use the system to calculate the dimension of T or its boundary (if T ^o ≠  ). By using this setup we also show that the Lebesgue measure of such T is a rational number, in contrast to the case where, for a self-affine tile, it is an integer.     

Automorphisms of higher‐dimensional Hadamard matrices

This article derives from first principles a definition of equivalence for higher‐dimensional Hadamard matrices and thereby a definition of the automorphism group for higher‐dimensional Hadamard matrices. Our procedure is quite general and could be applied to other kinds of designs for which there are no established definitions for equivalence or automorphism. Given a two‐dimensional Hadamard matrix H of order ν, there is a Product Construction which gives an order ν proper n‐dimensional Hadamard matrix P⁽ⁿ⁾(H). We apply our ideas to the matrices P⁽ⁿ⁾(H). We prove that there is a constant c > 1 such that any Hadamard matrix H of order ν > 2 gives rise via the Product Construction to cν inequivalent proper three‐dimensional Hadamard matrices of order ν. This corrects an erroneous assertion made in the literature that ”P⁽ⁿ⁾(H) is equivalent to “P⁽ⁿ⁾(H′) whenever H is equivalent to H′.” We also show how the automorphism group of P⁽ⁿ⁾(H) depends on the structure of the automorphism group of H. As an application of the above ideas, we determine the automorphism group of P⁽ⁿ⁾(Hk) when Hk is a Sylvester Hadamard matrix of order 2^k. For ν = 4, we exhibit three distinct families of inequivalent Product Construction matrices P⁽ⁿ⁾(H) where H is equivalent to H₂. These matrices each have large but non‐isomorphic automorphism groups. © 2008 Wiley Periodicals, Inc. J Combin Designs 16: 507–544, 2008     

Advanced basis construction in linear programming

This paper considers basis construction in a linear program when the number of activities with basic status is not equal to the number of rows in the particular scenario. This arises when starting with an ‘advanced basis’, obtained from a solution to another scenario. The goal here is to provide a triangular-seeking algorithm that takes advantage of structural properties during the construction of a basis agenda. For completeness, some facts, which are known but have not been published, are given about choosing an advanced basis and about spikes.     

《数学实验》课程建设的认识与实践

我们认为 :数学实验 ,就是对数学进行折腾 .我们提出一些饶有趣味而又有深刻背景的问题 ,让学生尝试自己去解决 ,借助于计算机 ,自己动手去折腾 ,在折腾过程中学习 ,观察现象和结果 ,猜测和验证规律 ,尝试和体验数学的探索、发现和应用     

Piezoelectricity of ordered (ScxGa1-xN) alloys from first principles

First-principles calculations are performed to compute the e₃₃ piezoelectric coefficients of GaN, ScN and (Sc_xGa_1-xN) alloys exhibiting an alternation of hexagonal GaN, with hexagonal ScN along the c-axis. For Sc compositions larger than 50%, each atom has nearly five nearest neighbors (i.e., the ground state exhibits a phase that is five-fold coordinated). On the other hand, Sc-deficient (Sc, Ga) N alloys adopt a ground-state that is four-fold coordinated). The magnitude of e₃₃ in the Sc-deficient ideally ordered (Sc_0.25Ga_0.75N) is found to be larger than the magnitude of the corresponding e₃₃ coefficients resulting from the compositional weighted average over the hexagonal (h-ScN) and the wurtzite (w-GaN) parent compounds. On the other hand, the e₃₃ coefficients of the Sc-rich ordered (Sc_0.75Ga_0.25N) is found to be negligibly small. In addition, e₃₃ piezoelectric coefficients in ordered (Sc_0.5Ga_0.5N) exhibit quite large magnitudes, due to the nonpolar to polar transition occurs at Sc composition x = 0.5, and thus can bridge the corresponding coefficients of (Ga, In) N and ferroelectric alloys. The microscopic origins for this huge enhancement in the piezoelectric behavior in Sc-low and Sc-intermediate alloys and the role of each atom are revealed and discussed.