Construction of relative difference sets and Hadamard groups

‘There exist normal \((2m,2,2m,m)\) relative difference sets and thus Hadamard groups of order \(4m\) for all \(m\) of the form $$\begin{aligned} m= x2^{a+t+u+w+\delta -\epsilon +1}6^b 9^c 10^d 22^e 26^f \prod _{i=1}^s p_i^{4a_i} \prod _{i=1}^t q_i^2 \prod _{i=1}^u \left( (r_i+1)/2)r_i^{v_i}\right) \prod _{i=1}^w s_i \end{aligned}$$ under the following conditions: \(a,b,c,d,e,f,s,t,u,w\) are nonnegative integers, \(a_1,\ldots ,a_r\) and \(v_1,\ldots ,v_u\) are positive integers, \(p_1,\ldots ,p_s\) are odd primes, \(q_1,\ldots ,q_t\) and \(r_1,\ldots ,r_u\) are prime powers with \(q_i\equiv 1\ (\mathrm{mod}\ 4)\) and \(r_i\equiv 1\ (\mathrm{mod}\ 4)\) for all \(i, s_1,\ldots ,s_w\) are integers with \(1\le s_i \le 33\) or \(s_i\in \{39,43\}\) for all \(i, x\) is a positive integer such that \(2x-1\) or \(4x-1\) is a prime power. Moreover, \(\delta =1\) if \(x>1\) and \(c+s>0, \delta =0\) otherwise, \(\epsilon =1\) if \(x=1, c+s=0\) , and \(t+u+w>0, \epsilon =0\) otherwise. We also obtain some necessary conditions for the existence of \((2m,2,2m,m)\) relative difference sets in partial semidirect products of \(\mathbb{Z }_4\) with abelian groups, and provide a table cases for which \(m\le 100\) and the existence of such relative difference sets is open.     

二次Lagrangian有限元方程的几何多重网格法

为了构造快速求解二次Lagrangian有限元方程的几何多重网格法,在选择二次Lagrangian有限元空间和一系列线性Lagrangian有限元空间分别作为最细网格层和其余粗网格层以及构造一种新限制算子的基础上,提出了一种新的几何多重网格法,并对它的计算量进行了估计.数值实验结果,与通常的几何多重网格法和AMG01法相比,表明了新算法计算量少且稳健性强.     

可口革囊星虫三种同工酶表达初步分析

应用聚丙烯酰胺凝胶电泳法，对可口革囊星虫的收吻肌、吻、肠、肾管和体壁5种组织或器官进行了同工酶分析．共分析了酯酶、过氧化物酶和超氧化物歧化酶等三种同工酶．结果表明：酯酶具有显著的组织特异性，其余两种酶相对不明显；可口革囊星虫的肠除了行使消化功能外，还和吻、肾管一起在清除自由基方面起着重要作用；提出将EST分析作为星虫动物门的一个分类学依据。     

铜合金中金相组织特征参数的测量

：根据体视学和定量金相分析的基本原理，利用Image—Pro Plus(IPP)图像分析软件测定了铜合金金相组织的相体积分数、晶粒度大小、粒子间距等特征参数，并提出了一种测量粒子间距的近似算法。     

次可分解算子的不变子空间格的丰富性

证明了一类次可分解算子的不变子空间格是丰富的,并举例说明存在Hilbert空间上的有界线性算子T,它有无穷多个不变子空间,但是它的不变子空间格Lat(T)不丰富．     

Two New Meroterpenes from the Mangrove Endophytic Fungus Aspergillus sp. 085241B

Two new meroterpenes, ‘acetoxydehydroaustin B’ ( 1 ) and ‘1,2‐dihydro‐acetoxydehydroaustin B’ ( 2 ) were isolated in the form of a mixed crystal from the mangrove endophytic fungus Aspergillus sp. 085241B. Their structures and absolute configurations were determined by extensive analysis of their spectra and X‐ray diffraction data. In a preliminary bioassay, the mixed crystal did not exhibit activities against cancer cell lines of MDA‐MB‐435, SKBR3, HepG2, HEP3B, PC‐3, and A549, as well as against α‐glucosidase and tyrosinase.     

ZnO nanorod arrays: Dependence of morphology upon ammonia

Well-aligned ZnO nanorod arrays were prepared on FTO substrate by hydrothermal method at low temperature for 5 h. The effect of ammonia on the length of ZnO nanorod was studied in detail. The resulting materials were extensively characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD) and UV-visible absorption spectra (scatter mode). With the increase of ammonia, the length of ZnO nanorod increases.     

Design and Synthesis of Chiral Molecular Tweezers Based on Deoxycholic Acid

Molecular tweezers is a novel type of artificial receptors, which not only offer the advantage of efficient construction but also their surfaces can be tailored for specific applications. The clefts of molecular tweezers are particularly effective in regard to complementarity with substrates since functional groups attached to the interior of the cleft converge on substrates held inside1. So, in recent years, the molecular tweezers receptors have attracted more and more attention in molecular …