All group‐based latin squares possess near transversals

In a latin square of order n, a near transversal is a collection of n ?1 cells which intersects each row, column, and symbol class at most once. A longstanding conjecture of Brualdi, Ryser, and Stein asserts that every latin square possesses a near transversal. We show that this conjecture is true for every latin square that is main class equivalent to the Cayley table of a finite group.     

Testing quasi-independence for truncation data

Quasi-independence is a common assumption for analyzing truncated data. To verify this condition, we propose a class of weighted log-rank type statistics that include existing tests proposed by Tsai (1990) and Martin and Betensky (2005) as special cases. To choose an appropriate weight function that may lead to a more power test, we derive a score test when the dependence structure under the alternative hypothesis is modeled via the odds ratio function proposed by Chaieb, Rivest and Abdous (2006). Asymptotic properties of the proposed tests are established based on the functional delta method which can handle more general situations than results based on rank-statistics or U-statistics. Extension of the proposed methodology under two different censoring settings is also discussed. Simulations are performed to examine finite-sample performances of the proposed method and its competitors. Two datasets are analyzed for illustrative purposes.     

Computing the full nonrigid group of tetra‐tert‐butyltetrahedrane using wreath product

The concept of symmetry group of nonrigid molecules as a permutation‐inversion group was formulated first by Longuet‐Higgins, although earlier works suggested the need for such a framework. Then Balasubramanian showed that these groups could be cast into elegant algebraic structures known as the wreath product of groups. In this study, we apply a similar method to that used by Balasubramanian to find the nonrigid group (NRG) of tetra‐tert‐butyltetrahedrane. Using the group theory package GAP, we calculate the conjugacy classes and character table of this molecule. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

C_2a~3П_■.d~3П_g 态振动能级和基态离解能的实验研究

测量了 c_2放电管中 d~3Π_(?)→a~3Π_(?)跃迁电振光谱带系.观察到了(2、0),(1、0)(0、0)和(0、1)各带的带头头和若干“尾带”,从而确定了 a~3Π_u、d~3Π_8二个态的较高振动能级.将 d~3Π_g 能级外推得到 c_2基态的离解能 D(?)=5.05eV.     

关于两个不考虑结合律的代数系统的讨论

从两个方面讨论了不考虑结合律的代数系统的结构和性质，给出了ｎ元置换的不动表的概念，证明了不动表的存在及其数目的计算方法，定义了一种新的代数系统－伪群，并进行了初步的讨论。     

Group classification of a family of second-order differential equations

We find the group of equivalence transformations for equations of the form y^″=A(x)y^′+F(y), where A and F are arbitrary functions. We then give a complete group classification of this family of equations using a direct method of analysis, together with the equivalence transformations.     

四膜虫细胞与过渡元素系

本文选用淡水纤毛虫—梨形四膜虫Sl株作实验,进一步研究过渡元素对细胞群体生长繁殖和抑制的影响。以未加元素作对照组比较时间t=37小时处各生长曲线的N/N_0值,得到细胞相对增殖率R与周期表中过渡元素浓度C的系列图。发现过渡元素对细胞生长分裂的促进浓度与他们在海水中的丰度之间,存在着相应消涨的关系,从而支持了生命起源和进化的海洋说;并从金属离子的水解形式和离子势方面,阐述第一过渡系元素在低浓度时的刺激促进作用与周期表中原子序数的依存关系。     

Full Non-Rigid Group and Symmetry of Dimethyltrichlorophosphorus

In this work, a simple method is described, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of NH3 groups attached to a rigid framework. The full non-rigid group (f-NRG) of dimethyltrichlorophosphorus with the symmetry group D3h was studied. It has been proven that it is a group of order 216 with 27 conjugacy classes and its character table computed. Finally, the Permutation-lnversion group of this molecule was calculated.     

Direct subduction of Q-conjugacy representations to give characteristic monomials for combinatorial enumeration

Characteristic monomials for a finite group are obtained by direct subductions of Q-conjugate representations. They are shown to give a generating function that is capable of solving enumeration problems. Received: 1 May 1998 / Accepted: 16 July 1998 / Published online: 18 September 1998     

A simple method to stably float a coupled system of optics tables

We demonstrate that one may safely float a composite system of mechanically coupled heavy-duty optics tables with a stability of ±λ/10 for several months without requiring the presence of an air compressor in the building. Furthermore, we demonstrate a simple and non-disruptive method to mechanically couple two floating tables such that the two-table system has sufficient stability for most optics experiments, and describe precautions that need to be taken in order to avoid mechanical damage to the tables. We checked the stability of the coupled system by use of a Michelson interferometer that spanned across the two tables.