On Schreier graphs of gyrogroup actions

The notion of a group action can be extended to the case of gyrogroups. In this article, we examine a digraph and graph associated with a gyrogroup action on a finite nonempty set, called a Schreier digraph and graph. We show that algebraic properties of gyrogroups and gyrogroup actions such as being gyrocommutative, being transitive, and being fixed-point-free are reflected in their Schreier digraphs and graphs. We also prove graph-theoretic versions of the three fundamental theorems involving actions: the Cauchy–Frobenius lemma (also known as the Burnside lemma), the orbit-stabilizer theorem, and the orbit decomposition theorem. Finally, we make a connection between gyrogroup actions and actions of symmetric groups by evaluation via Schreier digraphs and graphs.     

GO-MOCE: Greedy Order Method of Conditional Expectations for Max Sat

In this paper we present and study a new algorithm for the Maximum Satisfiability (Max Sat) problem. The algorithm is based on the Method of Conditional Expectations (MOCE, also known as Johnson’s Algorithm) and applies a greedy variable ordering to MOCE. Thus, we name it Greedy Order MOCE (GO-MOCE). We also suggest a combination of GO-MOCE with CCLS, a state-of-the-art solver. We refer to this combined solver as GO-MOCE-CCLS.We conduct a comprehensive comparative evaluation of GO-MOCE versus MOCE on random instances and on public competition benchmark instances. We show that GO-MOCE reduces the number of unsatisfied clauses by tens of percents, while keeping the runtime almost the same. The worst case time complexity of GO-MOCE is linear. We also show that GO-MOCE-CCLS improves on CCLS consistently by up to about 80%.We study the asymptotic performance of GO-MOCE. To this end, we introduce three measures for evaluating the asymptotic performance of algorithms for Max Sat. We point out to further possible improvements of GO-MOCE, based on an empirical study of the main quantities managed by GO-MOCE during its execution.     

偏最小二乘法在原子吸收光谱分析中的应用——钴和铟的同时测定

本文用偏最小二乘法（ＰＬＳ）校正了火焰原子吸收分析Ｉｎ２５２．１３７ｎｍ对Ｃｏ２５２．１３６ｎｍ的吸收线重叠干扰,对混合样中Ｃｏ和Ｉｎ的含量进行了测定,结果令人满意。     

On the cost of approximating all roots of a complex polynomial

This work examines the computational complexity of a homotopy algorithm in approximating all roots of a complex polynomialf. It is shown that, probabilistically, monotonic convergence to each of the roots occurs after a determined number of steps. Moreover, in all subsequent steps, each rootz is approximated by a complex numberx, where ifx ₀ =x, x _j =x _j–1 –f(x _j–1)/f(x _j–1),j = 1, 2,, then |x _j –z| < (1/|x ₀ –z|)|x _j–1–z|².     

Chemical applications of group theory and topology

The following procedure is described for investigating the qualitative dynamics of simple chemical systems: 1) A so-called influence diagram is generated representing the relationships between the reference reactants (phase-determining intermediates); 2) This influence diagram is used to generate a truth table indicating possible transitions between state vectors representing the signs of the time derivatives of of the reference reactant concentrations; 3) The truth table is used to determine a state transition diagram representing the flow topology around unstable equilibrium points; 4) The characteristic equation of the adjacency matrix of the influence diagram is solved in order to determine the presence of such unstable equilibrium points. The two types of qualitative dynamics possible for chemical systems containing two reference reactants and one feedback circuit are bifurcation between two attracting regions (bistability) and limit cycle oscillation. However, in two reference reactant systems oscillation requires an additional self-activating loop to generate the unstable equilibrium point required for its realization. Bistability and limit cycle oscillation are also two of the possible types of qualitative dynamics for chemical systems containing three reference reactants. However, chemical systems with three reference reactants and two or more feedback circuits can also contain interlocking limit cycles, which can lead to toroidal oscillations or chaos. The influence diagrams are given for the systems exhibiting these various types of dynamic behavior along with a summary of the important properties of all 729 possible influences for simple chemical systems containing three reference reactants.     

一种西佛碱侧链型液晶高分子的合成及表征

一种西佛碱侧链型液晶高分子的合成及表征邹友思，林国良，姚青青，戴李宗，潘容华（厦门大学化学系厦门３６１００５）关键词联苯，西佛碱，侧链型，液晶高分子，基团转移聚合Ｆｉｎｋｅｌｌｎａｎｎ等提出的柔性基去偶合概念’］已在侧链型液晶高分子的研究中得到了证实...     

高分子化学课程中若干论题的进展

高分子化学课程中下列五个论题被加以修正和补充:(1)1,2-二取代乙烯单体的聚合;(2)乙烯基单体聚合时的键连方式;(3)自由基聚合的自动加速;(4)引发转移和引发转移终止剂;(5)氢转移聚合和基因转移聚合。     

Comparison of side-on and end-on coordination of E2 ligands in complexes [W(CO)5E2] (E=N,P, As,Sb, Bi,Si-, Ge-, Sn-, Pb-)

Complexes of W(CO)(5) with neutral diatomic pnictogen ligands N(2), P(2), As(2), Sb(2), and Bi(2) and anionic Group 14 ligands Si(2) (2-), Ge(2) (2-), Sn(2) (2-), and Pb(2) (2-) coordinated in both side-on and end-on fashion have been optimized by using density functional theory at the BP86 level with valence sets of TZP quality. The calculated bond energies have been used to compare the preferential binding modes of each respective ligand. The results were interpreted by analyzing the nature of the interaction between the ligands and the metal fragment using an energy partitioning method. This yields quantitative information regarding the strength of covalent and electrostatic interactions between the metal and ligand, as well as the contributions by orbitals of different symmetry to the covalent bonding. Results show that all the ligands studied bind preferentially in a side-on coordination mode, with the exception of N(2), which prefers to coordinate in an end-on mode. The preference of the heavier homologues P(2)-Bi(2) for binding in a side-on mode over the end-on mode in the neutral complexes [(CO)(5)WE(2)] comes mainly from the much stronger electrostatic attraction in the former species. The energy difference between the side-on and end-on isomers of the negatively charged complexes with the ligands Si(2) (2-), Ge(2) (2-), Sn(2) (2-), and Pb(2) (2-) is much less and it cannot be ascribed to a particular bonding component.     

Group contributions to the thermodynamic properties of non-ionic organic solutes in dilute aqueous solution

The thermodynamic properties G _h ^o,H _h ^o, and C _p,h ^oassociated with the transfer of non-ionic organic compounds from gas to dilute aqueous solution and the limiting partial molar properties C _p ^o ,2 and V₂ ² of these compounds in water are described through a simple scheme of group contributions. A distinction is made between groups made only of carbon and hydrogen, and functional groups i.e. groups containing at least one atom different from carbon and hydrogen. Each group is assigned a contribution, for each property, through a least squares procedure which utilizes only molecules containing at most one functional group. Finally, for compounds containing more than one functional group, correction parameters are evaluated as the differences between the experimental values and those calculated by means of the group contributions. The different behavior of hydrophilic compared with hydrophobic groups is discussed for the various properties. A rationale for the correction parameters, i.e. for the effects of the interactions among hydrophilic groups on the thermodynamic properties, is attempted.     

Evaluation of measurement uncertainty for analytical procedures using a linear calibration function

In the EURACHEM/CITAC draft ”Quantifying uncertainty in analytical measurement” estimations of measurement uncertainty in analytical results for linear calibration are given. In this work these estimations are compared, i.e. the uncertainty deduced from repeated observations of the sample vs. the uncertainty deduced from the standard residual deviation of the regression. As a result of this study it is shown that an uncertainty estimation based on repeated observations can give more realistic values if the condition of variance homogeneity is not correctly fulfilled in the calibration range. The complete calculation of measurement uncertainty including assessment of trueness is represented by an example concerning the determination of zinc in sediment samples using ICP-atomic emission spectrometry. Received: 9 February 2002 Accepted: 17 April 2002