NUMERICAL ANALYSIS OF QUASICONFORMAL MAPPINGS BY CIRCLE PACKINGS

Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformai mappings in the plane is discussed.     

约束装箱问题的混合遗传算法求解

本将最佳适应法和遗传算法相结合，提出了一种新的启发式混合遗传算法对具有时间约束的装箱问题进行求解，给出了具体的算法步骤，试算结果表明基于启发式算法的混合遗传算法适合于求解各种约束条件下的大规模装箱问题。     

R￣d中Hausdorff维数和packing维数的确定

本文目的在于建立确定Ｒ￣ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ和ｐａｃｋｉｎｇ维数Ｄｉｍ的两个命题（定理１和定理２），进而寻求Ｒ￣ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ与ｐａｃｋｉｎｇ维数Ｄｉｍ相等的条件；这使得我们能够引入分形测度的测度论定义。     

Predicting the onset of DNA supercoiling using a non-linear hemitropic elastic rod

Elastic rod models provide a means to interpret single molecule DNA experiments as well as predict DNA behavior under physiological conditions. Here we use an elastic rod model to predict the stability boundary (critical torque vs. applied tension) for single molecule DNA experiments in which the molecule is subjected to applied tension and twist. We discuss the shortcomings of the usual isotropic rod model. We then derive a consistent non-linear material law from the general representation for a hemitropic (chiral) rod. Finally, we present results of a standard bifurcation analysis predicting the stability boundary. We find results from the non-linear hemitropic rod to match the data closely.     

Rigid nitronyl-nitroxide-labelled anchoring molecules: syntheses, structural and magnetic investigations

The syntheses of two rigid organic molecular rods bearing a nitronyl-nitroxide radical and a terminal nitrogen-based functionality like a pyridine or a cyano group are reported. Both new paramagnetic molecules are fully characterized, including crystal structure analysis. Furthermore their magnetic behaviours in the crystalline state are investigated and their spin concentration corroborate their excellent purity. While the pyridine functionalized rod is synthesized by converting the corresponding benzaldehyde to the phenyl-nitronyl-nitroxide radical, the synthesis of the cyano functionalized rod demonstrates the accessibility of highly sophisticated spin-labelled molecules via cross-coupling reaction with a meta-iodo-phenyl-nitronyl-nitroxide moiety.     

A hybrid genetic algorithm-heuristic for a two-dimensional orthogonal packing problem

In this paper we address a two-dimensional (2D) orthogonal packing problem, where a fixed set of small rectangles has to be placed on a larger stock rectangle in such a way that the amount of trim loss is minimized. The algorithm we propose hybridizes a placement procedure with a genetic algorithm based on random keys. The approach is tested on a set of instances taken from the literature and compared with other approaches. The computation results validate the quality of the solutions and the effectiveness of the proposed algorithm.     

A 3D-BPP approach for optimising stowage plans and terminal productivity

This paper addresses the problem of determining stowage plans for containers in a ship, that is the so-called master bay plan problem (MBPP).     

Convergence of optimal stochastic bin packing

Consider independent identically distributed random variables (X_i) valued in [0,1]. Let B(n) be the optimal (minimum) number of unit size bins needed to pack n items of size X₁, X₂,…,X_n. We prove that there exists a numerical constant C such that for t > 0,

$\text{Pr(∣B(n)?E(B(n))∣>t}\text{n}\text{)≤ C exp(? t).}$

The constant C does not depend on the distribution of X.     

Crystallization of chiral compounds. 1. Spectroscopic,thermochemical, and crystallographic investigation of homochiral and racemic glycidyl p-toluenesulfonate

Crystalline specimens of homochiral and racemic glycidyl p-toluenesulfonate were studied by IR spectroscopy, differential scanning calorimetry, and X-ray diffraction analysis. The melting phase diagram of glycidyl p-toluenesulfonate was constructed. The stacking effect in the crystals of the racemic sulfonate is responsible for a more dense molecular packing, with the result that a heterochiral type of crystallization becomes more favorable.     

Copolymer of Di (methacryloyloxymethyl) naphthalene and divinylbenzene as a column packing for high-performance liquid chromatography

Summary A new porous polyaromatic ester packing was synthetized for high performance liquid chromatography. The relationship between retention and chain length of the members of homologous series of alkylbenzenes, N-alkylanilines, alkylarylethers, alkylbenzoates and alkylarylketones on this new stationary phase using different eluents was investigated. Using the alkylarylketone scale the retention indices of the homologues and test compounds were calculated. The results were compared with those obtained for poly (styrene-divinylbenzene) polymers. For both types of packing the first members of each homologous series gave non-linear behaviour. The methylene group index increments are different for the studied homologous series; thus there is no simple additivity of the retention indices. The efficiency of the porous polymeric columns is a function of the capacity factor of the solute and the organic component of the eluent.