Formulas and numerical table for the radial part of overlap integrals with the same screening parameters of Slater-type orbitals

 The numerical properties of the radial part of overlap integrals with the same screening parameters in the form of polynomials in p = ξR over Slater-type orbitals have been studied and obtained by using three different methods. For that purpose, the characteristics of auxiliary functions were used first, then Fourier transform convolution theorem, and recurrence relations for the basic coefficients of A ^s _{n l λ, n ′ l ′λ} were used. The calculations of the radial part of overlap integrals with the same screening parameters were made in the range 1 ≤ n ≤ 75, 1 ≤ n′ ≤ 75, and 10⁻⁶ ≤ p. Received: 18 January 2001 / Accepted: 5 April 2001 / Published online: 27 June 2001     

The Distributions of the Frequency of Occurrence of Nucleotide Subsequences

The objective is to derive the probability distribution of the frequency of occurrence of a subsequence within a nucleotide sequence under the hypothesis that the four nucleotides occur at random and with equal probability. We also consider the Compound Poisson approximation for the same distribution. The exact probability distribution can be obtained by the finite Markov chain imbedding technique introduced by Fu and Koutras (1994), however we can manage the case as well if the probabilities are not all equal. The compound Poisson approximation by Stein-Chen's method can be used to develop an approximate probability distribution with proper setting of the definition of the sets of dependence. Such structure gives a bound on the total variation distance, which tends to get relatively larger as the frequency goes up. AMS 2000 Subject Classification: Primary: 60E05; Secondary: 60J10     

Comment: “On the computation of molecular auxiliary functions<Emphasis Type="Italic">A</Emphasis><Subscript>n</Subscript>and<Emphasis Type="Italic">B</Emphasis><Subscript>n</Subscript>”

Guseinov, Mamedov, Kara and Orbay (Pramana - J. Phys. 56, 691 (2001)) propose methods for evaluating the molecular auxiliary functionsA _n(p) andB _n(pt) for the range 17 ≤n ≤ 60 and 25 ≤pt ≤ 60. However, their procedure forA _n(p) is not new, and that forB _n(pt) is less efficient for their target range than another well-known method. Their approach does have merit for smaller non-zero values ofpt. Two minor errors in table 1 of their paper are also identified.     

Relation between the permeability and the degree of coil overlap of polymer in the bulk state

Based on the expression of the index of coil interpenetration (i.e.,the degree of coil overlap,ξ_b) of amorphous polymers in the bulk state proposed by Qian,theξ_b was rewritten asξ_b=ρ_b[η]_θ/1.66 via Flory's intrinsic viscosity equation at them conditions.Theξ_b ofpoly (vinyl chloride) (PVC) dense membranes with different molecular weights and cellulose diacetate (CA) dense membranes prepared using different solvents were determined.The permeability,permeation coefficient (P) of nitrogen and permeation flux (J) of liquid through both membranes,respectively,was measured.P and J decreased exponentially with increasingξ_b for PVC and CA membranes were revealed.     

A New Model for the Genesis of Natural Gases--Multi-source Overlap, Multi-stage Continuity, Type Controlled by Main Source and Nomenclature by Main Stage (Ⅰ)--Multi-source Overlap and Type Controlled by Main Source

Based on the geochemical studies of natural gases in the past ten years in China, the authors have proposed a new model for their genesis--multi-source overlap, multi-stage continuity, main source-controlling type and nomenclature by the main stage.Multi-source refers to a diversity of material sources involved in the formation of natural gases, including abiogenic and biogenic material sources. In regard to biogenic sources, either oil-generating or coal-generating organic matter would produce gaseous hydrocarbon reservoirs of commercial importance. Generally, natural gases originating from these sources can overlap to form gas reservoirs. Under specific circumstances mantle-source abiogenic gases could overlap biogenic gases to form gas reservoirs. In nature, natural gases predominated by gaseous hydrocarbons may be formed from a single end-member source. However, multi-source overlap is more typical of the genesis of natural gases.     

Monte Carlo simulations of magnetic particle suspensions with a simple assessment method for the particle overlap between magnetic spheroids

We have developed a simple assessment method for the overlap between spheroidal particles, which neither requires the complex manipulation of vectors and matrices that is indispensable in the ordinary methods, nor is based on a model potential. Moreover, we have developed an evaluation method for the interaction energy arising from the overlap of the steric layer coating spheroidal particles. This is based on a sphere-connected particle model, but some modifications are introduced in order to express an appropriate repulsive interaction energy at the deepest overlapping position. We have investigated the phase change in a magnetic spheroidal particle suspension for a two-dimensional system by means of Monte Carlo simulations. In the case of no external magnetic field, if the magnetic particle-particle interaction is sufficiently strong to favour cluster formation, long raft-like clusters tend to be formed in a dilute situation. With decreasing values of area fraction, a chain-like structure in a dense situation transforms into a raft-like structure within a narrow range of the particle area fraction. Similarly, the raft-like clusters are preferred in a weak applied magnetic field, but an increase in the field strength induces a phase change from a raft-like into a chain-like structure.

Highlights of the present paper:

1. A simple assessment method has been proposed for the overlap between two spheroidal particles.

2. The particle overlap assessment is free from a complex mathematical manipulation regarding vectors and matrices.

3. A modified sphere-connected model has been proposed in order to more accurately evaluate a repulsive interaction due to the overlap of the steric layers coating spheroidal particles.

4. 2D Monte Carlo simulations have been performed to elucidate the phenomenon of a phase change by magnetic spheroidal particles on a material plane surface.

5. A phase change between a raft-like and a chain-like aggregate structure is able to be controlled by the area fraction of particles and an external magnetic field.

     

On the Distribution of Overlaps in the Sherrington–Kirkpatrick Spin Glass Model

This paper describes some of the analytic tools developed recently by Ghirlanda and Guerra in the investigation of the distribution of overlaps in the Sherrington–Kirkpatrick spin glass model and of Parisi's ultrametricity. In particular, we introduce to this task a simplified (but also generalized) model on which the Gaussian analysis is made easier. Moments of the Hamiltonian and derivatives of the free energy are expressed as polynomials of the overlaps. Under the essential tool of self-averaging, we describe with full rigour, various overlap identities and replica independence that actually hold in a rather large generality. The results are presented in a language accessible to probabilists and analysts.     

排名聚合算法在少量长列表聚合中的性能比较分析

排名聚合将多个排名列表聚合成一个综合排名列表,可应用于推荐系统、链路预测、元搜索、提案评选等.当前已有工作从不同角度对不同排名聚合算法进行了综述、比较,但存在算法种类较少、数据统计特性不清晰、评价指标不够合理等局限性.不同排名聚合算法在提出时均声称优于已有算法,但是用于比较的方法不同,测试的数据不同,应用的场景不同,因此何种算法最能适应某一任务在很多情况下仍不甚清楚.本文基于Mallows模型,提出一套生成统计特性可控的不同类型的排名列表的算法,使用一个可应用于不同类型排名列表的通用评价指标,介绍9种排名聚合算法以及它们在聚合少量长列表时的表现.结果发现启发式方法虽然简单,但是在排名列表相似度较高、列表相对简单的情况下,能够接近甚至超过一些优化类方法的结果;列表中平局数量的增长会降低聚合排名的一致性并增加波动;列表数量的增加对聚合效果的影响呈现非单调性.整体而言,基于距离优化的分支定界方法 (FAST)优于其他各类算法,在不同类型的排名列表中表现非常稳定,能够很好地完成少量长列表的排名聚合.