Generalization of the muzzle wave similarity rules

The present paper describes an improvement of the muzzle wave similarity that permits treatment to unsteady and non sonic gun muzzle conditions. The revised formulation of the similarity is capable of characterizing the muzzle wave propagation even for significant variation of the muzzle conditions during the life time of the wave. Suitable scaling parameters are selected and tested yielding appropriate similarity rules at a significantly reduced number of tests whose applicability is confirmed by experimental data and comparison to an analytical theory. Received 9 October 1998 / Accepted 18 June 1999     

计量逻辑学中的近似推理

在多值逻辑系统中给出了计量逻辑学中单个公式到Γ结论集的距离公式,在此基础上,给出发散度的简化形式,讨论了计量逻辑学中三种近似推理模式之间的关系。     

Discrete elastica

This paper develops a discrete approach to the design of planar curves that minimize cost functions dependent upon their shape. The curves designed by using this approach are piecewise linear with equal length segments and obey various types of endpoint constraints.     

New structural parameters of fullerenes for principal component analysis

The Kekulé structure count and the permanent of the adjacency matrix of fullerenes are related to structural parameters involving the presence of contiguous pentagons p, q, r, q/p and r/p, where p is the number of edges common to two pentagons, q is the number of vertices common to three pentagons and r is the number of pairs of nonadjacent pentagons adjacent to another common pentagon. The cluster analysis of the structural parameters allows classification these parameters. Principal component analysis (PCA) of the structural parameters and the cluster analyses of the fullerenes permit their classification. PCA clearly distinguishes five classes of fullerenes. The cluster analysis of fullerenes is in agreement with PCA classification. Cluster analysis shows greatest similarity for the q–q/p and r–r/p pairs. PCA provides five orthogonal factors F ₁–F ₅. The use of F ₁ gives an error of 28%. The inclusion of F ₂ decreases the error to 2%.From the Proceedings of the 28th Congreso de Químicos Teóricos de Expresión Latina (QUITEL 2002)     

Similarity screening of molecular data sets

Summary Three-dimensional (3D)-database searches are now being widely applied to determine potential new active molecules. Many structural data sets obtained as a result of these searches are still large in size. In this paper we apply molecular similarity calculations as a rapid method to screen two such data sets. In the first investigation, synthetic candidates, produced as a result of a tendamistat -turn mimic search, were tested for their ability to imitate the -turn backbone. In the second study, structures extracted through a histamine pharmacophore query search were examined on the basis of their electronic similarity to histamine. Molecular similarity is shown to provide a rapid means of gaining insight into the composition of molecular data sets, with possible implications for future full 3D-database searches.     

边坡稳定性类比评价的定量实现

岩土边坡是一个受多因素影响、随时空变异的动态系统 ,它具有数据有限、不确定和没有原型等特点 ,因此 ,已有成功经验知识的运用在边坡稳定性评价中具有重要的意义。本文基于类比推理和灰色系统理论 ,提出了一种定量开发利用经验知识的新方法 ,并将其成功地应用于边坡稳定性分析和评价。结果表明 ,在运用经验知识方面 ,该法与目前广泛使用的神经网络方法有异曲同工之妙。此外 ,本文所提出的方法还具有简单、方便和实用等许多优点。     

GC-MS及主成分分析法用于咖啡香精的指纹图谱分析和微差样品的识别

采用正己烷溶剂萃取法提取咖啡香精中的挥发性和半挥发性成分,并通过气相色谱-质谱法建立了咖啡香精的色谱指纹图谱,共定性了22个组分,占总量的87％,采用共有峰率、组分含量的相对标准偏差及相似度等几个指标对6个不同批次的样品进行了评价,结果表明它们之间具有很大的一致性,通过相似度比较和主成分分析的投影显示法区分微差样品。该色谱指纹图谱可用作咖啡香精的质量控制。     

Exact solutions for the quintic nonlinear Schrödinger equation with time and space modulated nonlinearities and potentials

In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schrödinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions.     

复杂生态系统的模糊数学模型

生态系统是一个复杂的大系统，很多重要的生态学理论问题都是以生态位(niche)和生物群落概念为基础的。本文将生态位和群落抽象出来，看作是一个耗散结构。建立生态系统中基本概念的量化算子，利用系统模糊分析理论给出具有明确生物意义的生态位和群落的Fuzzy数学模型。并以此讨论生态系统中其他相关概念的数学模型、群落的水平和垂直格局及物种间在资源、斑块、时间三维模糊集上的互惠，共处和竞争关系。初步构建起复杂生态大系统的数学理论框架。     

Similarity solutions to nonlinear heat conduction and Burgers/Korteweg–deVries fractional equations

We analyze self-similar solutions to a nonlinear fractional diffusion equation and fractional Burgers/Korteweg–deVries equation in one spatial variable. By using Lie-group scaling transformation, we determined the similarity solutions. After the introduction of the similarity variables, both problems are reduced to ordinary nonlinear fractional differential equations. In two special cases exact solutions to the ordinary fractional differential equation, which is derived from the diffusion equation, are presented. In several other cases the ordinary fractional differential equations are solved numerically, for several values of governing parameters. In formulating the numerical procedure, we use special representation of a fractional derivative that is recently obtained.