基于混沌的三江平原月降水时间序列分析

三江平原是我国最大的淡水沼泽区,近年来降水的减少是导致湿地减少的一个重要的自然因素.别拉洪河是三江平原上比较有代表性的沼泽性河流.以别拉洪水文站的降水序列为例,通过相空间重构,分别计算了序列的关联维、最大Lyapunov指数以及Kolmogorov熵等几个序列特征量.计算表明:三江平原月降水序列中是存在明显的混沌特征的,这为以后建立三江平原月降水的混沌预测模型提供了理论依据.     

Quasi-particle theory of optical soliton interaction

The intra-channel collision of optical solitons, with non-Kerr law nonlinearities, is studied in this paper by the aid of quasi-particle theory. The perturbations terms that are considered in this paper are both of Hamiltonian as well as non-Hamiltonian type. The suppression of soliton–soliton interaction, in presence of these perturbation terms, is achieved. The nonlinearities that are studied in this paper are Kerr, power, parabolic and dual-power laws. The numerical simulations support the quasi-particle theory.     

The numerical analysis of the trapezoidal thread rolling process

The thread rolling is difficult technological process. Improve quality and contemporary reduce manufacture cost of the trapezoidal thread requires acquaintances of physical phenomena observed in the contact zone between rolls and deform work-pieces. Therefore, in this paper the physical and mathematical models of deformations (displacements and strains) and stress in the cold process of trapezoidal thread rolling, were developed. The process is considered as a geometrical and physical non-linear, initial as well as boundary value problem. The phenomena on a typical incremental step were described using a step-by-step incremental procedure, with an updated Lagrangian formulation. The state of strains was described by Green-Lagrange's tensor, while the state of stress by the second symmetrical Pioli-Kirchhoff's tensor. The object was treated as an elastic (in the reversible zone) and visco-plastic body (in non-reversible zone) with mixed hardening. The variational equation of motion in three dimensions for this case was proposed. Then, the finite elements methods (FEM) and dynamic explicit method (DEM) were used to obtain the solution. The application developed for in the ANSYS programme, which provides a complex time analysis for displacement, strains and stresses occurring in the object. The recommendations concern modeling the trapezoidal thread rolling process, where reduce degrees of freedom in numerical model is very important and provide convergence calculated results for maximum stress and strain values in the thread surface layer, were elaborated. The influence a various process conditions on the states deformation and stress for examples calculations, were presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nash and Stackelberg Differential Games

A large class of stochastic differential games for several players is considered in this paper.The class includes Nash differential games as well as Stackelberg differential games.A mix is possible.The...     

Wavelet Image Compressor—MinImage

Nowadays, still images are used everywhere in the digital world. The shortages of storage capacity and transmission bandwidth make efficient compression solutions essential. A revolutionary mathematics tool, wavelet transform, has already shown its power in image processing. MinImage, the major topic of this paper, is an application that compresses still images by wavelets. MinImage is used to compress grayscale images and true color images. It implements the wavelet transform to code standard BMP image files to LET wavelet image files, which is defined in MinImage. The code is written in C++ on the Microsoft Windows NT platform. This paper illustrates the design and implementation details in Min-Image according to the image compression stages. First, the preprocessor generates the wavelet transform blocks. Second, the basic wavelet decomposition is applied to transform the image data to the wavelet coefficients. The discrete wavelet transforms are the kernel component of MinImage and are discussed in detail. The different wavelet transforms can be plugged in to extend the functionality of MinImage. The third step is the quantization. The standard scalar quantization algorithm and the optimized quantization algorithm, as well as the dequantization, are described. The last part of MinImage is the entropy-coding schema. The reordering of the coefficients based on the Peano Curve and the different entropy coding methods are discussed. This paper also gives the specification of the wavelet compression parameters adjusted by the end user. The interface, parameter specification, and analysis of MinImage are shown in the final appendix.     

Integrating design problems in mathematics curriculum: an architecture college case study

This paper reports an attempt to improve results in the mathematics course in one of the architecture colleges in Israel through practise in applications. The effect of integrating structure design problems in the calculus curriculum on students' achievements and attitudes was examined. The applied topics in the curriculum were connected to calculus topics and studied through problembased learning activities. The integrated curriculum was implemented and the learning results in experimental and control groups were assessed by means of achievement tests, attitude questionnaires and student interviews. The learning achievements in the experimental group proved to be significantly higher than in the control group. The positive impact of learning applications on motivation, understanding, creativity and interest in mathematics is indicated.     

基于非局部应变梯度理论功能梯度纳米板的弯曲和屈曲研究

以纳米机器人等智能器件中的功能梯度纳米板结构为研究对象,基于非局部应变梯度理论,研究了其弯曲和屈曲问题.推导了一般情况下的功能梯度纳米板运动方程,弯曲和屈曲作为其特例可简化而成.分析了非局部尺度参数、材料特征尺度参数、梯度指数、纳米板尺寸等对弯曲挠度和临界屈曲载荷的影响.结果表明:不同高阶连续介质力学理论下的最大挠度都随梯度指数的增大而增大,正方形纳米板挠度较小,且板厚越大,弯曲挠度越小;最大挠度随非局部尺度参数的增大而增大,随材料特征尺度参数的增大而减小.临界屈曲载荷随梯度指数的增大而减小,随板厚、长宽比的增大而增大,随非局部尺度的增大而减小,随材料特征尺度的增大而增大.非局部应变梯度高阶弯曲和屈曲中存在结构软化与硬化机制,两个内特征参数之间具有耦合效应,当非局部尺度大于材料特征尺度时,非局部效应在功能梯度纳米板力学性能中占主导作用;当材料特征尺度大于非局部尺度时,应变梯度效应占主导作用.解析结果还证明了当非局部尺度等于材料特征尺度时,非局部应变梯度理论结果退化为经典结果.     

Associations and dissociations with time-dependent reaction coefficients in finite polymer mixtures: The model and analytical-numerical method for solution by successive approximations

The work deals with the association and dissociation reactions with time-dependent coefficients in finite mixtures of polymers dispersed in fluid media with solid components. The polymers are regarded to be formed by identical units, polymer-forming units (PFUs) and, thus, present homopolymers. The model takes into account the porosity of the dispersion-medium/polymer-mixture system. The work derives the model for the reactions in the finite mixtures. The model presents a non-autonomous quadratic finite ODE system in a time-independent hyperplane and is based on the conservation law for the total number of PFUs. A variety of engineering applications of the derived finite-mixture model are discussed. The simplest case of the finite mixtures, i.e., the monomer-dimer mixtures with time-independent reaction coefficients is completely analyzed. An analytical-numerical (AN) method of the successive-approximations (SA) type is proposed for solving the derived model. The AN/SA method includes explicit analytical expressions for each of the approximations in terms of the preceding approximation. The method is exact in the dissociation-only case. The approximations are expected to converge if the association-reaction coefficients are not too large and the zeroth approximations are not very far from the solution. The AN/SA method comprises two sequences of the approximations. If the first one converges uniformly in the entire time axis, then the limit function is a steady-state (or “dynamic equilibrium”) solution of the non-autonomous quadratic ODE system. The second sequence presumes that the first sequence is convergent in the above mentioned sense. The second sequence is intended for calculation of the solutions of initial-value problems for the above ODE system in a semi-infinite time interval. The main differences from common computational methods are formulated. The AN/SA method is quantitatively illustrated with a few examples of the settings in the aforementioned case of monomer-dimer mixtures, also in comparison with the explicit Euler method. The form of the AN/SA method allows especially efficient implementation on multi-processor/multi-core personal computers with graphic processing units even if the dimension of the state space is large. The developed model and method form a constructive framework for analysis or design of polymer mixtures dispersed in fluid-solid media. An application to prospective manufacturing of spatially heterogeneous polymer products is noted. A few directions for future research are proposed as well.     

A parametric method of constructing Poincaré mappings in hydrodynamic systems

The plane-parallel motion of the particles of an incompressible medium reduces to an investigation of a Hamilton system. The stream function is a Hamilton function. A Hamilton function, which depends periodically on time and corresponds to the agitation of an incompressible medium in a domain which varies periodically with time, is considered. This agitation of the medium is due to dynamic chaos. The transition to dynamic chaos is described by investigating the location of the Lagrangian particles over time intervals which are multiples of the period (Poincaré points (PP)). The set of PP can be obtained using a Poincaré mapping in the phase flow. The method which has been developed is used to investigate the plane-parallel motion of the particles in an incompressible fluid in a thin layer, bounded by a flat bottom, rectilinear side walls and an upper boundary which is deformed according to a specified periodic law. The motion of the particles is determined from Hamilton's system of equations. The Hamiltonian (the stream function) is found in the thin-layer approximation and depends on two dimensionless parameters: the amplitude of deformation and the tangential velocity in the deforming boundary. The characteristic boundary, which separates the domain of the chaotic motion of the PP from the domain of ordered motion, is determined numerically in the domain of the two parameters. The topological structure of the phase trajectories up to the transition to chaotic conditions is analysed using the Poincaré mapping, found with an accuracy up to the third order with respect to the amplitude. The phase trajectories of the PP, found analytically, turn out to be close to the trajectories of the initial Hamilton system, determined numerically. The mapping found in the domain of the two dimensionless parameters enables one to determine, qualitatively, the boundary of the transition to chaos.     

A Tale of Two Countries: Some Systems Perspectives on Japan and the United Kingdom in the Age of Information Technology

The British still excel in agriculture just as, a century or so ago, they did in manufacturing and, 30 years ago, in computing. The Japanese, who are also good at agriculture, came to excel in manufacturing and probably now lead the world in information technology. Now Britain is trying to catch up. The paper presents some views of the situation.     

Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains

The solvability in Sobolev spaces is proved for divergence form complex-valued higher order parabolic systems in the whole space, on a half-space, and on a Reifenberg flat domain. The leading coefficients are assumed to be merely measurable in one spacial direction and have small mean oscillations in the orthogonal directions on each small cylinder. The directions in which the coefficients are only measurable vary depending on each cylinder. The corresponding elliptic problem is also considered.     

“小麦发育后期茎秆抗倒性的数学模型”综述

2011年第8届全国研究生数学建模竞赛C题是一个农业生产中小麦倒伏问题,在给出3年原始测量数据的基础上要求建立小麦发育后期茎秆抗倒性的数学模型,内容包括小麦性状数据处理和弹性力学模型.综述为C题竞赛总结,含问题的提出、问题的解答与评阅情况、存在问题及研究建议.     

Review of ranking methods in the data envelopment analysis context

Within data envelopment analysis (DEA) is a sub-group of papers in which many researchers have sought to improve the differential capabilities of DEA and to fully rank both efficient, as well as inefficient, decision-making units. The ranking methods have been divided in this paper into six, somewhat overlapping, areas. The first area involves the evaluation of a cross-efficiency matrix, in which the units are self and peer evaluated. The second idea, generally known as the super-efficiency method, ranks through the exclusion of the unit being scored from the dual linear program and an analysis of the change in the Pareto Frontier. The third grouping is based on benchmarking, in which a unit is highly ranked if it is chosen as a useful target for many other units. The fourth group utilizes multivariate statistical techniques, which are generally applied after the DEA dichotomic classification. The fifth research area ranks inefficient units through proportional measures of inefficiency. The last approach requires the collection of additional, preferential information from relevant decision-makers and combines multiple-criteria decision methodologies with the DEA approach. However, whilst each technique is useful in a specialist area, no one methodology can be prescribed here as the complete solution to the question of ranking.     

Nonequilibrium processes in a polyatomic gas of moderate density in an external magnetic field

The dissipative and relaxation processes in a polyatomic gas of moderate density in an external magnetic field are considered using the methods of quantum kinetic theory. The momentum and the energy fluxes, as well as the transport coefficients; are obtained in the dissipative Navier-Stokes approximation by taking the first virial correction into account. The tensor coefficient of the shear viscosity in a gas of diamagnetic molecules is obtained as a function of the effective cross sections of binary and ternary collisions and of the value of the magnetic field. The Bloch equation for magnetization in a spatially homogeneous gas of linear diamagnetic molecules is derived. The relaxation times and the shift in the Larmor frequency due to intermolecular collisions are obtained.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 107, No. 2, pp. 307–319, May, 1996.Translated by V. I. Serdobol'skii.     

Modelling of thermoelastic Rayleigh waves in a solid underlying a fluid layer with varying temperature

The present paper is aimed at to study the propagation of surface waves in a homogeneous isotropic, thermally conducting and elastic solid underlying a layer of viscous liquid with finite thickness in the context of generalized theories of thermoelasticity. The secular equations for non-leaky Rayleigh waves, in compact form are derived after developing the mathematical model. The amplitude ratios of displacements and temperature change in both media at the surface (interface) are also obtained. The liquid layer has successfully been modeled as thermal load in addition to normal (hydrostatic pressure) one, which is the distinctive feature of the present study and missing in earlier researches. Finally, the numerical solution is carried out for aluminum-epoxy composite material solid (half-space) underlying a viscous liquid layer of finite thickness. The computer simulated results for dispersion curves, attenuation coefficient profiles, amplitude ratios of surface displacements and temperature change have been presented graphically, in order to illustrate and compare the theoretical results. The present analysis can be utilized in electronics and navigation applications in addition to surface acoustic wave (SAW) devices.     

Exact solution of thermal stress problem of an inhomogeneous hygrothermal piezoelectric hollow cylinder

The closed-form exact solution for the hygrothermal response of inhomogeneous piezoelectric hollow cylinders is obtained. The interaction of electric potentials, electric displacement and elastic deformations is presented. The present cylinder is subjected to both a mechanical load and an electric potential. The material properties coefficients of the present cylinder are assumed to be changed in the radial direction by different distribution forms. The field quantities like displacement, stresses and electric potentials in the inhomogeneous piezoelectric cylinders are determined. The significant of influences of material inhomogeneity, initial temperature, final moisture, and the load and electric ratios in the field quantities are investigated. The concluding remarks and suitable discussions are made.     

Stimulating student aesthetic response to mathematical problems by means of manipulating the extent of surprise

We investigated aesthetic responses of 60 middle school students as they engaged in a pair of similar looking geometry problems in one-on-one semi-structured interviews. The investigation was driven by three predictions. The first two predictions were about the association between the evaluative aesthetic response and surprise stemming from the solution to each problem. The third, main, prediction was that the problem with more surprising solution would be evaluated as more beautiful. The extent of surprise was manipulated by the order in which two problems were given. The third prediction came to be true in 90% of the cases, in which the first two predictions were fulfilled. The findings suggest that school students’ evaluative aesthetic response to mathematical problems can be stimulated in instructional settings. Implications for research and practice are drawn.     

Analysis of statically indeterminate non-uniform bar problem in post elastic domain by an iterative variational method

The present study investigates the growth of elastic–plastic front of a statically indeterminate non-uniform bar in post-elastic regime. The solutions of statically indeterminate bar problems are critical in general, because they are not amenable to a ready analytical solution. A clamped axially loaded bar problem becomes indeterminate when the load is concentric, and it result in a singularity point in the domain. In the present bar problem more such singularity points arise when the bar is in post-elastic state, at higher magnitude of concentrated load and the other points come from the yield front location. The computational domain is divided into sub-domains based on the location of singularity points. The formulation is based on von-Mises yield criterion and for linear strain hardening type material behavior. The governing equation is derived through an extension of a variational method in elasto-plastic regime and solution is obtained by using Galerkin's approximation principle. The approximate solution further needs an iterative method to locate the growth in the yield front. The solution algorithm is implemented with the help of MATLAB^® computational simulation software and validation of the formulation is carried out successfully for some reduced problems. The effect of geometry parameters like aspect ratio, slenderness ratio and the type of taperness on the post-elastic performance of the bar is investigated and the relevant results are obtained in dimensionless form. The term bar used in this paper is in generic sense and hence the formulation is applicable for all one dimensional elements, e.g., rods, pipes, truss members, etc.     

锥形微通道内液滴自输运特性及力学驱动机制研究

针对液体在微通道内的自输运特性,采用数值仿真与能量解析相结合的方法研究了液滴在锥形微通道内的自输运特性及力学驱动机制,得到微通道的锥形角、液滴与微通道内壁的接触角及微通道的润湿性对液滴自输运特性的影响关系.分析表明,微通道的锥形角、液滴与微通道内壁的接触角均能影响液滴的自输运方向及驱动力大小.对于亲水性微通道,微通道的锥形角、液滴与微通道内壁的接触角其作用效果呈现整体形态;对于疏水性微通道,微通道的锥形角、液滴与微通道内壁的接触角其作用效果呈现局域形态.这可为研究液体在微通道内的自输运机理及界面内液体细观流动机制奠定理论基础.     

基于ARIMA的油田A类物资市场价格预测

本文研究了油田A类物资的市场价格预测。采用时间序列方法中的ARIMA模型,结合油田物资历史价格数据,分析并提出了一套针对油田A类物资的市场价格预测模式。该模式包括两个模块:样本集模块和ARIMA模块。样本集模块的主要功能是样本集的输入和实时更新;ARIMA模块包括了价格预测模型的拟合、检验、预测、评价、动态反馈和调整等主要环节。在该模式的指导下,以大庆油田A类采购物资中的小螺纹钢(20-HRB335)(天津、石家庄和沈阳3个产地)为例,对2011年各月的市场价格进行了模拟预测,预测的平均相对误差分别控制在2.13%,1.64%和1.82%,该结果得到了用户的认可。该预测模式的运用对大庆油田物资集团制定合理的物资采购方案提供了依据。结论部分对该预测模式的意义及存在问题进行了分析,并给出改进建议。