谐和与有界噪声联合参激作用下的Visco-Elastic系统

研究了带visco-elastic项的非线性系统,在谐和与有界噪声联合参激作用下的响应和稳定性问题。用多尺度法分离了系统的快变项,并求出了系统的最大Liapunov指数和稳态概率密度函数,根据最大Liapunov指数可得系统解稳定的充分必要条件。讨论了系统的visco-elastic项对系统阻尼项和刚度项的贡献,给出了随机项和确定性参激强度等参数对系统响应影响的讨论。数值模拟表明该方法是有效的。     

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.     

谐和随机噪声联合作用下Van der PolDuffing振子的参数主共振

研究了Van der Pol－Duffing振子在谐和与随机噪声联合激励下的参数主共振响应和稳定性问题。用多尺度法分离了系统的快变项，并求出了系统的最大Liapunov指数和稳态概率密度函数，还分析了失稳、分 叉和跳跃现象，讨论了系统的阻尼项、非线性项、随机项和确定性参激强度等参数对系统响应的影响。数值模拟表明所提出的方法是有效的。     

Turbulence Model Predictions for the Inhomogeneous Mixing Layer

The plane mixing layer between two streams of different densities and velocities is studied using a complete, phenomenological model of turbulence. The model is an extension of that described by Saffman [11]. The properties of similarity solutions are computed, and compared with experimental data. The qualitative dependence on velocity ratio, density ratio, compressibility and adverse pressure gradient is predicted correctly. The quantitative agreement is satisfactory.     

Well-Posedness of Initial-Boundary Value Problems for Piezoelectric Equations

The well-posedness of the initial-boundary value problems for quasi-electrostatic equations in a bounded domain with Lipschitz boundary is proved. The quasi-electrostatic equation is the coupled system of the equations of motion and the equation of the quasistatic electric field. The mass density, the elastic, piezoelectric and dielectric tensors are bounded measurable functions in the domain, and these tensors satisfy the positivity and the symmetry. The initial conditions are given only for the mechanical displacement and its time derivative. The methods of proof are Galerkin's method, duality argument and energy inequality.     

On the Structure of Order Domains

The notion of an order domain is generalized. The behaviour of an order domain by taking a subalgebra, the extension of scalars, and the tensor product is studied. The relation of an order domain with valuation theory, Gröbner algebras, and graded structures is given. The theory of Gröbner bases for order domains is developed and used to show that the factor ring theorem and its converse, the presentation theorem, hold. The dimension of an order domain is related to the rank of its value semigroup.     

Impact of Technology Assimilation on Investment Policy: Dynamic Optimization and Econometric Identification

The paper introduces a dynamic model of optimization of R&D intensity under the effect of technology assimilation. The model involves R&D investments, technology stock, production, and technology productivity as main variables. The model characterizes the “growth” and “decline” trends that describe the interaction between R&D investments and transformation process of production factors. The technology stock is constructed as a function of indigenous and exogenous technology stocks and their growth rates. The research focuses on the issue of a reasonable balance between the indigenous technology stock and assimilated technology flow. Econometric linearization of the technology assimilation effect is used to construct a reasonable optimal control model. The existence of the value function for the problem of the optimal economic growth on the infinite horizon is proved and the basic features of the value function are outlined. The property of strong invariance for the main proportions of the model such as technology productivity and R&D intensity is proved. The model is calibrated on the aggregate data of the Japanese automotive industry. The research was sponsored by the SIMOT Program of the Japanese Ministry of Education, Science and Technology. The second author was supported by the Russian Fund for Basic Research, Grants 05-01-00601, 05-01-08034, by the Russian Fund for Humanities, Grant RFH 05-02-02118a, and by the Program for the Sponsorship of Leading Scientific Schools, Grant NSCH-791.2003.1.     

Parallel multi-frontal solver for p adaptive finite element modeling of multi-physics computational problems

The paper presents a parallel direct solver for multi-physics problems. The solver is dedicated for solving problems resulting from adaptive finite element method computations. The concept of finite element is actually replaced by the concept of the node. The computational mesh consists of several nodes, related to element vertices, edges, faces and interiors. The ordering of unknowns in the solver is performed on the level of nodes. The concept of the node can be efficiently utilized in order to recognize unknowns that can be eliminated at a given node of the elimination tree. The solver is tested on the exemplary three-dimensional multi-physics problem involving the computations of the linear acoustics coupled with linear elasticity. The three-dimensional tetrahedral mesh generation and the solver algorithm are modeled by using graph grammar formalism. The execution time and the memory usage of the solver are compared with the MUMPS solver.     

Damage and Failure of Metal/Fibre-Reinforced Polymer Tensile Specimens with Inelastic Interface

Hybrid specimens of metal and fibre-reinforced polymer are applied in automotive and aerospace industry. The simulation and analysis of damage of such engineering structures is the focus of this research. The investigation includes a computation of the extension of single lap tensile specimen, produced by ultrasonic metal welding. The specimen is manufactured from CF-PA66 - fibre-reinforced polymer and AlMg3 (AA5754), which is used as a metallic joining partner. The aluminium substrate is treated as an elastoplastic material. The polymer composite generally shows an orthotropic elastic behaviour. The interface material has been numerically modeled as an elastoplastic material with linear hardening, coupled with Lemaitre-type damage. The finite element method is used for the investigation of so-called interface elements. The geometry of the interface is a consequence of the welding sonotrode geometry. The behaviour of specimens with square and ring interface geometry are analysed. The influence of the interface geometry on the mechanical properties of the joint is shown. The increase of the damage parameter and the development of failure are described for both cases. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

住院病人构成动态分析与预测

本文对某一综合性教学医院１９８２～１９９１年住院病人进行疾病顺位动态分析与预测．结果表明：①肿瘤、消化、呼吸系统疾病顺位居高不下；②传染病、神经系统和感觉器官疾病顺位逐年下降；③循环、泌尿生殖系统疾病顺位有上升趋势　对疾病变化因素和统计预测进行了讨论．     

Automatic grading of students' ALGOL programming

The report describes an experiment on automatic grading of student algorithms, using an ALGOL compiler. The experiment is based on an evaluation of the efficiency and logical completeness of the algorithms, not on their formal correctness, which is supposed to be checked in advance by the individual student. The technique used is to embed the student algorithms within a larger grading program structure, which supplies test cases and performs checks and evaluation. The complete text of such a grading program is given. The experience gained through the experiment, and suggestions for further developments, are discussed.     

Effects of seasonal growth on delayed prey–predator model

The dynamic behavior of a delayed predator–prey system with Holling II functional response is investigated. The stability analysis has been carried out and existence of Hopf bifurcation has been established. The complex dynamic behavior due to time delay has been explored. The effects of seasonal growth on the complex dynamics have been simulated. The model shows a rich variety of behavior, including period doubling, quasi-periodicity, chaos, transient chaos, and windows of periodicity.     

Explicit Stability Zones for Cournot Game with 3 and 4 Competitors

The dynamical system of 3 and 4 competitors in a Cournot game is studied. The stability of its fixed points (Nash-equilibria) are also investigated. The stable and unstable regions are explicitly shown. The bifurcation characteristics are found. Periodic orbits with different periods 7, 25, 18, 13, 17 etc., are detected in both cases. The study of these models is very rich in bifurcation phenomena.     

Two-dimensional heat and mass transfer during drying of deformable media

Drying is an essential step in many production and treatment processes. The control of the dry product quality is more and more required in order to ensure effective use or handling of the material. The aim of this study is to develop a two-dimensional drying model which takes into account heat and mass transfer and the accompanying deformation of the dried material. The model tries to be relatively simple but sufficiently complete in order to predict and analyze the spatio-temporal distribution of the temperature, the moisture and the solid displacement during the process. The product was considered as a two-phases, homogeneous, hygroscopic, isotropic and highly shrinkable medium. The model was solved numerically by a finite difference method. The simulation allowed the obtention of the time and space evolutions of several parameters such as product temperature, moisture content and solid displacement.     

Geometrically nonlinear static and dynamic analysis of functionally graded skew plates

The present paper deals with nonlinear static and dynamic behavior of functionally graded skew plates. The equations of motion are derived using higher order shear deformation theory in conjunction with von-Karman’s nonlinear kinematics. The physical domain is mapped into computational domain using linear mapping and chain rule of differentiation. The spatial and temporal discretization is based on fast converging finite double Chebyshev series and Houbolt’s method. Quadratic extrapolation technique is employed to linearize the governing nonlinear equations. The spatial and temporal convergence and validation studies have been carried out to establish the efficacy of the present solution methodology. In case of dynamic analysis, the results are obtained for uniform step, sine, half sine, triangular and exponential type of loadings. The effect of volume fraction index, skew angle and boundary conditions on nonlinear displacement and moment response are presented.     

一维非稳态导热的火积耗散场分析

分别对无限大、半无限大物体与无限大平板非稳态导热过程的火积耗散场进行了分析,并将火积耗散场与熵产生场进行了比较.无限大物体总的火积耗散随时间的变化率为负定的,并对这一结论给出了证明.对于无限大物体,对耗散波峰的传播速度与波峰振幅进行了讨论.对于半无限大物体,分别对边界温度固定与边界热流固定两种导热情形下的火积耗散场进行了分析;对于无限大平板,分别对对流换热与绝热两种边界条件下的火积耗散场进行了分析.     

Intertemporal General Equilibrium Model of the Russian Economy Based on National Accounts Deaggregation

The paper describes a three-product intertemporal general equilibrium model of the Russian economy. The System Analysis of Evolving Economy (SAEE) approach to modelling economic processes developed in 1975 is described. Based on SAEE Intertemporal Equilibrium Model with Control of Capital (IEMCC) and three-product nonlinear deaggregation of Russian national accounts by consumption are described. The model agents of two types are introduced: mass (rational) and individual (scenario) agents. The former type includes Bank, Producer, Household, Owner, and Trader. The latter type includes State, Central Bank, Exporter, and Importer. The model is reduced to a boundary-value problem for a significantly nonlinear system of equations. These equations are derived from the initial hypothesis by means of the original economic modelling assistance system ECOMOD which is developed in the computer algebra system MAPLE. The model is adjusted with respect to official statistical quarterly data from 2004 till 2010. The calculation results are provided. The model proves the ability to model the Russian economy as a result of interactions of rational and individual macroeconomic agents.     

关于建立玉米叶片的数学模型的几种方法的讨论

分别运用拉格朗日插值法、最小二乘的三次多项式拟合法和经典三次样条插值法建立了玉米叶片的数学模型,并从收敛性、稳定性、光滑性等方面对三种方法进行了对比分析,通过对所给实例的绘图效果进行比较,指出了拉格朗日插值法、最小二乘的三次多项式拟合法和经典三次样条插值法在描述玉米叶片形态特征的效能上的利弊.     

Book Vignettes

Middleton , W. E. Knowles , A History of the Theories of Rain Salkind , Charles T., (Compiler): The MAA Problem Book II Stephenson , Marjory , Bacterial Metabolism Marshall , N. B., The Life of Fishes Parker , Francis D., The Structure of Number Systems Hardin , Garrett , Biology, Its Principles and Implications Miller , John P., and Scholten , Robert , Laboratory Studies in Geology Kovalik , Vladimir and Nada , The Ocean World Adler , Irving , The Wonders of Physics The Pirolechnia of Vannccio Biringuccio.     

A metacognitive intervention in mathematics at university level

The paper reports the main results of an instructional study. The study was aimed at improving the performance in mathematics of a group of university students of biology who repeatedly failed the final examination of a compulsory course in mathematics. The main difficulties of these students seemed to be metacognitive and affective in nature. The training therefore worked on metacognitive and affective features: knowledge about cognition, monitoring, beliefs, emotions and attitudes. The intervention was successful: at the end of the course all students passed the examination that they had failed so often. The results also suggest that it may be possible (and necessary) to ‘teach learning to learn’ mathematics.