Extensional wave motion in homogenous isotropic thermoelastic plate by using asymptotic method

The present investigation is concerned with the study of extensional wave motion in an infinite homogenous isotropic, thermoelastic plate by using asymptotic method. The governing equation for the extensional wave motions have been derived from the system of three-dimensional dynamical equations of linear coupled theory of thermoelasticity. All coefficients of the differential operator are expressed as explicit functions of the material parameters. The velocity dispersion equation for the extensional wave motion is deduced from the three-dimensional analog of Rayleigh–Lamb frequency equation for thermoelastic plate waves. The approximations for long and short waves and expression for group velocity are also derived. The thermoelastic Rayleigh–Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations whose equivalence is established to that of asymptotic method. The dispersion curves for phase velocity and attenuation coefficient are shown graphically for extensional wave motion of the plates.     

Existence results for dynamic adhesive contact of a rod

The existence and uniqueness of the weak solution to the model for the dynamics of a viscoelastic rod which is in adhesive contact with an obstacle is established. The model consists of a hyperbolic equation for the vibrations of the rod coupled with a nonlinear ordinary differential equation (ODE) for the evolution of the bonding function. The model allows for failure, i.e., complete debonding, in finite time. The existence of the weak solution is established by using an existence result for ODEs and the Schauder fixed-point theorem. The limit of an elastic rod when the viscosity vanishes is studied, too.     

A Note on the Stability of the Integral-Differential Equation of the Hyperbolic Type in a Hilbert Space

In this paper, the initial-value problem for integral-differential equation of the hyperbolic type in a Hilbert space H is considered. The unique solvability of this problem is established. The stability estimates for the solution of this problem are obtained. The difference scheme approximately solving this problem is presented. The stability estimates for the solution of this difference scheme are obtained. In applications, the stability estimates for the solutions of the nonlocal boundary problem for one-dimensional integral-differential equation of the hyperbolic type with two dependent limits and of the local boundary problem for multidimensional integral-differential equation of the hyperbolic type with two dependent limits are obtained. The difference schemes for solving these two problems are presented. The stability estimates for the solutions of these difference schemes are obtained.     

Mathematical modelling of flow control in a tundish using electro-magnetic forces

The control of flow in a tundish is important for improving the quality of the steel. Dams, Wiers and Pouring chamber are some of the devices used for controlling the flow in the tundish. The investigation about the role of electromagnetic forces as a replacement for these devices is an objective for the present work. Thus, 3-D MHD simulation was performed to study the effect of electromagnetic forces on flow behaviour in the tundish. The MHD model developed for carrying out the simulation was validated with the analytical solution of the Hartman problem. The results obtained shows improvement in the desired characteristics for inclusion flotataion with magnetic flow modifier of optimum strength of magnetic field.     

Trigonometric polynomial or exponential fitting approach?

The application of a trigonometric polynomial and an exponential fitting approach is compared for a three-point formula for second-order derivatives, for Simpson’s quadrature rule and for Numerov’s scheme for second-order differential equations. The expressions for the occurring parameters are constructed in both the approaches and the behaviour of these parameters with respect to the introduced frequency is studied. The errors for specific problems obtained in both the approaches as a function of the frequency are compared.     

Optimal control for systems described by hyperbolic equations with strong nonlinearity

An optimization control problem for a hyperbolic equation is considered. The system is nonlinear with respect to the state derivative. The regularization technique for the state equation is applied. The necessary conditions of optimality for the regularized control problem are proved. It uses the extended differentiability of the control-state mapping for the regularized equation. The convergence of the regularization method is proved. Thus the optimal control for the regularized problem with a small enough regularization parameter can be chosen as an approximate solution of the initial optimization problem.     

Nonlocal boundary-value problems for abstract parabolic equations: well-posedness in Bochner spaces

The well-posedness of the nonlocal boundary-value problem for abstract parabolic differential equations in Bochner spaces is established. The first and second order of accuracy difference schemes for the approximate solutions of this problem are considered. The coercive inequalities for the solutions of these difference schemes are established. In applications, the almost coercive stability and coercive stability estimates for the solutions of difference schemes for the approximate solutions of the nonlocal boundary-value problem for parabolic equation are obtained.     

The effect of the slip condition on flows of an Oldroyd 6-constant fluid

The steady flows of a non-Newtonian fluid are considered when the slippage between the plate and the fluid is valid. The constitutive equations of the fluid are modeled by those for an Oldroyd 6-constant fluid. They give rise to non-linear boundary value problems. The analytical solutions are obtained using powerful, easy-to-use analytic technique for non-linear problems, the homotopy analysis method. It is shown that solutions exist for all values of non-Newtonian parameters. The solutions valid for no-slip condition for all values of non-Newtonian parameters can be derived as the special cases of the present analysis. Finally, graphs are plotted and critical assessment is made for the cases of slip and no-slip conditions.     

The hyperbolic–elliptic equation with the nonlocal condition

The nonlocal boundary value problem for a hyperbolic–elliptic equation in a Hilbert space is considered. The stability estimate for the solution of the given problem is obtained. The first and second orders of difference schemes approximately solving this boundary value problem are presented. The stability estimates for the solution of these difference schemes are established. The theoretical statements for the solution of these difference schemes are supported by the results of numerical experiments. Copyright © 2013 John Wiley & Sons, Ltd.     

The Clique Complex and Hypergraph Matching

The width of a hypergraph is the minimal for which there exist such that for any , for some . The matching width of is the minimal such that for any matching there exist such that for any , for some . The following extension of the Aharoni-Haxell matching Theorem [3] is proved: Let be a family of hypergraphs such that for each either or , then there exists a matching such that for all . This is a consequence of a more general result on colored cliques in graphs. The proofs are topological and use the Nerve Theorem. Received June 14, 1999     

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.     

重建极性连续统理论的基本定律和原理(Ⅺ)——兼容性问题

对现有连续统场论中存在若干有关兼容性问题进行了简略的评论．根据重建的极性的连续统基本定律阐述三类兼容性问题．第一类是讨论各基本定律间的兼容性问题．第二类是讨论微极连续统基本定律兼容一般连续统基本定律的问题．第三类是讨论微极连续统基本定律兼容刚体动力学基本方程的问题．推导出的结果有助于深刻理解各种连续统理论的基本定律体系的结构和它们之间的联系．明确地指出,在传统的连续统场论的基本均衡定律的框架下,相容性问题是不可能自然地得到解决．     

A model and simulation for homeorhesis in the motion of a single individual

In contrast to nonliving systems, all living systems perform homeorhesis. The system state tends to the so-called necessary path, or creode, when the exogenous signals are in a certain system-relevant range. The present work develops the homeorhesis-aware dynamical model for the motion of a single individual (e.g., human). The model allows for the purposeful behaviour of the individual, the creode, the exogenous forces, and the individual-specific sensitivity to their influences. The model also describes the homeorhetic-dysfunction movements. The transparency of the model is such that it allows a physical analogue in the form of electronic circuits. The model is a first step towards the construction of sociologically relevant models for the prediction of human behaviour. It is indispensable for the analyses of dangerous scenarios where the experiments are impossible, for example when predicting the behaviour of panic-stricken crowds in life-threatening situations. The work illustrates the corresponding numerical-simulation results with a series of figures and suggests topics for future research.     

Some Remarks on Equivalence of Moduli of Smoothness

The present paper investigates polynomials for which the inverse inequality for moduli of smoothness holds. The technique for approach is different from the previous works for splines and is elegantly organized.     

Standardization and optimum structural design by dynamic programming

The paper is concerned with tools for optimum structural design that can taken into account the industrial production of structural elements. Standardization is considered here as the result of minimizing the cost as a function of both element sizes and numbers of identical elements. The optimum value of the design variables obtained by traditional minimum weight (volume) design is taken as the starting point for the present procedure. Dynamic programming is used for standardization decisions. The method seems to be particularly effective when the cost function for each element size can be regarded as the sum of a constant term (initial investment) and a term that is proportional to the number of identical elements (cost of production).The original idea for the present approach, developed in Section 2, was suggested by Professor N. Distefano. The author will always remember this with gratitude.The author expresses his thanks to Prof. Dr. W. Prager for reviewing the paper.     

Methodological Issues in Studying Effects of Networks in Organizations

Three methodological issues are discussed that are important for the analysis of data on networks in organizations. The first is the two-level nature of the data: individuals are nested in organizations. This can be dealt with by using multilevel statistical methods. The second is the complicated nature of statistical methods for network analysis. The third issue is the potential of mathematical modeling for the study of network effects and network evolution in organizations. Two examples are given of mathematical models for gossip in organizations. The first example is a model for cross-sectional data, the second is a model for longitudinal data that reflect the joint development of network structure and individual behavior tendencies.     

Hermitizable,isospectral complex matrices or differential operators

The main purpose of the paper is looking for a larger class of matrices which have real spectrum. The first well-known class having this property is the symmetric one, then is the Hermite one. This paper introduces a new class, called Hermitizable matrices. The closely related isospectral problem, not only for matrices but also for differential operators is also studied. The paper provides a way to describe the discrete spectrum, at least for tridiagonal matrices or one-dimensional differential operators. Especially, an unexpected result in the paper says that each Hermitizable matrix is isospectral to a birth–death type matrix (having positive sub-diagonal elements, in the irreducible case for instance). Besides, new efficient algorithms are proposed for computing the maximal eigenpairs of these class of matrices.     

Constitutive Modelling of Resins in the Stiffness Domain

An analytic method for inverting the constitutive compliance equations of viscoelasticity for resins is developed. These equations describe the HWKK/H rheological model, which makes it possible to simulate, with a good accuracy, short-, medium- and long-term viscoelastic processes in epoxy and polyester resins. These processes are of first-rank reversible isothermal type. The time histories of deviatoric stresses are simulated with three independent strain history functions of fractional and normal exponential types. The stiffness equations are described by two elastic and six viscoelastic constants having a clear physic meaning (three long-term relaxation coefficients and three relaxation times). The time histories of axiatoric stresses are simulated as perfectly elastic.The inversion method utilizes approximate constitutive stiffness equations of viscoelasticity for the HWKK/H model. The constitutive compliance equations for the model are a basis for determining the exact complex shear stiffness, whereas the approximate constitutive stiffness equations are used for determining the approximate complex shear stiffness. The viscoelastic constants in the stiffness domain are derived by equating the exact and approximate complex shear stiffnesses. The viscoelastic constants are obtained for Epidian 53 epoxy and Polimal 109 polyester resins. The accuracy of the approximate constitutive stiffness equations are assessed by comparing the approximate and exact complex shear stiffnesses. The constitutive stiffness equations for the HWKK/H model are presented in uncoupled (shear/bulk) and coupled forms. Formulae for converting the constants of shear viscoelasticity into the constants of coupled viscoelasticity are given as well.     

Analysis of a mathematical model for tumor growth under indirect effect of inhibitors with time delay in proliferation

In this paper, a mathematical model for tumor growth with time delay in proliferation under indirect effect of inhibitor is studied. The delay represents the time taken for cells to undergo mitosis. Nonnegativity of solutions is investigated. The steady-state analysis is presented with respect to the magnitude of the delay. Existence of Hopf bifurcation is proved for some parameter values. Local and global stability of the stationary solutions are proved for other ones. The analysis of the effect of inhibitor's parameters on tumor's growth is presented. The results show that dynamical behavior of solutions of this model is similar to that of solutions for corresponding non-retarded problems for some parameter values.     

Modeling Optimal Allocation of Deficit Irrigation: Application to Crop Production in Saudi Arabia

We develop an integrated dynamic programming—linear programming (LP) model to solve for optimal land exploitation for a given crop. The model applies deficit irrigation in order to increase the irrigated area at the expense of reducing the crop yield per unit area. The dynamic program guarantees that deficit irrigation is considered only when it is economically efficient. Moreover, it provides the best irrigation level for each growth stage of the crop, accounting for the varying impact of water stress overtime. The LP provides the best tradeoff between expanding the irrigated area and decreasing water share per hectare. The model objective is to maximize the total expected crop yield. The model is particularly applicable for regions suffering from irrigation water scarcity, such as Saudi Arabia. The implementation was made for crops in Al-Jouf Region, north of Saudi Arabia