Riemann problems for generalized gas dynamics

In this paper, a few classes of exact solutions are obtained using the differential constraints method for generalized gas dynamics equations. The solutions to Riemann problems for two different kinds of initial data are determined with a complete characterization of the solutions through shock waves and/or rarefaction waves.     

Comparisons between thermodynamic and one-dimensional combustion models of spark-ignition engines

A one-dimensional combustion model, employing a constant eddy diffusivity and a one-step chemical reaction, has been developed and applied to study the flame propagation in a spark-ignition engine. Calculations have been made at 1600 and 4200 rev min⁻¹ under fuel rich conditions and compared with available engine pressure data. One- and two-zone thermodynamic models have also been developed and applied to study the combustion process in the engine. The thermodynamic models have been compared with the one-dimensional model results and comparisons include the average mixture temperature, the temperatures of the burned and unburned gases and the flame surface area. These comparisons indicate that the one-dimensional model predictions are very sensitive to the eddy diffusivity and reaction rate data. The two-zone thermodynamic model predicts, first, a monotonically increasing flame surface area with time and, then, a monotonically decreasing surface area, whereas the one-dimensional model always predicts a monotonically increasing flame surface area. The average mixture temperature predicted by the one-zone thermodynamic model is higher than those of the two-zone and one-dimensional models during the compression stroke, while that of the one-dimensional model is higher than the temperatures predicted by the one- and two-zone models during the expansion stroke. The one-dmensional model predicts an accelerating flame even when the front approaches the cold cylinder wall. This yields a faster fuel consumption rate than those predicted by the one- and two-zone thermodynamic models which predict smoother burned fuel mass profiles.     

Some Riemann boundary value problems in Clifford analysis

In this paper, we mainly study the R_m (m>0) Riemann boundary value problems for functions with values in a Clifford algebra C?(V_{3, 3}). We prove a generalized Liouville‐type theorem for harmonic functions and biharmonic functions by combining the growth behaviour estimates with the series expansions for k‐monogenic functions. We obtain the result under only one growth condition at infinity by using the integral representation formulas for harmonic functions and biharmonic functions. By using the Plemelj formula and the integral representation formulas, a more generalized Liouville theorem for harmonic functions and biharmonic functions are presented. Combining the Plemelj formula and the integral representation formulas with the above generalized Liouville theorem, we prove that the R_m (m>0) Riemann boundary value problems for monogenic functions, harmonic functions and biharmonic functions are solvable. Explicit representation formulas of the solutions are given. Copyright © 2009 John Wiley & Sons, Ltd.     

Convergence of a finite difference method for combustion model problems

We study a finite difference scheme for a combustion model problem. A projection scheme near the combustion wave, and the standard upwind finite difference scheme away from the combustion wave are applied. Convergence to weak solutions with a combustion wave is proved under the normal Courant-Friedrichs-Lewy condition. Some con-     

Riemann problem for Chaplygin gas with combustion

We study the Riemann problem of the Chapman–Jouguet model for an ideal combustible Chaplygin gas. By analyzing the wave curves in the phase plane, we obtain constructively the unique solution of the Riemann problem under the global entropy conditions.     

A review of mathematical models in economic environmental problems

The paper presents a review of mathematical models used in economic analysis of environmental problems. This area of research combines macroeconomic models of growth, as dependent on capital, labour, resources, etc., with environmental models describing such phenomena like natural resources exhaustion or pollution accumulation and degradation. In simpler cases the models can be treated analytically and the utility function can be optimized using, e.g., such tools as the maximum principle. In more complicated cases calculation of the optimal environmental policies requires a computer solution. This revised version was published online in June 2006 with corrections to the Cover Date.     

Riemann boundary value problems on half space in Clifford analysis

In this paper, we discuss some properties of the Cauchy type integral operator defined over the half space of . As applications, we study a type of Riemann boundary value problem for solutions to polynomially generalized Cauchy–Riemann equations including with and as special cases over the half space of . Making use of Fischer‐type decomposition and the Clifford calculus for solutions to these equations, we will obtain explicit expressions of solutions to the kind of boundary value problems over the half space of . Copyright © 2012 John Wiley & Sons, Ltd.     

Sensitivity analysis for variational inequalities and nonlinear complementarity problems

This paper surveys the main results in the area of sensitivity analysis for finite-dimensional variational inequality and nonlinear complementarity problems. It provides an overview of Lipschitz continuity and differentiability properties of perturbed solutions for variational inequality problems, defined on both fixed and perturbed sets, and for nonlinear complementarity problems.     

Mixed-integer programming models for nesting problems

Several industrial problems involve placing objects into a container without overlap, with the goal of minimizing a certain objective function. These problems arise in many industrial fields such as apparel manufacturing, sheet metal layout, shoe manufacturing, VLSI layout, furniture layout, etc., and are known by a variety of names: layout, packing, nesting, loading, placement, marker making, etc. When the 2-dimensional objects to be packed are non-rectangular the problem is known as the nesting problem. The nesting problem is strongly NP-hard. Furthermore, the geometrical aspects of this problem make it really hard to solve in practice. In this paper we describe a Mixed-Integer Programming (MIP) model for the nesting problem based on an earlier proposal of Daniels, Li and Milenkovic, and analyze it computationally. We also introduce a new MIP model for a subproblem arising in the construction of nesting solutions, called the multiple containment problem, and show its potentials in finding improved solutions.     

Thermodynamically conditioned splitting schemes in combustion problems

Algorithms for solving the two-dimensional combustion problem for premixed flames are proposed and examined. The solution method is based on splitting into convective and diffusion parts according to the processes involved. A high-resolution explicit quasi-monotone scheme with flux correction is used for the hyperbolic part. For the parabolic part, the scheme is conservative and the source in the heat equation is set to be positive; i.e., the scheme ensures that the different thermodynamic consequences of the original equations hold; therefore, the scheme is thermodynamically conditioned. The applicability of the scheme to the full and purely gasdynamic problems is examined under various types of initial conditions and with various flux limiters. Numerical results are presented for one-and two-dimensional problems, including the Frank-Kamenetskii classical problem in two dimensions. The flame is shown to become turbulent in sufficiently wide pipes.     

The connectedness of the solutions set for generalized vector equilibrium problems

In this paper, we establish the connectedness of the sets of Henig efficient solutions, globally efficient solutions, weak efficient solutions, superefficient solutions and efficient solutions for a class of generalized vector equilibrium problems without the assumptions of monotonicity and compactness.     

A mean value theorem for generalized Riemann derivatives

Functional differences that lead to generalized Riemann derivatives were studied by Ash and Jones in (1987). They gave a partial answer as to when these differences satisfy an analog of the Mean Value Theorem. Here we give a complete classification.

     

EXISTENCE OF NONNEGATIVE SOLUTIONS FOR DEGENERATE ECOLOGICAL MODELS

In this paper,nonnegative solutions for the degenerate elliptic systems are considered.First,nonnegative solutions for scalar equation with spatial discontinuities are studied. Then themethod developed for scalar equation is applied to study elliptic systems. At last,the existence criteria of nonnegative solutions of elliptic systems are given.     

On some problems of weak consistency of quasi-maximum likelihood estimates in generalized linear models

In this paper,we explore some weakly consistent properties of quasi-maximum likelihood estimates(QMLE) concerning the quasi-likelihood equation in=1 Xi(yi-μ(Xiβ)) = 0 for univariate generalized linear model E(y |X) = μ(X'β).Given uncorrelated residuals {ei = Yi-μ(Xiβ0),1 i n} and other conditions,we prove that βn-β0 = Op(λn-1/2) holds,where βn is a root of the above equation,β0 is the true value of parameter β and λn denotes the smallest eigenvalue of the matrix Sn = ni=1 XiXi.We also show that the convergence rate above is sharp,provided independent non-asymptotically degenerate residual sequence and other conditions.Moreover,paralleling to the elegant result of Drygas(1976) for classical linear regression models,we point out that the necessary condition guaranteeing the weak consistency of QMLE is Sn-1→ 0,as the sample size n →∞.     

Uniqueness of solution to a free boundary problem from combustion

We investigate the uniqueness and agreement between different kinds of solutions for a free boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function defined in a domain and such that

0\}. \end{displaymath}">

We also assume that the interior boundary of the positivity set, \nobreak 0\}$">, so-called free boundary, is a regular hypersurface on which the following conditions are satisfied:

Here denotes outward unit spatial normal to the free boundary. In addition, initial data are specified, as well as either Dirichlet or Neumann data on the parabolic boundary of . This problem arises in combustion theory as a limit situation in the propagation of premixed flames (high activation energy limit).

The problem admits classical solutions only for good data and for small times. Several generalized concepts of solution have been proposed, among them the concepts of limit solution and viscosity solution. We investigate conditions under which the three concepts agree and produce a unique solution.

     

On the perturbation of least squares problems with equality constraints

Some new perturbation results are presented for least squares problems with equality constraints, in which relative errors are obtained on perturbed solutions, least squares residuals, and vectors of Lagrange multipliers of the problem, based on the equivalence of the problem to a usual least squares problem and optimal perturbation results for orthogonal projections.     

广义次对称矩阵反问题的最小二乘解

讨论了广义次对称矩阵反问题的最小二乘解,得到了解的一般表达式,并就该问题的特殊情形:矩阵反问题,得到了可解的充分必要条件及解的通式.此外,证明了最佳逼近问题解的存在唯一性,并给出了其解的具体表达式.     

双重广义线性模型的经验似然推断

基于截面经验似然方法,将双重广义线性模型的拟似然估计方程作为截面经验似然比函数的约束条件,构造了均值模型和散度模型未知参数的置信区间.最后通过数据模拟,将该方法与正态逼近方法比较,说明了该方法是有效和可行的.     

一类反应扩散方程奇摄动Robin问题的广义解

讨论了一类奇摄动反应扩散方程R ob in问题.在适当的条件下,研究了问题广义解的渐近性态.