Propagation of singularities in Cauchy problems for quasilinear thermoelastic systems in three space variables

By using microlocal analysis, the propagation of weak singularities in Cauchy problems for quasilinear thermoelastic systems in three space variables are investigated. First, paradifferential operators are employed to decouple the quasilinear thermoelastic systems. Second, by investigating the decoupled hyperbolic-parabolic systems and using the classical bootstrap argument, the property of finite propagation speeds of singularities in Cauchy problems for the quasilinear thermoelastic systems is obtained. Finally, it is shown that the microlocal weak singularities for Cauchy problems of the thermoelastic systems are propagated along the null bicharacteristics of the hyperbolic operators.     

Propagation characteristics of linearly polarized Bessel-Gaussian beams through an annular apertured paraxial ABCD optical system

By means of Collins diffraction integral formula in the paraxial approximation and based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical expression for linearly polarized Bessel-Gaussian beams passing through a paraxial ABCD optical system with an annular aperture has been derived. The results provide more convenient for studying their propagation and transformation than the usual way by using diffraction integral directly. By using the analytical expression and the diffraction integral formula some numerical simulations are done to illustrate for the propagation characteristics of a linearly polarized Bessel-Gaussian beam through an optical system with an annular aperture.     

Stability analysis of structurally unstable man–machine system involving time delays

In this paper, a structurally unstable man–machine system is considered and a rigorous mathematical analysis is performed to study the influence of time delays in the control force on stability of the equilibrium solution of this system. Results on stability, instability and conditions for the preservation of stability (instability), besides the existence of bifurcation are presented.     

Measure of Ordering in Statistical Systems

In this paper, we introduce a phenomenological measure of ordering in statistical systems. Using this characteristic, we construct a formal model of a system evolving according to the law of steepest ascent as the control parameter increases.     

求解非对称线性方程组的QMRGCGS方法

1 引言 求解非对称线性方程组Ax=b的双共轭梯度方法(BCG)[3]和它的变形共轭梯度平方方法(CGS)[6]都有典型的不规则收敛行为,后来Freund和Nachtigal提出一种BCG类方法,即拟极小剩余方法(QMR)[7],用来补救BCG方法的收敛性并且产生了光滑的收敛曲线。然而,象BCG方法一样,QMR方法要用到系数矩阵A及其转置A~T与向量的乘积,为了解决这一问题,Freund提出TFQMR方法,此方法具有拟极小剩余性,同时不需用到A~T与向量的乘积。     

Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamé Equations

We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature.     

Integrable Deformations of Tops Related to the Algebra so(p,q)

We propose an integrable deformation of the known model of two interacting tops on the algebra so(p,q). We consider particular cases including the generalized Lagrange and Kovalevskaya tops. We construct the Lax matrices and the corresponding classical R-matrices.     

Elliptic systems with nonlinearity q greater or equal than two with controlled growth. Global Hölder continuity of solutions to the Dirichlet problem

Hölder regularity up to the boundary of the solutions to the Dirichlet problem for second order elliptic systems with nonlinearity q>2 and with controlled growth is proved when n?q+2.     

Noninferior Nash Strategies for Multi-Team Systems

This paper is concerned with the optimization of systems that are controlled by several teams of decision makers. The decision makers within each team cooperate for the benefit of their team. On the other hand, the teams compete among themselves in order to achieve an objective that relates to the overall performance of the system. An approach that merges concepts from team theory and game theory for dealing with such systems and a solution called the noninferior Nash strategy are introduced. This multi-team solution provides a new framework for analyzing hierarchically controlled systems so as to address complicated coordination problems among the decision makers. The properties of the noninferior Nash solution in static multi-team systems are investigated and necessary conditions for its existence are derived. Analytical expressions for the noninferior Nash strategies are derived for a class of linear-quadratic static multi-team games. In order to deal with the issue of nonuniqueness of the solution, the concept of a noninferior Nash strategy with a team leader is introduced. Several examples are presented to illustrate the results.     

An existence theorem for neutral variational problems of Bolza

This note proves an existence theorem for a generalized Bolza-type problem that has time delays in both the state and velocity variables. The assumptions are stated in terms of a modification of the classical Hamiltonian, and extend ideas of Rockafellar to the delay case.