FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension

We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. Moreover, using a weaker notion of approximation, we show the existence of a fully polynomial-time approximation scheme for the problem of maximizing or minimizing an arbitrary polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. A conference version of this article, containing a part of the results presented here, appeared in Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, Miami, FL, January 22–24, 2006, pp. 743–748. The first author gratefully acknowledges support from NSF grant DMS-0608785, a 2003 UC-Davis Chancellor’s fellow award, the Alexander von Humboldt foundation, and IMO Magdeburg. The remaining authors were supported by the European TMR network ADONET 504438.     

Algorithm of orbit determination using one or two GPS satellites

The problem of orbit determination using one or two GPS satellites is discussed. Methods of getting initial values based on linear translation is presented; the Secant method and the descend Newton iterative procedure and the continuation algorithm are used synthetically to solve the nonlinear equations. Computer simulation shows that this algorithm can give preliminary state of satellite orbit with a certain precision in short time.     

Prevalent Behavior of Strongly Order Preserving Semiflows

Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or toward the set of equilibria (quasiconvergence). In this paper, we provide new formulations of these results in terms of the measure-theoretic notion of prevalence, developed in Christensen (Israel J. Math., 13, 255–260, 1972) and Hunt et al. (Bull. Am. Math. Soc., 27, 217–238, 1992). For monotone reaction–diffusion systems with Neumann boundary conditions on convex domains, we show the prevalence of the set of continuous initial conditions corresponding to solutions that converge to a spatially homogeneous equilibrium. We also extend a previous generic convergence result to allow its use on Sobolev spaces. Careful attention is given to the measurability of the various sets involved.     

The Markov modulated regulated Brownian motion: A second-order fluid flow model of a finite buffer

A second-order fluid flow model of a queue with finite capacity buffer and variable net input process is presented, based on the previous work of Karandikar and Kulkarni (1995). Queue length is modelled as a Brownian motion whose parameters are controlled by a finite state Markov chain. The process, termed a Markov modulated regulated Brownian motion (MMRBM), provides analytical solutions for steady state queue length distributions, overflow losses and idleness probabilities using boundary regulators. Applications of the model include queues with failure-prone servers and ATM statistical multiplexers with variable traffic loads. This revised version was published online in June 2006 with corrections to the Cover Date.     

Preparation and third-order nonlinear optical properties of self-organized complex oxide Ce:BaTiO3 quantum dots

Pulsed laser ablation epitaxial Strancky-Krastanow growth of self-organized complex oxide Ce:BaTiO3 quantum dots on MgO(100) substrates is demonstrated.Atomic force microscopy and X-ray diffraction are used to observe the structure and the growth process of the self-organized complex oxide quantum dots.The average dimension,height,and the density of self-organized complex oxide Ce:BaTiO3 quantum dots are given.The nonlinear refractive indexes of the wetting layer and the self-organized ordered quantum dots are determined by the single beam Z-scan method.The mechanisms of the nonlinear effect enhancement for these low-dimensional structure are discussed.     

神经网络在非线性规划中的应用

本文对蔡少棠[1 ] ,[2 ] 等提出的非线性规划神经网络作了改进 ,使得该神经网络适合于通用VLSI技术实现 .     

Membranes of revolution under partially vanishing normal load

This paper investigates the existence and uniqueness of solutions of some boundary value problems modeling the deformation of a membrane of revolution under a partially vanishing normal load. The frame of the membrane models we deal with is the Reissner theory of thin shells of revolution, in which strain-displacement relations are nonlinear, although it assumes a linear stress-strain relation.     

A numerical algorithm for simulation of the Q-switched fiber laser using the travelling wave model

We develop a finite-difference scheme for approximation of a system of nonlinear PDEs describing the Q-switching process. We construct it by using staggered grids. The transport equations are approximated along characteristics, and quadratic nonlinear functions are linearized using a special selection of staggered grids. The stability analysis proves that a connection between time and space steps arises only due to approximation requirements in order to follow exactly the directions of characteristics. The convergence analysis of this scheme is done in two steps. First, some estimates of the uniform boundedness of the discrete solution are proved. This part of the analysis is done locally, in some neighborhood of the exact solution. Second, on the basis of the obtained estimates, the main stability inequality is proved. The second-order convergence rate with respect to the space and time coordinates follows from this stability estimate. Using the obtained convergence result, we prove that the local stability analysis in the selected neighborhood of the exact solution is sufficient.     

Stationary diffusion in the membrane systems with the ongoing reversible chemical reactions

The diffusion phenomena were analyzed using the phenomenological equations of the thermodynamics of irreversible processes. The diffusion coefficient was thought to be dependent on local concentrations and pressure, unlike it was done in the linear theories. The reversible chemical reactions were modeled as intermolecular interaction. The ideal and regular solutions and solutions, described by the Margules's and Sketchard–Hammer's equations, were investigated and analytical solutions were found.     

The nonlinear strain measure of polyisobutylene melt in general biaxial flow and its comparison to the Doi-Edwards model

The nonlinear strain measure of a polyisobutylene (PIB) melt as determined by analysis of uniaxial, planar, ellipsoidal, and equibiaxial extensions is compared to the predictions of the molecular model of Doi and Edwards. It is found that the universal strain function of the Doi-Edwards model is unable to predict the nonlinear behavior of this polymer melt in general extensional flow. The qualitative agreement between predictions and experimental data for the strain dependence of shear stress and first normal stress difference in shear flow that was considered as powerful evidence for the correctness of the Doi-Edwards model seems to be accidental. The exaggerated strain dependence of the model suggests a need to reconsider the assumptions concerning the chain retraction process.Presented at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.Dedicated to Professor F.R. Schwarzl on the occasion of his 65th birthday