Chaos control of new Ikeda–Lorenz systems by GYC partial region stability theory

A new strategy to achieve chaos control by GYC partial region stability theory is proposed. By using the GYC partial region stability theory, the Lyapunov function is a simple linear homogeneous function of error states, the controllers are more simple and have less simulation error because they are in lower degree than that of traditional controllers. Simulation results for a new Ikeda–Lorenz system show the effectiveness of this strategy. Copyright © 2008 John Wiley & Sons, Ltd.     

Fuzzy statistic and comprehensive evaluating study for activity characterization of the active region

In this paper, the theory and method of the fuzzy mathematics are used to probe the connection between the activity of the active region and characterization of the sunspot groups, to build the subordinating function according to the relationship between them and to evaluate comprehensively the activity of the active region on the solar disk. The precise prediction of activity of the active regions has been obtained by data reduction and analysis. The predicting accuracy is higher than 95%. Forecast results indicate that the method of the fuzzy comprehensive evaluation is a good one for the solar activity prediction.     

Investigation of a macroeconomic model by the method of region analysis

A macroeconomic model on the relation between economic growth and the environment is investigated with the aim of illustrating how the method of region analysis can be used in solving practical problems formulated as regular optimal control problems with state constraints.This paper was written when the author was invited by Professor R. Bulirsch to work at the Munich University of Technology with the assistance of the Alexander Von Humboldt Foundation. The author would like to express his sincere gratitude to the Alexander Von Humboldt Foundation and to Professor Bulirsch.     

基于噪声误差模型的不规则区域室内定位和锚点分布优化

结合实际工业背景,研究了一类在不规则区域且误差不服从高斯分布的室内无线定位问题.给出了噪声误差模型, 在对多个传统定位算法进行性能分析的基础上,研究了待定位区域内锚点阵列的分布, 改进了多锚点阵列下的定位方法,并提出基于Delaunay三角剖分锚点分布优化模型和求解方法.     

Sharpness of the Korányi approach region

We prove a Littlewood-type theorem which shows the sharpness of the Korányi approach region for the boundary behavior of Poisson-Szegö integrals on the unit ball of . Our result is stronger than Hakim and Sibony (1983).

     

各地区城市市政工程情况统计分析及评估

本文利用数学计算软件SAS作主成分分析 ,将我国各地区城市市政工程情况进行排序、分类 ,再用对应分析法分别对各地区进行单项指标分析 ,最后对影响各地区城市市政工程情况的几个重要因素进行相关分析。以期为各地区城市市政工程的健康发展提供更好的思路     

Stability of an interconnected Schrödinger–heat system in a torus region

In this paper, we study the exponential stability of a two‐dimensional Schrödinger–heat interconnected system in a torus region, where the interface between the Schrödinger equation and the heat equation is of natural transmission conditions. By using a polar coordinate transformation, the two‐dimensional interconnected system can be reformulated as an equivalent one‐dimensional coupled system. It is found that the dissipative damping of the whole system is only produced from the heat part, and hence, the heat equation can be considered as an actuator to stabilize the whole system. By a detailed spectral analysis, we present the asymptotic expressions for both eigenvalues and eigenfunctions of the closed‐loop system, in which the eigenvalues of the system consist of two branches that are asymptotically symmetric to the line Reλ =? Imλ. Finally, we show that the system is exponentially stable and the semigroup, generated by the system operator, is of Gevrey class δ > 2. Copyright © 2016 John Wiley & Sons, Ltd.     

Superconvergence analysis of finite element method for Poisson–Nernst–Planck equations

This article concerns with the superconvergence analysis of bilinear finite element method (FEM) for nonlinear Poisson–Nernst–Planck (PNP) equations. By employing high accuracy integral identities together with mean value technique, the superclose estimates in H¹‐norm are derived for the semi‐discrete and the backward Euler fully‐discrete schemes, which improve the suboptimal error estimate in L²‐norm in the previous literature. Furthermore, the global superconvergence results in H¹‐norm are obtained through interpolation postprocessing approach. Finally, a numerical example is provided to confirm the theoretical analysis.     

Chebyshev pseudospectral method for computing numerical solution of convection–diffusion equation

A method for computing highly accurate numerical solutions of 1D convection–diffusion equations is proposed. In this method, the equation is first discretized with respect to the spatial variable, transforming the original problem into a set of ordinary differential equations, and then the resulting system is integrated in time by the fourth-order Runge–Kutta method. Spatial discretization is done by using the Chebyshev pseudospectral collocation method. Before describing the method, we review a finite difference-based method by Salkuyeh [D. Khojasteh Salkuyeh, On the finite difference approximation to the convection–diffusion equation, Appl. Math. Comput. 179 (2006) 79–86], and, contrary to the proposal of the author, we show that this method is not suitable for problems involving time dependent boundary conditions, which calls for revision. Stability analysis based on pseudoeigenvalues to determine the maximum time step for the proposed method is also carried out. Superiority of the proposed method over a revised version of Salkuyeh’s method is verified by numerical examples.     

Stability of efficiency evaluations in data envelopment analysis

Efficiency evaluations in data envelopment analysis are shown to be stable for arbitrary perturbations in the convex hulls of input and output data. Also, the corresponding restricted Lagrange multiplier functions are shown to be continuous. The results are proved using point-to-set mappings and a particular region of stability from input optimization.Research partly supported by National Science Foundation Grants, Office of Naval Research Grant, and by the Natural Sciences and Engineering Council of Canada.     

Mathematical analysis of the motion of a rigid body in a compressible Navier–Stokes–Fourier fluid

We study an initial and boundary value problem modelling the motion of a rigid body in a heat conducting gas. The solid is supposed to be a perfect thermal insulator. The gas is described by the compressible Navier–Stokes–Fourier equations, whereas the motion of the solid is governed by Newton's laws. The main results assert the existence of strong solutions, in an ‐ setting, both locally in time and globally in time for small data. The proof is essentially using the maximal regularity property of associated linear systems. This property is checked by proving the ‐sectoriality of the corresponding operators, which in turn is obtained by a perturbation method.     

The boundary element solution of the magnetohydrodynamic flow in an infinite region

We consider the magnetohydrodynamic (MHD) flow which is laminar, steady and incompressible, of a viscous and electrically conducting fluid on the half plane (y≥0)$(y\ge 0)$. The boundary y=0$y=0$ is partly insulated and partly perfectly conducting. An external circuit is connected so that current enters the fluid at discontinuity points through external circuits and moves up on the plane. The flow is driven by the interaction of imposed electric currents and a uniform, transverse magnetic field applied perpendicular to the wall, y=0$y=0$. The MHD equations are coupled in terms of the velocity and the induced magnetic field. The boundary element method (BEM) is applied here by using a fundamental solution which enables treating the MHD equations in coupled form with general wall conditions. Constant elements are used for the discretization of the boundary y=0$y=0$ only since the boundary integral equation is restricted to this boundary due to the regularity conditions at infinity. The solution is presented for the values of the Hartmann number up to M=700$M=700$ in terms of equivelocity and induced magnetic field contours which show the well-known characteristics of the MHD flow. Also, the thickness of the parabolic boundary layer propagating in the field from the discontinuity points in the boundary conditions, is calculated.     

Gel'fand–Tsetlin bases of orthogonal polynomials in Hermitean Clifford analysis

An explicit algorithmic construction is given for orthogonal bases for spaces of homogeneous polynomials, in the context of Hermitean Clifford analysis, which is a higher dimensional function theory centered around the simultaneous null solutions of two Hermitean conjugate complex Dirac operators. Copyright © 2011 John Wiley & Sons, Ltd.     

Convergence analysis of the Navier–Stokes alpha model

We consider the Navier–Stokes‐alpha (NS‐α) model as an approximation of turbulent flows under nonperiodic boundary conditions. We prove global existence and uniqueness of weak solutions of the particular model. Further, we give full discretization of the model using the finite element approximations. Finally, we prove convergence of the method to the continuous NS‐α solution as h → 0 for a constant α. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Vortex analysis of the periodic Ginzburg–Landau model

We study the vortices of energy minimizers in the London limit for the Ginzburg–Landau model with periodic boundary conditions. For applied fields well below the second critical field we are able to describe the location and number of vortices. Many of the results presented appeared in [H. Aydi, Doctoral Dissertation, Université Paris-XII, 2004], others are new.     

Numerical analysis of semi-linear parabolic systems in diffusion–reaction problems

In this paper, we investigate problems of approximation for the solution of a system of coupled semi-linear parabolic partial differential equations that model diffusion-reaction problems in chemical engineering. Given that the solutions belong to H^s (0, ∞), we consider finite-element approximations on bounded domains (0, R(h)) such that lim_h→0[R(h)] = ∞. Optimal convergence estimates are found to depend on the asymptotic behaviour of the solution and its regularity near t = 0. In the L²-norm, they cannot exceed an order of O((;h²/t^3/4) + h²[In h]²). For that purpose, a Wheeler-type argument is also generalized to non-coercive elliptic forms. Fully discrete schemes that preserve the positivity of the solutions are also considered. Due to the singularity at t = 0, they lead to estimates of the order O(τ^1/4 + h²/t^3/4).     

Convergence analysis of a linearized Crank–Nicolson scheme for the two‐dimensional complex Ginzburg–Landau equation

A linearized Crank–Nicolson‐type scheme is proposed for the two‐dimensional complex Ginzburg–Landau equation. The scheme is proved to be unconditionally convergent in the L² ‐norm by the discrete energy method. The convergence order is \begin{align*}\mathcal{O}(\tau^2+h_1^2+h^2_2)\end{align*}, where τ is the temporal grid size and h₁,h₂ are spatial grid sizes in the x ‐ and y ‐directions, respectively. A numerical example is presented to support the theoretical result. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Fredholm theory connected with a Douglis–Nirenberg system of differential equations over an exterior region in

We consider a boundary problem over an exterior subregion of for a Douglis–Nirenberg system of differential operators under limited smoothness asumptions and under the assumption of parameter‐ellipticity in a closed sector in the complex plane with vertex at the origin. We pose the problem in an Sobolev–Bessel potential space setting, , and denote by the operator induced in this setting by the boundary problem under null boundary conditions. We then derive results pertaining to the Fredholm theory for for values of the spectral parameter λ lying in as well as results pertaining to the invariance of the Fredholm domain of with p .     

Superconvergence analysis of FEMs for the Stokes–Darcy system

We consider a superconvergence analysis for quadratic finite element approximations of the Stokes–Darcy system. The superclose property of an extra half order is proven for uniform triangular meshes. Based on the result of the superclose property, global superconvergence is derived by applying a postprocessing technique. In addition, some numerical examples are presented to demonstrate our theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.