UNIFORM ESTIMATES OF SOLUTIONS OF(?)-EQUATION ON STEIN MANIFOLDS

By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman-Leray-Norguet formula for （p, q） differential forms on an open set with C^1 piecewise smooth boundary on a Stein manifold, and under suitable conditions gave the solutions of δ^--equation on a Stein manifold. In this article, using the method of Range and Siu [5], under suitable conditions, the authors complicatedly calculate to give the uniform estimates of solutions of δ^--equation for （p, q） differential forms on a Stein manifold.

UNIFORM SUPERCONVERGENCE ANALYSIS OF A TWO-GRID MIXED FINITE ELEMENT METHOD FOR THE TIME-DEPENDENT BI-WAVE PROBLEM MODELING D-WAVE SUPERCONDUCTORS

In this paper,a two-grid mixed finite element method(MFEM)of implicit Backward Euler(BE)formula is presented for the fourth order time-dependent singularly perturbed Bi-wave problem for d-wave superconductors by the nonconforming EQ_(1)^(rot) element.In this approach,the original nonlinear system is solved on the coarse mesh through the Newton iteration method,and then the linear system is computed on the fine mesh with Taylor’s expansion.Based on the high accuracy results of the chosen element,the uniform superclose and superconvergent estimates in the broken H^(1)-norm are derived,which are independent of the negative powers of the perturbation parameter appeared in the considered problem.Numerical results illustrate that the computing cost of the proposed two-grid method is much less than that of the conventional Galerkin MFEM without loss of accuracy.

The Integral Representations and Their Applications on the Analytic Varieties of Bounded Domains in Stein Manifolds

In this paper,we first obtain a unified integral representation on the analytic varieties of the general bounded domain in Stein manifolds(the two types bounded domains in[3]are regarded as its special cases).Secondly we get the integral formulas of the solution of∂-equation.And we use a new and unique method to give a uniform estimate of the solution of∂-equation,which is different from Henkin's method.

GLOBAL ENTROPY SOLUTIONS TO AN INHOMOGENEOUS ISENTROPIC COMPRESSIBLE EULER SYSTEM

In this article, we develop a new technique to prove the global existene of entropy solutions to an inhomogeneous isentropic compressible Euler equations through the compensated compactness and vanishing viscosity method. In particular, the entropy solutions are uniformly bounded independent of time.

THE GLOBAL COMBINED QUASI-NEUTRAL AND ZERO-ELECTRON-MASS LIMIT OF NON-ISENTROPIC EULER-POISSON SYSTEMS

We consider a non-isentropic Euler-Poisson system with two small parameters arising in the modeling of unmagnetized plasmas and semiconductors.On the basis of the energy estimates and the compactness theorem,the uniform global existence of the solutions and the combined quasi-neutral and zero-electron-mass limit of the system are proved when the initial data are close to the constant equilibrium state.In particular,the limit is rigorously justified as the two parameters tend to zero independently.

ON RADII OF ABSORBING SETS FOR KURAMOTOSIVASHINSKY EQUATION

In this article sharper estimates on the radii of absorbing sets for the Kuramoto_Sivashinsky equation are given. It is proved that radii of absorbing sets will decay to zero as the coefficient of viscosity tends to a certain critical value, which is more reasonable in the physical sence compared with classical results.

Fully Discrete Nonlinear Galerkin Methods for Kuramoto-Sivashinsky Equation and Their Error Estimates

In this paper,the uniform error estimates with respect to t∈[0, ∞ ) of the nonlinear Galerkin method are given for the long time integration of the Kuramoto-Sivashinsky equation. The nonlinear Galerkin method is used to study the asymptotic behaviour of Kuramoto-Sivashinsky equation and to construct the bifurcation diagrams.

Improving Energy and Power Efficiency Using NComputing and Approaches for Predicting Reliability of Complex Computing Systems

Opting to follow the computing-design philosophy that the best way to reduce power consumption and increase energy efficiency is to reduce waste, we propose an architecture with a very simple ready-implementation by using an NComputing device that can allow multi-users but only one computer is needed. This intuitively can save energy, space as well as cost. In this paper, we propose a simple and realistic NComputing architecture to study the energy and power-efficient consumption of desktop computer systems by using the NComputing device. We also propose new approaches to estimate the reliability of k-out-of-n systems based on the delta method. The k-out-of-n system consisting of n subsystems works if and only if at least k-of-the-n subsystems work. More specificly, we develop approaches to obtain the reliability estimation for the k-out-of-n systems which is composed of n independent and identically distributed subsystems where each subsystem （or energy-efficient usage application） can be assumed to follow a two-parameter exponential lifetime distribution function. The detailed derivations of reliability estimation of k-out-of-n systems based on the biased-corrected estimator, known as delta method, the uniformly minimum variance unbiased estimate （UMVUE） and maximum likelihood estimate （MLE） are discussed. An energy-management NComputing application is discussed to illustrate the reliability results in terms of the energy consumption usages of a computer system with qua（t-core, 8 GB of RAM, and a GeForce 9800GX-2 graphics card to perform various complex applications. The estimated reliability values of systems based on the UMVUE and the delta method differ only slightly. Often the UMVUE of reliability for a complex system is a lot more difficult to obtain, if not impossible. The delta method seems to be a simple and better approach to obtain the reliability estimation of complex systems. The results of this study also show that, in practice, the NComputing architecture improves both energy cost saving and energy efficient living spaces.

Uniform Estimate for The Tail Probabilities of Randomly Weighted Sums

Several authors have studied the uniform estimate for the tail probabilities of randomly weighted sumsa.ud their maxima. In this paper, we generalize their work to the situation thatis a sequence of upper tail asymptotically independent random variables with common distribution from the is a sequence of nonnegative random variables, independent of and satisfying some regular conditions. Moreover. no additional assumption is required on the dependence structureof {θi,i≥ 1）.

Uniform Lipschitz Estimates of Homogenization of Elliptic Systems in Divergence Form with Dini Conditions

The paper is devoted to the homogenization of elliptic systems in divergence form.We obtain uniform interior as well as boundary Lipschitz estimates in a bounded C1,γdomain when the coefficients are Dini continuous,inhomogeneous terms are divergence of Dini continuous functions and the boundary functions have Dini continuous derivatives.The results extend Avellaneda and Lin’s work[Comm.Pure Appl.Math.,40:803-847(1987)],where Holder continuity is the main assumption on smoothness of the data.

UNIFORM STABILITY AND ERROR ANALYSIS FOR SOME DISCONTINUOUS GALERKIN METHODS

In this paper,we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin(HDG)and weak Galerkin(WG)methods.By using the standard Brezzi theory on mixed methods,we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters.As a result,by taking appropriate limit of the stabilization parameters,we show that the HDG method converges to a primal conforming method and the WG method converges to a mixed conforming method.

Existence of the Uniformly Minimum Risk Unbiased Estimator in Seemingly Unrelated Regression System

For a seemingly Unrelated regression system with the assumption of normality,a necessary and sufficient condition for the existence of the Uniformly Minimum Risk Unbiased (UMRU)estimator of regression coefficients under strictly convex loss is obtained;it is proved that any unbiased estimator can not improve the least squares estimator;it is also shown that no UMRU estimator exists under missing observations.

UNIFORM ESTIMATES AND MULTISOLVABILITY OF A SEMILINEAR ELLIPTIC EQUATION

In this paper, the author gives the uniform estimates for the solutions of the semilinear elliptic equation △μ＋λe^μ= 0 with zero Dirichlet boundary condition,and then derive the uniqueness of the nonminimal solution assuming some conditions satisfied.

NONLINEAR GALERKIN METHODS FOR SOLVING TWO DIMENSIONAL NEWTON－BOUSSINESQ EQUATIONS

The nonlinear Galerkin methods for solving two-dimensional Newton-Boussinesq equations are proposed.The existence and uniqueness of global generalized solution of these equations, and the convergence of approximate solutions are also obtained.

Simultaneous optimal estimates of fixed effects and variance components in the mixed model

For a general linear mixed model with two variance components, a set of simple conditions is obtained, under which, (i) the least squares estimate of the fixed effects and the analysis of variance (ANOVA) estimates of variance components are proved to be uniformly minimum variance unbiased estimates simultaneously; (ii) the exact confidence intervals of the fixed effects and uniformly optimal unbiased tests on variance components are given; (iii) the exact probability expression of ANOVA estimates of variance components taking negative value is obtained.

A Family of Nonconforming Rectangular Elements for Strain Gradient Elasticity

We propose a family of nonconforming rectangular elements for the linear strain gradient elastic model.Optimal error estimates uniformly with respect to the small material parameter have been proved.Numerical results confirm the theoretical prediction.

THE IMPROVED FOURIER SPLITTING METHOD AND DECAY ESTIMATES OF THE GLOBAL SOLUTIONS OF THE CAUCHY PROBLEMS FOR NONLINEAR SYSTEMS OF FLUID DYNAMICS EQUATIONS

Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple togeth- er the elementary uniform energy estimates of the global weak solutions and a well known Gronwall＇s inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980＇s to study the op- timal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay esti- mates with sharp rates of the global weak solutions of the Cauchy problems for n-dimensional incompressible Navier-Stokes equations, for the n-dimensional magnetohydrodynamics equations and for many other very interesting nonlin- ear evolution equations with dissipations can be established.