Error estimation of prediction-correction legendre spectral approximation to incompressible fluid flow

1. IntroductionThere have been a lot of literatures concerning the existence, uniqueness, regularityof the solution of Navier-Stokes equation. Usually the primitive equation is considered,e.g.5 see 11,2]. Maily methods are used for its numerical simulation, e.g., see [2--7]. But wemeet several difficulties in calculation. For instance, if we use the finite difference method,then we have to evaluate the pressure at each time step. Some authors developed theartificial compressibility method or…     

MONOTONE APPROXIMATION TO A SYSTEM WITHOUT MONOTONE NONLINEARITY

1. IntroductionDue to the development of various studies in electromagnetism, biology and someother fields, nonlinear systems hajve been paid extellsive attention both analytically andnumerically, e.g., see [1--12]. As we kll')w, a reasonable numerical method should notonly have the approximation error of higher order, but also preserve the main feature ofthe original problem. In this case? the numerical results might fit the physical processbetter. Since the usual approximations simulate the …     

一类替换环的偏序$K_{0}$-群的无扭性

A ring R is called orthogonal if for any two idempotents e and f in R, the condition that e and f are orthogonal in R implies the condition that [eR] and [fR] are orthogonal in K0（R）^＋, i.e., [eR]∧[fR] = 0. In this paper, we shall prove that the K0-group of every orthogonal, IBN2 exchange ring is always torsion-free, which generalizes the main result in [3].     

HIGH ACCURACY NUMERICAL METHOD OF THIN-FILM PROBLEMS IN MICROMAGNETICS

In this paper, a new high accuracy numerical method for the thin-film problems of micron and submicron size ferromagnetic elements is proposed. For the computation of stray field, we use the finite element method(FEM) by introducing a semi-discrete artificial boundary condition [1, 2]. In our numerical experiments about the domain patterns and their movement, we can see that the results are accordant to that of experiments and other numerical methods. Our method are very convenient to deal with arbitrary shape of thin films such as a polygon with high accuracy.     

中介逻辑的命题演算系统(Ⅱ)

This paper is a continuation of [1]、[2]、[4]. In this paper, we shall con-tinue to constitute the formal theorems and the important substituting theorem(see theorem 16 in this paper) of the propositional calculus system of mediumlogic MP. The order numbers of following formal theorems follow those in reference[4]     

THE LONG-TIME BEHAVIOR OF SPECTRAL APPROXIMATE FOR KLEIN-GORDON-SCHROEDINGER EQUATIONS

Klein-Gordon-Schroedinger (KGS) equations are very important in physics. Some papers studied their well-posedness and numerical solution [1-4], and another works investigated the existence of global attractor in R^n and Ω包含于R^n (n≤3) [5-6,11-12]. In this paper, we discuss the dynamical behavior when we apply spectral method to find numerical approximation for periodic initial value problem of KGS equations. It includes the existence of approximate attractor AN, the upper semi-continuity on A which is a global attractor of initial problem and the upper bounds of Hausdorff and fractal dimensions for A and AN,etc.     

Finite Mixture Normal Models, with Application to Dose-Response Studies

In this paper, we consider the risk assessment problem under multi-levels and multiple mixture subpopulations. Our result is the generalization of the results of [1-5].1 Finite Mixture Normal ModelsIn dose-response studies, a class of phenomena that frequently occur are that experimental subjects (e.g., mice) may have different responses like 'none, mild, severe' after a toxicant experiment, or 'getting worse, no change, getting better' after a medical treatment, etc. These phenomena have attracted the attention of many researchers in recent years. Finite     

A class of quasilinear elliptic hemivariational inequalities

1. IntroductionIn this paper we shall deal with the quasilinear elliptic hemivaxiational inequalitieswhere the symbol OJ designates Clarke's generalized gradiellt of a locally Lipschitz functionalJ (see [1, 2]). The discontinuity is assumed to be in the lower order term OJ(u(x)). If Ais a linear operator and the disconiinuity is monotone, the problems have been studied,for example, in [3-6]. If A is a linear opertor and the discolltinuity is nonmonotone, thiskind of problems have been inve…     

On Trigonometric Splines

A great many papers concerning polynomial spline have been published in various mathematical journals.But, as we know, there are a few papers discussing trigonometric splines.The aim of this paper is to investigate some kinds of trigonometric splines, which can be regarded as a generalization of the polynomial splines discussed in[1],[2].From the results obtained in this paper we will see the similarity and differences between them.     

STABILITY OF DELAY DIFFERENCE EQUATIONS IN BANACH SPACES

1 IntroductionDiscrete reaction--diffusion type partial difference equations llave recentlybeen introduced by a number of authors as modeIs for the study of spatiotem-poral chaos (see e.g. [2,3j). Stability criteria have also been derived fOr suchequatioIls which invoIve two time-level processes (see e.g. [1l) as well as three-level processes (see e.g. [9]). In this paper, we will study no11linear three--levc1partia1 diffcrence equations in an abstract setting and derive stability criteriafo…     

Haar锥逼近的交错定理及其在系数有界逼近中的应用

本文首先推广了Ｐ．Ｐｅｉｓｋｅｒ １９８３年给出的Ｈａａｒ锥的定义及Ｈａａｒ锥一致逼近的交错定量，然后得到了Ｈａａｒ锥根数的一种求法。利用这些结果，讨论了系数有界限逼近的特征问题，特别是给出了系数有界限的代数多项式逼近与广义Ｂｅｒｎｓｔｅｉｎ多项式逼近的使用十分方便的交错定理。     

An empirical extension of the M/G/1 heavy traffic approximation

Numerical evaluation of waiting time distributions for M/G/1 systems is somewhat difficult. This paper examines a simple variation of the heavy traffic formula which may be useful at modest levels of traffic intensity. One can justify the heavy traffic approximation by expressing the Laplace transform of the service time distribution as a Maclaurin series and then truncating to three terms. The spectrum factorization and inversion leads in a straightforward fashion to the heavy traffic approximation. If one carries two additional terms from the Maclaurin series, the characteristic equation is a cubic with exactly one real negative root. This root provides an easy way to extend the heavy traffic formula to cases where the traffic is not so heavy. This paper studies the quality of this approximation and includes some numerical evaluation based on data actually encountered.     

Assembly-like queues with finite capacity: Bounds,asymptotics and approximations

In this paper we study a queueing model of assembly-like manufacturing operations. This study was motivated by an examination of a circuit pack testing procedure in an AT & T factory. However, the model may be representative of many manufacturing assembly operations. We assume that customers fromn classes arrive according to independent Poisson processes with the same arrival rate into a single-server queueing station where the service times are exponentially distributed. The service discipline requires that service be rendered simultaneously to a group of customers consisting of exactly one member from each class. The server is idle if there are not enough customers to form a group. There is a separate waiting area for customers belonging to the same class and the size of the waiting area is the same for all classes. Customers who arrive to find the waiting area for their class full, are lost. Performance measures of interest include blocking probability, throughput, mean queue length and mean sojourn time. Since the state space for this queueing system could be large, exact answers for even reasonable values of the parameters may not be easy to obtain. We have therefore focused on two approaches. First, we find upper and lower bounds for the mean sojourn time. From these bounds we obtain the asymptotic solutions as the arrival rate (waiting room, service rate) approaches zero (infinity). Second, for moderate values of these parameters we suggest an approximate solution method. We compare the results of our approximation against simulation results and report good correspondence.     

NON-ISOTROPIC JACOBI SPECTRAL METHODS FOR UNBOUNDED DOMAINS

Some specific non-isotropic Jacobi approximations in multiple-dimensions are investigated, which are used for numerical solutions of differential equations on various unbounded domains. The convergence of proposed schemes are proved. Some efficient algorithms are provided. Numerical results are presented to illustrate the efficiency of this new approach.     

Optimal dividends with incomplete information in the dual model

In [Gerber, H.U., Shiu, E.S.W., Smith, N., 2008. Methods for estimating the optimal dividend barrier and the probability of ruin. Insurance: Math. Econ. 42 (1), 243-254], methods were analyzed for estimating the optimal dividend barrier (in the sense of de Finetti). In particular, De Vylder approximations and diffusion approximations are discussed. These methods are useful when only the first few moments of the claim amount distribution are known.The purpose of this paper is to examine these and other methods (such as the gamma approximations and the gamproc approximations) in the dual model, see [Avanzi, B., Gerber, H.U., Shiu, E.S., 2007. Optimal dividends in the dual model. Insurance: Math. Econ. 41 (1), 111-123]. The dual model is obtained if the roles of premiums and claims are exchanged. In other words, the company has random gains, which constitute a compound Poisson process, and expenses occur continuously at a constant rate. The approximations can easily be implemented, and their accuracy is surprisingly good. Several numerical illustrations enhance the paper.     

Well-Posedness and Finite Element Approximations for Elliptic SPDEs with Gaussian Noises

The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by white or colored Gaussian noises. The noise term is approximated through the spectral projection of the covariance operator, which is not required to be commutative with the Laplacian operator.Through the convergence analysis of SPDEs with the noise terms replaced by the projected noises, the well-posedness of the SPDE is established under certain covariance operator-dependent conditions. These SPDEs with projected noises are then numerically approximated with the finite element method. A general error estimate framework is established for the finite element approximations. Based on this framework, optimal error estimates of finite element approximations for elliptic SPDEs driven by power-law noises are obtained. It is shown that with the proposed approach, convergence order of white noise driven SPDEs is improved by half for one-dimensional problems, and by an infinitesimal factor for higher-dimensional problems.     

RD-Rational Approximations of the Matrix Exponential

Restricted Denominator (RD) rational approximations to the matrix exponential operator are constructed by interpolation in points related to Krylov subspaces associated to a rational transform of the particular matrix considered. Convergence analysis are provided. Numerical experiments show the effectiveness of the proposed methods in applications involving discretizations of differential operators.     

Upper bounds for the risk in the α — t utility function

Fishburn's α — t model is an important example of a utility function involving a target for a random variable. Simple upper bounds for the risk function in this model are proposed for cases in which the probability distribution is either unknown, or produces complicated or intractable statements of the model.     

A complete asymptotic expansion for a sequence of certain sums

In the present note we derive a complete asymptotic expansion for a sequence of certain sums. A special case of our results solves a problem recently proposed in the Research Group in Mathematical Inequalities and Applications (RGMIA) mailing list. Moreover, the result is connected with a certain combinatorial problem.     

A heuristic technique for the transient behavior of Markovian queueing systems

Through an examination of numerical solutions to Markovian queueing systems, it has been shown that the expected queue length eventually approaches its equilibrium value in an approximately exponential manner. Based on this observation a heuristic is proposed for approximating the transient expected queue length for Markovian systems by scaling the numerical solution of an M/M/1 system.