Projective Approximation of Double Limit Points for Nonlinear Problems

In [2], general approximation results for the solution in a neighborhood of a simple limit point are given. In this paper we give projective approximation results for the solutions in a neighborhood of a double limit point. Application of these results to a nonlinear partial differential equation and numerical results are given.     

Steady solution of solitary wave and linear shear current interaction

The steady solution of a solitary wave propagating in the presence of a linear shear background current is investigated by the Green–Naghdi (GN) equations. The steady solution is obtained by use of the Newton–Raphson method. Three aspects are investigated; they are the wave speed, wave profile and velocity field. The converged GN results are compared with results from the literature. It is found that for the opposing-current case of the solitary wave with a small amplitude, the results of the GN equations match results from the literature well, while for the solitary wave with a large amplitude, results from the literature are seen to be not as accurate. In the following-current case, though the amplitude of the solitary wave is small, the GN results are shown to be accurate. The velocity along the water column at the wave crest and the velocity field for different cases are calculated by the GN equations. The results of the GN equations show obvious differences when compared with the results obtained by superposing the no-current results and linear shear current linearly. We find that for the same current strength, the vortex is stronger for the steep solitary-wave case than that for the small solitary-wave case.     

Positivity and stability of the essential spectrum for singular transport semigroups with non-vacuum boundary conditions

In this paper we prove some compactness results for a large class of singular transport equations. Our approach relies on some comparison results for positive operators. Our results extend and complete several earlier works. We also provide simpler proofs for several known results in the literature.     

Some dual characterizations of Farkas-type results for fractional programming problems

In this paper, we present some Farkas-type results for a fractional programming problem. To this end, by using the properties of dualizing parametrization functions, Lagrangian functions and the epigraph of the conjugate functions, we introduce some new notions of regularity conditions and then obtain some dual forms of Farkas-type results for this fractional programming problem. We also obtain sufficient conditions for alternative type theorems. As an application of these results, we obtain the corresponding results for a convex optimization problem.     

On the negative value of information in informationally inefficient markets: Calculations for large number of traders

In informationally inefficient markets, classical decision theory assumes the value of information to be positive. Recent developments, however, contradict this paradigm. Schredelseker [Schredelseker, K., 2001. Is the usefulness approach useful? Some reflections on the utility of public information. In: McLeay, S., Riccaboni, A. (Eds.), Contemporary Issues in Accounting Regulation, Kluwer Academic Publishers, Boston, pp. 135–153] proposed a simulation model wherein a single security is traded among non-cooperating and asymetrically informed traders. One of the main results was the fact that badly informed traders could expect higher returns than traders with more information. But Schredelseker was able to give exact results for a small number of traders only. The aim of this paper is to give reliable results for a sufficiently large number of traders for both the expected gain and the probability of gain larger than zero. We are using combinatorial methods in order to get exact results for badly informed traders and simulation techniques for results of traders with higher level of information. The exact results are used (error between exact results and simulation results for the first traders) to determine the number of samples which have to be drawn with the simulation algorithm.     

Properties of serial kanban systems

In this paper we show some structural results of a kanban system by using results about the underlying GSMP. The main results from this connection are: dominance of allocations, optimal partition, upper and lower bounds on throughput, consistency of the IPA derivative, convexity of throughput as a function of service time parameters and concavity of throughput with respect to number of kanbans. Although the dominance and the partition results were obtained previously by sample path arguments, the proofs here are less cumbersome and generalize the earlier results. The second-order properties for kanban lines are new. These results form a basis for results in multi-product lines where proofs by sample paths require extensive notation.     

Effective bandwidths: Call admission,traffic policing and filtering for ATM networks

In this paper we review and extend the effective bandwidth results of Kelly [28], and Kesidis, Walrand and Chang [29, 6]. These results provide a framework for call admission schemes which are sensitive to constraints on the mean delay or the tail distribution of the workload in buffered queues. We present results which are valid for a wide variety of traffic streams and discuss their applicability for traffic management in ATM networks. We discuss the impact of traffic policing schemes, such as thresholding and filtering, on the effective bandwidth of sources. Finally we discuss effective bandwidth results for Brownian traffic models for which explicit results reveal the interaction arising in finite buffers.     

The spline collocation method for parabolic boundary integral equations on smooth curves

Summary. We consider the spline collocation method for a class of parabolic pseudodifferential operators. We show optimal order convergence results in a large scale of anisotropic Sobolev spaces. The results cover the classical boundary integral equations for the heat equation in the general case where the spatial domain has a smooth boundary in the plane. Our proof is based on a localization technique for which we use our recent results proved for parabolic pseudodifferential operators. For the localization we need also some special spline approximation results in anisotropic Sobolev spaces. Received May 17, 2001 / Revised version received February 19, 2002 / Published online April 17, 2002     

泛函积分方程的正解与应用

运用锥拉伸与压缩不动点定理,研究一类泛函积分方程的正解．把所得结果应用于研究常微分方程积分边值问题正解的存在性,所得结果推广和本质上改进了马如云等作者最近的一些结果．     

Truncated random variables with application to random surfaces

There has been considerable interest in obtaining discrete results for random surfaces. Standard results have been published in journals of physics or engineering which have emphasised the applications. This paper gives a detailed background of the mathematical methods needed so that the central connection, namely truncated random variables, between these standard results can be understood. Distributions of discrete peak measures are obtained from the distributions of discrete profile measures of a random Gaussian surface by applying results for the distributions of truncated random variables. This enable the moments to be obtained from known results for the truncated distributions.     

向量优化中广义增广拉格朗日对偶理论及应用

作者介绍了一种基于向量值延拓函数的广义增广拉格朗日函数,建立了基于广义增广拉格朗日函数的集值广义增广拉格朗日对偶映射和相应的对偶问题,得到了相应的强对偶和弱对偶结果,将所获结果应用到约束向量优化问题.该文的结果推广了一些已有的结论.     

Superconvergence of mixed finite element semi-discretizations of two time-dependent problems

We will show that some of the superconvergence properties for the mixed finite element method for elliptic problems are preserved in the mixed semi-discretizations for a diffusion equation and for a Maxwell equation in two space dimensions. With the help of mixed elliptic projection we will present estimates global and pointwise in time. The results for the Maxwell equations form an extension of existing results. For both problems, our results imply that post-processing and a posteriori error estimation for the error in the space discretization can be performed in the same way as for the underlying elliptic problem.     

Sufficient structure conditions for uniqueness of viscosity solutions of semilinear and quasilinear equations

In this article, we introduce a new approach for proving Maximum Principle type results for viscosity solutions of second-order, fully nonlinear possibly degenerate elliptic equations. This approach leads, in particular, to a better understanding of the conditions on the equation which are necessary to obtain such results. It allows us to provide new comparison results for semilinear and quasilinear equations.     

Sequential Lagrangian Conditions for Convex Programs with Applications to Semidefinite Programming

In this paper it is shown that, in the absence of any regularity condition, sequential Lagrangian optimality conditions as well as a sequential duality results hold for abstract convex programs. The significance of the results is that they yield the standard optimality and duality results for convex programs under a simple closed-cone condition that is much weaker than the well-known constraint qualifications. As an application, a sequential Lagrangian duality, saddle-point conditions, and stability results are derived for convex semidefinite programs.The authors are grateful to the referee and Professor Franco Giannessi for valuable comments and constructive suggestions which have contributed to the final preparation of the paper.     

Systems of quasi-variational relations with applications

In this paper, we introduce a system of quasi-variational relations (in short, SQVR) and present several examples which show that it is a very general and unified model of several problems. We establish the existence of solutions of SQVP, in general, and several other problems, in particular. As an application of our results, we derive maximal element theorems and a collectively fixed point theorem for a family of multivalued maps. As further applications, we study Ky Fan type inequality / inclusion problem for vector valued bifunctions which includes constrained Nash equilibrium problem as a special case. We also present a common fixed point theorem for a family of multivalued maps. The results of this paper improve and generalize several known results on (system of) quasi-equilibrium problems, (system of) quasi-variational inclusions, constrained Nash equilibrium problem, collectively fixed point theorem and KKM type theorems for a family of multivalued maps. Our results also contain several results which appeared in recent literature.     

Dynamical Systems and Adaptive Timestepping in ODE Solvers

Initial value problems for ODEs are often solved numerically using adaptive timestepping algorithms. These algorithms are controlled by a user-defined tolerance which bounds from above the estimated error committed at each step. We formulate a large class of such algorithms as discrete dynamical systems which are discontinuous and of higher dimension than the underlying ODE. By assuming sufficiently strong finite-time convergence results on some neighbourhood of an attractor of the ODE we prove existence and upper semicontinuity results for a nearby numerical attractor as the tolerance tends to zero.This assumption of sufficiently strong finite-time convergence results is then examined for adaptive algorithms that use a pair of explicit Runge-Kutta methods of different order to estimate the one-step error. For arbitrary Runge-Kutta pairs the necessary finite-time convergence results fail to hold on a set of points in the phase space that includes all the equilibria of the ODE. Therefore, in general, the asymptotic convergence results cannot be applied to attractors containing equilibria. However, for a particular class of Runge-Kutta pairs, the finite-time convergence results can be strengthened to include neighbourhoods of equilibrium points for which the Jacobian is invertible.     

非正非线性算子方程正解的存在性及其应用

首先使用全局分歧理论得到了含参数非线性算子方程解集无界连通分支存在的结果,然后根据算子的正连通性得到了一类非正非线性算子方程正解的存在结果.使用本文的主要结果在无需假设非线性项为正的条件下可以得到某些微分边值问题正解的存在结果.     

SUPERCONVERGENCE AND A POSTERIORI ERROR ESTIMATES FOR BOUNDARY CONTROL GOVERNED BY STOKES EQUATIONS

In this paper, the superconvergence results are derived for a class of boundary con-trol problems governed by Stokes equations. We derive superconvergence results for boththe control and the state approximation. Base on superconvergence results, we obtainasymptotically exact a posteriori error estimates.     

Positive periodic solutions of singular systems with a parameter

The existence and multiplicity of positive periodic solutions for second-order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our results provide a unified treatment for the problem and significantly improve several results in the literature. The proof of our results is based on the Krasnoselskii fixed point theorem in a cone.     

Minimizing cyclic cutwidth of graphs using a memetic algorithm

Cyclic cutwidth minimization problem (CCMP) consists of embedding a graph onto a circle such that the maximum cutwidth in a region is minimized. It is an NP-complete problem and for some classes of graphs, exact results of cyclic cutwidth have been proved in literature. However, no algorithm has been reported for general graphs. In this paper, a memetic algorithm is proposed for CCMP in which we have designed six construction heuristics in order to generate a good initial population and also local search is employed to improve the solutions in each generational phase. The algorithm achieves optimal results for the classes of graphs with known exact results. Extensive experiments have also been conducted on some classes of graphs for which exact results are not known such as the complete split graph, join of hypercubes, toroidal meshes, cone graph and some instances of Harwell-Boeing graphs which are a subset of public domain Matrix Market library. Trends observed in the experimental results for some of the classes of graphs have led to conjectures for cyclic cutwidth.