entropy production in second order three point schemes we discuss semi discrete three point finite difference methods for the numerical solution of system of conservation laws which are second order accurate in space in the sense of truncation error particular discretizations of the numerical entropy flux associated with such schemes are studied clarifying the importance of this discretization with regard to the production of numerical entropy using a numerical entropy flux constructed in a canonical way we prove that a wide class of finite difference methods cannot satisfy a discrete entropy inequality together with a well known result of schonbek concerning lax wendroff type schemes our result indicates a strong relationship between entropy production and oscillations in numerical solutions

convergence of fluctuation splitting schemes for two dimensional scalar conservation laws with a kinetic solver the fluctuation splitting schemes fss in short have been introduced by roe and sildikover to solve advection equations on rectangular grids and then extended to triangular grids by roe deconinck struij for a two dimensional nonlinear scalar conservation law we consider the case of a triangular grid and of a kinetic approach to reduce the discretization of the nonlinear equation to a linear equation and apply a particular fss called n scheme we show that the resulting scheme converges strongly in l 2 loc in a finite volume sense

an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search recently more research works are focused on multi objective particle swarm optimization algorithm mopso due to its ability of global and local search for solving multi objective optimization problems moops however most of existing mopsos cannot achieve satisfactory results in solution quality this paper proposes an efficient hybrid multi objective particle swarm optimization with a multi objective dichotomy line search mols named mols mopso to deal with such problem mols mopso combines an effective particle updating strategy with the local search of mols the effective particle updating strategy is used for global search to deal with premature convergence and diversity maintenance within the swarm the mols is periodically activated for fast local search to converge toward the pareto front the exploratory capabilities are enhanced more efficiently by keeping a desirable balance between global search and local search so as to ensure sufficient diversity and well distribution amongst the solutions of the non dominated fronts while retaining at the same time the convergence to the pareto optimal front comparing mols mopso with various state of the art multi objective optimization algorithms developed recently the comparative study shows the effectiveness of mols mopso which not only assures a better convergence to the pareto frontier but also illustrates a good diversity and distribution of solutions

on the convergence of a finite element method for a nonlinear hyperbolic conservation law we consider a space time finite element discretization of a time dependent nonlinear hyperbolic conservation law in one space dimension burgers equation the finite element method is higher order accurate and is a petrov galerkin method based on the so called streamline diffusion modification of the test functions giving added stability we first prove that if a sequence of finite element solutions converges boundedly almost everywhere as the mesh size tends to zero to a function u then u is an entropy solution of the conservation law this result may be extended to systems of conservation laws with convex entropy in several dimensions we then prove using a compensated compactness result of murat tartar that if the finite element solutions are uniformly bounded then a subsequence will converge to an entropy solution of burgers equation we also consider a further modification of the test functions giving a method with improved shock capturing finally we present the results of some numerical experiments

linear preservers of minimal rank abstract it is proved that a linear transformation on the vector space of upper triangular matrices that maps the set of matrices of minimal rank 1 into itself and either has the analogous property with respect to matrices of full minimal rank or is bijective is a triangular equivalence or a flip about the south west north east diagonal followed by a triangular equivalence the result can be regarded as an analogue of marcus moyls theorem in the context of triangular matrices

a posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multi dimensions in this paper we shall derive a posteriori error estimates in the l 1 norm for upwind finite volume schemes for the discretization of nonlinear conservation laws on unstructured grids in multi dimensions this result is mainly based on some fundamental a priori error estimates published in a recent paper by c chainais hillairet the theoretical results are confirmed by numerical experiments

geometric multiplicities of completions of partial triangular matrices abstract a sufficient condition for a set of positive integers g 1 g 2 g n to be the geometric multiplicites of given eigenvalues for some strictly lower triangular completions of a partial matrix is given a method is proposed which allows one to reduce the investigation of geometric multiplicities of completed matrix with different eigenvalues to the nilpotent case

an analysis of some high accuracy finite element methods for hyperbolic problems some high accuracy finite element methods for hyperbolic problems are studied in this paper it is proven that over a finite element mesh the convergence order of linear finite element solutions for both linear and nonlinear equations can be higher than one even if the exact solutions are discontinuous the theoretical tools for the convergence analysis are some superclose error estimates that are also developed in this paper for nonsmooth solutions

convergence of a shock capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions convergence of a shock capturing streamline diffusion nite element method for a conservation law in two space dimensions

finite dimensional wiener hopf equations and factorizations of matrices abstract let a be the algebra of all n n matrices over the real or complex numbers let a be the subalgebra of upper triangular matrices and a the subalgebra of strictly lower triangular matrices denote by p the projection of a onto a with kernel a in this paper we investigate the wiener hopf equation p ax y where y a is given and x a is a solution

on the transport diffusion algorithm and its applications to the navier stokes equations this paper deals with an algorithm for the solution of diffusion and or convection equations where we mixed the method of characteristics and the finite element method globally it looks like one does one step of transport plus one step of diffusion or projection but the mathematics show that it is also an implicit time discretization of thepde in lagrangian form we give an error bound h t h h t in the interesting case that holds also for the navier stokes equations even when the reynolds number is infinite euler equation

controllability and completion of partial upper triangular matrices over rings abstract for a given partial upper triangular matrix a and a matrix b over a ring we characterize the existence of a completion ac of a such that the pair ac b is controllable in terms of irreducibility

jordan structures of upper equivalent matrices abstract jordan structures of strictly lower triangular completions of matrices over an algebraically closed field are studied we give in terms of majorization a sufficient condition for the existence of a completion which preserve the spectrum of the original matrix and has prescribed jordan structure the case of nilpotent matrix was considered previously by krupnik and leibman

completions of partial jordan and hessenberg matrices abstract jordan forms of completions of partial jordan matrices are studied our approach is based on an algorithm for constructing completions of a given partial jordan matrix having prescribed eigenvalues and multiplicities an upper bound is given for the number of entries that must be made nonzero to produce such completions the algorithm is further interpreted in terms of the graph associated with a matrix some of the results are extended to a larger class of partial hessenberg matrices

symmetric systems with semi simple structure algebra the quaternionic case linear systems over the quaternions is discussed the theory of real semisimple symmetric systems is outlined

pole shifting for families of linear systems depending on at most three parameters abstract we prove that for any family of n dimensional controllable linear systems continuously parametrized by up to three parameters and for any continuous selection of n eigenvalues in complex conjugate pairs there is some dynamic controller of dimension 3 n which is itself continuously parametrized and for which the closed loop eigenvalues are these same eigenvalues each counted four times an analogous result holds also for smooth parametrizations

optimal multiple objective resource allocation using hybrid particle swarm optimization and adaptive resource bounds technique the multiple objective resource allocation problem morap seeks for an allocation of resource to a number of activities such that a set of objectives are optimized simultaneously and the resource constraints are satisfied morap has many applications such as resource distribution project budgeting software testing health care resource allocation etc this paper addresses the nonlinear morap with integer decision variable constraint to guarantee that all the resource constraints are satisfied we devise an adaptive resource bound technique to construct feasible solutions the proposed method employs the particle swarm optimization pso paradigm and presents a hybrid execution plan which embeds a hill climbing heuristic into the pso for expediting the convergence to cope with the optimization problem with multiple objectives we evaluate the candidate solutions based on dominance relationship and a score function experimental results manifest that the hybrid pso derives solution sets which are very close to the exact pareto sets the proposed method also outperforms several representatives of the state of the art algorithms on a simulation data set of the morap

a fuzzy dynamic approach to the multicriterion resource allocation problem abstract in this paper a new approach using fuzzy dynamic programming is proposed for solving the multiple criteria resource allocation problems it has been concluded that solutions obtained by this approach are always efficient hence an optimal compromise solution can be introduced a characteristic feature of the presented approach is that the objective function scalarization can be taken into account by using fuzzy set notations a numerical example is given to clarify the developed approach

the nonlinear resource allocation problem in this paper we study the nonlinear resource allocation problem defined as the minimization of a convex function over one convex constraint and bounded integer variables this problem is encountered in a variety of applications including capacity planning in manufacturing and computer networks production planning capital budgeting and stratified sampling despite its importance to these and other applications the nonlinear resource allocation problem has received little attention in the literature therefore we develop a branch and bound algorithm to solve this class of problems first we present a general framework for solving the continuous variable problem then we use this framework as the basis for our branch and bound method we also develop reoptimization procedures and a heuristic that significantly improve the performance of the branch and bound algorithm in addition we show how the algorithm can be modified to solve nonconvex problems so that a concave objective function can be handled

on a conjecture about the jordan form of completions of partial upper triangular matrices abstract we give a counterexample to a conjecture about the possible jordan normal forms of nilpotent matrices where the entries in the upper triangular part are prescribed

convergence of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions we prove convergence of a class of higher order upwind finite volume schemes on unstructured grids for scalar conservation laws in several space dimensions the result is applied to the discontinuous galerkin method due to cockburn hou and shu

minimal rank completions for block matrices abstract this paper deals with the following problem of completion of block matrices let aij i j be given matrices find additional matrices aij such that the completion a aij ni j 1 has lowest possible rank the structure of the set of all minimal rank completions is studied special attention is paid to the toeplitz case together with its connection to the partial realization problem

jordan forms of completions of partial upper triangular matrices abstract the possible jordan forms of completions of a matrix prescribed in its upper triangular part are studied it is shown that there always exists a nonderogatory completion for such a matrix jordan forms of nilpotent completions are considered as well

it cemop an iterative co evolutionary algorithm for multiobjective optimization problem with nonlinear constraints over the past few years researchers have developed a number of multiobjective evolutionary algorithms moeas although most studies concentrate on solving unconstrained optimization problems there exit a few studies where moeas have been extended to solve constrained optimization problems most of them were based on penalty functions for handling nonlinear constraints by genetic algorithms however the performance of these methods is highly problem dependent many methods require additional tuning of several parameters in this paper we present a new optimization algorithm which is based on concept of co evolution and repair algorithm for handling nonlinear constraints the algorithm maintains a finite sized archive of nondominated solutions which gets iteratively updated in the presence of new solutions based on the concept of e dominance the use of e dominance also makes the algorithms practical by allowing a decision maker to control the resolution of the pareto set approximation by choosing an appropriate e value which guarantees convergence and diversity the results provided by the proposed algorithm for six benchmark problems are promising when compared with exiting well known algorithms also our results suggest that our algorithm is better applicable for solving real world application problems

a dynamic approach to multiple objective resource allocation problem a new approach using dynamic programming is developed for solving the multiple objective resource allocation problem there are two key issues being addressed in this approach the first one is to develop a methodology of fuzzy evaluation and fuzzy optimization for multiple objective systems the procedure of getting the marginal evaluation for each objective and aggregating them synthetically into a global evaluation is presented in this paper the second one is to design a dynamic optimization algorithm by incorporating the method of fuzzy evaluation and fuzzy optimization with the conventional dynamic programming technique a characteristic feature of the approach presented is that various objectives are synthetically considered by the fuzzy systematic technique instead of the frequently employed weighted average method numeric examples are also given to clarify the developed approach and to demonstrate its effectiveness

matrices with prescribed eigenvalues and principal submatrices abstract we give a necessary and sufficient condition for the existence of a square matrix with prescribed eigenvalues and prescribed complementary principal blocks

a note on entropy inequalities and error estimates for higher order accurate finite volume schemes on irregular families of grids recently cockburn coquel and lefloch proved convergence and error estimates for higher order finite volume schemes their result is based on entropy inequalities which are derived under restrictive assumptions on either the flux function or the numerical fluxes moreover they assume that the spatial grid satisfies a standard regularity assumption using instead entropy inequalities derived in previous work by kroner noelle and rokyta and a weaker condition on the grid we can generalize and simplify the error estimates

an error estimate for finite volume methods for multidimensional conservation laws in this paper an l ll error estimate for a class of finite volume methods for the approximation of scalar multidimensional conservation laws is obtained these methods can be formally high order accurate and are defined on general triangulations the error is proven to be of order ft 4 where h represents the size of the mesh via an extension of kuznetsov approximation theory for which no estimate of the total variation and of the modulus of con tinuity in time are needed the result is new even for the finite volume method constructed from monotone numerical flux functions

on the jordan form of completions of partial upper triangular matrices abstract rodman and shalom present in linear algebra appl 168 221 249 1992 two completion conjectures for partial upper triangular matrices in this paper we show that one of them is not true in general and we prove its validity for some particular cases we also prove the equivalence between the two conjectures in the case of partial hessenberg matrices

a two grid combined finite element upwind finite volume method for a nonlinear convection dominated diffusion reaction equation in this paper we first present a combined finite element upwind finite volume method for a fully nonlinear convection dominated diffusion reaction equation and derive its a priori optimal error estimate in h 1 norm and sub optimal error estimate in l 2 norm for piecewise linear finite element combining with the first order upwind finite volume scheme then we study a type of two grid method for the nonlinear convection dominated transport equation together with the combined finite element upwind finite volume method on the fine grid t h and the streamline diffusion finite element scheme on the coarse grid t h which not only significantly reduces the computational cost on nonlinear iterations but also remains the numerical computation stabilized and the approximation accuracy unchanged a priori error estimate of such designed two grid method in h 1 norm is proved to be o h h 3 2 showing that the two grid method achieves the optimal approximation as long as the mesh sizes satisfy h o h 3 2 finally a numerical example is carried out to verify the accuracy and efficiency of the present numerical method

an effective modified binary particle swarm optimization mbpso algorithm for multi objective resource allocation problem morap a modified binary particle swarm optimization mbpso algorithm is proposed for solving the multi objective resource allocation problem morap first the generation mechanism for initial particles is established to guarantee that the algorithm can begin to search optimal particle in the feasible solution space second we develop the update mechanism for iterative particles which includes setting up the memory array modifying sig function and verifying the constraint condition to assure that the regenerated particles meet the constraint and algorithm can quickly converge third the selection mechanism for pbesti and gbest is proposed which uses the dynamic neighborhood strategy to ensure that the algorithm to find pareto optimal solutions through comparing the example simulation results of our mbpso with hga and aco published in references we find that proposed mbpso outperforms hga and aco finally the effectiveness of the different improved methods is analyzed and the synergism effect and the convergence behavior of the mbpso algorithm show its good performances

approximation based fuzzy multi objective models with expected objectives and chance constraints application to earth rock work allocation in this paper we introduce a measure me which is more suitable for real life decision making problems under fuzzy environments then we establish a general fuzzy multi objective model with expected objectives and chance constraints ecm based on the me to handle the model and obtain solutions we propose two approximation models by dividing the fuzzy feasible region using rough set theory in particular we focus on a linear ecm and several properties and two equivalent models are presented finally as an illustration we apply the proposed models and approaches to an earth rock work allocation problem at the longfeng hydropower construction project

an algorithm for nilpotent completions of partial jordan matrices abstract an algorithm to obtain a completion of a partial upper triangular matrices with prescribed eigenvalues and their multiplicities and the jordan chains of the completed matrix is introduced this algorithm extends some results of rodman and shalom in linear algebra and appl 168 1992 221 249

factorization of block matrices abstract an lu type factorization theorem due to elsner and to gohberg and goldberg is generalized to block matrices one form of the general factorization takes the form lmu where l is block lower triangular u is block upper triangular and m is a subpermutation matrix each of whose blocks is diagonal a factorization is also given where the middle term is a block diagonal subpermutation matrix and the factorization is applied to wiener hopf equations the nonuniqueness of the middle term in the factorization is analyzed a special factorization for self adjoint block matrices is also obtained

multiobjective fuzzy competence set expansion problem by multistage decision based hybrid genetic algorithms the problem of competence set expansion involves determining the optimal expansion path under the minimum cost and has been widely used for the problem of process planning as we know the conventional competence set model only considers the problems of the single objective and the static situations in practice however the multiobjective and the dynamic situations usually occur in the optimal expansion path problems furthermore due to the subjective judgment and the restriction of information the degree of uncertainty should also be considered in this paper a multiobjective and multistage fuzzy competence set model is proposed to overcome the problems above simultaneously in order to efficiently obtain the optimal expansion path hybrid genetic algorithms hga are employed here in addition a particular job shop scheduling example is used to demonstrate the proposed method on the basis of the numerical results we can conclude that the proposed method can provide a sound fuzzy competence set model by considering the multiobjective and the multistage situations simultaneously

on the number of invariant polynomials of partially prescribed matrices abstract we study the number of invariant polynomials of a i j i j 1 2 when the submatrices a 1 1 a 1 2 a 2 2 are prescribed

a domain decomposition method for two phase transport model in the cathode of a polymer electrolyte fuel cell using kirchhoff transformation we develop a dirichlet neumann alternating iterative domain decomposition method for a 2d steady state two phase model for the cathode of a polymer electrolyte fuel cell pefc which contains a channel and a gas diffusion layer gdl this two phase pefc model is represented by a nonlinear coupled system which typically includes a modified navier stokes equation with darcy s drag as an additional source term of the momentum equation and a convection diffusion equation for the water concentration with discontinuous and degenerate diffusivity for both cases of dry and wet gas channel we employ kirchhoff transformation and dirichlet neumann alternating iteration with appropriate interfacial conditions on the gdl channel interface to treat the jump nonlinearities in the water equation numerical experiments demonstrate that fast convergence as well as accurate numerical solutions are obtained simultaneously owing to the implementation of the above described numerical techniques along with a combined finite element upwind finite volume discretization to automatically control the dominant convection terms arising in the gas channel

matrices with prescribed rows and invariant factors abstract in this paper we solve the problem of the existence of an n n matrix over an arbitrary field when its invariant polynomials and either some rows or columns are prescribed the solution is given in terms of invariant factor inequalities and of majorization inequalities involving controllability indices and the degrees of the invariant polynomials

the toda flow on a generic orbit is integrable on construit des variables action angle pour le flot de toda sur des orbites generiques de l action coadjointe du groupe triangulaire inferieur sur son algebre de lie duale

convergence of a staggered lax friedrichs scheme for nonlinear conservation laws on unstructured two dimensional grids based on nessyahu and tadmor s nonoscillatory central difference schemes for one dimensional hyperbolic conservation laws 16 for higher dimensions several finite volume extensions and numerical results on structured and unstructured grids have been presented the experiments show the wide applicability of these multidimensional schemes the theoretical arguments which support this are some maximum principles and a convergence proof in the scalar linear case a general proof of convergence as obtained for the original one dimensional nt schemes does not exist for any of the extensions to multidimensional nonlinear problems for the finite volume extension on two dimensional unstructured grids introduced by arminjon and viallon 3 4 we present a proof of convergence for the first order scheme in case of a nonlinear scalar hyperbolic conservation law

superconvergence of discontinuous galerkin methods for hyperbolic systems in this paper the discontinuous galerkin method for the positive and symmetric linear hyperbolic systems is constructed and analyzed by using bilinear finite elements on a rectangular domain and an o h 2 order superconvergence error estimate is established under the conditions of almost uniform partition and the h 3 regularity for the exact solutions the convergence analysis is based on some superclose estimates derived in this paper finally as an application the numerical treatment of maxwell equation is discussed and computational results are presented

one sided difference approximations for nonlinear conservation laws we analyze one sided or upwind finite difference approximations to hyperbolic partial differential equations and in particular nonlinear conservation laws second order schemes are designed for which we prove both nonlinear stability and that the entropy condition is satisfied for limit solutions we show that no such stable approximation of order higher than two is possible these one sided schemes have desirable properties for shock calculations we show that the proper switch used to change the direction in the upwind differencing across a shock is of great importance new and simple schemes are developed for which we prove qualitative properties such as sharp monotone shock profiles existence uniqueness and stability of discrete shocks numerical examples are given

matrices with prescribed lower triangular part abstract we give a necessary and sufficient condition for the existence of a square matrix with prescribed characteristic polynomial and prescribed entries on and below the main diagonal

error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method in this paper we derive a priori and a posteriori error estimates for cell centered finite volume approximations of nonlinear conservation laws on polygonal bounded domains numerical experiments show the applicability of the a posteriori result for the derivation of local adaptive solution strategies

an effective genetic algorithm approach to multiobjective resource allocation problems moraps dynamic programming dp is a mathematical procedure designed primarily to improve the computational efficiency of solving select mathematical programming problems by decomposing them into smaller and hence computationally simpler subproblems in solving multiple objectives dynamic programming problem modp classical approaches reduce the multiple objectives into a single objective of minimizing a weighted sum of objectives the determination of these weights indicate the relative importance of the various objective also if the problem scale increases it become difficult to be dealt with even in the case of single objective because of the rapid expansion of the number of states to be considered in this paper we investigated the possibility of using genetic algorithms gas to solve multiobjective resource allocation problems moraps this procedure eliminates the need of any user defined weight factor for each objective also the proposed approach is developed to deal with the problems with both single or multiple objectives the simulation results for multiobjective resource allocation problems morap shows that genetic algorithms gas may hopefully be a new approach for such kinds of problems

symmetric systems structure of the state space it is shown that every module of every finite dimensional associative algebra is associated with the state space of some class of symmetric systems the general structure of symmetric systems is investigated

nilpotent completions of partial upper triangular matrices in this paper five questions related with the existence of nilpotent completions of partial upper triangular matrices lower irreducibles and with trace equal to zero are presented and solved

a hybrid binary particle swarm optimization for the obnoxious p median problem abstract the obnoxious p median problem can be formulated as a constrained binary linear program it is np hard and has a lot of real world applications in this paper a hybrid binary particle swarm optimization is proposed to solve the obnoxious p median problem a new position updating rule is presented to inherit the good structure of previous high quality solutions furthermore two tabu based mutation operators are used to avoid the premature convergence and guide the search to a promising area a greedy repair procedure is developed to repair infeasible solutions in addition an iterated greedy local search procedure is utilized to enhance the exploitation ability extensive experiments are done on a set of 72 benchmark instances from the literature experimental results and comparisons with some existing algorithms demonstrate the effectiveness of the proposed algorithm in particular the proposed algorithm finds new best solutions for 15 instances compared with existing algorithms the proposed algorithm is able to find better average objective function value in a short average computing time

a finite volume scheme with shock fitting for the steady euler equations abstract analysis of two alternative finite volume formulations in respect of accuracy on non uniform meshes and number of spurious modes leads to a preference for the more compact cell vertex scheme over the cell centre scheme the resulting equations are solved iteratively by using a lax wendroff procedure as a smoother for a multigrid algorithm then application of boundary conditions in a natural way leads rapidly to all individual residuals being driven close to zero except at shocks at shocks the residuals should not be zero and a shock fitting procedure is introduced to avoid this inconsistency sharp accurate solutions on a relatively coarse mesh are obtained for a channel low problem in which the zierep singularity is displayed and for the naca 0012 aerofoil

matrices with prescribed characteristic polynomial and principal blocks ii abstract in this paper we present some new sufficient conditions for the existence of a square matrix with prescribed characteristic polynomial and two complementary principal submatrices

on the convergence of shock capturing streamline diffusion finite element methods for hyperbolic conservation laws we extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shock capturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the meh size with this term present we prove a maximum norm bound for finite element solutionsof burgers equation an thus complete an earlier convergence proof for this equation we further prove using entropy variables that a strong limit of finite element solutions is a weak solution of the system of conservation laws and satisfies the entropy inequality asociated with the entropy variables results of some numerical experiments for the time dependent compressible euler equations in two dimensions are also reported

mixed covolume methods for quasi linear second order elliptic problems we consider covolume methods for the mixed formulations of quasi linear second order elliptic problems covolume methods for the mixed formulations of linear elliptic problem was first considered by russell rigorous block centered discretizations on irregular grids improved simulation of complex reservoir systems tech report 3 project report reservoir simulation research corporation tulsa ok 1995 and tested extensively in cai et al comput geosci 1 1997 pp 289 315 jones a mixed finite volume element method for accurate computation of fluid velocities in porous media ph d thesis university of colorado denver 1995 the analysis was carried out by chou and kwak siam j numer anal 37 2000 pp 758 771 for linear symmetric problems where they showed optimal error estimates in l2 norm for the pressure and in h div norm for the velocity in this paper we extend their results to quasi linear problems by following milner s argument math comp 44 1985 pp 303 320 through an adaptation of the duality argument of douglas and roberts math comp 44 1985 pp 39 52 for mixed covolume methods