stable coexistence states in the volterra lotka competition model with diffusion we study the existence uniqueness and stability of coexistence states in the lotka volterra model with diffusion for two competing species we assume that the parameters describing the interactio

parameter ranges for the existence of solutions whose state components have specified nodal structure in coupled multiparameter systems of nonlinear sturm liouville boundary value problems

on the existence and uniqueness of positive solutions for competing species models with diffusion in this paper we consider strictly positive solutions of competing species systems with diffusion under dirichlet boundary conditions we obtain a good understanding of when strictly positive solutions exist obtain new nonuniqueness results and a number of other results showing how complicated these equations can be in particular we consider how the shape of the underlying domain affects the behaviour of the equations the purpose of this paper is to obtain much better results on the existence and uniqueness of strictly positive stationary that is time independent solutions of

numerical computation of a control function in a partial differential equation this study presents several finite difference schemes for solving the three dimensional parabolic equation with a control function these techniques are developed for indentifying u u x y z t and p p t the temperature parameter which satisfy u t 2u x 2 2u y 2 2u z 2 p t email protected x y z t in rx 0 t u x y z 0 f x y z x y z r 0 1 3 u is known on the boundary of r and also u x 0 y 0 z 0 t e t 0

an stable numerical algorithm for identifying the solution of an inverse problem in this paper we consider an inverse parabolic problem with space dependent coefficient mathematical model of the problem consists a parabolic equation in which the condition is unknown at the one of the boundary and to be determined from an overspecified data measured at an interior point inside the body uniqueness of the solution of under study inverse problem will be shown our concern for the numerical procedure for this inverse problem is based on a finite differences scheme stability conditions for numerical solution to inverse problem are stated the approach of proposed method is approximated the unknown function by a set of chebyshev polynomials where the unknown set of expansion coefficients in unknown function are determined from the minimizing the least squares method some numerical examples will be given in the last section

bifurcation of steady state solutions in predator prey and competition systems we discuss steady state solutions of systems of semilinear reaction diffusion equations which model situations in which two interacting species u and v inhabit the same bounded region it is easy to find solutions to the systems such that either u or v is identically zero such solutions correspond to the case where one of the species is extinct by using decoupling and global bifurcation theory techniques we prove the existence of solutions which are positive in both u and v corresponding to the case where the populations can co exist

on positive solutions of some pairs of differential equations this paper is a sequel to the author s paper 6 which studied positive solutions of a pair of differential equations introduced by conway gardner and smoller 4 their equations were equations for population problems in biology their significance is discussed further in 141 the purpose of the present paper is to obtain further results for the conwat gardner smoller equations and to show how the methods in 6 can be modified to decide exactly when the classical predator prey system as in blat and brown 2 has a strictly positive solution we also show how the methods can be applied to a number of other problems in particular our results answer some questions in conway s secondly we show how the asymptotic methods developed in 6 can be used to study the existence and uniqueness of strictly positive solutions of competing species problems our results suggest that this is a much more complicated problem than the predator prey problem we do obtain a condition which is except for a few special cases necessary and sufficient for the existence of a strictly positive solution however the condition is complicated and rather implicit thirdly we prove the uniqueness of the strictly positive solution in the conway smoller system if d is small and n 1 that is the case of ordinary differential equations this partially answers a question in 4 our proof is a local result and can be used in other situations for example it can be used to show that in certain cases of asocial nonlinearities where our notation follows 4 sect 4 there are exactly two strictly positive solutions for small d we also show how our method applies to more general predator prey problems in section 1 we find necessary and sufficient conditions for the existence of strictly positive solutions of predator prey systems in section 2 we study competing species models by iteration and asymptotic methods finally in section 3 we prove our uniqueness results in an appendix we briefly discuss how the methods of section 3 apply to more general models

a new holstein primakoff realisation of sp 4 r a new holstein primakoff type realisation of the non compact lie algebra sp 4 r is given in a completely explicit analytic and closed form the construction is related to the representations where the casimir invariants of the subalgebras sp1 2 2 r are diagonal rather than the invariants of the maximal compact subalgebra u 2

finite volume method for solving a one dimensional parabolic inverse problem in this paper finite volume method is used to solve a one dimensional parabolic inverse problem with source term and neumann boundary conditions for the first time some advantages of this approach are developing difference schemes and maintaining certain properties of the physics of the problems especially for the treatment of the source term and the unknown boundary conditions numerical results show that our method is more effective

coherent state theory of the noncompact symplectic group an extended coherent state theory is presented for the noncompact sp 3 r group which reveals a simple relationship between the sp 3 r algebra and its contracted u 3 boson limit the relationship is used to derive a remarkably accurate analytic expression for sp 3 r matrix elements for the generic lowest weight representations the expression is shown to be exact whenever the states involved are multiplicity free with respect to the u 3 subalgebra it is further shown how exact matrix elements are easily calculated in general dyson and holstein primakoff type u 3 boson expansions are given

boson realization of sp 4 i the matrix formulation holstein and primakoff derived long ago the boson realization of a su 2 lie algebra for an arbitrary irreducible representation irrep of the su 2 group the corresponding result for su 1 1 sp 2 is also well known this raises the question of whether it is possible to obtain in an explicit analytic and closed form and for any integer d the boson realization of a sp 2d lie algebra for an arbitrary irrep of the sp 2d group which is a problem of considerable physical interest the case d 2 already illustrates the problem in its full generality and thus in this paper we concentrate on sp 4 the dyson realization is well known and the passage to bosons satisfying the appropriate hermiticity conditions can be done by a similarity transformation through an operator k what we want though is an explicit boson realization for sp 2d similar to the one that exists for sp 2 in sec vi we show how we can get it for sp 4 if the operator k is known unfortunately while the matrix form of k2 can be ex

monotonicity and uniqueness results in identifying an unknown coefficient in a nonlinear diffusion equation we consider the problem of identifying an unknown diffusion coefficient in a nonlinear diffusion equation from overspecified data measured on the boundary conditions ensuring compatibility of the data are derived and it is shown that the mapping which carries the diffusion coefficient into the data is isotonic this result is then used to derive a uniqueness result for the inverse problem and for an associated identification problem some results of numerical experiments are presented to illustrate the various results

finding a control parameter in one dimensional parabolic equations an inverse problem concerning diffusion equation with source control parameter is considered several finite difference schemes are presented for identifying the control parameter which produces at each time a desired temperature at a given point in a spatial domain these schemes are based on the second order 3 point forward time centred space ftcs explicit formula and the fourth order 5 point ftcs explicit scheme and the second order 3 point backward time centred space btcs implicit technique and the fourth order 3 3 crandall s implicit formula the 5 point ftcs scheme has a bounded range of stability but its fourth order accuracy is significant the 3 point btcs method uses less central processor cpu time than the 3 3 crandall s technique but it is only second order accurate the basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach developed from the 1974 work of warming and hyett this allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes the results of a numerical experiment are presented and accuracy and the cpu time needed for the parabolic inverse problem are discussed

numerical approximation of solution of an inverse heat conduction problem based on legendre polynomials in this paper we consider an inverse heat conduction problem ihcp the given heat conduction equation the boundary condition and the initial condition are presented in a dimensionless form a set of temperature measurements at a single sensor location inside the heat conduction body is required using a linear transformation the ill posed ihcp becomes a cauchy problem this problem will be solved by applying legendre polynomials results show that an excellent estimation can be obtained within a couple of minutes cpu time at pentium iv 2 4 ghz pc

application of sinc collocation method for solving an inverse problem in this article the identification of an unknown time dependent source term in an inverse problem of parabolic type with nonlocal boundary conditions is considered the main approach is to change the inverse problem to a system of volterra integral equations the resulting integral equations are convolution type which by using sinc collocation method are replaced by a system of linear algebraic equations the convergence analysis is included and it is shown that the error in the approximate solution is bounded in the infinity norm by the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system to show the efficiency of the present method an example is presented the method is easy to implement and yields very accurate results

a method for solving an inverse biharmonic problem this paper deals with the problem of determining of an unknown coefficient in an inverse boundary value problem using a nonconstant overspecified data it has been shown that the solution to this inverse problem exists and is unique

on positive solutions of some pairs of differential equations ii on etudie l existence de solutions strictement positives de systemes predateur proie on demontre l unicite de la solution strictement positive dans le systeme de conway smoller

an inverse heat conduction problem with a nonlinear source term abstract in this paper the nonlinear problem of an inhomogeneous heat equation with linear boundary conditions will be considered the surface heat flux history of a heated conducting body will be identified the approach of the proposed method is to approximate the unknown function using linear polynomial pieces which are determined consecutively from the solution of the minimization problem on the basis of overspecified data some numerical examples will also be presented

a numerical solution technique for a one dimensional inverse nonlinear parabolic problem abstract this study is intended to provide a new numerical algorithm for solving a one dimensional inverse nonlinear parabolic problem at the beginning of the study taylor s series expansion is employed to linearize nonlinear terms and then finite difference method is used to discretize the problem domain the present approach is to rearrange the matrix forms of the differential governing equations and estimate unknown functions the least squares method is adopted to find the solution it is assumed that no prior information is available on the functional form of the unknown coefficient in the present study thus it is classified as the function estimation results show that an excellent estimation on the unknown functions of the inverse problem which can be obtained within a couple of minutes cpu time at pentium iv 2 4 ghz pc

application of finite difference method to analysis an ill posed problem abstract in this paper a numerical solution of an inverse non dimensional heat conduction problem will be considered by using a sensor located at a point inside the body and measuring the temperature at a point x x 1 0 x 1

d type anticipatory iterative learning control for a class of inhomogeneous heat equations in this paper a d type anticipatory iterative learning control ilc scheme is applied to the boundary control of a class of inhomogeneous heat equations where the heat flux at one side is the control input while the temperature measurement at the other side is the control output by transforming the inhomogeneous heat equation into its integral form and exploiting the properties of the embedded jacobi theta functions the learning convergence of ilc is guaranteed through rigorous analysis without any simplification or discretization of the 3d dynamics in the time space as well as iteration domains the adopted ilc scheme makes full use of the process repetition and deals with state independent or state dependent uncertainties meanwhile due to the feedforward characteristic of ilc the proposed scheme not only makes anticipatory compensation possible to overcome the heat conduction delay in boundary output tracking but also eliminates the gain margin limitation encountered in feedback control in the end an illustrative example is presented to demonstrate the performance of the proposed ilc scheme

residual minimization least squares method for inverse heat conduction abstract a numerical method is systematically developed for resolving an inverse heat conduction problem in the presence of noisy discrete data this paper illustrates the effect of imposing constraints on the unknown function of interest a volterra integral equation of the first kind is derived and used as the starting point for residual minimization least squares methodology symbolic manipulation is exploited for purposes of augmenting the computational methodology preliminary indications suggest that the imposition of physical constraints on the system drastically reduces the level of mathematical sophistication needed for accurately approximating the unknown function of interest these constraints are actually available in many design studies or from models which are derived by physical processes

application jacobi spectral method for solving the time fractional differential equation abstract our aim from this article is to propose a spectral method for numerically solving a general form of time fractional differential equation with boundary conditions our method is based on the shifted jacobi polynomials and has four steps as follows at first the problem is converted to a new problem with homogeneous conditions step 1 then an integro differential equation is obtained which is equivalent with the new problem step 2 next all the known and unknown functions which are existing in the integro differential equation are approximated via the shifted jacobi polynomials step 3 utilizing operational matrices of shifted jacobi polynomials and collocation method a system of nonlinear algebraic equations is achieved which is solved by newton s iterative method step 4 in order to show and verify the accuracy and performance of the proposed method we examine our method on some illustrative examples

numerical solution of one dimensional parabolic inverse problem this paper is concerned with numerical techniques for the solution of a one dimensional parabolic inverse problem with a control parameter the discrete approximation of the problem is based on the finite difference schemes these techniques are presented for identifying the control parameter which produces at each time a desired temperature at a given point in a spatial domain the main idea behind the finite difference methods for obtaining the solution of a given partial differential equation is to approximate the derivatives appearing in the equation by a set of values of the function at a selected number of points the most usual way to generate these approximations is through the use of taylor series the methods developed here are based on the modified equivalent partial differential equation as described by warming and hyett j comput phys 14 2 1974 159 this approach allows the simple determination of the theoretical order of accuracy thus allowing methods to be compared with one another also from the truncation error of the modified equivalent equation it is possible to eliminate the dominant error terms associated with the finite difference equations that contain free parameters weights thus leading to more accurate methods the results of a numerical experiment are presented and accuracy and the central processor cpu time needed for the parabolic inverse problem are discussed

boson representations of the real symplectic group and their applications to the nuclear collective model both non hermitian dyson and hermitian holstein primakoff representations of the sp 2d r algebra are obtained when the latter is restricted to a positive discrete series irreducible representation d n 2 1 n 2 for such purposes some results for boson representations recently deduced from a study of the sp 2d r partially coherent states are combined with some standard techniques of boson expansion theories the introduction of usui operators enables the establishment of useful relations between the various boson representations two dyson representations of the sp 2d r algebra are obtained in compact form in terms of d d 1 2 pairs of boson creation and annihilation operators and of an extra u d spin characterized by the irreducible representation 1 d in contrast to what happens when 1 d it is shown that the holstein primakoff representation of the sp 2d r algebra cannot be written in such a compact form for a generic irreducible representation explicit expansions are

complementarity relation between the usp 2ν and so 2d lie groups the object of this paper consists of finding a complementary group with respect to usp n within either irreducible representation 1 2 dn or 1 2 dn 13 2 of the real symplectic group sp 2dn r for such purpose the author deals with the full orthogonal group o n n 2 nu or 2 nu 1 and the unitary symplectic group usp n n 2 nu in a unified way by introducing an appropriate metric a similar treatment applied to their complementary group determination leads to the well known sp 2d r group in the o n case and to the so 2d group in the usp n case

wavelet and fourier methods for solving the sideways heat equation we consider an inverse heat conduction problem the sideways heat equation which is a model of a problem where one wants to determine the temperature on both sides of a thick wall but where one side is inaccessible to measurements mathematically it is formulated as a cauchy problem for the heat equation in a quarter plane with data given along the line x 1 where the solution is wanted for 0 leq x 1 the problem is ill posed in the sense that the solution if it exists does not depend continuously on the data we consider stabilizations based on replacing the time derivative in the heat equation by wavelet based approximations or a fourier based approximation the resulting problem is an initial value problem for an ordinary differential equation which can be solved by standard numerical methods e g a runge kutta method we discuss the numerical implementation of fourier and wavelet methods for solving the sideways heat equation theory predicts that the fourier method and a method based on meyer wavelets will give equally good results our numerical experiments indicate that also a method based on daubechies wavelets gives comparable accuracy as test problems we take model equations with constant and variable coefficients we also solve a problem from an industrial application with actual measured data

global higher bifurcations in coupled systems of nonlinear eigenvalue problems on etablit des conditions pour l existence d une bifurcation n aire globale de dimension elevee dans des systemes generaux de problemes aux valeurs propres non lineaires multiparametre qui conservent la structure de couplage des modeles de lotka volterra diffusifs etat stationnaire

boson realisation of symplectic algebras the boson realisation of the two dimensional symplectic lie algebra sp 2 for a given irreducible representation irrep of the sp 2 group has been known for a long time more recently the boson realisation of the 2d dimensional symplectic lie algebras sp 2d have been derived for particular irreps of the sp 2d group the author outlines the corresponding result for an arbitrary irrep of sp 2d

bosonic realisation of sp 4 r and the spectrum of two particle quantum systems a new bosonic holstein primakoff type realisation of sp 4 r is applied in the development of 1 n expansions of non relativistic spin independent two particle hamiltonians as a non trivial example the spectrum of helium like ions is considered and the energies of the low lying levels with given values of total angular momentum are computed the calculation is explicitly performed in an approximation up to the second degree in the small expansion parameter

numerical solution of inverse heat conduction problem with nonstationary measurements the inverse heat conduction problem involves the calculation of surface heat flux and or temperature histories from transient measured temperatures inside solid in this paper the temperature is not specified at x 0 in an inverse heat conduction problem we choose an additional moving boundary condition this problem may be subdivided into two separate problems one of these problems is a moving boundary problem which is solved exactly by means of fundamental solution of heat equation the second problem is an inverse moving boundary problem which is solved with the residual minimization least squares method by using numerical examples we show the accuracy of our method