global boundedness for a delay differential equation on etudie l inequation t u u t x u t x 1 u t x on montre que les solutions non negatives du probleme de dirichlet dans un intervalle borne restent bornees lorsque le temps croit indefiniment dans un domaine de plus grande dimension cette propriete n a lieu que si le retard n est pas trop grand

abstract functional differential equations and reaction diffusion systems functional differential equations and reaction diffusion systems r h martin jr and h l smith abstract several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays suppose q is a bounded domain in rn with aq smooth and a is the laplacian operator on q also let m be a positive integer z a positive number and f fi m a continuous bounded function from 0 xc x q x c z 0 m into rm where c t 0 is the space of continuous functions from z 0 into r the purpose of this paper is to apply abstract results for semilinear functional differential equations in banach spaces to reactiondiffusion systems with time delays having the form a tu x t diau x t i t x ut x t a xeq i 1 m rdd ai x ui x t au i x t 81 x t t a x eaq u x a 0 x x 0 5 t 0 di 0 and ca q 0 o is c and i q x 0 oo r is c2 here an is the outward normal derivative on aq and if di 0 it is assumed that no boundary conditions are specified for this i also tu x t denotes the partial with respect to t whereas ut x denotes the member of c z 0 defined by 0 u x t 0 u x t 0 m our techniques provide basic existence criteria but the main point is that they can also be effectively applied to obtain estimates for solutions especially received by the editors october 7 1987 and in revised form october 7 1988 1980 mathematics subject classification 1985 revision primary 35r10 34k30

oscillation of nonlinear partial difference equations with delays abstract in this paper we first derive a discrete gaussian formula and then apply the formula to two classes of nonlinear parabolic and hyperbolic partial difference equations with delays to obtain sufficient conditions under which every solution of the two classes of nonlinear partial difference equations with delays is oscillatory

associative monotonic operations in fuzzy set theory abstract the properties of binary operations in a real interval are considered and used in the discussion of generalized operations on fuzzy sets on fuzzy numbers and on fuzzy probabilistic sets

arithmetic operations of non normal fuzzy sets using gradual numbers abstract this paper will study the arithmetic operations of non normal fuzzy sets using the concept of gradual numbers that can be regarded as the elements of gradual sets we shall present the idea in which the fuzzy sets can be formulated as consisting of gradual elements like the usual set consisting of usual elements when the universal set is taken to be the real number system the gradual element is also called a gradual number in this case the arithmetic operations of non normal fuzzy sets can be defined by using the gradual numbers

some comments on tridiagonal p r toeplitz matrices abstract the aim of this note is to extend the notion of a tridiagonal p r toeplitz matrix recently introduced and to provide procedures for short proofs to results on the invertibility of such matrices

a fast elementary algorithm for computing the determinant of toeplitz matrices in recent years a number of fast algorithms for computing the determinant of a toeplitz matrix were developed the fastest algorithm we know so far is of order k 2 log n k 3 where n is the number of rows of the toeplitz matrix and k is the bandwidth size this is possible because such a determinant can be expressed as the determinant of certain parts of the n th power of a related k i k companion matrix in this paper we give a new elementary proof of this fact and provide various examples we give symbolic formulas for the determinants of toeplitz matrices in terms of the eigenvalues of the corresponding companion matrices when k is small

operations on fuzzy sets an axiomatic approach abstract we introduce intersection and union of fuzzy sets constructed by means of operations on the unit interval which may depend on the considered element of the universe of discourse a similar approach for complementation was given by lowen 7 the main result is that element dependent operations are not compatible with the preservation of the intersection and union under the inverse image of a function finally we consider fuzzy algebras built with these set theoretic operations

spatiotemporal dynamics and spatial pattern in a diffusive intraguild predation model with delay effect abstract based on biological meaning a kind of diffusive intraguild predation igp resource ig prey and ig predator model with delay effect is investigated in this paper the model has holling type i functional response between resource ig prey and resource ig predator holling type ii functional response between ig prey and ig predator we first give sufficient conditions on the stability of possible nonnegative constant steady state solutions for the proposed model which give us a complete picture of the global dynamics then we investigate hopf bifurcation near the unique positive constant steady state solution by taking delay as bifurcation parameter and derive the hopf bifurcation threshold it is shown that the delay can induce three types of bistability node node bistability node cycle bistability and cycle cycle bistability periodic oscillations and irregular oscillations triggering spatiotemporal chaos in the diffusive igp model numerical simulations are performed to illustrate our theoretical results and suggest that delay can even trigger the emergence of self organised spatiotemporal patterns which evolve from spiral patterns to irregular spatial patterns via spatiotemporal hopf bifurcation in addition the impact of diffusion on the model s dynamics under certain time delay are also explored

global stability and hopf bifurcations of a beddington deangelis type predator prey system with diffusion and delays the dynamics of a diffusive predator prey system with the beddington deangelis functional response and two delays are considered by choosing the sum of two delays as a bifurcation parameter the stability of the constant equilibria and the existence of hopf bifurcations are investigated by analyzing the characteristic equations and the formulas determining the direction and the stability of the bifurcating periodic solutions are derived by using the center manifold and the normal form theory of partial functional differential equations particularly the sufficient conditions of the global stability of the positive equilibrium are given by the upper lower solutions method

generalized aizerman myshkis problem for abstract differential delay equations abstract we consider a class of semilinear functional differential equations in a hilbert space conditions for the absolute stability are established moreover it is shown that these conditions separate equations that satisfy the generalized aizerman myshkis hypothesis the suggested approach is based on a combined usage of the properties of operators on tensor products of hilbert spaces and recent estimates for the norm of the resolvent our results are new even in the finite dimensional case we also discuss applications of the mentioned results to coupled systems of parabolic equations with delay and integro differential equations with delay

the generalized quasi linearization method for reaction diffusion equations on an unbounded domain the method of generalized quasi linearization has been well developed for ordinary differential equations in this paper we extend the method of generalized quasi linearization to reaction diffusion equations on an unbounded domain the iterates which are solutions of linear equations starting from lower and upper solutions converge uniformly and monotonically to the unique solution of the nonlinear reaction diffusion equation in an unbounded domain initially an existence theorem for the linear nonhomogeneous reaction diffusion equation in an unbounded domain has been proved under improved conditions the quadratic convergence has been proved by using a comparison theorem of reaction diffusion equations with ordinary differential equations this avoids the computational complexity of the quasi linearization method since the computation of green s function at each stage of the iterates is avoided

nonlocal problems involving spatial structure for coupled reaction diffusion systems the purpose of this work is to investigate the uniqueness and existence of solutions for a system of nonlinear parabolic equations weakly coupled with ordinary differential equations in bounded domains subject to nonlocal boundary conditions that involve values of the unknown functions inside of the spatial domain the solutions of such problems allow for considering not only physical chemical or biological properties but also spatial structure of the modelled system the uniqueness of classical solutions of the nonlocal boundary problems for coupled reaction diffusion systems is proved by means of comparison principles for differential inequalities the existence of the unique solution is obtained via a monotone iterative method applications are given to some model problems in epidemiology and ecology with the nonlocal boundary conditions based on the inverse distance weighting interpolation and cokriging

construction of fuzzy σ algebras using triangular norms abstract generalizing the definitions given by the author fuzzy sets and systems4 1980 83 93 we introduce and study t fuzzy algebras t being any triangular norm the main result is that for a large class of triangular norms each t fuzzy algebra is generated i e consists of all functions x 0 1 being measurable with respect to some algebra on x

global asymptotic stability of 3 species lotka volterra models with diffusion and time delays abstract this paper is concerned with three 3 species time delayed lotka volterra reaction diffusion models with homogeneous neumann boundary condition some simple conditions are obtained for the global asymptotic stability of the nonnegative semitrivial constant steady state solutions these conditions are explicit and easily verifiable and they involve only the reaction rate constants and are independent of the diffusion and time delays the result of global asymptotic stability not only implies the nonexistence of positive steady state solution but also gives some extinction results of the models in the ecological sense the instability of some nonnegative semitrivial constant steady state solutions is also shown the conclusions for the reaction diffusion systems are directly applicable to the corresponding ordinary differential systems

on the smoothing property of linear delay partial differential equations abstract we consider linear partial differential equations with an additional delay term which under spatial discretization lead to ordinary differential equations with fixed delay of retarded type this means that the semi discrete solution gains smoothness over time for the concept of classical mild and weak solutions we analyse whether this effect also takes place in the original system we show that some systems behave in a neutral way only as a result the smoothness of the exact solution remains unchanged instead of gaining smoothness over time

a priori bounds and stability in the retarded nonlinear wave equation the object of this work is to give sufficient conditions to ensure that the zero solution of certain generalizations of u t 4x g u x t h t x flu o 0 xg x oifx o f b 0 and g x 0 2 a g f and h are at least continuous 3 we impose the boundary conditions u t o u t l o so that u t o u t l o 4 although mixed boundary conditions are generally satisfactory among other things it is crucial to have

existence and stability of periodic quasisolutions in nonlinear parabolic systems with discrete delays the existence of periodic quasisolutions and the dynamics for a couple system of semilinear parabolic equations with discrete time delays and periodic coefficients are investigated using the method of upper and lower solutions it is shown that if the reaction function in the system possesses a mixed quasimonotone property and the periodic boundary value system has a pair of coupled t upper and lower solutions then the periodic boundary value problem has a pair of periodic quasisolutions and the sector between the quasisolutions is an attractor of the delayed periodic parabolic system under some additional conditions the periodic quasisolutions are exactly true periodic solutions of the periodic boundary value system finally three models arising from ecology are given to illustrate the obtained results

connective generators for archimedian triangular operators abstract triangular norms form the kernel of fuzzy logic and fuzzy systems here in this paper my main motivation is to provide three new connective generators that can generate different classes of fuzzy connectives in this study i have tried to show that there are many possible fuzzy connective generators that can be associative and yet monotonic the study contemplates mainly on three different connective generators these generators use simple monotonic and continuous functions that are both bounded in the domain 0 1 and the range 0 1

eigenproblems for tridiagonal 2 toeplitz matrices and quadratic polynomial mappings abstract given a system of monic orthogonal polynomials mops p n x n 0 we characterize all the sequences of monic orthogonal polynomials q n x n 0 such that q 1 x x b q 2 n x p n 2 x n 0 1 2 where 2 is a fixed polynomial of degree exactly 2 and b is a fixed complex number with an appropriate choice of the mops p n x n 0 our results enables us to solve the eigenproblem of a tridiagonal 2 toeplitz matrix giving an alternative proof to a recent result by m j c gover we also find the relations between the jacobi matrices corresponding to the mops p n x n 0 and q n x n 0 finally we show that if p n x n 0 is a semiclassical orthogonal polynomial sequence then so is q n x n 0 and in particular we analyze the classical case in detail

asymptotic constancy of solutions of linear parabolic volterra difference equations abstract in this paper we obtain some sufficient conditions under which every solution of a class of linear parabolic volterra difference equations of neutral type tends to a constant as n we also consider the asymptotic constancy of solutions for a class of linear ordinary volterra difference equations of neutral type the results obtained improve and generalize some known results

functional differential equations and jensen s inequality on etudie les proprietes de stabilite et de limitation de l equation differentielle fonctionnelle x t f t x t ou x t s x t s pour h s 0 et h une constante positive fixee on utilise la methode de lyapunov directe

periodic solutions of parabolic systems with time delays existence of maximal and minimal periodic solutions of a coupled system of parabolic equations with time delays and with nonlinear boundary conditions is discussed the proof of the existence theorem is based on the method of upper and lower solutions and its associated monotone iterations this method is constructive and can be used to develop a computational algorithm for numerical solutions of the periodic parabolic system an application is given to a competitor competitor mutualist model which consists of a coupled system of three reaction diffusion equations with time delays

explicit inverse of a tridiagonal k toeplitz matrix we obtain explicit formulas for the entries of the inverse of a nonsingular and irreducible tridiagonal k toeplitz matrix a the proof is based on results from the theory of orthogonal polynomials and it is shown that the entries of the inverse of such a matrix are given in terms of chebyshev polynomials of the second kind we also compute the characteristic polynomial of a which enables us to state some conditions for the existence of a 1 our results also extend known results for the case when the residue mod k of the order of a is equal to 0 or k 1 numer math 10 1967 pp 153 161

entries of continuous functions of large hermitian tridiagonal 2 toeplitz matrices abstract in this paper we present an eigenvalue decomposition for any real symmetric tridiagonal 2 toeplitz matrix of odd order where the eigenvector matrix is orthogonal using this decomposition we study the entries of continuous functions of large real symmetric tridiagonal 2 toeplitz matrices furthermore we also study in the present paper the entries of continuous functions of large hermitian toeplitz matrices with at most three non zero diagonals

eigenvalues of a certain class of tridiagonal matrices we make a short comment on a paper involving the minimal eigenvalues of a specialized version of 2 toeplitz tridiagonal matrices

global attractivity in population dynamics we established sufficient conditions for the global attractivity of the positive equilibrium of the delay differential equation n t mu n t i 1m pi exp n t i t 0 m 1 for m 1 equation 1 was used by wazewska czyzewska and lasota as a model for the survival of red blood cells in an animal

inverses of k toeplitz matrices with applications to resonator arrays with multiple receivers abstract we find closed form algebraic formulas for the elements of the inverses of tridiagonal 2 and 3 toeplitz matrices which are symmetric and have constant upper and lower diagonals these matrices appear respectively as the impedance matrices of resonator arrays in which a receiver is placed over every 2 or 3 resonators consequently our formulas allow to compute the currents of a wireless power transfer system in closed form allowing for a simple exact and symbolic analysis thereof small numbers are chosen for illustrative purposes but the elementary linear algebra techniques used can be extended to k toeplitz matrices of this special form with k arbitrary hence resonator arrays with a receiver placed over every k resonators can be analysed in the same way

systems of parabolic equations with continuous and discrete delays abstract in this paper we investigate the global existence and the dynamics of a coupled system of nonlinear parabolic equations where the nonlinear reaction function may depend on both continuous infinite or finite and discrete delays it is shown that if the reaction function is locally lipschitz continuous and the system possesses a pair of coupled upper and lower solutions then there exists a unique global solution to the system without any quasimonotone condition on the reaction function for systems with mixed quasimonotone reaction functions we use the monotone method to establish more dynamic property of the parabolic system in terms of the quasisolutions of the corresponding elliptic system this approach yields a global attractor of the parabolic system and under some additional conditions this attractor leads to the existence and asymptotic stability of a solution of the elliptic system application to three model problems in population dynamics and chemical reactions is given

integral equations as evolution equations abstract we study a class of time dependent linear integrodifferential equations ve with the evolution equation approach we determine the generators of a time dependent evolution equation de which is equivalent to the given integrodifferential equation under very general assumptions we prove the well posedness and continuity of ve from the stability of de the related question of convergence of a family of approximate solutions is examined as an application we include an example of hyperbolic integro partial differential equation to illustrate the theory

on a constant diagonals matrix in this paper we consider a constant diagonals matrix the matrix was discussed in witula and slota r witula d slota on computing the determinants and inverses of some special type of tridiagonal and constant diagonals matrices appl math comput 189 1 2007 514 527 the authors gave some results on determinant and the inverse of the matrix for some special cases we give lu factorization and then compute determinant of the matrix we determine eigenvalues of the matrix further we obtain some relationships between permanent of the matrix and terms of a certain recurrence relation

reaction diffusion systems with time delays monotonicity invariance comparison and convergence in a recent paper we have obtained differential inequality results developed comparison theorems and established invariance criteria for mild solutions of abstract functional differential equations in a banach space the primary application for these results is to reaction diffusion systems in which the reaction nonlinearity contains time delays in the present paper we apply these results to reaction diffusion systems with time delays of the form u t d u f x u t x x u u n 0 x where is a bounded open set in r n with smooth boundary u r n d diag d 1 d n with d i 0

parabolic systems in unbounded domains i existence and dynamics abstract in this paper we investigate the existence uniqueness and asymptotic behavior of a solution for a class of coupled nonlinear parabolic equations in a general unbounded domain that includes the whole space r n the exterior of a bounded domain and a half space in r n the asymptotic behavior of the solution is with respect to a pair of quasi solutions of the corresponding elliptic system and when these two quasi solutions coincide the solution of the parabolic system converges to a unique solution of the elliptic system

locally toeplitz sequences spectral properties and applications abstract the notion of locally toeplitz sequence of matrices is introduced which extends the notion of toeplitz sequence of matrices the singular value distribution and in the hermitian case the eigenvalue distribution is completely characterized for locally toeplitz sequences and their sums obtaining weighted szeg formulas which extend well known results due to tyrtyshnikov concerning toeplitz matrices indeed any toeplitz sequence t n f where f is bounded is proved to be a locally toeplitz sequence moreover sufficient conditions are given for the product of two locally toeplitz sequences to be also locally toeplitz by combining these theoretic results we are able to explicitly compute the asymptotic spectral distribution of a large class of matrices arising in the applications including the algebra generated by toeplitz sequences and virtually all matrices resulting from the discretization of a unidimensional differential operator with non constant coefficients finally a large number of examples is discussed

asymptotic behavior of solutions for a cooperation diffusion model with a saturating interaction this paper is concerned with a lotka volterra cooperation diffusion model with a saturating interaction term for one species the goal of the paper is to investigate the asymptotic behavior of the time dependent solution in relation to the corresponding steady state solutions under homogeneous neumann boundary condition some simple and easily verifiable conditions are given to the rate constants so that for every nontrivial nonnegative initial function the corresponding time dependent solution converges to one of the nonnegative constant steady state solutions as time tends to infinity this convergence result leads to the existence and uniqueness of a positive or nonnegative steady state solution and the global asymptotic stability of a given nonnegative constant steady state solution in terms of ecological dynamics it also gives some coexistence permanence and extinction results for the model

spatio temporal complexity of a delayed diffusive model for plant invasion abstract in this paper we develop a diffusive plant invasion model with delay under the homogeneous neumann boundary condition first the existence and uniqueness of a non negative solution persistence property and local asymptotic stability of the constant steady states are established then by analyzing the associated characteristic equation the stability of steady states and the existence of hopf bifurcation are demonstrated under special circumstance the discontinuous hopf bifurcation is also investigated furthermore the existence and non existence of nonconstant positive steady states of this model are studied through considering the effect of large diffusivity finally in order to verify our theoretical results some numerical simulations are also included it shows that the numerically observed behaviors are in good agreement with the theoretically proposed results on the basis of numerical simulations we provide some useful comparisons for the readers between our results and the existing ones and discuss the effects of the delay and the diffusion term on dynamic behaviors numerical results indicate that diffusion can make the system unstable and increasing delay may cause the plant to go extinct

flow invariance for nonlinear partial differential delay equations several fundamental results on existence flow invariance regularity and linearized stability of solutions to the nonlinear partial differential delay equation u t bu t f u t t 0 uo with b c x x x w accretive are developed for a general banach space x in contrast to existing results with the history response f globally defined and at least lipschitz on bounded sets the results are tailored for situations with f defined on possibly thin subsets of the initial history space e only and are applied to place several classes of population models in their natural l 1 setting the main result solves the open problem of a subtangential condition for flow invariance of solutions in the fully nonlinear case paralleling those known for the cases of a no delay b ordinary delay equations with b 0 and c the semilinear case

symmetric functional differential equations and neural networks with memory we establish an analytic local hopf bifurcation theorem and a topological global hopf bifurcation theorem to detect the existence and to describe the spatial temporal pattern the asymptotic form and the global continuation of bifurcations of periodic wave solutions for functional differential equations in the presence of symmetry we apply these general results to obtain the coexistence of multiple large amplitude wave solutions for the delayed hopfield cohen grossberg model of neural networks with a symmetric circulant connection matrix

comments on the spectrum of a tridiagonal k toeplitz matrix abstract in this note we will discuss some errors presented in a recent paper on r periodic tridiagonal matrices in addition we present several results that had been previously reported in mathematical literature

diffusion effect and stability analysis of a predator prey system described by a delayed reaction diffusion equations in this paper we consider a delayed reaction diffusion equations which describes a two species predator prey system with diffusion terms and stage structure by using the linearization method and the method of upper and lower solutions we study the local and global stability of the constant equilibria respectively the results show that the free diffusion of the delayed reaction diffusion equations has no effect on the populations when the diffusion is too slow otherwise the free diffusion has a certain influence on the populations however the influence can be eliminated by improving the parameters to satisfy some suitable conditions

universal estimate of the gradient for parabolic equations we suggest a modification of the estimate for weighted sobolev norms of solutions of parabolic equations such that the matrix of the higher order coefficients is included into the weight for the gradient more precisely we found the upper limit estimate that can be achieved by variations of the zero order coefficient as an example of applications an asymptotic estimate was obtained for the gradient at initial time the constant in the estimates is the same for all possible choices of the dimension domain time horizon and the coefficients of the parabolic equation as an another example of application existence and regularity results are obtained for parabolic equations with time delay for the gradient

spectral properties of certain tridiagonal matrices abstract we study spectral properties of irreducible tridiagonal k toeplitz matrices and certain matrices which arise as perturbations of them

instability in diffusive ecological models with nonlocal delay effects abstract we propose a reaction diffusion system with nonlocal delays to model the growth of plankton communities feeding on a limiting nutrient supplied at a constant rate two delays are incorporated into the model one describes the delayed nutrient recycling process and the other models the delayed growth response of the plankton it is assumed that both delays are nonlocal in the sense that there are delayed not only in time but also in space local and bifurcation analyses are carried out it has been shown that turing type spatial patterns occur when the diffusion coefficients vary and temporal or spatial temporal patterns occur when the delay involved in the growth response changes

multiple boolean algebras and their application to fuzzy sets abstract a cycle of semilattices is a set e together with p semilattice operations which can be linearly ordered so that each operation is distributive to the following and the last is distributive to the first a multiple boolean algebra is defined to be a cycle of semilattices satisfying certain additional requirements 1 i each operation has an absorbing and an identity element 2 ii there is a bijection e e carrying each operation into the next and the last into the first 3 iii an axiom is satisfied that generalizes the fact that in boolean algebras the meet and the join of an element with its complement are equal to the zero and the identity elements respectively it is shown that for every n 1 and p 2 there exist multiple boolean algebras of order p and cardinality p n the new theoretical construct can be applied to the theory of fuzzy sets if a suitable finite subset of the unit interval 0 1 is taken as the set of the grades of membership the set of the fuzzy subsets in a universe can be equipped with additional binary operations in such manner that it becomes isomorphic to a pair of multiple boolean algebras one conjugate to the other

coupled nonlinear parabolic systems with time delays a coupled system of parabolic equations with time delays is investigated by the method of upper lower solutions it is shown by using upper and lower solutions as coupled initial iterations that the corresponding sequences converge monotonically to a unique solution of the system this convergence leads to an existence comparison theorem which is useful for studying the asymptotic behavior of the solution this method is extended to a coupled system of integro differential equations and systems of parabolic ordinary equations applications are given to some model problems in ecology and nuclear engineering including the stability property of a steady state solution

a small set of axioms for residuated logic we show that a set of three axioms together with modus ponens suffices to build up a formal system for the class r of all quadruples l t j in which l is a partially ordered set with a top element and t is a triangular norm on l that has a residuated implication j we show that this r is not a variety

orthogonal polynomials on the unit circle via a polynomial mapping on the real line let f n n 0 be a sequence of monic orthogonal polynomials on the unit circle opuc with respect to a symmetric and finite positive borel measure email protected on 0 email protected and let 1 a 0 a 1 a 2 be the associated sequence of verblunsky coefficients in this paper we study the sequence email protected n n 0 of monic opuc whose sequence of verblunsky coefficients is 1 b 1 b 2 b n 1 a 0 b n 1 b 2 b 1 a 1 b 1 b 2 b n 1 a 2 b n 1 b 2 b 1 a 3 where b 1 b 2 b n 1 are n 1 fixed real numbers such that b email protected 1 1 for all j 1 2 n 1 so that email protected n n 0 is also orthogonal with respect to a symmetric and finite positive borel measure email protected on the unit circle we show that the sequences of monic orthogonal polynomials on the real line oprl corresponding to f n n 0 and email protected n n 0 by szego s transformation are related by some polynomial mapping giving rise to a one to one correspondence between the monic opuc email protected n n 0 on the unit circle and a pair of monic oprl on a subset of the interval 1 1 in particular we prove email protected q email protected n 1 q email protected q n q email protected q n q q n q supported on a subset of the union of 2n intervals contained in 0 email protected such that any two of these intervals have at most one common point and where up to an affine change in the variable z n 1 and email protected n are algebraic polynomials in email protected of degrees n 1 and n respectively defined only in terms of a 0 b 1 b n 1 this measure induces a measure on the unit circle supported on the union of 2n arcs pairwise symmetric with respect to the real axis the restriction to symmetric measures or real verblunsky coefficients is needed in order that szego s transformation may be applicable

dynamics of nonlinear parabolic systems with time delays abstract the dynamics of a coupled system of semilinear parabolic equations with discrete time delays is investigated using the method of upper and lower solutions it is shown that if the reaction function in the system possesses a mixed quasimonotone property and the corresponding elliptic system has a pair of coupled upper and lower solutions then there is a monotone iteration process which yields a pair of quasisolutions of the elliptic system and the sector between the quasisolutions is an attractor of the delayed parabolic system under some additional conditions this sector is a global attractor and the solution of the parabolic system converges to a true solution of the elliptic system the same conclusions are obtained for a coupled system of parabolic ordinary equations with time delays applications are given to three model problems arising from ecology and nuclear engineering these model problems possess multiple steady state solutions and sufficient conditions are given to ensure the stability and instability of these solutions

generalized locally toeplitz sequences spectral analysis and applications to discretized partial differential equations abstract starting from the finite difference discretization of an elliptic second order pde as i j 1 d x i a i j x x j u x b x over a bounded domain we introduce the notion of generalized locally toeplitz sequence of matrices the singular value distribution the eigenvalue distribution in the hermitian case is studied and characterized for generalized locally toeplitz sequences in terms of weighted multidimensional szeg formulas this extends preceding results attributed to tilli which concern the unilevel case the application of this theoretic analysis to the numerical solution of pdes is finally discussed

inversion of k tridiagonal matrices with toeplitz structure in this paper we consider an inverse problem with the k tridiagonal toeplitz matrices a theoretical result is obtained that under certain assumptions the explicit inverse of a k tridiagonal toeplitz matrix can be derived immediately two numerical examples are given to demonstrate the validity of our results

finite difference solutions of reaction diffusion equations with continuous time delays abstract this paper is an extension of the monotone iterative methods for finite difference equations with discrete time delays to a class of nonlinear finite difference system with continuous time delays the system under consideration is a finite difference approximation of a class of reaction diffusion equations with continuous time delays in the nonlinear reaction under either dirichlet or neumann robin boundary conditions various monotone iterative schemes which depend on the property of the nonlinear reaction mechanism are developed for the computation of numerical solutions it is shown by the method of upper and lower solutions that the two sequences obtained from each iterative scheme converge monotonically from above and below respectively to a unique solution of the finite difference system applications are given to two model problems known as the diffusive logistic equation and the fisher s diffusion equation in population genetics

explicit inverses of some tridiagonal matrices abstract we give explicit inverses of tridiagonal 2 toeplitz and 3 toeplitz matrices which generalize some well known results concerning the inverse of a tridiagonal toeplitz matrix

global asymptotic behaviour in some functional parabolic equations the global asymptotic behavior in some functional parabolic equations was presented the sufficient condition for the global convergence to a spatially uniform equilibrium in the system of functional partial differential equations was provided results were observed to be valid for all non negative spatio temporal kernels which also satisfied a uniform normailzation condition

on positive solutions of the lotka volterra cooperating models with diffusion abstract in this paper using the existence and comparison conclusion for the time periodic quasimonotone nondecreasing systems given by pao c v and iterative method we investigate the time periodic lotka volterra cooperating model and present some existence uniqueness and nonexistence results we also use similar methods to treat the corresponding stationary system to give parallel results

periodic solutions of parabolic systems with nonlinear boundary conditions this paper is concerned with the existence and stability of periodic solutions for a coupled system of nonlinear parabolic equations under nonlinear boundary conditions the approach to the problem is by the method of upper and lower solutions and its associated monotone iterations this method leads to the existence of maximal and minimal periodic solutions which can be computed from a linear iteration process in the same fashion as for parabolic initial boundary value problems a sufficient condition for the stability of a periodic solution is also given these results are applied to three model problems arising from chemical kinetics ecology and population biology

real coextensions as a tool for constructing triangular norms we present in this paper a universal method of constructing left continuous triangular norms l c t norms the starting point is an arbitrary possibly finite totally ordered monoid fulfilling the conditions that are characteristic for l c t norms commutativity negativity and quanticity we show that under suitable conditions we can extend this structure by substituting each element for a real interval the process can be iterated and if the final structure obtained in this way is order isomorphic to a closed real interval its monoidal operation can up to isomorphism be identified with a l c t norm we specify the constituents needed for the construction in an explicit way we furthermore illustrate the method on the basis of a number of examples

the determination of companion matrices characterizing toeplitz and r toeplitz matrices abstract it is shown that the unknown elements in the companion matrix used to characterize a nonsingular toeplitz matrix are easily found from the elements of the inverse of the toeplitz matrix similar formulae are obtained for the two companion like matrices characterizing an r toeplitz matrix this case includes the result for a block toeplitz matrix

spatially inhomogeneous steady state solutions for systems of equations describing interacting populations for x e i2 and t 0 where 0 is a bounded region in r n 1 2 3 and a denotes the laplacian models the interaction of two species co existing in q the densities of the species at time t and at the point x e q are given by u x t and v x t the constants d dz 0 give the rates at which the species diffuse the constants a and b give if positive the birth rates and if negative the mortality rates of the species so that system 1 1 has a unique solution we must specify initial conditions i e u x 0 and li x 0 and boundary conditions we shall be interested in the case of dirichlet boundary conditions i e in the case where u x f and t x t are specified functions of x on x co existing populations may interact in various ways e g they may compete or co operate with each other or one may be a predator preying on the other the nature of the interaction is reflected by the properties of the terms f u tl and g u c for example if the 1 population preys on the ii population an increase in l would lead to a decrease in u and so it would be natural to assume that zf k 0 throughout we shall assume that

oscillation of a class of partial functional population model abstract this paper is concerned with the oscillation of a class of partial functional population model and some sufficient conditions for all positive solutions of the model to oscillate about the positive equilibrium are obtained the approach is based on the upper and lower solution method of the partial functional differential equations and the oscillation theory of the functional differential equation moreover some numerical simulations are also given to illustrate our results

the eigenproblem of a tridiagonal 2 toeplitz matrix abstract the characteristic polynomial of a tridiagonal 2 toeplitz matrix is shown to be closely connected to polynomials which satisfy the three point chebyshev recurrence relationship this is an extension of the well known result for a tridiagonal toeplitz matrix when the order of the matrix is odd the eigenvalues are found explicitly in terms of the chebyshev zeros the eigenvectors are found in terms of the polynomials satisfying the three point recurrence relationship

explicit expression for powers of tridiagonal 2 toeplitz matrix of odd order abstract in this paper we give the eigenvalue decomposition for odd order tridiagonal 2 toeplitz matrix and derive the explicit expression for integer powers of such matrix

asymptotic behavior of solutions for a class of predator prey reaction diffusion systems with time delays the aim of this paper is to investigate the asymptotic behavior of solutions for a class of three species predator prey reaction diffusion systems with time delays under homogeneous neumann boundary condition some simple and easily verifiable conditions are given to the rate constants of the reaction functions to ensure the convergence of the time dependent solution to a constant steady state solution the conditions for the convergence are independent of diffusion coefficients and time delays and the conclusions are directly applicable to the corresponding parabolic ordinary differential system and to the corresponding system without time delays

solution estimates for abstract nonlinear time variant differential delay equations abstract semilinear time variant functional differential equations in a banach space are considered a solution estimate is derived by that estimate explicit conditions for boundedness of solutions and stability are established

characterisation and properties of r toeplitz matrices abstract an r toeplitz rt matrix can be regarded as a block toeplitz matrix with order some multiple of r from which a bottom border and a right hand border have been removed it is shown that some known properties of toeplitz matrices extend to this new class in particular a necessary and sufficient condition is given in terms of a linear matrix equation for a nonsingular matrix to have rt form from which it follows that the elements of the inverse are completely determined by those in its first and last r rows and columns in addition some results are presented for cases when the inverse of an rt matrix has certain banded forms

parabolic systems in unbounded domains ii equations with time delays abstract this paper extends the results of an earlier article concerning the existence uniqueness comparison and dynamics problems for a coupled system of parabolic equations in unbounded domains including the whole space r n the present extension is for a system of functional parabolic ordinary equations where the reaction function is allowed to depend on the unknown function with time delay which may be discrete or continuous finite or infinite applications are made to some model problems with emphasis on the convergence fo the time dependent solution to a steady state solution and the decay property of the solution as x

on the order of triangular norms comments on a triangular norm hierarchy by e cretu in cretu fuzzy sets and systems 120 2001 371 the members of the families of frank dubois prade yager and hamacher t norms respectively are compared in a pointwise way with the minimum the product and the lukasiewicz t norm all these results are well known and trivial moreover these families of t norms cannot only be compared with the three basic t norms above but all these families are monotone with respect to their index a fact which is also well known and straightforward to prove with the exception of the family of frank t norms whose monotonicity has been first proven in butnariu and klement triangular norm based measures and games with fuzzy coalitions kluwer dordrecht 1993

stability of abstract nonlinear nonautonomous differential delay equations with unbounded history responsive operators we consider a class of nonautonomous functional differential equations in a banach space with unbounded nonlinear history responsive operators which have the local lipshitz property conditions for the boundedness of solutions lyapunov stability absolute stability and input output one are established our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators

on some tridiagonal k toeplitz matrices algebraic and analytical aspects applications in this paper we use the analytic theory for 2 and 3 toeplitz matrices to obtain the explicit expressions for the eigenvalues eigenvectors and the spectral measure associated to the corresponding infinite matrices as an application we consider two solvable models related with the so called chain model some numerical experiments are also included

spectra of certain jacobi operators we discuss the spectra and in particular the essential spectra of some bounded self adjoint jacobi operators associated with orthogonal polynomial sequences obtained via polynomial mappings

time delayed parabolic system in a two species competitive model with stage structure a two species competitive model with stage structure is discussed the dynamics of coupled system of semilinear parabolic equations with time delays are investigated results on the local and global stabilities of the axial equilibria and positive equilibrium are given our results show that the introduction of diffusion does not affect the permanence and extinction of the species though the introduction of stage structure brings negative effect on it

small gain stability analysis of certain hyperbolic parabolic pde loops abstract this work provides stability results in the spatial sup norm for hyperbolic parabolic loops in one spatial dimension the results are obtained by an application of the small gain stability analysis two particular cases are selected for the study because they contain challenges typical of more general systems to which the results are easily generalizable but at the expense of less pedagogical clarity and more notational clutter i the feedback interconnection of a parabolic pde with a first order zero speed hyperbolic pde with boundary disturbances and ii the feedback interconnection by means of a combination of boundary and in domain terms of a parabolic pde with a first order hyperbolic pde the first case arises in the study of the movement of chemicals underground and includes the wave equation with kelvin voigt damping as a subcase the second case arises when we apply backstepping to a pair of hyperbolic pdes that is obtained by ignoring diffusion phenomena moreover the second case arises in the study of parabolic pdes with distributed delays in the first case we provide sufficient conditions for iss in the spatial sup norm with respect to boundary disturbances in the second case we provide delay independent sufficient conditions for exponential stability in the spatial sup norm