optimal control of non homogenous prey predator models during infinite and finite time intervals we propose a lattice to describe dynamics of two animal species population one being a prey and the other a predator the problem of controlling steady states of non homogenous prey predator model during finite and infinite time intervals is studied using lyapunov bellman technique the optimal control law is derived from the conditions that ensure the asymptotic stabilization of the steady states of this model using bellman s equation the densities of both prey and predator populations are obtained as functions of time graphical and numerical example studies of the obtained results are presented

on the global convergence of trust region algorithms for unconstrained minimization many trust region algorithms for unconstrained minimization have excellent global convergence properties if their second derivative approximations are not too large 2 we consider how large these approximations have to be if they prevent convergence when the objective function is bounded below and continuously differentiable thus we obtain a useful convergence result in the case when there is a bound on the second derivative approximations that depends linearly on the iteration number

qualitative analysis for a ratio dependent predator prey model with disease and diffusion abstract this paper is purported to study a reaction diffusion system arising from a ratio dependent predator prey model with disease we study the dynamical behavior of the predator prey system the conditions for the permanent and existence of steady states and their stability are established we can obtain the bounds for positive steady state of the corresponding elliptic system the non existence results of non constant positive solutions are derived

stopping rules and backward error analysis for bound constrained optimization termination criteria for the iterative solution of bound constrained optimization problems are examined in the light of backward error analysis it is shown that the problem of determining a suitable perturbation on the problem s data corresponding to the definition of the backward error is analytically solvable under mild assumptions moreover a link between existing termination criteria and this solution is clarified indicating that some standard measures of criticality may be interpreted in the sense of backward error analysis the backward error problem is finally considered from the multicriteria optimization point of view and some numerical illustration is provided

spin and wedge representations of infinite dimensional lie algebras and groups abstract we suggest a purely algebraic construction of the spin representation of an infinite dimensional orthogonal lie algebra sections 1 and 2 and a corresponding group section 4 from this we deduce a construction of all level one highest weight representations of orthogonal affine lie algebras in terms of creation and annihilation operators on an infinite dimensional grassmann algebra section 3 we also give a similar construction of the level one representations of the general linear affine lie algebra in an infinite dimensional wedge space along these lines we construct the corresponding representations of the universal central extension of the group sln k t t 1 in spaces of sections of line bundles over infinite dimensional homogeneous spaces section 5

permanence and stability of a diffusive predator prey model with disease in the prey abstract we investigate a 3 dimensional system of the predator prey dynamics with disease for the prey this system is a reaction diffusion model with ratio dependent michaelis menten functional response and diffusion in a bounded domain by applying the comparison principle liapunov function and linearized method we are able to achieve the sufficient conditions of the permanence the global stability of the boundary equilibria and the positive equilibrium and the local stability of the positive equilibrium numerical simulations are also given to illustrate the applications

a robust trust region method for nonlinear optimization with inequality constraint a new trust region algorithm for inequality constrained optimization is presented which solves two linear programming subproblems and a serious of quadratic subproblems at each successful iteration to obtain a acceptable trial step the algorithm can circumvent the difficulties associated with the possible inconsistency of trust region subproblem moreover the algorithm can converge to a point which satisfies a certain first order necessary condition even when the original problems itself is infeasible some global convergence properties are proved without regularity assumption and local superlinear convergence of the algorithm is obtained under standard conditions preliminary numerical results are reported on some classic problems

hopf bifurcation and stability of periodic solutions in a delayed eco epidemiological system abstract in this paper a delayed predator prey epidemiological system with disease spreading in predator population is considered by regarding the delay as the bifurcation parameter and analyzing the characteristic equation of the linearized system of the original system at the positive equilibrium the local asymptotic stability of the positive equilibrium and the existence of local hopf bifurcation of periodic solutions are investigated moreover we also study the direction of hopf bifurcations and the stability of bifurcated periodic solutions an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations finally numerical simulations supporting the theoretical analysis are also included

non monotone trust region algorithms for nonlinear optimization subject to convex constraints this paper presents two new trust region methods for solving nonlinear optimization problems over convex feasible domains these methods are distinguished by the fact that they do not enforce strict monotonicity of the objective function values at successive iterates the algorithms are proved to be convergent to critical points of the problem from any starting point extensive numerical experiments show that this approach is competitive with the lancelot package

multivariate scattered data fitting during the week of 2 8 march 1995 a meeting entitled international conference on scattered data fitting was held in cancun mexico the meeting was attented by 42 researchers from europe and the americas and 34 lectures were presented this special issue of journal of computational and applied mathematics includes 14 papers based on presentations at the conference

bispectral algebras of commuting ordinary differential operators we develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank n it combines and unifies the ideas of duistermaat grunbaum and wilson our construction is completely algorithmic and enables us to obtain all previously known classes or individual examples of bispectral operators the method also provides new broad families of bispectral algebras which may help to penetrate deeper into the problem

a trust region strategy for minimization on arbitrary domains we present a trust region method for minimizing a general differentiable function restricted to an arbitrary closed set we prove a global convergence theorem the trust region method defines difficult subproblems that are solvable in some particular cases we analyze in detail the case where the domain is a euclidean ball for this case we present numerical experiments where we consider different hessian approximations

differential equations in the spectral parameter we determine all the potentialsv x for the schrodinger equation 2 v x k2 such that some family of eigenfunctions satisfies a differential equation in the spectral parameterk of the formb k k o x o for each suchv x we determine the algebra of all possible operatorsb and the corresponding functions x

a trust region algorithm for parametric curve and surface fitting abstract let a family of curves or surfaces be given in parametric form via the model equation x s where x rn r m and s s rd d such that the manifold m s s s is a best fit toscattered data zi i 1y rn in the sense that for some s i i 1 n the sum of the squared least distances i 1 n z i s i 2 2 from the data points to the manifold m is minimal among all such manifolds for robustness our algorithm uses a globally convergent trust region approach in which at each iteration an approximation to the objective function is minimized in a given neighborhood of the current iterate the set s may be all of rd or a closed convex subset in particular it may be chosen so that our theory is applicable to splines

bispectral operators of prime order the aim of this paper is to solve the bispectral problem for bispectral operators whose order is a prime number more precisely we give a complete list of such bispectral operators we use systematically the operator approach and in particular dixmier ideas on the first weyl algebra when the order is 2 the main theorem is exactly the result of duistermaat grunbaum on the other hand our proofs seem to be simpler

global convergence of a class of trust region algorithms for optimization with simple bounds this paper extends the known excellent global convergence properties of trust region algorithms for unconstrained optimization to the case where bounds on the variables are present weak conditions on the accuracy of the hessian approximations are considered it is also shown that when the strict complementarily condition holds the proposed algorithms reduce to an unconstrained calculation after finitely many iterations allowing a fast asymptotic rate of convergence

on the convergence of a new trust region algorithm in this paper we present a new trust region algorithm for general nonlinear constrained optimization problems the algorithm is based on the l infty exact penalty function under very mild conditions global convergence results for the algorithm are given local convergence properties are also studied it is shown that the penalty parameter generated by the algorithm will be eventually not less than the l 1 norm of the lagrange multipliers at the accumulation point it is proved that the method is equivalent to the sequential quadratic programming method for all large k hence superlinearly convergent results of the sqp method can be applied numerical results are also reported

modelling and analysis of a delayed predator prey model with disease in the predator in this paper we study a predator prey model with a transmissible disease spreading in the predator population and a time delay representing the gestation period of the predator by analyzing corresponding characteristic equations the local stability of each of feasible equilibria and the existence of hopf bifurcations at the disease free equilibrium and the coexistence equilibrium are established respectively by means of lyapunov functionals and lasalle s invariance principle sufficient conditions are derived for the global stability of the predator extinction equilibrium and the disease free equilibrium and the global attractiveness of the coexistence equilibrium of the system respectively numerical simulations are carried out to support the theoretical analysis

a new active set algorithm for box constrained optimization an active set algorithm asa for box constrained optimization is developed the algorithm consists of a nonmonotone gradient projection step an unconstrained optimization step and a set of rules for branching between the two steps global convergence to a stationary point is established for a nondegenerate stationary point the algorithm eventually reduces to unconstrained optimization without restarts similarly for a degenerate stationary point where the strong second order sufficient optimality condition holds the algorithm eventually reduces to unconstrained optimization without restarts a specific implementation of the asa is given which exploits the recently developed cyclic barzilai borwein cbb algorithm for the gradient projection step and the recently developed conjugate gradient algorithm cg descent for unconstrained optimization numerical experiments are presented using box constrained problems in the cuter and minpack 2 test problem libraries

analysis of a three species eco epidemiological model abstract this paper formulates and analyzes a predator prey model with disease in the prey mathematical analyses of the model equations with regard to invariance of nonnegativity boundedness of solutions nature of equilibria permanence and global stability are analyzed it is also shown that for some parameter values the positive equilibrium is asymptotically stable but for other parameter values it is unstable and a surrounding periodic solution appears by hopf bifurcation a concluding discussion with numerical simulation is then presented

qualitative analysis for a diffusive predator prey model with a transmissible disease in the prey population in this paper we study a diffusive predator prey model with a transmissible disease in the prey population we offer a complete discussion of the dynamical properties under the homogeneous neumann boundary condition we analyze local and global stabilities of nonnegative constant steady states and long time behaviors of the positive solutions moreover we study the existence nonexistence and bifurcation of nonconstant positive stationary solutions finally some numerical simulations are presented to support and strengthen our analytical analysis

noncommutative bispectral darboux transformations we prove a general theorem establishing the bispectrality of noncommutative darboux transformations it has a wide range of applications that establish bispectrality of such transformations for differential difference and q difference operators with values in all noncommutative algebras all known bispectral darboux transformations are special cases of the theorem using the methods of quasideterminants and the spectral theory of matrix polynomials we explicitly classify the set of bispectral darboux transformations from rank one differential operators and airy operators with values in matrix algebras these sets generalize the classical calogero moser spaces and wilson s adelic grassmannian

ecoepidemic models with disease incubation and selective hunting in this paper we consider ecoepidemic models in which the basic demographics is represented by predator prey interactions with the disease modeled by an sei system at first we consider a basic lotka volterra type of interaction then we also introduce competition for resources among individuals of the prey population several variations of the model are presented in which the prey intra specific population pressure assumes different forms depending on the virulence of the disease indeed the latter may affect the exposed and infected individuals so much that they may not be able to compete with the sound ones for resources a further distinguishing feature of this investigation lies in the way in which the predator actively selects the prey for hunting for instance in some cases predators may discard the diseased ones as less palatable while in other situations they would instead search expressly for the infected since these are weaker individuals and thus easier to hunt the equilibria of the systems are analyzed showing that in some cases bifurcations arise contrary to what happens to similar classical holling type i ecoepidemic models these persistent oscillations seem to be triggered by the number of subpopulations present in the system which is larger than those introduced in the former models counting also the latent class furthermore adding predation to an sei epidemic model has profound effects on the stability of its equilibria in particular once the predators are introduced into an sei epidemic at a stable endemic equilibrium their presence destabilizes this equilibrium making the previous stable conditions unrecoverable

a lax representation for the vertex operator and the central extension integrable hierarchies viewed as isospectral deformations of an operatorl may admit symmetries they are time dependent vector fields transversal to and commuting with the hierarchy and forming an algebra in this work the commutation relations for the symmetries are shown to be based on a non commutative lie algebra splitting theorem the symmetries viewed as vector fields onl are expressed in terms of a lax pair

convergence properties of an augmented lagrangian algorithm for optimization with a combination of general equality and linear constraints we consider the global and local convergence properties of a class of augmented lagrangian methods for solving nonlinear programming problems in these methods linear and more general constraints are handled in different ways the general constraints are combined with the objective function in an augmented lagrangian the iteration consists of solving a sequence of subproblems in each subproblem the augmented lagrangian is approximately minimized in the region defined by the linear constraints a subproblem is terminated as soon as a stopping condition is satisfied the stopping rules that we consider here encompass practical tests used in several existing packages for linearly constrained optimization our algorithm also allows different penalty parameters to be associated with disjoint subsets of the general constraints in this paper we analyze the convergence of the sequence of iterates generated by such an algorithm and prove global and fast linear convergence as well as show that potentially troublesome penalty parameters remain bounded away from zero

implicit polynomial representation through a fast fitting error estimation this paper presents a simple distance estimation for implicit polynomial fitting it is computed as the height of a simplex built between the point and the surface i e a triangle in 2 d or a tetrahedron in 3 d which is used as a coarse but reliable estimation of the orthogonal distance the proposed distance can be described as a function of the coefficients of the implicit polynomial moreover it is differentiable and has a smooth behavior hence it can be used in any gradient based optimization in this paper its use in a levenberg marquardt framework is shown which is particularly devoted for nonlinear least squares problems the proposed estimation is a generalization of the gradient based distance estimation which is widely used in the literature experimental results both in 2 d and 3 d data sets are provided comparisons with state of the art techniques are presented showing the advantages of the proposed approach

the long time behavior of a predator prey model with disease in the prey by stochastic perturbation in this paper we formulate a predator prey model with disease in the prey by stochastic perturbation using lyapunov analysis methods we discuss the asymptotic behavior of this solution furthermore we investigate whether that there exists a stationary distribution for this system and if it has the ergodic property finally we make simulations to illustrate our analytical results

bispectral darboux transformations the generalized airy case abstract this paper considers darboux transformations of a bispectral operator which preserve its bispectrality a sufficient condition for this to occur is given and applied to the case of generalized airy operators of arbitrary order r 1 as a result the bispectrality of a large family of algebras of rank r is demonstrated an involution on these algebras is exhibited which exchanges the role of spatial and spectral parameters generalizing wilson s rank one bispectral involution spectral geometry and the relationship to the sato grassmannian are discussed

a predator prey disease model with immune response in infected prey abstract in this paper a predator prey disease model with immune response in the infected prey is formulated the basic reproduction number of the within host model is defined and it is found that there are three equilibria extinction equilibrium infection free equilibrium and infection persistent equilibrium the stabilities of these equilibria are completely determined by the reproduction number of the within host model furthermore we define a basic reproduction number of the between host model and two predator invasion numbers predator invasion number in the absence of disease and predator invasion number in the presence of disease we have predator and infection free equilibrium infection free equilibrium predator free equilibrium and a co existence equilibrium we determine the local stabilities of these equilibria with conditions on the reproduction and invasion reproduction numbers finally we show that the predator free equilibrium is globally stable

infinite dimensional grassmannian structure of two dimensional quantum gravity we study the infinite dimensional grassmannian structure of 2d quantum gravity coupled to minimal conformal matters and show that there exists a large symmetry thew 1 symmetry using this symmetry structure we prove that the square root of the partition function which is a function of thep reduced kp hierarchy satisfies the vacuum condition of thew 1 algebra we further show that this condition is reduced to the vacuum condition of thew p algebra when the redundant variables for thep reduction are eliminated this mechanism also gives a prescription for extracting thew p algebra from thew 1 algebra

a class of methods for fitting a curve or surface to data by minimizing the sum of squares of orthogonal distances given a family of curves or surfaces in rs an important problem is that of finding a member of the family which gives a best fit to m given data points a criterion which is relevant to many application areas is orthogonal distance regression where the sum of squares of the orthogonal distances from the data points to the surface is minimized for certain types of fitting problem attention has recently focussed on the use of an iteration process which forces orthogonality to hold at every iteration and uses steps of gauss newton type within this framework a number of different methods has recently emerged and the purpose of this paper is to place these methods into a unified framework and to make some comparisons

bifurcation of an eco epidemiological model with a nonlinear incidence rate abstract a predator prey system with disease in the prey is considered assume that the incidence rate is nonlinear we analyse the boundedness of solutions and local stability of equilibria by using bifurcation methods and techniques we study bogdanov takens bifurcation near a boundary equilibrium and obtain a saddle node bifurcation curve a hopf bifurcation curve and a homoclinic bifurcation curve the hopf bifurcation and generalized hopf bifurcation near the positive equilibrium is analyzed one or two limit cycles is also discussed

convergence properties of trust region methods for linear and convex constraints we develop a convergence theory for convex and linearly constrained trust region methods which only requires that the step between iterates produce a sufficient reduction in the trust region subproblem global convergence is established for general convex constraints while the local analysis is for linearly constrained problems the main local result establishes that if the sequence converges to a nondegenerate stationary point then the active constraints at the solution are identified in a finite number of iterations as a consequence of the identification properties we develop rate of convergence results by assuming that the step is a truncated newton method our development is mainly geometrical this approach allows the development of a convergence theory without any linear independence assumptions

a trust region method for norm constrained problems a trust region method for the solution of nonlinear optimization problems with norm constraints is analyzed such optimization problems arise in parameter identification and nonlinear eigenvalue problems the characteristics of these applications motivate the formulation and analysis of the trust region method the algorithms studied here allow for inexact gradient information and the use of subspace methods for the approximate solution of subproblems characterizations and the descent properties of trust region steps are given criteria for the existence of successful iterations under inexact gradient information and under the use of subspace methods are established and global convergence of the method is proven

newton s method for large bound constrained optimization problems we analyze a trust region version of newton s method for bound constrained problems our approach relies on the geometry of the feasible set not on the particular representation in terms of constraints the convergence theory holds for linearly constrained problems and yields global and superlinear convergence without assuming either strict complementarity or linear independence of the active constraints we also show that the convergence theory leads to an efficient implementation for large bound constrained problems

dynamic behavior of an eco epidemic system with impulsive birth in the paper we investigate an eco epidemic system with impulsive birth the conditions for the stability of infection free periodic solution are given by applying floquet theory of linear periodic impulsive equation and we give the conditions of persistence by constructing a consequence of some abstract monotone iterative schemes by using the method of coincidence degree a set of sufficient conditions are derived for the existence of at least one strictly positive periodic solution finally numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level thus we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels

tau functions as highest weight vectors for algebra for each we construct a highest weight module of the lie algebra the highest weight vectors are specific tau functions of the nth gelfand dickey hierarchy we show that these modules are quasifinite and we give a complete description of the reducible ones together with a formula for the singular vectors

a ratio dependent predator prey model with disease in the prey in this paper a ratio dependent predator prey system with disease in the prey is formulated and analyzed mathematical analyses of the model equations with regard to invariance of nonnegativity boundedness of solutions nature of equilibria permanence and global stability are analyzed specially we shall show that ratio dependent predator prey models are rich in boundary dynamics and most importantly we shall show that a periodic solution can occur whether the system is permanent or not that is there are solutions which tend to disease free equilibrium while bifurcating periodic solution exists

stability and hopf bifurcation analysis of an eco epidemic model with a stage structure abstract in this paper an eco epidemiological model with a stage structure is considered the asymptotical stability of the five equilibria the existence of stability switches about positive equilibrium is investigated it is found that hopf bifurcation occurs when the delay passes though a critical value some explicit formulae determining the stability and the direction of the hopf bifurcation periodic solutions bifurcating from hopf bifurcations are obtained by using the normal form theory and center manifold theory some numerical simulations for justifying the theoretical analysis are also provided finally biological explanations and main conclusions are given

a predator prey model with disease in the prey after the seminal models of vito volterra and alfred james lotka in the mid 1920s for predator prey interactions mutualist and competitive mechanisms have been studied extensively in the recent years by researchers there are so many references in this context we have just cited here some books e g see 14 16 18 and the refer ences therein similarly after the pioneering work of kermack mckendrick on sirs susceptible infective removal susceptible epidemiological models have also received much attention from scientists relevant references in this context are also vast and we shall again mention here some books see 1 2 4 to mention a few but little attention has been paid so far to merge these two important areas of research see 7 21 in this paper we shall put emphasis in such an eco epidemiological system we consider a three species eco epidemiological system namely sound prey suscep tible infected prey infective and predator we consider the case when the predator mainly eats the infected prey this is in accordance with a previous model by hadeler and freedman 7 which describes a predator prey model where the prey is infected by a parasite and the prey in turn infects the predator with that parasite the infec tion weakens the prey and increases its susceptibility to predation while no predator impairing elect is accounted for while the paper is mainly theoretical and does not address any specific situation the reader may and several examples in 7 we derive persistence and extinction conditions of the populations and we also determine conditions for which the system enters a hopf type bifurcation moreover we observe that the bifurcated branches are supercritical in some parametric region space in a special case when the predator response function is a holling type ii function

bispectral kp solutions and linearization of calogero moser particle systems rational and soliton solutions of the kp hierarchy in the subgrassmanniangr1 are studied within the context of finite dimensional dual grassmannians in the rational case properties of the tau function which are equivalent to bispectrality of the associated wave function are identified in particular it is shown that there exists a bound on the degree of all time variables in if and only if is a rank one bispectral wave function the action of the bispectral involution in the generic rational case is determined explicitly in terms of dual grassmannian parameters using the correspondence between rational solutions and particle systems it is demonstrated that is a linearizing map of the calogero moser particle system and is essentially the map introduced by airault mckean and moser in 1977 2

asymptotic behavior of a three species eco epidemiological model perturbed by white noise abstract this paper considers a three species eco epidemiological model perturbed by white noise stochastic stability and long time behavior around the equilibrium of deterministic eco epidemiological model are analyzed by lyapunov methods numerical simulations for a set of parameter values are presented to illustrate the analytical findings

projected newton methods for optimization problems with simple constraints we consider the problem min f x x geqq 0 and propose algorithms of the form x k 1 x k alpha k d k nabla f x k where cdot denotes projection on the positive orthant alpha k is a stepsize chosen by an armijo like rule and d k is a positive definite symmetric matrix which is partly diagonal we show that d k can be calculated simply on the basis of second derivatives of f so that the resulting newton like algorithm has a typically superlinear rate of convergence with other choices of d k convergence at a typically linear rate is obtained the algorithms are almost as simple as their unconstrained counterparts they are well suited for problems of large dimension such as those arising in optimal control while being competitive with existing methods for low dimensional problems the effectiveness of the newton like algorithm is demonstrated via computational examples involving as many as 10 000 variables extensions to general linearly constrained pr

differential equations in the spectral parameter for matrix differential operators we use matrix darboux transformation to generate a class of matrix differential operators l that have the following property there exist a family x k of eigenfunctions of l also satisfying a differential equation in the spectral parameter k of the form b k k x whereb k k is a diffrential and is a non constant function of x we also obtain nth order scalar operators which have this property

on the identification of active constraints nondegeneracy conditions that guarantee that the optimal active constraints are identified in a finite number of iterations are studied results of this type have only been established for a few algorithms and then under restrictive hypothesis the main result is a characterization of those algorithms that identify the optimal constraints in a finite number of iterations this result is obtained with a nondegeneracy assumption which is equivalent in the standard nonlinear programming problem to the assumption that there is a set of strictly complementary lagrange multipliers as an important consequence of the authors results the way that this characterization applies to gradient projection and sequential quadratic programming algorithms is shown

on the accurate identification of active constraints we consider nonlinear programs with inequality constraints and we focus on the problem of identifying those constraints which will be active at an isolated local solution the correct identification of active constraints is important from both a theoretical and a practical point of view such an identification removes the combinatorial aspect of the problem and locally reduces the inequality constrained minimization problem to an equality constrained problem which can be more easily dealt with we present a new technique which identifies active constraints in a neighborhood of a solution and which requires neither complementary slackness nor uniqueness of the multipliers we also present extensions to variational inequalities and numerical examples illustrating the identification technique

optimal control of stochastic lattice of prey predator models we propose a stochastic lattice model to describe the dynamics of two animal species population one being a prey and the other a predator the system follows a stochastic dynamics composed of three markovain processes the first one describes the birth of prey the second describes the death of prey and simultaneous birth of predator the third describes spontaneous death of predator the master equation is used to derive the time evolution of one and two site correlations the stability of the stationary states of one site correlations is studied the optimal control functions that ensure the asymptotic stability of unstable stationary states are derived in the case of one site approximation the densities of the vacant sites prey sites and predator sites are obtained as functions of time for the controlled model

a nonlocal and time delayed reaction diffusion eco epidemiological predator prey model abstract in this paper we propose and investigate a nonlocal and time delayed reaction diffusion predator prey model with disease spread in the prey which incorporates spatial heterogeneity and assimilation lag of consumed prey biomass into predator biomass the si type subsystem of prey without predator is first studied and we establish the threshold dynamics in terms of the basic reproduction number based on epidemiology then we show a series of sufficient conditions for the co existence of prey and predator species the global extinction of predator species and the global extinction of both the prey and predator species finally a special example is explored via numerical simulations where the influences of nonlocal effect spatial heterogeneity and time delay on the invasion of the predator species are probed

stability and hopf bifurcation of a mathematical model describing bacteria fish interaction in marine environment abstract in this work we present and study a model of a host parasite system in marine environment which describes the population dynamics of fish tilapia which can be infected by botulinum the mathematical model is structured by levels of infection using the characteristic curves method we transform the model into a system of distributed delay differential equations we study the existence of hopf bifurcation following the method presented by hassard et al 1981 5 we prove analytically the stability of limit cycle periodic solutions we present numerical and computer simulations of the model

on additional symmetries of the kp hierarchy and sato s backlund transformation a short proof is given to the fact that the additional symmetries of the kp hierarchy defined by their action on pseudodifferential operators according to fuchssteiner chen lee lin orlov shulman coincide with those defined by their action on functions as sato s backlund transformations a new simple formula for the generator of additional symmetries is also presented

quasifinite highest weight modules over the lie algebra of differential operators on the circle we classify positive energy representations with finite degeneracies of the lie algebraw 1 and construct them in terms of representation theory of the lie algebra hat gl infty r m of infinites matrices with finite number of non zero diagonals over the algebrar m t t m 1 the unitary ones are classified as well similar results are obtained for the sin algebras

periodic and almost periodic solution for a non autonomous epidemic predator prey system with time delay in this paper we studied a non autonomous predator prey system with discrete time delay where there is epidemic disease in the predator by using some techniques of the differential inequalities and delay differential inequalities we proved that the system is permanent under some appropriate conditions when all the coefficients of the system is periodic we obtained the existence and global attractivity of the positive periodic solution by mawhin s continuation theorem and constructing a suitable lyapunov functional furthermore when the coefficients of the system are not absolutely periodic but almost periodic sufficient conditions are also derived for the existence and asymptotic stability of the almost periodic solution

global analysis and numerical simulations of a novel stochastic eco epidemiological model with time delay abstract in this paper a new stochastic eco epidemiological model is proposed and investigated and the high dimensional model includes time delay and a general incidence rate which make the study more complex first the existence and uniqueness of the global positive solution with any positive initial value are verified second using stochastic analysis methods and some differential inequality techniques we explore the long time asymptotic properties of the stochastic delayed system furthermore we prove that the solution of the stochastic delayed system has a unique stationary distribution and it has ergodic property third the sufficient conditions of permanence in mean or extinction for the ecological populations are obtained finally we introduce a series of computer simulations to show the performance of the theoretical results

global convergence of trust region interior point algorithms for infinite dimensional nonconvex minimization subject to pointwise bounds a class of interior point trust region algorithms for infinite dimensional nonlinear optimization subject to pointwise bounds in l p banach spaces 2 le p le infty is formulated and analyzed the problem formulation is motivated by optimal control problems with l p controls and pointwise control constraints the interior point trust region algorithms are generalizations of those recently introduced by coleman and li siam j optim 6 1996 pp 418 445 for finite dimensional problems many of the generalizations derived in this paper are also important in the finite dimensional context all first and second order global convergence results known for trust region methods in the finite dimensional setting are extended to the infinite dimensional framework of this paper

differential equations in the spectral parameter darboux transformations and a hierarchy of master symmetries for kdv we study a certain family of schrodinger operators whose eigenfunctions satisfy a differential equation in the spectral parameter of the formb x we show that the flows of a hierarchy of master symmetries for kdv are tangent to the manifolds that compose the strata of this class ofbispectral potentials this extends and complements a result of duistermaat and grunbaum concerning a similar property for the adler and moser potentials and the flows of the kdv hierarchy

diseased prey predator model with general holling type interactions choice of interaction function is one of the most important parts for modelling a food chain many models have been proposed as a diseased prey predator model with holling type i or type ii or type iii interactions but there is no model with general holling type interactions in this paper we study a diseased prey predator model with general holling type interactions local stability conditions of equilibrium points are derived we obtain the permanence and impermanence conditions of the system the conditions for global stability of the system are also derived the system exhibits limit cycle period 2 higher periodic oscillations and chaotic behaviour for different values of holling parameters one parameter bifurcation analysis is done with respect to general holling parameters and infection rate we utilize the matcont package to analyse the detailed bifurcation scenario as the two important interaction parameters are varied it is interesting to note that a diseased system becomes a disease free system for proper choice of interaction functions our results give an idea for constructing a realistic food chain model through proper choice of general holling parameters

a limited memory quasi newton trust region method for box constrained optimization by means of wolfe conditions strategy we propose a quasi newton trust region method to solve box constrained optimization problems this method is an adequate combination of the compact limited memory bfgs and the trust region direction while the generated point satisfies the wolfe conditions and therefore maintains a positive definite approximation to the hessian of the objective function the global convergence and the quadratic convergence of this method are established under suitable conditions finally we compare our algorithms iwtral and ibwtral with an active set trust region algorithm astral xu and burke 2007 on the cutest box constrained test problems presented by gould et al 2015 numerical results show that the presented method is competitive and totally interesting for solving box constrained optimization

two metric projection methods for constrained optimization this paper is concerned with the problem min f x mid x in x where x is a convex subset of a linear space h and f is a smooth real valued function on h we propose the class of methods x k 1 p x k alpha k g k where p denotes projection on x with respect to a hilbert space norm cdot g k denotes the frechet derivative of f at x k with respect to another hilbert space norm cdot k on h and alpha k is a positive scalar stepsize we thus remove an important restriction in the original proposal of goldstein 1 and levitin and poljak 2 where the norms cdot and cdot k must be the same it is therefore possible to match the norm cdot with the structure of x so that the projection operation is simplified while at the same time reserving the option to choose cdot k on the basis of approximations to the hessian of f so as to attain a typically superlinear rate of convergence the resulting methods are particularly attrac