equivalence of hardy submodules generated by polynomials abstract in this paper we obtain a complete classification under unitary equivalence for hardy submodules on the polydisk which are generated by ideals of polynomials let i be an ideal of polynomials in n variables since i is generated by finitely many polynomials i has a greatest common divisor p so i can be uniquely written as i p l which is called the beurling form of i let i 1 p 1 l 1 i 2 p 2 l 2 we prove that i 1 and i 2 are unitarily equivalent if and only if there are polynomials q 1 and q 2 with z q 1 d n z q 2 d n such that p 1 q 1 p 2 q 2 on t n and p 1 l 1 p 1 l 2 consequently two principal submodules p 1 and p 2 are unitarily equivalent if and only if there are polynomials q 1 and q 2 with z q 1 d n z q 2 d n such that p 1 q 1 p 2 q 2 on t n furthermore we give a complete similarity classification for submodules generated by homogeneous ideals finally we point out that in the case of the hardy module on the unit ball i 1 and i 2 are unitarily equivalent if and only if they are equal if i 1 and i 2 are homogeneous ideals then i 1 and i 2 are quasi similar if and only if i 1 i 2

essentially normal homogeneous quotient modules on the polydisc abstract in the present paper we give a complete characterization of all essentially normal homogeneous quotient modules of the hardy space on the unit polydisc it turns out that our approach also applies to quotients of weighted bergman modules

positive almost periodic solutions of some delay integral equations the delay integral equation x t tt f s x s ds which arises in models for the spread of epidemics is studied with the aim of establishing the existence of positive almost periodic solutions for large values of when f t x is uniformly almost periodic in t for x in compact subsets of r under reasonable assumptions on f it is shown that there exist two positive numbers 0 they do exist a priori bounds on the set of positive solutions and uniqueness results are also obtained

dynamics for a class of general hematopoiesis model with periodic coefficients abstract sufficient conditions are obtained for the existence and global attractivity of a unique positive periodic solution x t of x t a t x t b t 1 x n t t t 0 where n 1 a and b are continuous positive periodic function also some sufficient conditions are established for oscillation of all positive solutions of about x t for the proof of existence and uniqueness of x t the method used here is better than contraction mapping principle

the dynamics of some discrete population models in this paper we are interested in providing sufficient conditions guaranteeing the fact that all positive solutions of the discrete delay difference equation a ii 1 aa f a e converge as n 00 in e a is a constant real number with 0 0 sufficiently small thus formally equation e comes from x t h x t h yx t d x t r for small h if we set z f x ht then the preceding equation for t n and r h m becomes yh 1 1 h y n hd y n m which is of the form e where a 1 yh and f u hd u u 2 0 clearly h 0 is small if and only if a e 0 1 1069 h

on stepanov like pseudo almost automorphic functions abstract we prove new composition theorems for stepanov like almost automorphic and stepanov like pseudo almost automorphic functions an application is given to a class of evolution equations with stepanov like pseudo almost automorphic perturbations

on the topological structure of almost automorphic and asymptotically almost automorphic solutions of differential and integral equations in abstract spaces abstract the main purpose of this paper is to deal with almost automorphic and asymptotically almost automorphic solutions of the initial value problem as well as the nonlinear volterra integral equation in banach spaces we obtain a collection of existence results of such solutions to these equations we investigate also a topological structure of such solution sets moreover we prove aronszajn type theorems for solutions of the initial value problem as well as the nonlinear volterra integral equation defined on the whole real line

characteristic spaces and rigidity for analytic hilbert modules abstract it is well known that a polynomial in one variable is completely determined by its zeros counting multiplicities we generalize this result to an ideal of polynomials in several variables by introducing the characteristic spaces of the ideal one finds that the ideal is completely determined by its characteristic spaces on a characteristic set in particular a primary ideal is completely determined by its characteristic space at any zero point some straightforward applications of the above results yield the algebraic reduction theorem for analytic hilbert modules in several variables also we obtain some general rigidity results for analytic hilbert modules by using the techniques of af envelopes of analytic hilbert modules

subalgebras of c algebras iii multivariable operator theory a d contraction is a d tuple t1 td of mutually commuting operators acting on a common hilbert space h such that t1 1 t2 2 td d 1 2 d for all 1 2 d h these are the higher dimensional counterparts of contractions we show that many of the operator theoretic aspects of function theory in the unit disk generalize to the unit ball bd in complex d space including von neumann s inequality and the model theory of contractions these results depend on properties of the d shift a distinguished d contraction which acts on a new h2 space associated with bd and which is the higher dimensional counterpart of the unilateral shift h 2 and the d shift are highly unique indeed by exploiting the noncommutative choquet boundary of the d shift relative to its generated c algebra we find that there is more uniqueness in dimension d 2 than there is in dimension one

existence of positive almost periodic solutions to the hematopoiesis model in this paper we study and obtain the existence of a positive almost periodic solution to the nonlinear differential equation with delays that describes the so called hematopoiesis model the main tool utilized to establish our existence result consists of the fixed point theorem in a cone two examples are given at the end of the paper to illustrate our main result

essential normality of polynomial generated submodules hardy space and beyond abstract recently douglas and wang proved that for each polynomial q the submodule q of the bergman module generated by q is essentially normal 11 using improved techniques we show that the hardy space analogue of this result holds and more

mackey glass model of hematopoiesis with monotone feedback revisited for the blood cell production modeldxdt ax t f 0 q n q n x n t t we review known results permanence of solutions oscillation and stability of a positive equilibrium or a positive periodic solution are analyzed for non autonomous generalizations of this equation with both concentrated and distributed delays

pseudo almost automorphic mild solutions to semilinear integral equations in a banach space abstract in this paper we consider the existence of pseudo almost automorphic solutions of the semilinear integral equation x t t a t s a x s f s x s d s t r in a banach space x where a l 1 r a is the generator of an integral resolvent family of linear bounded operators defined on the banach space x and f r x x is a pseudo almost automorphic function the main results are proved by using integral resolvent families combined with the theory of fixed points

almost periodic solutions of lasota wazewska type delay differential equation sufficient conditions are derived for the existence of a globally attractive almost periodic solution of a single species model given by the nonautonomous lasota wazewska type delay differential equations x t txt ptfxt in which 0 p t 0 t are continuous almost periodic functions and f is a decreasing positive c1 function conditions of the uniform asymptotical stability for some associated nonautonomous delay differential equations x t txt ptxt are also discussed

a harmonic analysis approach to essential normality of principal submodules guo and the second author have shown that the closure i in the drury arveson space of a homogeneous principal ideal i in c z1 zn is essentially normal in this note the authors extend this result to the closure of any principal polynomial ideal in the bergman space in particular the commutators and cross commutators of the restrictions of the multiplication operators are shown to be in the schatten p class for p n the same is true for modules generated by polynomials with vector valued coefficients further the maximal ideal space xi of the resulting c algebra for the quotient module is shown to be contained in z i bn where z i is the zero variety for i and to contain all points in bn that are limit points of z i bn finally the techniques introduced enable one to study a certain class of weight bergman spaces on the ball

beurling type quotient modules over the bidisk and boundary representations this paper mainly concerns beurling type quotient modules of h2 d2 over the bidisk by establishing a theorem of function theory over the bidisk it is shown that a beurling type quotient module is essentially normal if and only if the corresponding inner function is a rational inner function having degree at most 1 1 furthermore we apply this result to the study of boundary representations of toeplitz algebras over quotient modules it is proved that the identity representation of c sz sw is a boundary representation of b sz sw in all nontrivial cases this extends a result of arveson to toeplitz algebras on beurling type quotient modules over the bidisk cf w arveson subalgebras of c algebras acta math 123 1969 141 224 w arveson subalgebras of c algebras ii acta math 128 1972 271 308 the paper also establishes k homology defined by beurling type quotient modules over the bidisk

hilbert polynomials and arveson s curvature invariant abstract we define and study hilbert polynomials for certain holomorphic hilbert spaces we obtain several estimates for these polynomials and their coefficients our estimates inspire us to investigate the connection between the leading coefficients of hilbert polynomials for invariant subspaces of the symmetric fock space and arveson s curvature invariant for coinvariant subspaces we are able to obtain some formulas relating the curvature invariant with other invariants in particular we prove that arveson s version of the gauss bonnet chern formula is true when the invariant subspaces are generated by any polynomials

a new existence theory for positive periodic solutions to functional differential equations abstract this paper deals with a new existence theory for positive periodic solutions to a kind of nonautonomous functional differential equation by employing the fixed point theorem in cones applying the general theorems established to several biomathematical models the paper improves some previous results and obtains some new results

the isomorphism problem for some universal operator algebras abstract this paper addresses the isomorphism problem for the universal non self adjoint operator algebras generated by a row contraction subject to homogeneous polynomial relations we find that two such algebras are isometrically isomorphic if and only if the defining polynomial relations are the same up to a unitary change of variables and that this happens if and only if the associated subproduct systems are isomorphic the proof makes use of the complex analytic structure of the character space together with some recent results on subproduct systems restricting attention to commutative operator algebras defined by a radical ideal of relations yields strong resemblances with classical algebraic geometry these commutative operator algebras turn out to be algebras of analytic functions on algebraic varieties we prove a projective nullstellensatz connecting closed ideals and their zero sets under some technical assumptions we find that two such algebras are isomorphic as algebras if and only if they are similar and we obtain a clear geometrical picture of when this happens this result is obtained with tools from algebraic geometry reproducing kernel hilbert spaces and some new complex geometric rigidity results of independent interest the c envelopes of these algebras are also determined the banach algebraic and the algebraic classification results are shown to hold for the wot closures of these algebras as well

method of reduction of order for solving singularly perturbed two point boundary value problems in this paper a method of reduction of order is proposed for solving singularly perturbed two point boundary value problems with a boundary layer at one end point it is distinguished by the following fact the original singularly perturbed boundary value problem is replaced by a pair of initial value problems classical fourth order runge kutta method is used to solve these initial value problems several linear and non linear singular perturbation problems have been solved and the numerical results are presented to support the theory

a new approach for positive almost periodic solutions to a class of nicholson s blowflies model this paper is concerned with the existence of almost periodic solutions for a class of nicholson s blowflies model by transforming the model into an equivalent integral equation and using a fixed point theorem in cones we establish a new result about the existence of positive almost periodic solutions for the model comparing with some earlier works on almost periodic solutions for nicholson s blowflies models our approach is novel

stability of time periodic solution of the navier stokes equation on the half space under oscillatory moving boundary condition abstract navier stokes system on the half space with periodically oscillating boundary has a time periodic solution which depends on time variable and vertical variable only it is proved that the time periodic solution is asymptotically stable when the reynolds number is sufficiently small and the decay estimates of the perturbations are established in the frameworks of both strong and weak solutions

massera type theorem for almost automorphic solutions of functional differential equations of neutral type abstract in this work we study the existence of almost automorphic solutions for functional differential equations of neutral type we prove that the existence of a bounded solution on r implies the existence of an almost automorphic solution

almost automorphic solutions of nonautonomous evolution equations abstract in this paper we establish some new theorems about the existence of almost automorphic solutions to nonautonomous evolution equations u t a t u t f t and u t a t u t f t u t in banach spaces as we will see our results allow for a more general a t to some extent an example is also given to illustrate our results in addition by means of an example we show that one cannot ensure the existence of almost automorphic solutions to u t a t u t f t even if the evolution family u t s generated by a t is exponentially stable and f a a x

essential normality essential norms and hyperrigidity abstract let s s 1 s d denote the compression of the d shift to the complement of a homogeneous ideal i of c z 1 z d arveson conjectured that s is essentially normal in this paper we establish new results supporting this conjecture and connect the notion of essential normality to the theory of the c envelope and the noncommutative choquet boundary the unital norm closed algebra b i generated by s 1 s d modulo the compact operators is shown to be completely isometrically isomorphic to the uniform algebra generated by polynomials on v z i b d where z i is the variety corresponding to i consequently the essential norm of an element in b i is equal to the sup norm of its gelfand transform and the c envelope of b i is identified as the algebra of continuous functions on v b d which means it is a complete invariant of the topology of the variety determined by i in the ball motivated by this determination of the c envelope of b i we suggest a new more qualitative approach to the problem of essential normality we prove the tuple s is essentially normal if and only if it is hyperrigid as the generating set of a c algebra which is a property closely connected to arveson s notion of a boundary representation we show that most of our results hold in a much more general setting in particular for most of our results the ideal i can be replaced by an arbitrary not necessarily homogeneous invariant subspace of the d shift

oscillations of delay difference equations consider the delay difference equation n 1 n pn n k 0 n 0 1 2 where pn is a sequence of real numbers and k is a positive integer new oscillation criteria for this equation are established an extension of the results to difference equations with several delays is also presented

asymptotic behavior of solutions of the compressible navier stokes equations on the half space asymptotic behavior of solutions of the compressible navier stokes equations on the half space r n n 2 is considered around a given constant equilibrium a solution formula for the linearized problem is derived and l p estimates for solutions of the linearized problem are obtained for 2 p it is shown that as in the case of the cauchy problem the leading part of the solution of the linearized problem is decomposed into two parts one that behaves like diffusion waves and the other one purely diffusively there however are some aspects different from the cauchy problem especially in considering spatial derivatives it is also shown that the solution of the linearized problem approaches for large times the solution of the nonstationary stokes problem in some l p spaces and as a result a solution formula for the nonstationary stokes problem is obtained large time behavior of solutions of the nonlinear problem is then investigated in l p spaces for 2 p by applying the results on the linearized analysis and the weighted energy method the results indicate that there may be some nonlinear interaction phenomena not appearing in the cauchy problem

a further result on the oscillation of delay difference equations in this paper we are concerned with the delay difference equations of the form yn 1 yn pnyn k 0 n 0 1 2 where pn 0 and k is a positive integer we prove by using a new technique that n 0 i nn kpi ln i nn k pi 1 sign i nn k pi i n 1n k pi ln i n 1n k pi 1 sign i n 1n k pi guarantees that all solutions of equation oscillate which improves many previous well known results in particular our theorems also fit the case where n 1i n kpi kk 1 k 1 k 1 in addition we present a nonoscillation sufficient condition for equation

existence of positive almost automorphic solutions to nonlinear delay integral equations abstract this paper is concerned with the existence of positive almost automorphic solutions to some nonlinear delay integral equations we first establish a new fixed point theorem for mixed monotone operator in a cone and then with its help we obtain existence theorems of positive almost automorphic solutions some examples are given to illustrate our results as one will see even in the case of almost periodicity our theorems extend some earlier results and moreover the approach dealing with the integral equation arising in an epidemic problem in this paper is also new

oscillations and global attractivity in delay differential equations of population dynamics abstract the oscillatory and asymptotic behavior of all positive solutions of x t 0 n n x n t x t about its positive steady state x are studied where x t denotes the density of mature cells in blood circulation is the time delay between the production of immature cells in the bone marrow and 0 n are positive constants

l2 decay for the navier stokes flow in halfspaces on etudie le comportement asymptotique dans l 2 des solutions faibles des equations de navier stokes dans des demi espaces

the dirac operator of a commuting d tuple abstract given a commuting d tuple t t1 td of otherwise arbitrary operators on a hilbert space there is an associated dirac operator dt significant attributes of the d tuple are best expressed in terms of dt including the taylor spectrum and the notion of fredholmness in fact all properties of t derive from its dirac operator we introduce a general notion of dirac operator in dimension d 1 2 that is appropriate for multivariable operator theory we show that every abstract dirac operator is associated with a commuting d tuple and that two dirac operators are isomorphic iff their associated operator d tuples are unitarily equivalent by relating the curvature invariant introduced in a previous paper to the index of a dirac operator we establish a stability result for the curvature invariant for pure d contractions of finite rank it is shown that for the subcategory of all such t that are a fredholm and and b graded the curvature invariant k t is stable under compact perturbations we do not know if this stability persists when t is fredholm but ungraded although there is concrete evidence that it does

an analytic grothendieck riemann roch theorem we extend the boutet de monvel toeplitz index theorem to complex manifolds with isolated singularities following the relative k homology theory of baum douglas and taylor for manifolds with boundary we apply this index theorem to study the arveson douglas conjecture let bmbm be the unit ball in cmcm and i an ideal in the polynomial algebra c z1 zm c z1 zm we prove that when the zero variety zizi is a complete intersection space with only isolated singularities and intersects with the unit sphere s2m 1s2m 1 transversely the representations of c z1 zm c z1 zm on the closure of i in la2 bm and also the corresponding quotient space qiqi are essentially normal furthermore we prove an index theorem for toeplitz operators on qiqi by showing that the representation of c z1 zm c z1 zm on the quotient space qiqi gives the fundamental class of the boundary zi s2m 1zi s2m 1 in the appendix we prove with kai wang that if f la2 bm vanishes on zi bmzi bm then f is contained inside the closure of the ideal i in la2 bm

multiplier algebras of complete nevanlinna pick spaces dilations boundary representations and hyperrigidity abstract we study reproducing kernel hilbert spaces on the unit ball with the complete nevanlinna pick property through the representation theory of their algebras of multipliers we give a complete description of the representations in terms of the reproducing kernels while representations always dilate to representations of the ambient c algebra we show that in our setting we automatically obtain coextensions in fact we show that in many cases this phenomenon characterizes the complete nevanlinna pick property we also deduce operator theoretic dilation results which are in the spirit of work of agler and several other authors moreover we identify all boundary representations compute the c envelopes and determine hyperrigidity for certain analogues of the disc algebra finally we extend these results to spaces of functions on homogeneous subvarieties of the ball

positive periodic solutions of functional differential equations abstract we consider the existence multiplicity and nonexistence of positive periodic solutions for the periodic equation x t a t g x x t b t f x t t where a b c r 0 are periodic 0 a t dt 0 0 b t dt 0 f g c 0 0 and f u 0 for u 0 g x is bounded t is a continuous periodic function define f 0 lim u 0 f u u f lim u f u u i0 number of zeros in the set f 0 f and i number of infinities in the set f 0 f we show that the equation has i0 or i positive periodic solution s for sufficiently large or small 0 respectively

oscillation and global attractivity in hematopoiesis model with periodic coefficients in this paper we shall consider the nonlinear delay differential equation p t email protected t p m email protected 1 p n email protected email protected t p t where k is a positive integer b t and c t are positive periodic functions of period w in the nondelay case we shall show that has a unique positive periodic solution email protected t and we will study the global attractivity of email protected t in the delay case we shall establish some sufficient conditions for oscillation of all positive solutions of about email protected t and establish some sufficient conditions for the global attractivity of email protected t our results in this paper extend as well as improve the results in the autonomous case

some fixed point theorems and applications on utilise la theorie du degre de leray schauder pour etablir des theoremes de points fixes et on donne des applications a des equations integrales non lineaires

essential normality for quotient modules and complex dimensions abstract for analytic sets m introduced in 9 we show that the corresponding quotient module q of the bergman module is p essentially normal for all p dim c m which verifies the geometric arveson douglas conjecture in this case this result makes it possible to study the helton howe trace invariants on both q and the corresponding submodule r

time periodic solution to a two phase model with magnetic field in a periodic domain abstract in the paper we consider a two phase model with magnetic field and a time periodic external force in a periodic domain in r n the existence of the time periodic solutions to the model is obtained by the topological degree theory and parabolic regularization method

quotient modules for some hilbert modules over the bidisk in this note we will prove the essential normality of some type of quotient hilbert modules over the bidisk moreover we will study some properties of the compression of the multiplication operators to the quotient hilbert modules

essentially normal hilbert modules and k homology this paper mainly concerns the essential normality of graded submodules essentially all of the basic hilbert modules that have received attention over the years are p essentially normal including the d shift hilbert module the hardy and bergman modules of the unit ball arveson conjectured graded submodules over the unit ball inherit this property and provided motivations to seek an affirmative answer some positive results have been obtained by arveson and douglas however the problem has been resistant in dimensions d 2 3 this paper shows that the arveson s conjecture is true in any dimension the paper also gives an affirmative answer in the case of the graded principal submodule finally the paper is associated with k homology invariants arising from graded quotient modules by which geometry of the quotient modules and geometry of algebraic varieties are connected in dimensions d 2 3 it is shown that k homology invariants determined by graded quotients are nontrivial the paper also establishes results on p smoothness of k homology elements and gives an explicit expression for k homology invariant in dimension d 2

samuel multiplicity and the structure of semi fredholm operators abstract two numerical invariants refining the fredholm index are introduced for any semi fredholm operator in such a way that their difference calculates the fredholm index these two invariants are inspired by samuel multiplicity in commutative algebra and can be regarded as the stabilized dimension of the kernel and cokernel a geometric interpretation of these invariants leads naturally to a 4 4 uptriangular matrix model for any semi fredholm operator on a separable hilbert space this model can be regarded as a refined local version of the apostol s 3 3 triangular representation for arbitrary operators some classical results such as gohberg s punctured neighborhood theorem can be read off directly from our matrix model banach space operators are also considered

geometric arveson douglas conjecture abstract we prove the arveson douglas essential normality conjecture for graded hilbert submodules that consist of functions vanishing on a given homogeneous subvariety of the ball smooth away from the origin our main tool is the theory of generalized toeplitz operators of boutet de monvel and guillemin

quotients of standard hilbert modules we initiate a study of hilbert modules over the polynomial algebra that are obtained by completing with respect to an inner product having certain natural properties a standard hilbert module is a finite multiplicity version of one of these standard hilbert modules occupy a position analogous to that of free modules of finite rank in commutative algebra and their quotients by submodules give rise to universal solutions of nonlinear relations essentially all of the basic hilbert modules that have received attention over the years are standard including the hilbert module of the shift the hardy and bergman modules of the unit ball modules associated with more general domains in and those associated with projective algebraic varieties we address the general problem of determining when a quotient of an essentially normal standard hilbert module is essentially normal this problem has been resistant our main result is that it can be linearized in that the nonlinear relations defining the submodule can be reduced appropriately to linear relations through an iteration procedure and we give a concrete description of linearized quotients

the structure of inner multipliers on spaces with complete nevanlinna pick kernels let k be the reproducing kernel for a hilbert space h k of analytic functions on bd the open unit ball in cd d 1 k is called a complete np kernel if k0 1 and if 1 1 k z is positive definite on bd bd let d be a separable hilbert space and consider h k d h k d and think of it as a space of d valued h k functions a theorem of mccullough and trent j funct anal 178 2000 226 249 partially extends the beurling lax halmos theorem for the invariant subspaces of the hardy space h2 d they show that if k is a complete np kernel and if d is a separable hilbert space then for any scalar multiplier invariant subspace m of h k d there exists an auxiliary hilbert space e and a multiplication operator h k e h k d such that is a partial isometry and m h k e such multiplication operators are called inner multiplication operators and they satisfy the orthogonal projection onto m in this paper we shall show that for many interesting complete np kernels the analogy with the beurling lax halmos theorem can be strengthened we show that for almost every z bd the nontangential limit z of the multiplier bd b e d associated with an inner multiplication operator is a partial isometry and that rank z is equal to a constant almost everywhere the result applies to certain weighted dirichlet spaces and to the space h2d which is determined by the kernel k z 11 z d z bd in particular our result implies that the curvature invariant of arveson proc natl acad sci usa96 1999 11 096 11 099 of a pure contractive hilbert module of finite rank is an integer this answers a question of w arveson proc natl acad sci usa96 1999 11096 11099

dixmier trace for toeplitz operators on symmetric domains abstract for toeplitz operators on bounded symmetric domains of higher rank there is no obvious way to define the dixmier trace within the toeplitz c algebra since commutators are in general not compact in this paper we solve this problem by constructing a hilbert quotient module corresponding to partitions of length 1 which leads to commutators in the macaev class l n we also obtain an explicit formula for the dixmier trace of such commutators in terms of the underlying boundary geometry which involves a new type of flag manifold defined in jordan theoretic terms

fredholm and invertible tuples of operators the deformation problem using j l taylor s definition of joint spectrum we study fredholm and invertible tuples of operators on a hilbert space we give the foundations for a several variables theory including a natural generalization of atkinson s theorem and an index which well behaves we obtain a characterization of joint invertibility in terms of a single operator and study the main examples at length we then consider the deformation problem and solve it for the class of almost doubly commuting fredholm pairs with a semi fredholm coordinate 1 introduction 1 let t be a bounded linear operator on a banach space t is said to be invertible if there exists an operator s on such that ts st 1 the identity operator on 9c by the open mapping theorem this is equivalent to ker t 0 and r t range of t the last formulation does not rely upon the existence of an inverse for t but rather on the action of the operator t when t is replaced by an tuple of commuting operators several definitions of nonsingular ity exist j l taylor 19 has obtained one which reflects the actions of the operators by considering the koszul complex associated with the tuple 2 in this paper we develop a general several variables theory on the basis of taylor s work and study commuting and almost commuting commuting mod ulo the compacts tuples of operators on a hilbert space we obtain a characterization of joint invertibility in terms of the invertibility of a single operator which is essential for our approach from that we get a number of corollaries which generalize nicely the known elementary results in one variable at the same time the referred characterization allows us to define a continuous invariant under compact perturbations integer valued index on the class of fred holm tuples those almost commuting tuples which are invertible in the calkin algebra this index extends the classical one for fredholm operators we prove that an almost commuting tuple of essentially normal operators with all commu tators in trace class has index zero 2 and that a natural generalization of atkinson s theorem holds for tuples

existence of positive pseudo almost periodic solutions to a class of neutral integral equations abstract in this work a new fixed point theorem in partially ordered banach spaces is established and then used to prove the existence of positive pseudo almost periodic solutions to a class of neutral integral equations our existence theorem extends some recent results due to e ait dads p cieutat l lhachimi positive pseudo almost periodic solutions for some nonlinear infinite delay integral equations mathematical and computer modelling 49 2009 721 739 to a more general class of integral equations

existence and global attractivity of unique positive periodic solution for a lasota wazewska model abstract in this paper we consider the lasota wazewska model x t a t x t i 1 m p i t e q i t x t i t by using a fixed point theorem some criteria are established for the existence of the unique positive periodic solution x of the above equation in particular we not only give the conclusion of convergence of x n to x where x n is a successive sequence but also show that x is a global attractor of all other positive solutions

existence and global attractivity of unique positive periodic solution for a model of hematopoiesis sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis then some criteria are established for the existence uniqueness and global attractivity of almost periodic solutions of almost periodic system

almost periodic solutions of neutral functional differential equations in this paper we study a non autonomous neutral functional differential equation in a banach space applying the theory of semigroups of operators to evolution equations and krasnoselskii s fixed point theorem we establish the existence and uniqueness of a mild almost periodic solution of the problem under consideration

nonexistence and existence of positive solutions for difference equations with unbounded delay consider the delay difference equation xn 1 xn pnx n 0 0 1 2 where n z n n for n n and limn n pn r some existence results of positive solutions and oscillation criteria for this equation are obtained

a new result on the existence of positive almost periodic solution for generalized hematopoiesis model abstract this paper is concerned with a generalized nonlinear hematopoiesis model with variable delays by utilizing mixed monotone operator fixed point theorem in a cone we establish some criteria to ensure that the existence of positive almost periodic solution two examples are given to illustrate the obtained results

positive solutions of nonlinear integral equations arising in infectious diseases on considere l equation integrale non lineaire x t t t f s x s ds on utilise la theorie d indice du point fixe et la technique monotone pour etablir trois theoremes sur les solutions le premier affirme l existence de deux solutions non negatives non triviales de periode les deux autres concernent l existence et l unicite des solutions positives non triviales sous certaines conditions

oscillation and global attractivity in hematopoiesis model with delay time in this paper we shall consider the nonlinear delay differential equations with delay time p t bp m t t 1 p n t t cp t that is proposed as a model of hematopoiesis blood cell production where p t denotes the density of mature cells in blood circulation and the time delay t is the time between the production of immature cells in the bone marrow and their maturation for release in the circulating bloodstreams our aim is to give sufficient condition for oscillation of all positive solutions of about the positive steady state and obtain some sufficient conditions for the global attractivity our results extend and improve the well known oscillation results of when m 0

the navier stokes equations in the weak l n space with time dependent external force abstract we consider the navier stokes equations with time dependent external force either in the whole time or in positive time with initial data with domain either the whole space the half space or an exterior domain of dimension n ge 3 we give conditions on the external force sufficient for the unique existence of small solutions in the weak l n space bounded for all time in particular this result gives sufficient conditions for the unique existence and the stability of small time periodic solutions or almost periodic solutions this result generalizes the previous result on the unique existence and the stability of small stationary solutions in the weak l n space with time independent external force

a cell population model described by impulsive pdes existence and numerical approximation this paper considers a cell population model described by impulsive pdes existence and numerical approximation of solutions are investigated by showing that the related operator a x ddx on c0 generates a strongly conitunous semigroups under general assumption on a x we prove the existence of the solution of the nonlinear problem with impulses and given approximation of the solution of the homogenuous equation

permanence oscillation and attractivity of the discrete hematopoiesis model with variable coefficients abstract in this paper we consider the nonlinear delay difference equation with periodic coefficients p n 1 p n n p n n 1 p n m and demonstrate that solutions are permanent the existence of a positive periodic solution is proven and sufficient conditions for the attractivity of this solution are obtained oscillation and nonoscillation about the positive periodic solution is considered