a non hyponormal operator generating stieltjes moment sequences abstract a linear operator s in a complex hilbert space h for which the set d s of its c vectors is dense in h and s n f 2 n 0 is a stieltjes moment sequence for every f d s is said to generate stieltjes moment sequences it is shown that there exists a closed non hyponormal operator s which generates stieltjes moment sequences what is more d s is a core of any power s n of s this is established with the help of a weighted shift on a directed tree with one branching vertex the main tool in the construction comes from the theory of indeterminate stieltjes moment sequences as a consequence it is shown that there exists a non hyponormal composition operator in an l 2 space over a finite measure space which is injective paranormal and which generates stieltjes moment sequences the independence assertion of barry simon s theorem which parameterizes von neumann extensions of a closed real symmetric operator with deficiency indices 1 1 is shown to be false

a relationship subnormal polynomially hyponormal and semi weakly hyponormal weighted shifts abstract let x x a b c be a one step backward extension sequence of stampfli s subnormal completion where 0 x a b c and let w x be the associated weighted shift in this paper we prove that w x is subnormal if and only if w x is polynomially hyponormal which also is equivalent to that w x is completely semi weakly hyponormal

testing the descriptive validity of possibility theory in human judgments of uncertainty many works in the past showed that human judgments of uncertainty do not conform very well to probability theory the present paper reports four experiments that were conducted in order to evaluate if human judgments of uncertainty conform better to possibility theory at first two experiments investigate the descriptive properties of some basic possibilistic measures then a new measurement apparatus is used the scale to compare possibilistic vs probabilistic disjunction and conjunction results strongly suggest that a human judgment is qualitative in essence closer to a possibilistic than to a probabilistic approach of uncertainly the paper also describes a qualitative heuristic for conjunction which was used by expert radiologists

subnormality for arbitrary powers of 2 variable weighted shifts whose restrictions to a large invariant subspace are tensor products the lifting problem for commuting subnormals lpcs asks for necessary and sufficient conditions for a pair of subnormal operators onhilbert space to admit commuting normal extensions we study lpcs within the class of commuting 2 variable weighted shifts t t1 t2 with subnormal components t1 and t2 acting on the hilbert space 2 z 2 with canonical orthonormal basis fe k1 k2 gk1 k2 0 the core of a commuting 2 variable weighted shift t c t is the restriction of t to the invariant subspace generated by all vectors e k1 k2 with k1 k2 1 we say that c t is of tensor form if it is unitarily equivalent to

the truncated complex moment problem let 2n denote a sequence of complex numbers 00 01 10 0 2n 2n 0 00 0 ij ji and let k denote a closed subset of the complex plane c the truncated complex k moment problem for entails determining whether there exists a positive borel measure on c such that ij zizj d 0 i j 2n and supp k for k kp a semi algebraic set determined by a collection of complex polynomials p pi z z mi 1 we characterize the existence of a finitely atomic representing measure with the fewest possible atoms in terms of positivity and extension properties of the moment matrix m n and the localizing matrices mpi we prove that there exists a rankm n atomic representing measure for 2n supported in kp if and only if m n 0 and there is some rankpreserving extension m n 1 for which mpi n ki 0 where deg pi 2ki or 2ki 1 1 i m

lyapunov functionals for delay differential equations model of viral infections we study global properties of a class of delay differential equations model for virus infections with nonlinear transmissions compared with the typical virus infection dynamical model this model has two important and novel features to give a more complex and general infection process a general nonlinear contact rate between target cells and viruses and the removal rate of infected cells are considered and two constant delays are incorporated into the model which describe i the time needed for a newly infected cell to start producing viruses and ii the time needed for a newly produced virus to become infectious mature respectively by the lyapunov direct method and using the technology of constructing lyapunov functionals we establish global asymptotic stability of the infection free equilibrium and the infected equilibrium we also discuss the effects of two delays on global dynamical properties by comparing the results with the stability conditions for the model without delays further we

weighted shifts induced by hamburger moment sequences abstract we indicate how our subject emerges from the confluence of several streams of analysis including the classical moment problems the theory of positive matrices and subnormal operator theory some new properties h n n 1 2 and a hamburger type weighted shift are considered via a hamburger moment sequence we discuss examples to show the various h n are distinct study flatness backward n step extensions and perturbations of weighted shifts and given three initial weights 0 1 2 with 0 2 1 we produce a completion a weighted shift of hamburger type but not subnormal extending a subnormal completion by stampfli in the case 0 1 2

unbounded subnormal weighted shifts on directed trees ii abstract a new method of verifying the subnormality of unbounded hilbert space operators based on an approximation technique is proposed diverse sufficient conditions for subnormality of unbounded weighted shifts on directed trees are established an approach to this issue via consistent systems of probability measures is invented the role played by determinate stieltjes moment sequences is elucidated lambert s characterization of subnormality of bounded operators is shown to be valid for unbounded weighted shifts on directed trees that have sufficiently many quasi analytic vectors which is a new phenomenon in this area

when does the k hyponormality of a 2 variable weighted shift become subnormality abstract in this article we construct a sequence of nontrivial classes of 2 variable weighted shifts g k k 2 such that the k hyponormality of an arbitrary power of a member w from g k is equivalent to its subnormality

subnormality of unbounded composition operators over one circuit directed graphs exotic examples abstract a recent example of a non hyponormal injective composition operator in an l 2 space generating stieltjes moment sequences invented by three of the present authors was built over a non locally finite directed tree the main goal of this paper is to solve the problem of whether there exists such an operator over a locally finite directed graph and in the affirmative case to find the simplest possible graph with these properties simplicity refers to local valency the problem is solved affirmatively for the locally finite directed graph g 2 0 which consists of two branches and one loop the only simpler directed graph for which the problem remains unsolved consists of one branch and one loop the consistency condition the only efficient tool for verifying subnormality of unbounded composition operators is intensively studied in the context of g 2 0 which leads to a constructive method of solving the problem the method itself is partly based on transforming the krein and the friedrichs measures coming either from shifted al salam carlitz q polynomials or from a quartic birth and death process

a representation theorem for cyclic analytic two isometries a bounded linear operator t on a complex separable hilbert space z is called a 2 isometry if t 2t2 2t t i o we say that t is analytic if nn 0 tnt 0 in this paper we show that every cyclic analytic 2 isometry can be represented as multiplication by z on a dirichlet type space d 8 here ze denotes a finite positive borel measure on the unit circle for two measures u and v the 2 isometries obtained as multiplication by z on d 8 and d v are unitarily equivalent if and only if u v we also investigate similarity and quasisimilarity of these 2 isometries and we apply our results to the invariant subspaces of the dirichlet shift

jointly hyponormal pairs of commuting subnormal operators need not be jointly subnormal we construct three different families of commuting pairs of subnormal operators jointly hyponormal but not admitting commuting normal extensions each such family can be used to answer in the negative a 1988 conjecture of r curto p muhly and j xia we also obtain a sufficient condition under which joint hyponormality does imply joint subnormality

schur product techniques for the subnormality of commuting 2 variable weighted shifts abstract in this paper we study the subnormality of 2 variable weighted shifts using the schur product techniques in matrices and the convolution of two continuous functions as a consequence we find the berger measure of the subnormal weighted shift obtained from the schur product of two subnormal weighted shifts as applications we first give non trivial large classes satisfying the curto muhly xia conjecture see the conjecture given below for 2 variable weighted shifts we next show when the 2 hyponormality of 2 variable weighted shifts becomes subnormality

modeling uncertainty in monetary poverty fuzzy sets theory has successfully accommodated the lack of clear cut boundaries of poverty and its gradual nature on the other hand uncertainties related to lack of knowledge and imprecision in poverty data need also to be accounted for the accuracy of poverty analysis is highly subject to how well these features are adequately addressed we argue that possibility theory is an appropriate framework to deal with incomplete knowledge in poverty indeed considering the possibility of poverty instead of the probability of poverty allows us to achieve a more realistic handling of this phenomenon empirical possibility distributions of monetary poverty states are derived based on our previous works and alpha cut analysis is used to explore their features also collective possibilistic poverty measures for each state are computed along with an aggregate possibilistic poverty ratio this possibilistic modeling is applied to the analysis of poverty in tunisia in 2005 and 2010

m isometric operators and their local properties abstract in this paper we give necessary and sufficient conditions for a bounded linear hilbert space operator to be an m isometry for an unspecified m written in terms of conditions that are applied to one vector at a time we provide criteria for orthogonality of generalized eigenvectors of an a priori unbounded linear operator t on an inner product space that correspond to distinct eigenvalues of modulus 1 we also discuss a similar question of when jordan blocks of t corresponding to distinct eigenvalues of modulus 1 are orthogonal

stability and hopf bifurcation for a virus infection model with delayed humoral immunity response abstract in this paper we investigate the dynamical behavior of a virus infection model with delayed humoral immunity by using suitable lyapunov functional and the lasalle s invariance principle we establish the global stabilities of the two boundary equilibria if r 0 1 the uninfected equilibrium e 0 is globally asymptotically stable if r 1 1 r 0 the infected equilibrium without immunity e 1 is globally asymptotically stable when r 1 1 we obtain the sufficient conditions to the local stability of the infected equilibrium with immunity e 2 the time delay can change the stability of e 2 and lead to the existence of hopf bifurcations the stabilities of bifurcating periodic solutions is also studied we check our theorems with numerical simulations in the end

a solution to the cauchy dual subnormality problem for 2 isometries abstract the cauchy dual subnormality problem asks whether the cauchy dual operator t t t t 1 of a 2 isometry t is subnormal in the present paper we show that the problem has a negative solution the first counterexample depends heavily on a reconstruction theorem stating that if t is a 2 isometric weighted shift on a rooted directed tree with nonzero weights that satisfies the perturbed kernel condition then t is subnormal if and only if t satisfies the unperturbed kernel condition the second counterexample arises from a 2 isometric adjacency operator of a locally finite rooted directed tree again by thorough investigations of positive solutions of the cauchy dual subnormality problem in this context we prove that if t is a 2 isometry satisfying the kernel condition or a quasi brownian isometry then t is subnormal we construct a 2 isometric adjacency operator t of a rooted directed tree such that t does not satisfy the kernel condition t is not a quasi brownian isometry and t is subnormal

hyponormality for commuting pairs of operators abstract in this paper we study propagation phenomena for mono weakly hyponormal 2 variable weighted shifts next we describe the positivity and determinant of an immediate ancestor of the classical hilbert matrix finally using its positivity we construct a family of examples which shows and elucidates the gap between k hyponormality and k 1 hyponormality for commuting pairs of operators for each k 1

on the sum of two subnormal kernels abstract we show by means of a class of examples that if k 1 and k 2 are two positive definite kernels on the unit disc such that the multiplication by the coordinate function on the corresponding reproducing kernel hilbert space is subnormal then the multiplication operator on the hilbert space determined by their sum k 1 k 2 need not be subnormal this settles a recent conjecture of gregory t adams nathan s feldman and paul j mcguire in the negative we also discuss some cases for which the answer is affirmative

berger measure for s a b c d abstract in this note we get the berger measure of the weighted shift s a b c d with weights n a n b c n d a b c d 0 and n 0 as well as its p subshift then we will give examples from analytic function theory to illustrate that the necessary condition given by curto and yoon 2006 12 for subnormality of 2 variable weighted shift is not sufficient furthermore we will do some calculations about subnormal backward extension of s a b c d

cubically hyponormal weighted shifts and their examples we obtain criteria for cubical hyponormality which provide a tool for finding examples being distinct the classes of 2 hyponormal cubically hyponormal and quadratically hyponormal operators

subnormality of bergman like weighted shifts abstract for a b c d 0 with a d b c 0 we consider the unilateral weighted shift s a b c d with weights n a n b c n d n 0 using schur product techniques we prove that s a b c d is always subnormal more generally we establish that for every p 1 all p subshifts of s a b c d are subnormal as a consequence we show that all bergman like weighted shifts are subnormal

asymptotic behaviour and cyclic properties of weighted shifts on directed trees abstract in this paper we investigate a new class of bounded operators called weighted shifts on directed trees introduced recently in 11 this class is a natural generalization of the so called weighted bilateral unilateral and backward shift operators in the first part of the paper we calculate the asymptotic limit and the isometric asymptote of a contractive weighted shift on a directed tree and that of the adjoint then we use the asymptotic behaviour and similarity properties in order to obtain cyclicity results we also show that a weighted backward shift operator is cyclic if and only if there is at most one zero weight

operators intertwining with isometries and brownian parts of 2 isometries abstract for two operators a and t a 0 on a hilbert space h satisfying t a t a and the a regularity condition a t a 1 2 t a 1 2 we study the subspace n a a 2 in connection with n a t t a for t belonging to different classes our results generalize those due to c kubrusly concerning the case when t is a contraction and a s t is the asymptotic limit of t also the particular case of a 2 isometry in the sense of s richter as well as j agler and m stankus is considered for such operators under the same regularity condition we completely describe the reducing brownian unitary and isometric parts as well as the invariant brownian isometric part some examples are provided in order to illustrate the limits of the theoretical results

complex dynamic behavior in a viral model with delayed immune response the rich dynamics of a viral infection model is studied under the assumption that the immune response is retarded it is shown that if the basic reproductive ratio of the virus is less than one the infection free equilibrium is globally asymptotically stable analytical and numerical results show that if the basic reproductive ratio of the virus is greater than one the combined effect of the strength of the lytic component the time delay of the immune response and the birth rate of susceptible host cells is to create a rich dynamics which includes the occurrence of stable periodic solutions and chaotic dynamical behavior the route from periodic oscillations to chaos is investigated these results can be used to explain irregular real time series data on the immune state of patients

perturbation of the q numerical radius of a weighted shift operator abstract we formulate the taylor series expansion for the q numerical radius of a weighted shift operator with periodic weights near q 0 coefficients up to the fourth order in the expansion are found via the perturbation theory of hermitian matrices

complete nevanlinna pick property of dirichlet type spaces we prove that all dirichlet type spaces of functions analytic in the unit disk whose derivatives are square area integrable with superharmonic weights have complete nevanlinna pick reproducing kernels as a corollary we obtain a commutant lifting theorem for cyclic analytic two isometries c 2002 elsevier science usa

stability and hopf bifurcation of a hiv infection model with ctl response delay in this paper we consider a hiv infection model with ctl response delay and analyze the effect of time delay on stability of equilibria we obtain the global stability of the infection free equilibrium and give sufficient conditions for the local stability of the ctl absent equilibrium and ctl present equilibrium by choosing the ctl response delay t as a bifurcation parameter we prove that the ctl present equilibrium is locally asymptotically stable in a range of delays and a hopf bifurcation occurs as t crosses a critical value numerical simulations are given to support the theoretical results

k hyponormality of multivariable weighted shifts we characterize joint k hyponormality for 2 variable weighted shifts using this characterization we construct a family of examples which establishes and illustrates the gap between k hyponormality and k 1 hyponormality for each k 1 as a consequence we obtain an abstract solution to the lifting problem for commuting subnormals

analysis of a diffusive virus infection model with humoral immunity cell to cell transmission and nonlinear incidence abstract in this paper we investigate a reaction diffusion virus infection model with humoral immunity and nonlinear incidence in heterogeneous and homogenous environments the model includes simultaneously the virus to cell and cell to cell transmissions of the infection the well posedness of solutions including the existence of global solutions and the ultimate boundedness is established the virus infection reproduction number r 0 is calculated when r 0 1 it is proved that the infection free steady state is globally asymptotically stable otherwise when r 0 1 then the infection with antibody free response is uniformly persistent furthermore the antibody free infection equilibrium is also globally asymptotically stable in spatially homogeneous case in order to investigate the effect of humoral immunity the virus infection with antibody response model in the spatially homogeneous environment is considered the antibody response reproduction number r 1 is calculated the threshold criteria on the uniform persistence of total model and the global asymptotic stability of the antibody response infection equilibrium are established finally the numerical examples are presented to illustrate the theoretical results and verify the conjectures

nonmonotonic reasoning conditional objects and possibility theory abstract this short paper relates the conditional object based and possibility theory based approaches for reasoning with conditional statements pervaded with exceptions to other methods in nonmonotonic reasoning which have been independently proposed namely lehmann s preferential and rational closure entailments which obey normative postulates the infinitesimal probability approach and the conditional modal logics based approach all these methods are shown to be equivalent with respect to their capabilities for reasoning with conditional knowledge although they are based on different modeling frameworks it thus provides a unified understanding of nonmonotonic consequence relations more particularly conditional objects a purely qualitative counterpart to conditional probabilities offer a very simple semantics based on a 3 valued calculus for the preferential entailment while in the purely ordinal setting of possibility theory both the preferential and the rational closure entailments can be represented

which 2 hyponormal 2 variable weighted shifts are subnormal it is well known that a 2 hyponormal unilateral weighted shift with two equal weights must be flat and therefore subnormal by contrast a 2 hyponormal 2 variable weighted shift which is both horizontally flat and vertically flat need not be subnormal in this paper we identify a large class s of flat 2 variable weighted shifts for which 2 hyponormality is equivalent to subnormality one measure of the size of s is given by the fact that within s there are hyponormal shifts which are not subnormal

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

hypercyclicity of shifts on weighted lp spaces of directed trees abstract in this paper we study the hypercyclicity of forward and backward shifts on weighted l p spaces of a directed tree in the forward case only the trivial trees may support hypercyclic shifts in which case the classical results of salas 21 apply for the backward case nontrivial trees may support hypercyclic shifts we obtain necessary conditions and sufficient conditions for hypercyclicity of the backward shift and in the case of a rooted tree on an unweighted space we show that these conditions coincide

module tensor product of subnormal modules need not be subnormal let d d c d d c be a diagonal positive definite kernel and let h h denote the associated reproducing kernel hilbert space of holomorphic functions on the open unit disc dd assume that zf hzf h whenever f hf h then hh is a hilbert module over the polynomial ring c z c z with module action p f pfp f pf we say that h h is a subnormal hilbert module if the operator mzmz of multiplication by the coordinate function z on h h is subnormal n salinas 1988 11 asked whether the module tensor product h 1 c z h 2h 1 c z h 2 of subnormal hilbert modules h 1h 1 and h 2h 2 is again subnormal in this regard we describe all subnormal module tensor products la2 d ws1 c z la2 d ws2 where la2 d ws denotes the weighted bergman hilbert module with radial weight ws z 1s z 2 1 s s z d s 0 in particular the module tensor product la2 d ws c z la2 d ws is never subnormal for any s 6s 6 thus the answer to this question is no

k hyponormality of finite rank perturbations of unilateral weighted shifts in this paper we explore finite rank perturbations of unilateral weighted shifts w first we prove that the subnormality of w is never stable under nonzero finite rank perturbations unless the perturbation occurs at the zeroth weight second we establish that 2 hyponormality implies positive quadratic hyponormality in the sense that the maclaurin coefficients of d n s det p n w sw 2 w sw 2 p n are nonnegative for every n 0 where p n denotes the orthogonal projection onto the basis vectors e 0 e n finally for strictly increasing and w 2 hyponormal we show that for a small finite rank perturbation a of a the shift w remains quadratically hyponormal

flat phenomena of 2 variable weighted shifts abstract we study the class of mono weakly 2 hyponormal 2 variable weighted shifts t t 1 t 2 resp hyponormal with quadratically hyponormal t 1 and t 2 with two consecutive equal weights in the weight sequence of each of the coordinate operators we show that under natural assumptions on the coordinate operators the presence of consecutive equal weights in t 1 and t 2 leads to the flatness in a way that resembles the situation for 1 variable weighted shifts

operator theory and algebraic geometry on presente des resultats en theorie des operateurs multivariable dont les demonstrations se relient a des techniques issues de la geometrie algebrique

locally weighted regression an approach to regression analysis by local fitting abstract locally weighted regression or loess is a way of estimating a regression surface through a multivariate smoothing procedure fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series with local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions such as polynomials the goal of this article is to show through applications how loess can be used for three purposes data exploration diagnostic checking of parametric models and providing a nonparametric regression surface along the way the following methodology is introduced a a multivariate smoothing procedure that is an extension of univariate locally weighted regression b statistical procedures that are analogous to those used in the least squares fitting of parametric functions c several graphical methods that are useful tools for understanding loess estimates and checking the a

schur product techniques for commuting multivariable weighted shifts abstract in this paper we study the hyponormality and subnormality of 2 variable weighted shifts using the schur product techniques in matrices as applications we generalize the result in r curto j yoon jointly hyponormal pairs of subnormal operators need not be jointly subnormal trans amer math soc 358 2006 5135 5159 theorem 5 2 and give a non trivial large class satisfying the curto muhly xia conjecture r curto p muhly j xia hyponormal pairs of commuting operators oper theory adv appl 35 1988 1 22 for 2 variable weighted shifts further we give a complete characterization of hyponormality and subnormality in the class of flat contractive 2 variable weighted shifts t t 1 t 2 with the condition that the norm of the 0th horizontal 1 variable weighted shift of t is a given constant

nearly subnormal operators and moment problems abstract we use separation of cones techniques and ideas from multivariable operator theory to show that polynomial hyponormality does not imply subnormality for hilbert space operators as an application we obtain a new result in the theory of power moments in two dimensions

a new characterization of subnormality for a class of 2 variable weighted shifts with 1 atomic core abstract given a pair t t 1 t 2 of commuting subnormal hilbert space operators the lifting problem for commuting subnormals lpcs calls for necessary and sufficient conditions for the existence of a commuting pair n n 1 n 2 of normal extensions of t 1 and t 2 this is an old problem in operator theory the aim of this paper is to study lpcs there are three well known subnormal characterizations for operators the berger theorem the bram halmos characterization and franks result in our paper we study a new subnormal characterization which is related to these three well known ones for a class of 2 variable weighted shifts thus we can provide a large nontrivial class of 2 variable weighted shifts in which k hyponormal some k 1 and subnormal are equal and the class is invariant under the action h l t h l t 1 h t 2 l h l 1

existence of non subnormal polynomially hyponormal operators in 1950 p r halmos motivated in part by the successful development of the theory of normal operators introduced the notions of subnormality and hyponormality for bounded hilbert space operators an operator t is subnormal if it is the restriction of a normal operator to an invariant subspace t is hyponormal if t t tt it is a simple matrix calculation to verify that subnormality implies hyponormality but the converse is false one reason is that subnormality is invariant under polynomial calculus indeed analytic functional calculus while hyponormality is not if one then defines t to be polynomially hyponormal when p t is hyponormal for every polynomial p e c z the following question arises naturally

hyponormality and subnormality for powers of commuting pairs of subnormal operators let h0 respectively h denote the class of commuting pairs of subnormal operators on hilbert space respectively subnormal pairs and for an integer k 1 let hk denote the class of k hyponormal pairs in h0 we study the hyponormality and subnormality of powers of pairs in hk we first show that if t1 t2 h1 the pair t12 t2 may fail to be in h1 conversely we find a pair t1 t2 h0 such that t12 t2 h1 but t1 t2 h1 next we show that there exists a pair t1 t2 h1 such that t1mt2n is subnormal for all m n 1 but t1 t2 is not in h this further stretches the gap between the classes h1 and h finally we prove that there exists a large class of 2 variable weighted shifts t1 t2 namely those pairs in h0 whose cores are of tensor form cf definition 3 4 for which the subnormality of t12 t2 and t1 t22 does imply the subnormality of t1 t2

a new approach to the 2 variable subnormal completion problem we study the subnormal completion problem scp for 2 variable weighted shifts we use tools and techniques from the theory of truncated moment problems to give a general strategy to solve scp we then show that when all quadratic moments are known equivalently when the initial segment of weights consists of five independent data points the natural necessary conditions for the existence of a subnormal completion are also sufficient to calculate explicitly the associated berger measure we compute the algebraic variety of the associated truncated moment problem it turns out that this algebraic variety is precisely the support of the berger measure of the subnormal completion

stability properties and hopf bifurcation of a delayed viral infection model with lytic immune response a class of more general delayed viral infection model with lytic immune response is proposed based on some important biological meanings the effect of time delay on stabilities of the equilibria is given the sufficient criteria for local and global asymptotic stabilities of the viral free equilibrium and the local asymptotic stabilities of the no immune response equilibrium are given we also get the sufficient criteria for stability switch of the positive equilibrium numerical simulations are carried out to explain the mathematical conclusions

quadratically hyponormal weighted shifts with recursive tail abstract we characterize positive quadratic hyponormality of the weighted shift w x associated to the weight sequence x 1 1 x u v w with stampfli recursive tail and produce an interval in x with non empty interior in the positive real line for quadratic hyponormality but not positive quadratic hyponormality for such a shift

embry truncated complex moment problem abstract let t be a cyclic subnormal operator on a hilbert space h with cyclic vector x 0 and let ij t i t j x 0 x 0 for any i j n 0 the bram halmos characterization for subnormality of t involved a moment matrix m n in a parallel approach we construct a moment matrix e n corresponding to embry s characterization for subnormality of t we discuss the relationship between m n and e n via the full moment problem next given a collection of complex numbers ij 0 i j 2 n i j n with 00 0 and ji ij we consider the truncated complex moment problem for this entails finding a positive borel measure supported in the complex plane c such that ij z i z j d z we show that this moment problem can be solved when e n 0 and e n admits a flat extension e n k where k 1 when n is odd and k 2 when n is even

the classical moment problem as a self adjoint finite difference operator abstract this is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators among the advantages of this approach is that the nevanlinna functions appear as elements of a transfer matrix and convergence of pade approximants appears as the strong resolvent convergence of finite matrix approximations to a jacobi matrix as a bonus of this we obtain new results on the convergence of certain pade approximants for series of hamburger

wold type decompositions and wandering subspaces for operators close to isometries for operators t satisfying certain inequalities we obtain a weak analog of the classical wold kolmogorov decomposition theorem representing t as a direct sum of a unitary operator and a shift operator acting in some hilbert space of analytic functions the concept of a dual operator is introduced which reflects relationships between shift operators acting in two hilbert spaces of analytic functions dual to each other with respect to the cauchy pairing among different aspects of this duality we consider relationships between hereditary inequalities and properties of reproducing kernels

disintegration of measure techniques for commuting multivariable weighted shifts we employ techniques from the theory of disintegration of measures to study the lifting problem for commuting n tuples of subnormal weighted shifts we obtain a new necessary condition for the existence of a lifting and generate new pathology associated with bringing together the berger measures associated to each individual weighted shift for subnormal 2 variable weighted shifts we then find the precise relation between the berger measure of the pair and the berger measures of the shifts associated to horizontal rows and vertical columns of weights

quartically hyponormal weighted shifts need not be 3 hyponormal we give the first example of a quartically hyponormal unilateral weighted shift which is not 3 hyponormal

global dynamics of a cell mediated immunity in viral infection models with distributed delays abstract in this paper we investigate global dynamics for a system of delay differential equations which describes a virus immune interaction in vivo the model has two distributed time delays describing time needed for infection of cell and virus replication our model admits three possible equilibria an uninfected equilibrium and infected equilibrium with or without immune response depending on the basic reproduction number for viral infection r 0 and for ctl response r 1 such that r 1 r 0 it is shown that there always exists one equilibrium which is globally asymptotically stable by employing the method of lyapunov functional more specifically the uninfected equilibrium is globally asymptotically stable if r 0 1 an infected equilibrium without immune response is globally asymptotically stable if r 1 1 r 0 and an infected equilibrium with immune response is globally asymptotically stable if r 1 1 the immune activation has a positive role in the reduction of the infection cells and the increasing of the uninfected cells if r 1 1

global stability in a viral infection model with lytic and nonlytic immune responses this paper investigates the global stability of a viral infection model with lytic and nonlytic immune responses if the basic reproductive ratio of the virus is less than or equal to one by the lasalle s invariance principle and center manifold theorem the disease free steady state is globally asymptotically stable if the basic reproductive ratio of the virus is greater than one then the virus persists in the host and the disease steady state is locally asymptotically stable furthermore by the method of lyapunov function the global stability of the disease steady state is established at the same time if we neglect the efficacy of the lytic component using a geometrical approach we obtain a different type of conditions for the global stability of the disease steady state

the mean transform of bounded linear operators abstract in this paper we introduce the mean transform of bounded linear operators acting on a complex hilbert space and then explore how the mean transform of weighted shifts behaves in comparison with the aluthge transform