pointwise lipschitzian mappings in uniformly convex and uniformly smooth banach spaces abstract let x be a uniformly convex and uniformly smooth banach space let t c c be an asymptotic pointwise nonexpansive mapping where c is a bounded closed and convex subset of x in this paper we investigate conditions sufficient for the weak convergence of the generalized mann and ishikawa processes to a fixed point of t

master equation for a quantum system driven by a strong periodic field in the quasienergy representation abstract the evolution of a quantum system weakly coupled with a thermal reservoir and influenced by an external periodic field is formulated in the quasienergy representation where the strong external periodic field disappears and the original model is transformed to a time dependent system weakly coupled with thermal reservoir based on this time dependent subdynamics we derive a master equation of the reduced density operator for the driven quantum system this equation is valid in the weak coupling limit our method can be useful for obtaining the master equation of any system coupled with a thermal reservoir and driven by strong external periodic fields

spectral decomposition of the renyi map the authors construct a generalized spectral decomposition of the frobenius perron operator of the general beta adic renyi map using a general iterative operator method applicable in principle to any mixing dynamical system they also explicitly define appropriate rigged hilbert spaces which provide mathematical meaning to the formally obtained spectral decomposition the explicit construction of the eigenvalues and eigenvectors allows one to show that the essential spectral radius of the frobenius perron operator decreases as the smoothness of the domain increases the reason for the change of the spectrum from the unit disk to isolated eigenvalues is the existence of coherent states of the frobenius perron operator which are not infinitely differentiable

concatenating decoherence free subspaces with quantum error correcting codes an operator sum representation is derived for a decoherence free subspace dfs and used to i show that dfs s are the class of quantum error correcting codes qecc s with fixed unitary recovery operators and ii find explicit representations for the kraus operators of collective decoherence we demonstrate how this can be used to construct a concatenated dfs qecc code which protects against collective decoherence perturbed by independent decoherence the code yields an error threshold which depends only on the perturbing independent decoherence rate s0031 9007 99 09301 1

statistical mechanics of a large dynamical system interacting with an external time dependent field generalised correlation subdynamics abstract we recently showed that it is possible using an explicitly time dependent formalism to separate the density matrix or distribution function of a large isolated dynamical system into a complete set of mutually orthogonal projections each obeying its own independent subdynamics in the presence of an external time dependent field these subspaces are themselves coupled for this situation we now obtain under mild integrability conditions the new time dependent projectors for the complete set of generalised correlations under which the projections t again obey independent subdynamics this result is a generalisation of the work of balescu and misguich which was confined to the vacuum case 0 it considerably broadens the scope of the subdynamics theory which may now be applied to the study of irreversible processes in macroscopic systems evolving under the influence of external fields such ramifications will be discussed in future publications

ergodic retractions for amenable semigroups in banach spaces with normal structure abstract in this paper we discuss the existence of nonexpansive retraction onto the set of common fixed points assume that t s s s is an amenable semigroup of nonexpansive mappings on a closed convex subset c in a reflexive banach space e such that the set f of common fixed points of is nonempty among other things it is shown that if either c has normal structure or the t s s are affine then there exists a nonexpansive retraction p from c onto f such that p t t t t p p for each t s and every closed convex invariant subset of c is also p invariant in the case that the mappings are affine p is also affine and p x c o t t x t s for each x c and it is unique regarding the latter property our results extend corresponding results of t suzuki some remarks on the set of common fixed points of one parameter semigroups of nonexpansive mappings in banach spaces with the opial property nonlinear anal 58 2004 441 458 and r e bruck a common fixed point theorem for a commuting family of nonexpansive mappings pacific j math 53 1974 59 71

kinetic equation non perturbative approach and decoherence free subspace for quantum open system a schrodinger lionville type of equation for an quantum open system is presented the equation has a correlated part and many master equations can be derived from it as special cases most significantly it can be applied to construct a decoherence free subspace for quantum computing the original schrodinger lionville equation for the total system is related to it by a non unitary similarity transformation which enables us to propose a non perturbative method for solving the eigenvalue problem for the total hamiltonian in addition it also enables one to uncover a simple procedure to treat the eigenvalue problem of an open system under strong interaction the correlated part of the equation is not necessarily self adjoint so that there exists a complex spectrum for the corresponding hamiltonian liouvillian which enables the time evolution of states to be asymmetric this then exposes just the correlation required to produce evolution which coincides with the second law of thermodynamics c 2002 published by elsevier science b v

universal approximation using radial basis function networks there have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables some of these studies deal with cases in which the hidden layer nonlinearity is not a sigmoid this was motivated by successful applications of feedforward networks with nonsigmoidal hidden layer units this paper reports on a related study of radial basis function rbf networks and it is proved that rbf networks having one hidden layer are capable of universal approximation here the emphasis is on the case of typical rbf networks and the results show that a certain class of rbf networks with the same smoothing factor in each kernel node is broad enough for universal approximation

nonlinear adaptive trajectory tracking using dynamic neural networks in this paper the adaptive nonlinear identification and trajectory tracking are discussed via dynamic neural networks by means of a lyapunov like analysis we determine stability conditions for the identification error then we analyze the trajectory tracking error by a local optimal controller an algebraic riccati equation and a differential one are used for the identification and the tracking error analysis as our main original contributions we establish two theorems the first one gives a bound for the identification error and the second one establishes a bound for the tracking error we illustrate the effectiveness of these results by two examples the second order relay system with multiple isolated equilibrium points and the chaotic system given by duffing equation

on an analogue of zarantonello s inequality and a nonlinear mean ergodic theorem abstract let x be a uniformly convex banach space c be a bounded closed subset of x and t c x be a contraction then it is shown that for all xi c i 0 i 1 2 n with i 1n i 1 there exists a strictly increasing convex function n of r with n 0 0 such that n t i 1n ixi i 1n itxi 1 i j n i j xi xj txi txj as an application of this inequality the mean ergodic theorem for contractions in uniformly convex banach spaces is proved

asymptotic behavior of commutative semigroups of nonexpansive mappings in banachspaces on etablit des theoremes de convergence pour des semigroupes generaux d applications non dilatation dans le cadre des espaces de banach on demontre un theoreme ergodique non lineaire de type rode pour des semigroupes commutatifs

on the time dependent formulation of analytical continuation in non equilibrium statistical mechanics abstract on the basis of the dynamics of correlations approach to the solution of the liouville von neumann equation we develop within the familiar classification of correlations scheme a time dependent formalism which leads naturally to an analytical continuation procedure thereby allowing explicit evaluation of each term in the formal series solution this procedure throws new light on the so called i rule and opens the way to the treatment of the full correlation subdynamics for time dependent phenomena which will be discussed in future publications

resonances of dynamical systems and fredholm riesz operators on rigged hilbert spaces abstract resonances of dynamical systems are defined as the singularities of the analytically continued resolvent of the restriction of the frobenius perron operator to suitable test function spaces a sufficient condition for resonances to arise from a meromorphic continuation to the entire plane is that the frobenius perron operator is a fredholm riesz operator on a rigged hilbert space after a discussion of spectral theory in locally convex topological vector spaces we illustrate the approach for a simple chaotic system namely the renyi map

strong convergence of mann s type iterations for nonexpansive semigroups in general banach spaces abstract in this paper we prove a strong convergence theorem of mann s type for commutative nonexpansive semigroups in general banach spaces using this theorem we obtain some strong convergence theorems in general banach spaces

an ergodic theorem for semigroups of nonexpansive mappings in a hilbert space abstract j b baillon c r acad sci paris ser a 280 1975 1511 1514 proved an ergodic theorem for a single nonexpansive mapping in a hilbert space which is a nonlinear version of von neumann s mean ergodic theorem in this paper we study the ergodic behavior of a semigroup of nonexpansive mappings we try to find a sequence of means on the semigroup generalizing the cesaro means on n such that the corresponding sequence of nonexpansive mappings converges to a projection onto the set of common fixed points our method of proof is an appropriate modification of a pazy s proof israel j math 26 1977 197 204 of baillon s theorem

kinetic time irreversible evolution of the unstable π meson abstract in liouville formalism the expression for density matrix determining the time evolution of unstable meson in the framework of unified formulation of quantum and kinetic dynamics is defined the eigenvalues problem is investigated in the framework of prigogine s principles of description of nonequilibrium processes at microscopic level the problem was solved on the basis of complex spectral representation it was shown that the approach leads to pauli master equation for the weakly interacting system

uniform approximation and the circle criterion the input output maps g of causal time invariant systems are considered and a complete characterization of those maps that can be uniformly approximated by the maps of certain simple structures is given the criterion is that g must satisfy certain continuity and approximately finite memory conditions it is proved that the conditions are satisfied by the input output maps of control systems of a familiar type containing a sector nonlinearity for which the circle condition for stability is met in particular this shows that such feedback systems with inputs drawn from a certain large set of bounded functions possess arbitrarily good finite volterra series or radial basis function approximations

general iterative methods for a one parameter nonexpansive semigroup in hilbert space abstract let h be a hilbert space and f a fixed contractive mapping with coefficient 0 1 a a strongly positive linear bounded operator with coefficient 0 consider two iterative methods that generate the sequences x n y n by the algorithm respectively i x n i n a 1 t n 0 t n t s x n d s n f x n ii y n 1 i n a 1 t n 0 t n t s y n d s n f y n where n and t n are two sequences satisfying certain conditions and t s s 0 is a one parameter nonexpansive semigroup on h it is proved that the sequences x n y n generated by the iterative method i and ii respectively converge strongly to a common fixed point x f which solves the variational inequality a f x x z 0 z f

resonances and the extension of dynamics to rigged hilbert space abstract we propose a unified operator theoretic formulation of resonances and resonance states in rigged hilbert space our approach shows how resonances are the basis for the extension of dynamics for unstable systems and in a synthesis and a generalization of the work of the brussels austin groups directed by prigogine with the work of bohm and gadella on gamow vectors and with the extension theory developed by the st petersburg group directed by pavlov we illustrate the approach for prototypes of resonances namely resonances of the power spectrum scattering resonances and resonances associated with the unstable bloch states

quantum systems with diagonal singularity their logic and intrinsic irreversibility abstract the work of the brussels austin group on irreversibility over the last years has shown that quantum large poincare systems with diagonal singularity lead to an extension of quantum theory beyond the conventional hilbert space framework and logic we characterize the algebra of observables and the states and the logic of the extended quantum theory of intrinsically irreversible systems with diagonal singularity

on the extension of the general theorem in the dynamics of correlations to the statistical mechanics of large systems evolving in time dependent external fields the formal subdynamics approach to irreversibility in nonequilibrium statistical mechanics is cursorily reviewed emphasis being placed on a recently developed time dependent formalism which generalises naturally from isolated systems to systems open to external influence by means of a diagrammatic approach the authors apply this theoretical framework to begin the study of gases and plasmas evolving in the presence of time dependent external fields the general theorem in the dynamics of correlations is extended to include these cases and a corollary is deduced which enables one to eliminate from consideration a large class of diagrams in the thermodynamic limit finally they discuss briefly some consequences of the formalism which may serve as avenues for the investigation of problems of physical interest

identification of linear systems with nonlinear distortions this paper studies the impact of nonlinear distortions on linear system identification it collects a number of previously published methods in a fully integrated approach to measure and model these systems from experimental data first a theoretical framework is proposed that extends the linear system description to include the impact of nonlinear distortions the nonlinear system is replaced by a linear model plus a nonlinear noise source the class of nonlinear systems covered by this approach is described and the properties of the extended linear representation are studied these results are used to design the experiments to detect the level of the nonlinear distortions to measure efficiently the best linear approximation to reveal the even or odd nature of the nonlinearity to identify a parametric linear model and to improve the model selection procedures in the presence of nonlinear distortions

steady state errors in nonlinear control systems control systems containing a memoryless nonlinear element are addressed the steady state response to certain inputs when the circle condition for stability is met is characterized

iterative algorithms for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of families and semigroups of nonexpansive mappings abstract we introduce iterative algorithms for finding a common element of the set of solutions of a system of equilibrium problems and of the set of fixed points of a finite family and a left amenable semigroup of nonexpansive mappings in a hilbert space we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality which is the optimality condition for a minimization problem our results extend for example the recent result of v colao g marino h k xu an iterative method for finding common solutions of equilibrium and fixed point problems j math anal appl 344 2008 340 352 to systems of equilibrium problems

the extension of classical dynamics for unstable hamiltonian systems abstract classical dynamics can be formulated in terms of trajectories or in terms of statistical ensembles whose time evolution is described by the liouville equation it is shown that for the class of large nonintegrable poincare systems lps the two descriptions are not equivalent practically all dynamical systems studied in statistical mechanics belong to this class the basic step is the extension of the liouville operator l h outside the hilbert space to functions singular in their fourier transformation this function space plays an important role in statistical mechanics as functions of the hamiltonian and therefore equilibrium distribution functions belong to this class physically these functions correspond to situations characterized by persistent interactions as they are realized in macroscopic physics persistent interactions are introduced in contrast to transient interactions studied in quantum mechanics by the s matrix approach asymptotically free in and out states the eigenvalue problem for the liouville operator l h is solved in this generalized function space for lps we obtain a complex irreducible spectral representation complex means that the eigenvalues are complex numbers whose imaginary parts refer to the various irreversible processes such as relaxation times diffusion irreducible means that these representations cannot be implemented by trajectory theory as the result the dynamical group of evolution splits into two semigroups moreover the laws of classical dynamics take a new form as they have to be formulated on the statistical level they express possibilities and no more certitudes two examples of typical classical systems i e interacting particles and anharmonic lattices are studied

the retractions onto the common fixed points of some families and semigroups of mappings abstract assume that c is a closed convex subset of a reflexive banach space e and t i i i is a family of self mappings on c of type such that f the common fixed point set of is nonempty from our results in this paper it can be derived that a if i i f t i is contained in a 3 dimensional subspace of e then f is a nonexpansive retract of c b if is commutative there exists a retraction r of type from c onto f such that r t i t i r r i and every closed convex invariant subset of c is r invariant the same result holds for a non commutative right amenable semigroup under some additional assumptions moreover the existence of a t i ergodic retraction r of type from c x i l e x i c i i onto f in l e for the family is discussed we also apply some of our results to find ergodic retractions for nonexpansive affine mappings

order and disorder in the approach to equilibrium of a classical gas we study the approach to equilibrium of a classical gas the initial condition corresponds to a maxwell velocity distribution but to a nonequilibrium binary correlation we consider two cases in the first there are initially no spatial correlations while in the second initial correlations correspond to long range spatial order we show that the gas leaves the maxwell velocity distribution function in the process of building up equilibrium correlations the spatial correlations in the equilibrium state are seen to emerge from a self organization process in the gas non markovian effects play an essential role in this process by coupling the velocity distribution and the binary correlations for the case of initial long range correlations we obtain anti boltzmann behavior in the evolution of the velocity distribution as the boltzmann entropy decreases from the nonequilibrium to the equilibrium state for this case we also have nontrivial behavior on a short time scale due to the non markovian effects the approach used here is based on the theory of subdynamics as developed in previous publications the results obtained show the interplay between irreversible processes leading to disorder and to order in a classical gas

subdynamics in the time dependent formalism abstract by means of the recently derived analytical continuation procedure of coveney and george together with henin s theorem in the dynamics of correlations we show that the complete correlation subdynamics of a large dynamical system may be obtained within an explicitly time dependent formalism this result represents a significant extension of the earlier work of balescu and misguich insofar as the time dependent problem is concerned and bring us a stage nearer to a subdynamics based description of irreversible processes in open systems which are described by a time dependent liouville operator

poincare s theorem and subdynamics for driven systems abstract large dynamical systems with explicit time dependence will be studied for these systems which we call driven systems there exist resonances between internal frequencies and or between internal and external frequencies as in the time independent case the usual canonical or unitary perturbation theory leads to divergences due to the resonances as a result there exist no trajectories analytic in both the coupling constant and the initial data this is a generalization of poincare s theorem on non integrability and extends the notion of large poincare systems lps i e systems with a continuous spectrum and a continuous set of resonances here the resonances involve external frequencies along the line of the subdynamics theory developed by prigogine and his co workers we study lps within the liouville space formalism we construct projection operators which decompose the equations of motion and are analytic in the coupling constant our approach recovers coveney s theory of time dependent subdynamics but is based on recursion formulas which significantly simplify the construction of the projection operators these projectors are non hermitian and provide a description with broken time symmetry as an application we study the modification of the well known three stages of the decay process from a time dependent perturbation

a state space approach to analysis of almost periodic nonlinear systems with sector nonlinearities the nonlinear system considered in this paper consists of two components a linear system and a time varying nonlinear element in the feedback connection and is almost periodic it is shown using a state space approach or lyapunov approach that if the well known circle criterion is satisfied then there exists an almost periodic solution which is uniformly asymptotically stable in the large furthermore it is also shown that the spectra of the almost periodic solution can be characterized by those of the input and the time varying nonlinearity

solution of the linearised vlasov equation for collisionless plasmas evolving in external fields of arbitrary spatial and time dependence i the authors solve perturbatively the linearised vlasov equation describing inhomogeneous collisionless plasmas evolving in time dependent external fields the method employs an explicitly time dependent formalism and is facilitated by the use of diagrammatic techniques it leads to a straightforward algorithm for computing the contribution to the solution order by order in the external field they provide the solution to first order

a note on the pq theorem and the extrapolation of signals the problem of determining a bandlimited function from its values on a finite interval is ill conditioned in the sense that although the pertinent inverse map exists it is discontinuous at every point whenever certain closely related general problems are well conditioned in the sense that the inverse operator is continuous they can be solved using a special case of a known algorithm in particular attention is directed to the relation between the pq theorem its hilbert space projection operator setting and later work

canonical nonequilibrium ensembles and subdynamics a method for constructing a canonical nonequilibrium ensemble for systems in which correlations decay exponentially has recently been proposed by coveney and penrose in this paper we show that the method is equivalent to the subdynamics formalism developed by prigogine and others when the dimension of the subdynamic kinetic subspace is finite the comparison between the two approaches helps to clarify the nature of the various operators used in the brussels formalism we discuss further the relationship between these two approaches with particular reference to a simple discrete time dynamical system based on the baker s transformation which we call the baker s urn

non hermitian hamiltonians in decoherence and equilibrium theory there are many formalisms to describe quantum decoherence however many of them give a non general and ad hoc definition of pointer basis or moving preferred basis and this fact is a problem for the decoherence program in this paper we will consider quantum systems under a general theoretical framework for decoherence and we will present a tentative definition of the moving preferred basis these ideas are implemented in a well known open system model the obtained decoherence and the relaxation times are defined and compared with those of the literature for the lee friedrichs model this article is part of a special issue of journal of physics a mathematical and theoretical devoted to quantum physics with non hermitian operators

gamow vectors for degenerate scattering resonances in this paper we construct gamow vectors for resonances given by poles of the analytic continuation of the s matrix of any finite order we study their modes of decay or growth we obtain jordan block structures for the extended hamiltonians and evolution operators on the subspaces spanned by these gamow vectors we perform this study within the context of the rigged hilbert space extension of quantum theory we construct an explicit friedrichs model with a double pole resonance to illustrate the general formulation

subdynamics and nonintegrable systems work on the application of poincare s theorem to large classical or quantum systems with a continuous spectrum is continued in situations where it is applicable poincare s theorem prevents the construction of a complete set of eigenprojectors which would be hermitian as well as analytic in the coupling constant in contrast the theory of subdynamics as developed by the brussels group permits the construction of a unique set of projectors for t 0 giving up the requirement of hermiticity which is replaced by star hermiticity the theory of subdynamics is presented in a new self contained way starting from the commutation relation lh lh where lh is the liouvillian this presentation is far more direct and avoids some of the lengthy discussions associated with previous presentations based mainly on the resolvent of the liouvillian subdynamics appears to be of interest from many points of view it generalizes the concept of spectral representation while permitting to retain all the degrees of freedom present in the unperturbed hamiltonian in contrast degrees of freedom are lost when going to the spectral representation e g in the friedrichs model subdynamics permits us to solve the initial value problem associated with the liouville equation retaining the non markovian contributions which appear in the standard presentation finally it introduces a classification of large dynamical systems classical or quantum into integrable and nonintegrable ones it is therefore of direct interest for a number of basic problems which belong to the class of nonintegrable dynamical systems such as the interaction of matter with light the applications of this technique to these problems will be worked out in subsequent papers

convergence of iterates of nonexpansive mappings and orbits of nonexpansive semigroups abstract let x be a uniformly convex banach space and let c be a bounded closed and convex subset of x assume that c has nonempty interior and is locally uniformly rotund let t be a nonexpansive self mapping of c if t has no fixed point in the interior of c then there exists a unique point x on the boundary of c such that each sequence of iterates of t converges in norm to x we also establish an analogous result for nonexpansive semigroups

a mean ergodic theorem for nonlinear semigroups which are asymptotically nonexpansive in the intermediate sense abstract let x be a uniformly convex banach space such that its dual x has the kadec klee property c a bounded closed convex subset of x and t t t t 0 a one parameter nonlinear semigroup which is asymptotically nonexpansive in the intermediate sense we show that every continuous almost orbit of t is weakly almost convergent to a common fixed point of t a discrete version of our main result is also included

state feedback control of nonlinear systems a simple approach a simple methodology for the design of state feedback controllers for nonlinear continuous time systems is introduced the objective is to develop controllers that drive a nonlinear system from an initial condition into an assigned region of state space it is shown that such state feedback controllers can be derived by solving a set of inequalities obtained directly from quantities given in the controlled system s equation the results are applied to the design of state feedback controllers that achieve robust asymptotic stabilisation for a rather general class of nonlinear systems

weak convergence of almost orbits of asymptotically nonexpansive commutative semigroups we give three equivalent conditions for weak convergence of almost orbits of an asymptotically nonexpansive commutative semigroup acting on a nonempty bounded closed convex subset of a uniformly convex banach space whose dual has the kadec property

nonlinear ergodic theorems for semigroups of non lipschitzian mappings in banach spaces let c be a nonempty closed convex subset of a uniformly convex banach space and let s t t t 0 be a nonlinear semi group of non lipschitzian mappings on c which is asymptotically non expansive in the intermediate sense in this paper we study weak almost convergence of almost orbits of s

intrinsic irreversibility of quantum systems with diagonal singularity the work of the brussels austin group on irreversibility over the last years has shown that quantum large poincare systems with diagonal singularity lead to an extension of quantum theory beyond the conventional hilbert space framework and logic we characterize the algebra of observables the states and the logic of the extended quantum theory of intrinsically irreversible systems with diagonal singularity we illustrate the general ideas for the friedrichs model

irreversible liouville equation and nonperturbative approach in quantum computing having analyzed the role of time ordering boundary conditions in deriving irreversible kinetic equation a general irreversible liouville equation is proposed by this equation a variety of irreversible kinetic equations such as a stochastic diffusion equation a irreversible project liouville equation can be constructed we also develop a nonperturbative method to solve the eigenvalue problem for this equation application in controlling decoherence for quantum computing is also studied c 2004 elsevier b v all rights reserved

generalized spectral decomposition of the β adic baker s transformation and intrinsic irreversibility abstract we construct a generalized spectral decomposition of the frobenius perron operator of the adic baker s transformation using a general iterative operator method applicable in principle for any mixing dynamical system the eigenvalues in the decomposition are related to the decay rates of the autocorrelation functions and have magnitudes less than one we explicitly define appropriate generalized function spaces which provide mathematical meaning to the formally obtained spectral decomposition the unitary frobenius perron evolution of densities when extended to the generalized function spaces splits into two semigroups one decaying in the future and the other in the past this split which reflects the asymptotic evolution of the forward and backward k partitions shows the instrinsic irreversibility of the baker s transformation

weak convergence and non linear ergodic theorems for reversible semigroups of non lipschitzian mappings abstract letgbe a semitopological semigroup letcbe a closed convex subset of a uniformly convex banach spaceewith afrechetdifferentiable norm and t tt t g be a continuous representation ofgas asymptotically nonexpansive type mappings ofcinto itself such that the common fixed point setf t of t incis nonempty we prove in this paper that ifgis right reversible then for every almost orbitu of t formula consists of at most one point further formula is nonempty for eachx cif and only if there exists a nonexpansive retractionpofcontof t such thatpts tsp pfor alls gandp x is in the closed convex hull of tsx s g x c this result is applied to study the problem of weak convergence of the net u t t g to a common fixed point of t

nonexpansive retractions and nonlinear ergodic theorems in banach spaces on donne des theoremes ergodiques non lineaires pour des semigroupes commutatifs d applications non dilatation sans utiliser le concept de moyenne compacte

alternative formulation of classical and quantum dynamics for non integrable systems we continue our work on large poincare systems lps characterized by a continuous spectrum and a continuous set of resonances poincare s theorem prevents the existence of solutions of the eigenvalue problem associated with the hamiltonian as well as the liouville operator which would be analytic in the coupling constant in simple cases such as the friedrichs model studied in a recent paper poincare s divergences can be avoided using a natural time ordering of the dynamical states in the hilbert space however in general the time ordering has to be performed in the liouville space of density matrices

lie admissible perturbation methods for open quantum systems abstract we consider open quantum systems described by a hamiltonian of the type h0 v where is a small parameter for such systems we develop perturbative methods of solution of the corresponding liouville von neumann and schrodinger equations by introducing dissipation operators which connect conservative to dissipative systems in the case of the density matrix the corresponding operator is nothing but the non unitary transformation of misra prigogine and courbage our perturbative approach possesses a lie admissible structure since the dissipation operators obey time evolution equations whose brackets are the product of a lie admissible algebra explicit solutions for such operators are found in the form of series expansions in the matrix formulation of the above results is also given

oscillation criteria of a class of partial difference equations with delays this paper is concerned with the linear delay partial difference equation aa m 1 n 1 ba m 1 n ca n m n l da m n p m na m s n t 0 where s and t are two nonnegative integers a b c and d are positive constants and p i j i j e n 0 is a double real sequence sufficient conditions for this equation to be oscillatory are derived

asymptotic behavior of uniformly asymptotically almost nonexpansive curves in a hilbert space abstract we extend the notion of uniformly asymptotically almost nonexpansive curves which was first introduced in rouhani and kim j nonlinear convex anal 4 2003 175 for a commutative semigroup to a general semitopological semigroup study the asymptotic behavior of such curves in a hilbert space and apply our results to study the asymptotic behavior for almost orbits of semigroups of asymptotically nonexpansive type mappings over a general semitopological semigroup in a hilbert space since in this case the semigroup is not directed the proofs in rouhani and kim j nonlinear convex anal 4 2003 175 do not extend to this case and new methods have to be used for the proofs in addition to rouhani j math anal appl 147 1990 465 j math anal appl 151 1990 226 nonlinear anal 44 2001 627 nonlinear anal 51 2002 735 and rouhani and kim j nonlinear convex anal 4 2003 175 our results extend and unify many previously known results j math anal appl 127 1987 206 proc amer math soc 104 1988 431 nonlinear anal 29 1997 539 topol methods nonlinear anal 5 1995 305 j math anal appl 105 1985 514 nonlinear anal 26 1996 1411 pacific j math 126 1987 277 j math anal appl 206 1997 451 chinese ann math 6 1996 729 nonlinear anal 14 1990 69 j math anal appl 85 1982 172 proc amer math soc 81 1981 253 proc amer math soc 97 1986 55 canad j math 44 1992 880 j math anal appl 142 1989 242 proc amer math soc 117 1993 385

general formalism for the spectral decomposition of the hamiltonian in a quantum fractal network we present a general formulation for the spectral decomposition of the hamiltonian operator of a quantum fractal network qfn the qfn can be constructed by placing artificial neurons on each site of the fractal lattice an artificial neuron may consist of a cell of a quantum cellular automata or a quantum dot which confines a single electron the coulomb interaction or the spin spin interaction between neurons can be used to transmit signals and perform logic operations the local external field may be as input signal to influence output of the system we obtain explicitly the recursive formulae of the eigenvalues and eigenvectors between sublattices the intertwining relation between the collision operator and the hamiltonian operator by combining subdynamics and a reduced lattice approach furthermore the perturbation method to obtain the spectral decomposition for the time dependent hamiltonian is also discussed finally as an example we calculate the eigenvalues and eigenvectors of the hamiltonian operator for a sierpinski gasket based on our formulation analysis of the recursive formula for the spectrum of the sierpinski gasket reveals how its spectral structure changes in boundary conditions

asymptotic behavior for almost orbits of a reversible semigroup of non lipschitzian mappings in a metric space let m be a metric space and a hausdorff topology on m such that m is compact let s be a right reversible semitopological semigroup and t s s s a representation of s as asymptotically nonexpansive type self mappings of m and u a bounded almost orbit of we study the convergence of the net u s s s in m when the triplet m satisfies various types of opial conditions our results extend and unify many previously known results 2002 elsevier science usa all rights reserved

quantum theory of non integrable systems in 1889 h poincare introduced a basic distinction between integrable and non integrable dynamical systems this distinction refers to the role of resonances which may lead to divergences a specially important class of non integrable systems are large poincare systems lps which have a continuous spectrum and present continuous sets of resonances as has been shown earlier lps play an essential role both in classical and quantum mechanics essentially all nontrivial problems of field theory as well as kinetic theory belong this class we consider here the well known friedrichs model in which an unstable discrete level is coupled to a continuum poincare s theorem prevents the existence of solutions of the eigenvalue problem associated to the hamiltonian which would be analytic in the coupling constant

weak almost periodicity and the strong ergodic limit theorem for periodic evolution systems the first ergodic theorems for semigroups of nonlinear operators date back to work done by j b baillon cl 23 in 1975 1976 where he proved in 2 that i i lim l t j t s i x dt exists for an odd nonlinear contraction semigroup s t a 0 in real hilbert space in subsequent years various authors have extended his results to motions and almost orbits of nonlinear strongly continuous semigroups in uniformly convex banach spaces e g see 4 10 22 24 26 27 30 31 33 351 as well as 4 10 241 for yet further references these results apply to strong and integral solutions of the quasi autonomous nonlinear cauchy problem