the ngp stability of runge kutta methods for systems of neutral delay differential equations this paper deals with the stability analysis of implicit runge kutta methods for the numerical solutions of the systems of neutral delay differential equations we focus on the behavior of such methods with respect to the linear test equations where tau 0 l m and n are d times d complex matrices we show that an implicit runge kutta method is ngp stable if and only if it is a stable

quasilinear multistep methods and variable step predictor corrector methods for neutral functional differential equations the theory of quasilinear multistep methods and predictor corrector methods for neutral functional differential equations is developed the theorem about the asymptotic behaviour of the global discretization error of quasilinear methods which forms a theoretical basis for step control strategy for predictor corrector methods for neutral equations is given some problems of implementation of these methods are also addressed and the results of numerical experiments are presented

nonlocality asymmetry and distinguishing bipartite states entanglement is a useful resource because some global operations cannot be locally implemented using classical communication we prove a number of results about what is and what is not locally possible we focus on orthogonal states which can always be globally distinguished we establish the necessary and sufficient conditions for a general set of 2 ifmmode times else texttimes fi 2 quantum states to be locally distinguishable and for a general set of 2 ifmmode times else texttimes fi n quantum states to be distinguished given an initial measurement of the qubit these results reveal a fundamental asymmetry to nonlocality which is the origin of nonlocality without entanglement and we present a very simple proof of this phenomenon

numerical solution of neutral functional differential equations by adams methods in divided difference form a variable step and variable order algorithm for the numerical solution of neutral functional differential equations is described this general purpose algorithm is based on the variable step formulation of the adams methods represented in divided difference form the adams bashforth and adams moulton methods are implemented in predictor corrector mode the detection of derivative discontinuities relies on the estimates of the local discretization errors the restarting of the integration at each discontinuity point relies on the step size and order changing strategy based on the estimates of the local discretization errors this algorithm reduces the overhead cost by implementing the adams methods in divided difference form this algorithm increases the reliability and efficiency by obtaining asymptotically correct estimates of the local discretization errors for the lower adjacent orders without any extra function evaluation by using local extrapolation the results from three test examples are presented

approximate solution of ordinary differential equations and their systems through discrete and continuous embedded runge kutta formulae and upgrading of their order abstract the eight main contributions of the author to the field of approximate solutions of ordinary differential equations described herein are all application oriented with the purposes of simplification and the increase in efficiency and effectiveness of the runge kutta processes generated they range from the determination of an initial trial step size to be adopted to expedite the approximation process through embedded runge kutta algorithms to a more recent procedure for upgrading the order of runge kutta processes these contributions encompass all classes of differential equations of all orders such as explicit implicit single or systems and their treatment by runge kutta processes of scalar or vector type with the related equivalence conditions of discrete or continuous kind including the computer derivations of nonlinear algebraic equations associated with the runge kutta processes specifically the author developed the first fifth order runge kutta formulae with fourth order embedded and the first c 1 approximate solution through interpolation and runge kutta formulae which he improved by developing c 1 embeddings with runge kutta formulae without the use of interpolative techniques

stability of linear multistep methods for nonlinear neutral delay differential equations in banach space this paper is devoted to investigating the nonlinear stability properties of linear multistep methods for the solution to neutral delay differential equations in banach space two approaches to numerically treating the neutral term are considered which allow us to prove several results on numerical stability of linear multistep methods these results provide some criteria for choosing the step size such that the numerical method is stable some examples of application and a numerical experiment which further confirms the main results are given

uniform k monotonicity and k order continuity in symmetric spaces with application to approximation theory abstract we investigate k order continuity in a symmetric space e using the fundamental function of e we also show a connection between reflexivity and k order continuity in symmetric spaces next we present several results devoted to a characterization of uniform k monotonicity and decreasing increasing uniform k monotonicity in symmetric spaces we also discuss a relationship between decreasing resp increasing uniform monotonicity and decreasing resp increasing uniform k monotonicity next we deliberate a correlation between uniform k monotonicity and uniform rotundity in symmetric spaces finally employing k monotonicity properties and k order continuity we provide solvability and stability of the best approximation problem in the sense of the hardy littlewood polya relation in symmetric spaces

perturbed proximal point algorithms for generalized quasivariational inclusions abstract in this paper we study a class of generalized quasivariational inclusions by using the properties of the resolvent operator associated with a maximal monotone mapping in hilbert space we have established an existence theorem of solutions for generalized quasivariational inclusions suggesting a new iterative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solution of the generalized quasivariational inclusions as special cases some known results in this field are also discussed

the numerical solution of volterra functional differential equations of neutral type in this paper methods of adams moulton type for neutral functional differential equations are investigated a general convergence theorem is presented and the order of convergence of these methods is examined some numerical examples are given

relationships between k monotonicity and rotundity properties with application abstract in this paper we investigate a relationship between fully k rotundity properties uniform k monotonicity properties reflexivity and k order continuity in symmetric spaces e we also answer a crucial question whether fully k rotundity properties might be restricted in definition to e d the positive cone of all nonnegative and decreasing elements of e we present a complete characterization of decreasing uniform k monotonicity and k order continuity in e it is worth mentioning that we also establish several auxiliary results describing reflexivity in lorentz spaces p w and k order continuity in orlicz spaces l finally we show an application of discussed geometric properties to the approximation theory

optimal entanglement criterion for mixed quantum states we develop a strong and computationally simple entanglement criterion the criterion is based on an elementary positive map phi which operates on state spaces with even dimension n or 4 it is shown that phi detects many entangled states with a positive partial transposition ppt and that it leads to a class of optimal entanglement witnesses this implies that there are no other witnesses which can detect more entangled ppt states the map phi yields a systematic method for the explicit construction of high dimensional manifolds of bound entangled states

approximation schemes for the linear quadratic optimal control problem associated with delay equations the linear regulator problem for delay equations is discussed we propose a theoretical solution involving riccati integral equations and then axiomatically discuss a general approximation scheme the details are given for spline and averaging approximations

waveform relaxation methods for functional differential systems of neutral type abstract we investigate continuous time and discretized waveform relaxation iterations for functional differential systems of neutral type it is demonstrated that continuous time iterations converge linearly for neutral equations and superlinearly when the right hand side is independent of the history of the derivative of the solution the error bounds for discretized iterations are also obtained and some implementation aspects are discussed numerical results are presented which indicate a potential speedup of this technique as compared with the classical approach based on discrete variable methods

on the design of a stable adaptive filter for state estimation in high dimensional systems design of specific parametrized gain structures provides a new tool for ensuring stability of reduced order filter for high dimensional systems which is optimized adaptively in the minimum prediction error framework

a new criterion for indecomposability of positive maps we give a criterion for a positive mapping on the space of operators on a hilbert space to be indecomposable we show that this criterion can be applied to two families of positive maps these families of maps can then be used to form separability criteria for bipartite quantum states that can detect the entanglement of bound entangled quantum states

approximation schemes for nonlinear neutral optimal control systems abstract we discuss methods of approximating stable neutral functional differential equations and associated optimal control problems by sequences of optimal control problems for ordinary differential equations by introducing a class of mollified neutral functional differential equations convergence of the linear interpolating spline and the averaging approximation scheme is proved a number of numerical examples are included

a class of linear partial neutral functional differential equations with nondense domain abstract we consider a system of linear partial neutral functional differential equations with nondense domain a natural generalized notion of solutions is provided by the integral solutions we derive a variation of constants formula which allows us to transform the integral solutions of the neutral equation to solutions of an abstract volterra integral equation the basic existence and uniqueness results are given and the solutions are shown to generate an integrated semigroup

spline approximation for retarded systems and the riccati equation the purpose of this paper is to introduce a new spline approximation scheme for retarded functional differential equations the special feature of this approximation scheme is that it preserves the product space structure of retarded systems and approximates the adjoint semigroup in a strong sense these facts guarantee the convergence of the solution operators for the differential riccati equation in a strong sense numerical findings indicate a significant improvement in the convergence behaviour over both the averaging and the previous spline approximation scheme

algorithms of solutions for completely generalized mixed implicit quasi variational inclusions in this paper by applying resolvent operator technique an existence theorem of solutions for a class of completely generalized mixed implicit quasi variational inclusions involving relaxed lipschitz generalized pseudo contractive and relaxed monotone set valued mappings is proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria is also given these results of existence algorithm and convergence are new and unify and generalize some corresponding results in recent literatures

a factorization on the semi infinite interval ii applications to stable regulator problems abstract a factorization approach to the synthesis of feedback control laws for stable regulator problems is developed new feedback representations are obtained for hereditary problems with and without control delay also new derivations of representations of the optimal gain for regulator problems in hilbert space are presented

characterizations of kadec klee properties in symmetric spaces of measurable functions we present several characterizations of kadec klee properties in symmetric function spaces on the half line based on the k functional of j peetre in addition to the usual kadec klee property we study those symmetric spaces for which sequential convergence in measure respectively local convergence in measure on the unit sphere coincides with norm convergence

stability analysis of one step methods for neutral delay differential equations in this paper stability properties of one step methods for neutral functional differential equations are investigate stability regions are characterized for runge kutta methods with respect to the linear test equation begin gathered y left t right ay left t right by left t tau right cy left t tau right t geqq 0 hfill y left t right g left t right tau leqq t leqq 0 hfill end gathered 0 where a b andc are complex parameters in particular it is shown that everya stable collocation method for ordinary differential equations can be extended to a method for neutrals delay differential equations with analogous stability properties the so called np stable method we also investigate how the approximation to the derivative of the solution affects stability properties of numerical methods for neutral equations

distinguishability of quantum states by positive operator valued measures with positive partial transpose we study the distinguishability of bipartite quantum states by positive operator valued measures with positive partial transpose ppt povms the contributions of this paper include 1 we give a negative answer to an open problem of showing a limitation of a previous known method for detecting nondistinguishability 2 we show that a maximally entangled state and its orthogonal complement no matter how many copies are supplied cannot be distinguished by the ppt povms even unambiguously this result is much stronger than the previous known ones and 3 we study the entanglement cost of distinguishing quantum states it is proved that 2 3 00 1 3 11 is sufficient and necessary for distinguishing three bell states by the ppt povms an upper bound of entanglement cost of distinguishing a d d pure state and its orthogonal complement is obtained for separable operations based on this bound we are able to construct two orthogonal quantum states which cannot be distinguished unambiguously by separable povms but finite copies would make them perfectly distinguishable by local operations and classical communication we further observe that a two qubit maximally entangled state is always enough for distinguishing a d d pure state and its orthogonal complement by the ppt povms no matter the value of d in sharp contrast an entangled state with schmidt number at least d is always needed for distinguishing such two states by separable povms as an application we show that the entanglement cost of distinguishing a d d maximally entangled state and its orthogonal complement must be a maximally entangled state for d 2 which implies that teleportation is optimal and in general it could be chosen as o logd d

special factorization and riccati integral equations abstract a class of operator riccati integral equations is associated with a factorization problem in a certain banach algebra recent results concerning factorization in this algebra are used to obtain existence uniqueness and continuous dependence results for the riccati equations

local monotonicity structure of symmetric spaces with applications abstract in this paper we discuss several monotonicity properties in banach lattices we start with several general results on local structure of symmetric banach function spaces discussing in particular whether a point x e has some local property if and only if its nonincreasing rearrangement x has the same property section 2 in that section we also prove some general facts for nonincreasing rearrangements which may be of independent interest next we apply these results to find complete criteria for local monotonicity structure of lorentz spaces p and orlicz lorentz spaces sections 3 local structure of lorentz spaces 4 1 local structure of orlicz lorentz spaces 4 2 local uniform structure of lorentz spaces we conclude with the description of global monotonicity structure of lorentz spaces p section 4 3 we finish with the applications of upper monotonicity and lower monotonicity points to local best dominated approximation problems in banach lattices section 5

set valued resolvent equations and mixed variational inequalities in this paper we introduce and study a new class of variational inequalities which is called the generalized set valued mixed variational inequality the resolvent operator technique is used to establish the equivalence among generalized set valued variational inequalities fixed point problems and the generalized set valued resolvent equations this equivalence is used to study the existence of a solution of set valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems the results proved in this paper represent a significant refinement and improvement of the previously known results in this area

stability of runge kutta methods for delay integro differential equations we study stability of runge kutta rk methods for delay integro differential equations with a constant delay on the basis of the linear equation du dt lu t mu t k t t u d where l m k are constant complex matrices in particular we show that the same result as in the case k 0 koto bit 34 1994 262 267 holds for this test equation i e every a stable rk method preserves the delay independent stability of the exact solution whenever a step size of the form h m is used where m is a positive integer

segmented tau approximation for test neutral functional differential equations we use the segmented formulation of the tau method to approximate the solutions of the neutral delay differential equationy t ay t by email protected cy email protected f t t 0 y t email protected t t 0 which represents for different values of a b c and t a family of functional differential equations that some authors have considered as test equations in different numerical experimentations the tau method introduced by lanczos is an important example of how to get approximations of functions defined by a differential equation in the formulation of a step by step tau version is expected that the error is minimized at the matching points of successive steps through the study of recent papers it seems to be demonstrated that the step by step tau method is a natural and promising strategy for the numerical solution of functional differential equations in preliminary experimentation significant improvements have been obtained when compared with the numerical results obtained elsewhere

error estimation and step size control for delay differential equation solvers based on continuously embedded runge kutta sarafyan methods abstract this paper considers the use of continuously embedded runge kutta sarafyan methods for the solution of delay differential equations it discusses simple ways to improve the error estimation and step size selection strategies for delay solvers based on sarafyan methods numerical results are given which demonstrate the manner in which these estimates improve the accuracy of the solvers in a natural way

bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication we show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally the number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement a similar general condition is also shown for pure and mixed states these results offer a rare operational interpretation for three abstractly defined distancelike measures of multipartite entanglement

stability analysis of numerical methods for linear neutral volterra delay integro differential system this paper is concerned with the stability of numerical methods for linear neutral volterra delay integro differential system a sufficient condition such that the system is asymptotically stable is derived furthermore it is proved that every linear q method with email protected 1 2 1 and a stable bdf method preserve the delay independent stability of its exact solutions finally the numerical experiments are given to demonstrate the conclusions

numerical treatment of delay differential equations by hermite interpolation a class of numerical methods for the treatment of delay differential equations is developed these methods are based on the wellknown runge kutta fehlberg methods the retarded argument is approximated by an appropriate multipoint hermite interpolation the inherent jump discontinuities in the various derivatives of the solution are considered automatically problems with piecewise continuous right hand side and initial function are treated too real life problems are used for the numerical test and a comparison with other methods published in literature

generalized quasi variational like inclusions with nonconvex functionals in this paper two new concepts of h subdifferential and h proximal mappings of a proper functional is introduced in hilbert spaces the existence and lipschitz continuity of h proximal mapping of a proper functional are proved by applying these concepts we introduce and study a class of generalized quasi variational like inclusions with a nonconvex functional a new iterative algorithms for finding the approximate solutions and the convergence criteria of the iterative sequences generated by the algorithm are also given these algorithm and existence result generalize many known results in the literature

local indistinguishability more nonlocality with less entanglement we provide a first operational method for checking local indistinguishability of orthogonal states it originates from that in ghosh et al phys rev lett 87 5807 2001 though we deal with pure states our method shows that probabilistic local distinguishing is possible for a complete multipartite orthogonal basis if and only if all vectors are product also it leads to local indistinguishability of a set of orthogonal pure states of 3 multiply sign in circle 3 which shows that one can have more nonlocality with less entanglement where more nonlocality is in the sense of increased local indistinguishability of orthogonal states this is to our knowledge the only known example where d orthogonal states in d multiply sign in circle d are locally indistinguishable

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

limitations on separable measurements by convex optimization we prove limitations on locc and separable measurements in bipartite state discrimination problems using techniques from convex optimization specific results that we prove include an exact formula for the optimal probability of correctly discriminating any set of either three or four bell states via locc or separable measurements when the parties are given an ancillary partially entangled pair of qubits an easily checkable characterization of when an unextendable product set is perfectly discriminated by separable measurements along with the first known example of an unextendable product set that cannot be perfectly discriminated by separable measurements and an optimal bound on the success probability for any locc or separable measurement for the recently proposed state discrimination problem of yu duan and ying

entanglement cost of two qubit orthogonal measurements the entanglement cost of a bipartite measurement is the amount of shared entanglement two participants need to use up in order to carry out the given measurement by means of local operations and classical communication we numerically investigate the entanglement cost of generic orthogonal measurements on two qubits our results strongly suggest that for almost all measurements of this kind the entanglement cost is strictly greater than the average entanglement of the eigenstates associated with the measurements implying that the nonseparability of a two qubit orthogonal measurement is generically distinct from the nonseparability of its eigenstates

local approach to kadec klee properties in symmetric function spaces abstract we prove several results concerning local approach to kadec klee properties with respect to global local convergence in measure in symmetric banach function spaces which may be of independent interest moreover we prove characterizations of these properties in the lorentz spaces finally we show applications of h g and h l points to the local best dominated approximation problems in banach lattices

distinguishability and indistinguishability by local operations and classical communication it is well known that orthogonal quantum states can be distinguished perfectly however if we assume that these orthogonal quantum states are shared by spatially separated parties the distinguishability of these shared quantum states may be completely different we show that a set of linearly independent quantum states formula see text where u m n are generalized pauli matrices cannot be discriminated deterministically or probabilistically by local operations and classical communication on the other hand any l maximally entangled states from this set are locally distinguishable if l l 1 or 2d the explicit projecting measurements are obtained to locally discriminate these states as an example we show that four werner states are locally indistinguishable

generalized set valued variational inclusions and resolvent equations in this paper we establish the equivalence between the generalized set valued variational inclusions the resolvent equations and the fixed point problem using the resolvent operator technique this equivalence is used to suggest and analyze some iterative algorithms for solving the generalized set valued variational inclusions and related optimization problems

local distinguishability of any three quantum states we prove that any three linearly independent pure quantum states can always be locally distinguished with nonzero probability regardless of their dimension entanglement or multipartite structure almost always all three states can be unambiguously identified the only exceptional case where one state is locally knowable but the other two are not is found among multi qubit states

construction of highly stable parallel two step runge kutta methods for delay differential equations it is shown that any a stable two step runge kutta method of order p and stage order q p for ordinary differential equations can be extended to the p stable method of uniform order p p for delay differential equations

extended backward differentiation methods in the numerical solution of the neutral volterra integro differential equations the numerical solution of first order volterra integro differential equations of neutral type with continuous kernel is considered preliminary results from the application of extended backward differentiation methods are given and comparisons are made with adams bashforth adams moulton predictor corrector methods and collocation methods

on geometric structure of symmetric spaces abstract in this article we discuss local approach to strict k monotonicity and local uniform rotundity in symmetric spaces we prove several general results on local structure of symmetric spaces e showing relation between strict monotonicity and strict k monotonicity and the kadec klee property for global convergence in measure we also present the full criteria for points of upper k monotonicity in lorentz spaces p w for degenerated weight function w next we characterize local uniform rotundity in symmetric spaces e proving several correspondences between x e a point of local uniform rotundity and its decreasing rearrangement x and absolute value x finally we apply these results to find complete criteria for local uniform rotundity of lorentz spaces p w

spline approximation for systems of linear neutral delay differential equations abstract we derive a new finite dimensional semidiscrete approximation scheme for systems of linear neutral delay differential equations and prove convergence results our construction extends to neutral delay equations results which were previously only available for retarded delay equations

distinguishability of quantum states by separable operations in this paper we study the distinguishability of multipartite quantum states by separable operations we first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations an analytical version of this condition is derived for the case of d 1 pure states where d is the total dimension of the state space under consideration a number of interesting consequences of this result are then carefully investigated remarkably we show there exists a large class of 2 otimes 2 separable operations not being realizable by local operations and classical communication before our work only a class of 3 otimes 3 nonlocal separable operations was known bennett phys rev a 59 1070 1999 we also show that any basis of the orthogonal complement of a multipartite pure state is indistinguishable by separable operations if and only if this state cannot be a superposition of one or two orthogonal product states i e has an orthogonal schmidt number not less than three thus generalize the recent work about indistinguishable bipartite subspaces watrous phys rev lett 95 080505 2005 notably we obtain an explicit construction of indistinguishable subspaces of dimension 7 or 6 by considering a composite quantum system consisting of two qutrits resp three qubits which is slightly better than the previously known indistinguishable bipartite subspace with dimension 8

four locally indistinguishable ququad ququad orthogonal maximally entangled states we explicitly exhibit a set of four ququad ququad orthogonal maximally entangled states that cannot be perfectly distinguished by means of local operations and classical communication before our work it was unknown whether there is a set of d locally indistinguishable d d orthogonal maximally entangled states for some positive integer d we further show that a 2 2 maximally entangled state can be used to locally distinguish this set of states without being consumed thus demonstrate a novel phenomenon of entanglement discrimination catalysis based on this set of states we construct a new set k consisting of four locally indistinguishable states such that k m with 4 m members is locally distinguishable for some m greater than one as an immediate application we construct a noisy quantum channel with one sender and two receivers whose local zero error classical capacity can achieve the full dimension of the input space but only with a multi shot protocol

generalized multivalued quasi variational inequalities in this paper we introduce and study a new class of variational inequalities known as generalized multivalued quasi variational inequalities this class is the most general and unifying one using essentially the projection technique we establish the equivalence between this class and the implicit wiener hopf equations this equivalence is used to suggest a number of iterative algorithms for solving the generalized multivalued quasi variational inequalities the convergence analysis of these algorithms is also studied the results proved in this paper represent a significant improvement and refinement of the previously known results in this area

distinguishability of bell states more than two multipartite orthogonal states cannot always be discriminated if only local operations and classical communication locc are allowed we show that four bell states cannot be discriminated by locc even probabilistically using the separability properties of a four party unlockable bound entangled state using an existing inequality among the measures of entanglement we show that any three bell states cannot be discriminated with certainty by locc exploiting the inequality we calculate the distillable entanglement of a certain class of 4 multiply sign in circle 4 mixed states

unextendible product bases uncompletable product bases and bound entanglement we report new results and generalizations of our work on unextendible product bases upb uncompletable product bases and bound entanglement we present a new construction for bound entangled states based on product bases which are only completable in a locally extended hilbert space we introduce a very useful representation of a product basis an orthogonality graph using this representation we give a complete characterization of unextendible product bases for two qutrits we present several generalizations of upbs to arbitrary high dimensions and multipartite systems we present a sufficient condition for sets of orthogonal product states to be distinguishable by separable superoperators we prove that bound entangled states cannot help increase the distillable entanglement of a state beyond its regularized entanglement of formation assisted by bound entanglement

on the resolvent of linear nonautonomous partial functional differential equations abstract we give sufficient conditions for the existence of the resolvent operator for nonautonomous linear partial differential equations with delay where the highest order derivatives are undelayed furthermore we analyse the connection between the resolvent and the solution operator of the homogeneous equation

dissipative approximations to neutral ddes abstract we approximate the solution of a neutral dde with the solution of a retarded dde to exploit the fact that retarded ddes are much easier to solve numerically after demonstrating the validity of the approach we develop a m atlab program ddensd that solves ddes of neutral type the new approach and a simple user interface make it easy to solve a wide range of test problems from the literature to moderate accuracy

a twofold spline approximation for finite horizon lqg control of hereditary systems in this paper an approximation scheme is developed for the solution of the linear quadratic gaussian lqg control on a finite time interval for hereditary systems with multiple noncommensurate delays and distributed delay the solution here proposed is achieved by means of two approximating subspaces the first one to approximate the riccati equation for control and the second one to approximate the filtering equations since the approximating subspaces have finite dimension the resulting equations can be implemented the convergence of the approximated control law to the optimal one is proved simulation results are reported on a wind tunnel model showing the high performance of the method

distinguishing bipartitite orthogonal states using locc best and worst cases two types of results are presented for distinguishing pure bipartite quantum states using local operations and classical communications we examine sets of states that can be perfectly distinguished in particular showing that any three orthogonal maximally entangled states in c3 c3 form such a set in cases where orthogonal states cannot be distinguished we obtain upper bounds for the probability of error using locc taken over all sets of k orthogonal states in cn cm in the process of proving these bounds we identify some sets of orthogonal states for which perfect distinguishability is not possible

iterative methods for generalized nonlinear variational inequalities abstract in this paper we establish the equivalence between the generalized nonlinear variational inequalities and the generalized wiener hopf equations this equivalence is used to suggest and analyze a number of iterative algorithms for solving generalized variational inequalities we also discuss the convergence analysis of the proposed algorithms as a special case we obtain various known results from our results

adams methods for neutral functional differential equations in this paper adams type methods for the special case of neutral functional differential equations are examined it is shown thatk step methods maintain orderk 1 for sufficiently small step size in a sufficiently smooth situation however when these methods are applied to an equation with a non smooth solution the order of convergence is only one some computational considerations are given and numerical experiments are presented

spline approximations for linear nonautonomous delay systems we develop a semi discrete approximation framework for linear nonautonomous nonhomogeneous functional differential equations of retarded type the approximation schemes are constructed and convergence results are obtained through the approximation of an associated abstract evolution operator computer implementation of the schemes is outlined and a spline based method included in the framework is constructed extensions of the semi discrete methods to schemes incorporating full discretization and difference equation approximation are also discussed numerical results for several examples demonstrating the feasibility of the schemes are presented

convergence of one leg methods for neutral delay integro differential equations the error analysis of one leg methods for a class of nonlinear neutral delay integro differential equations ndides is given it is proved that an a stable one leg method with an appropriate quadrature rule applied to ndides is convergent of order at least min p q 12 if the one leg method is consistent of order p2 in the classical sense for odes and the error order of the quadrature rule is o hq 1 numerical examples further confirm the theoretical results

a family of indecomposable positive linear maps based on entangled quantum states abstract we introduce a new family of indecomposable positive linear maps based on entangled quantum states central to our construction is the notion of an unextendible product basis the construction lets us create indecomposable positive linear maps in matrix algebras of arbitrary high dimension

convergence of runge kutta methods for neutral delay integro differential equations the present paper is concerned with the convergence of numerical methods to solve initial value problems of neutral delay integro differential equations ndides the error estimation of runge kutta methods for a class of nonlinear systems of ndides are derived some numerical experiments are given which confirm the theoretical results

unextendible product bases and bound entanglement an unextendible product basis upb for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state we give examples of upbs and show that the uniform mixed state over the subspace complementary to any upb is a bound entangled state we exhibit a tripartite 2 3 2 3 2 upb whose complementary mixed state has tripartite entanglement but no bipartite entanglement i e all three corresponding 2 3 4 bipartite mixed states are unentangled we show that members of a upb are not perfectly distinguishable by local positive operator valued measurements and classical communication s0031 9007 99 09360 6

stability of the radau ia and lobatto iiic methods for neutral delay differential system abstract numerical stability is considered for several runge kutta methods to systems of neutral delay differential equations the linear stability analysis is adopted to the system adapted with the equistage interpolation process as well as the continuous extension the runge kutta methods are shown to have the numerical stability similar to the analytical asymptotic stability with arbitrary stepsize when certain assumptions hold for the logarithmic matrix norm on the coefficient matrices of the ndde system

advance in the theory of variable stepsize variable formula methods for ordinary differential equations the theory of the constant stepsize constant formula methods cscfm s for solving initial value problems for ordinary differential equations ode s is well developed however the integration methods are often used as variable stepsize variable formula methods vsvfm s in the codes for automatic solution of ode s this fact explains why it is necessary to develop a rigorous theory for the vsvfm s also results obtained until now in the efforts to develop a theory for the vsvfm s are presented in a systematic way and compared with the well known results for cscfm s the comparison is used to outline the directions in which further efforts in the attempt to improve the theoretical results and to obtain new results are most needed the integration methods can be separated into two large groups implicit methods and explicit methods including here the predictor corrector schemes it is discussed what kind of results are needed for each of these two groups assume that a set f of cscfm s is given from a practical point of view it is highly desirable that the cscfm s belonging to set f have the following property if every cscfm from set f is consistent zero stable and convergent then any vsvfm induced by the cscfm s of set f is also consistent zero stable and convergent for a sufficiently large class of grids a theorem concerning a class of cscfm s with this property is presented the application of this theorem in the selection of methods for solving large systems of ode s arising after the space discretization of air pollution models is discussed it is explained why the vsvfm s based on this class provide a very efficient computational process in the treatment of air pollution models

convergence analysis of the solution of retarded and neutral delay differential equations by continuous numerical methods we have recently developed a generic approach to solving retarded and neutral delay differential equations ddes the approach is based on the use of an explicit continuous runge kutta formula and employs defect control the approach can be applied to problems with state dependent delays and vanishing delays in this paper we determine convergence properties for the numerical solution associated with methods that implement this approach we first analyze such properties for retarded ddes and then the analysis is extended to the case of neutral ddes ndes such an extension is particularly important since ndes have received little attention in the literature the main result we establish is that the global error of the numerical solution can be efficiently and reliably controlled by directly monitoring the magnitude of the associated defect our analysis can also be applied directly to other numerical methods which use defect error control based on runge kutta formulas for ddes

preserving stability implicit euler method for nonlinear volterra and neutral functional differential equations in banach space this paper is concerned with the contractivity and asymptotic stability properties of the implicit euler method iem for nonlinear functional differential equations fdes these properties are first analyzed for volterra fdes and then the analysis is extended to the case of neutral fdes nfdes such an extension is particularly important since nfdes are more general and have received little attention in the literature the main result we establish is that the iem with linear interpolation can completely preserve these stability properties of the analytical solution to such fdes

spline approximations for neutral functional differential equations based on an abstract approximation theorem for text c 0 semigroups trotter kato theorem we present an algorithm where linear autonomous functional differential equations of neutral type are approximated by sequences of ordinary differential equations of increasing dimensions numerical examples using cubic splines and cubic hermite splines illustrate the theoretical results

numerical approximation for the infinite dimensional discrete time optimal linear quadratic regulator problem an abstract approximation framework is developed for the finite and infinite horizon discrete time linear quadratic regulator problems for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional hilbert space the schemes included in the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law convergence arguments are given examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered spline based finite element schemes for these classes of problems together with numerical results are presented and discussed