stability of homomorphisms for a 3d cauchy jensen type functional equation on c ternary algebras abstract in this paper we investigate homomorphisms between c ternary algebras and derivations on c ternary algebras associated with the following cauchy jensen type additive functional equation f x y 2 z f x z 2 y f y z 2 x 2 f x f y f z

extension of the berlekamp massey algorithm to n dimensions abstract we present an algorithm for finding a minimal set of linear recurring relations which are valid for a given n dimensional array over any field where the minimality is defined with respect to the partial order over the n dimensional lattice the algorithm is an extension of our two dimensional version of the berlekamp massey algorithm to more than two dimensions the n dimensional theory is based on more general concepts which can be reduced into those of the two dimensional theory in the previous paper in a typical case the resulting set of polynomials characterizing the minimal linear recurring relations proves to be a groebner basis of the ideal defined by the array and consequently the structure of an n dimensional linear feedback shift register with the minimum number of storage devices which can generate the array is determined by it

fast decoding of algebraic geometric codes up to the designed minimum distance we present a decoding algorithm for algebraic geometric codes from regular plane curves in particular the hermitian curve which corrects all error patterns of weight less than d 2 with low complexity the algorithm is based on the majority scheme of feng and rao 1993 and uses a modified version of sakata s 1988 generalization of the berlekamp massey algorithm

decoding binary 2 d cyclic codes by the 2 d berlekamp massey algorithm a method of decoding two dimensional 2 d cyclic codes by applying the 2 d berlekamp massey algorithm is proposed to explain this decoding method the author introduces a subclass of 2 d cyclic codes which are called 2 d bch codes due to their similarity with bch codes it is shown that there are some short 2 d cyclic codes with a better cost parameter value the merit of the approach is verified by showing several simple examples of 2 d cyclic codes

the numerical solution of linear multi term fractional differential equations systems of equations in this paper we show how the numerical approximation of the solution of a linear multi term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity we begin by showing how our method applies to a simple class of problems and we give a convergence result we solve the bagley torvik equation as an example we show how the method can be applied to a general linear multi term equation and give two further examples

multipliers and dual operator algebras abstract in a previous paper we showed how the main theorems characterizing operator algebras and operator modules fit neatly into the framework of the noncommutative shilov boundary and more particularly via the left multiplier operator algebra of an operator space as well as giving new characterization theorems the approach of that paper allowed many of the hypotheses of the earlier theorems to be eliminated recent progress of the author with effros and zarikian now enables weak versions of these characterization theorems for example we prove a result analogous to sakai s famous characterization of von neumann algebras as the c algebras with predual namely that the weakly closed unital not necessarily selfadjoint subalgebras of b h for a hilbert space h are exactly the unital operator algebras which possess an operator space predual this removes one of the hypotheses from an earlier characterization due to le merdy we also show that the multiplier operator algebras of dual operator spaces are dual operator algebras using this we refine several known results characterizing dual operator modules

fast generalized minimum distance decoding of algebraic geometry and reed solomon codes generalized minimum distance gmd decoding is a standard soft decoding method for block codes we derive an efficient general gmd decoding scheme for linear block codes in the framework of error correcting pairs special attention is paid to reed solomon rs codes and one point algebraic geometry ag codes for rs codes of length n and minimum hamming distance d the gmd decoding complexity turns out to be in the order o nd where the complexity is counted as the number of multiplications in the field of concern for ag codes the gmd decoding complexity is highly dependent on the curve in consideration it is shown that we can find all relevant error erasure locating functions with complexity o o sub 1 nd where o sub 1 is the size of the first nongap in the function space associated with the code a full gmd decoding procedure for a one point ag code can be performed with complexity o dn sup 2

a generalized forney formula for algebraic geometric codes this correspondence contains a straightforward generalization of decoding of bch codes to the decoding of algebraic geometric codes couched in terms of varieties ideals and grobner bases this consists of 1 a berlekamp massey type lattice shifting row reduction algorithm with majority voting similar to algorithms in the current literature 2 a realization that it produces a minimal grobner basis b for the error locator ideal i v relative to a particular weighted total degree monomial ordering 3 a factoring of that basis into several minimal plex bases that facilitates finding the variety v of error positions and 4 a direct generalization of forney s formula to calculate error magnitudes using functions spl sigma p which are by products of this factoring

anomalous transport in external fields continuous time random walks and fractional diffusion equations extended the continuous time random walk ctrw in a homogeneous velocity field and in arbitrary force fields is studied within the extended ctrw scheme anomalous transport properties due to long tailed waiting time or jump length distributions are consistently introduced the connections with generalised diffusion equations in a potential field are discussed these equations being of fractional order in particular the problems of a constant and a hookean linear force i e of a linear and a parabolic potential are worked out

morita rieffel equivalence and spectral theory for integrable automorphism groups of c algebras abstract given a c dynamical system a g we discuss conditions under which subalgebras of the multiplier algebra m a consisting of fixed points for are morita rieffel equivalent to ideals in the crossed product of a by g in case g is abelian we also develop a spectral theory giving a necessary and sufficient condition for to be equivalent to the dual action on the cross sectional c algebra of a fell bundle in our main application we show that a proper action of an abelian group on a locally compact space is equivalent to a dual action

fractional calculus and continuous time finance in this paper we present a rather general phenomenological theory of tick by tick dynamics in financial markets many well known aspects such as the levy scaling form follow as particular cases of the theory the theory fully takes into account the non markovian and non local character of financial time series predictions on the long time behaviour of the waiting time probability density are presented finally a general scaling form is given based on the solution of the fractional diffusion equation

on the number of correctable errors for some ag codes an algorithm that for codes from a regular plane curve corrects up to d 2 m sup 2 8 m 4 9 8 errors where d is the designed distance and m is the degree of the curve was presented in an earlier work see ibid vol 35 p 811 21 1989 it is now shown that this bound is the best possible for the algorithm considered

continuous time random walks in finite domains and general boundary conditions some formal considerations the present work studies continuous time random walks ctrws in a finite domain a broad class of boundary conditions of which absorbing and reflecting boundaries are particular cases is considered it is shown how any ctrw in this class can be mapped to a ctrw in an infinite domain this may allow applying well known techniques for infinite ctrws to the problem of obtaining the fluid limit for finite domain ctrws where the fluid limit or hydrodynamic limit refers to the partial differential equation describing the long time and large distance behaviour of the system as an illustration the fluid limit equation and its propagator are obtained explicitly in the case of purely reflecting boundaries we also derive the modification of the riemann liouville fractional differential operators implementing the reflecting boundary conditions

on the minimal partial realization of 2d discrete linear shift invariant systems the partial realization problem for 2d discrete linear shift invariant systems is discussed the authors attempt to establish a reasonable definition of minimality and propose a method for finding the degree and the system function of a minimal realization of a 2d linear system characterized by a given 2d impulse response array the method used is based on the 2d berlekamp massey algorithm which has a close connection with the 2d hankel matrix derived from the 2d array while it compares in efficiency with other methods for identification and approximation of 2d linear systems it gives a novel approach to the problem in the sense that one does not need any knowledge or assumptions concerning the system degree

numerical methods for the solution of partial differential equations of fractional order anomalous diffusion is a possible mechanism underlying plasma transport in magnetically confined plasmas to model this transport mechanism fractional order space derivative operators can be used here the numerical properties of partial differential equations of fractional order 1 2 are studied two numerical schemes an explicit and a semi implicit one are used in solving these equations two different discretization methods of the fractional derivative operator have also been used the accuracy and stability of these methods are investigated for several standard types of problems involving partial differential equations of fractional order

finding recursions for multidimensional arrays we produce a concise description of sakata s algorithm for finding recursion relations that are valid for an n dimensional array the new analysis extends to limit points which are excluded by previous authors we show that under a natural hypothesis the algorithm becomes stationary below each limit point and in particular constructs a full set of recursion relations for a recursive array at some finite point the method used to justify the algorithm stresses the duality between the fundamental extension operation of sakata and the s polynomial operation of buchberger

approximate homomorphisms and derivations between c ternary algebras in 1940 ulam proposed the famous ulam stability problem in this paper we introduce a general cauchy jensen functional equation and prove the generalized ulam stability of c ternary homomorphisms and c ternary derivations in c ternary algebras for the general cauchy jensen equation

fast decoding of multipoint codes from algebraic curves multipoint codes are a broad class of algebraic geometry codes derived from algebraic functions which have multiple poles and or zeros on an algebraic curve thus they are more general than one point codes which are an important class of algebraic geometry codes in the sense that they can be decoded efficiently using the berlekamp massey sakata algorithm we present a fast method for decoding multipoint codes from a plane curve particularly a hermitian curve our method with some adaptation can be applied to decode multipoint codes from a general algebraic curve embedded in the n dimensional affine space fqn over a finite field fq so that those algebraic geometry codes can be decoded efficiently if the dimension n of the affine space including the defining curve is small

decoding of codes defined by a single point on a curve a decoding algorithm for certain codes from algebraic curves is presented the dual code which is used for decoding is formed by evaluating rational functions having poles at a single point a theoretical foundation is developed from which an improved bound for the minimum distance and results on decoding up to that bound are derived the decoding is done by a computationally efficient berlekamp massey type algorithm which is intrinsic to the curve

governing equations and solutions of anomalous random walk limits fachbereich mathematik university of dortmund 44221 dortmund germany received 5 june 2002 published 30 december 2002 continuous time random walks model anomalous diffusion coupling allows the magnitude of particlejumps to depend on the waiting time between jumps governing equations for the long time scaling limits ofthese models are found to have fractional powers of coupled space and time differential operators explicitsolutions and scaling properties are presented for these equations which can be used to model ow in porousmedia and other physical systems doi 10 1103 physreve 66 060102 pacs number s 05 40 2a 02 50 cw 05 60 2k 47 55 mhi introduction

systemes dynamiques non commutatifs et moyennabilite on introduit la notion de fonction de type positif relativement a un systeme dynamique c dont les proprietes sont analogues a celles des fonctions de type positif classiques on montre que dans le cas d un groupe discret g agissant sur une algebre de von neumann m la moyennabilite de l action est equivalente a l existence d une suite bornee de fonctions de type positif sur g a support fini a valeurs dans le centre z m de m qui converge vers 1 pour la topologie de la convergence simple ultrafaible

operator space structure of jc triples and tros i we embark upon a systematic investigation of operator space structure of jc triples via a study of the tros ternary rings of operators they generate our approach is to introduce and develop a variety of universal objects including universal tros by which means we are able to describe all possible operator space structures of a jc triple via the concept of reversibility we obtain characterisations of universal tros over a wide range of examples we apply our results to obtain explicit descriptions of operator space structures of cartan factors regardless of dimension

uniqueness universality and homogeneity of the noncommutative gurarij space we realize the noncommutative gurarij space ng defined by oikhberg as the fraisse limit of the class of finite dimensional 1 exact operator spaces as a consequence we deduce that the noncommutative gurarij space is unique up to completely isometric isomorphism homogeneous and universal among separable 1 exact operator spaces we also prove that ng is the unique separable nuclear operator space with the property that the canonical triple morphism from the universal tro to the triple envelope is an isomorphism we deduce from this fact that ng does not embed completely isometrically into an exact c algebra and it is not completely isometrically isomorphic to a c algebra or to a tro we also provide a canonical construction of ng which shows that the group of surjective complete isometries of ng is universal among polish groups analog results are proved in the commutative setting and more generally for m n spaces in particular we provide a new characterization and canonical construction of the gurarij banach space

a fixed point method for perturbation of bimultipliers and jordan bimultipliers in c ternary algebras let a be a c ternary algebra a c bilinear t a a a is called a c ternary algebra bi multiplier if it satisfies t abc d t a b cd t a bcd abt c d for all a b c d a also the mapping t a a a is a called c ternary algebra jordan bimultiplier if it satisfies t aaa a t a a aa t a aaa aat a a for all a a using the fixed point method we investigate the generalized hyers ulam rassias stability of bimultipliers and jordan bimultipliers in c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias proc am math soc 72 297 1978

δ sequences and evaluation codes defined by plane valuations at infinity we introduce the concept of sequence a sequence generates a well ordered semigroup s in z or r we show how to construct and compute parameters for the dual code of any evaluation code associated with a weight function defined by from the polynomial ring in two indeterminates to a semigroup s as above we prove that this is a simple procedure which can be understood by considering a particular class of valuations of function fields of surfaces called plane valuations at infinity we also give algorithms to construct an unlimited number of sequences of the different existing types and so this paper provides the tools to know and use a new large set of codes

homomorphisms in c ternary algebras and jb triples abstract in this paper we investigate homomorphisms between c ternary algebras and derivations on c ternary algebras and homomorphisms between j b triples and derivations on j b triples associated with the following apollonius type additive functional equation f z x f z y 1 2 f x y 2 f z x y 4

duality and operator algebras automatic weak continuity and applications abstract we investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras and give several applications of the surprising fact that certain maps are always weak continuous on dual spaces in particular if x is a subspace of a c algebra a and if a a satisfies ax x then we show that the function x ax on x is automatically weak continuous if either a x is a dual operator space or b a x x and x is a dual banach space these results hinge on a generalization to banach modules of tomiyama s famous theorem on contractive projections onto a c subalgebra applications include a new characterization of the weakly closed possibly nonunital and nonselfadjoint operator algebras and a generalization of the theory of w modules to the framework of modules over such algebras we also give a banach module characterization of weakly closed spaces of operators which are invariant under the action of a von neumann algebra

fluid limit of nonintegrable continuous time random walks in terms of fractional differential equations the fluid limit of a recently introduced family of nonintegrable nonlinear continuous time random walks is derived in terms of fractional differential equations in this limit it is shown that the formalism allows for the modeling of the interaction between multiple transport mechanisms with not only disparate spatial scales but also different temporal scales for this reason the resulting fluid equations may find application in the study of a large number of nonlinear multiscale transport problems ranging from the study of self organized criticality to the modeling of turbulent transport in fluids and plasmas

algebraic geometry codes the theory of error correcting codes derived from curves in an algebraic geometry was initiated by the work of goppa as generalizations of bose chaudhuri hocquenghem bch reed solomon rs and goppa codes the development of the theory has received intense consideration since that time and the purpose of the paper is to review this work elements of the theory of algebraic curves at a level sufficient to understand the code constructions and decoding algorithms are introduced code constructions from particular classes of curves including the klein quartic elliptic and hyperelliptic curves and hermitian curves are presented decoding algorithms for these classes of codes and others are considered the construction of classes of asymptotically good codes using modular curves is also discussed

efficient forney functions for decoding ag codes using a forney formula to solve for the error magnitudes in decoding algebraic geometric ag codes requires producing functions spl sigma sub p which are 0 at all but one point p of the variety of the error locator ideal the best such function is produced here in a reasonably efficient way from a lex grobner basis this lex basis is in turn produced efficiently from a weighted grevlex basis by using the fglm algorithm these two steps essentially complete the efficient decoding scheme based on a forney formula started in the author s previous work see ibid vol 42 p 1263 8 1996

strict optimal rational approximants of multisequences the synthesis problem of multisequences of elements of a field f is studied a new way of approximation by rational functions to multisequences is introduced different from the usual approach by optimal rational approximant profile in the proposed strict optimal rational approximant of a multisequence the components of the optimal rational approximant are not required to have the same denominator an algorithm to obtain a strict optimal rational approximant profile is established the relation between optimal rational approximant and strict optimal rational approximant is studied

stochastic foundations of fractional dynamics it is shown that fractional diffusion equations arise very naturally as the limiting dynamic equations of all continuous time random walks with decoupled temporal and spatial memories and with either temporal or spatial scale invariance fractal walks thus enlarging their stochastic foundations hitherto restricted to a particular case of fractal walk r hilfer and l anton phys rev e 51 r848 1995

physical pictures of transport in heterogeneous media advection dispersion random walk and fractional derivative formulations 1 the basic conceptual picture and theoretical basis for development of transport equations in porous media are examined the general form of the governing equations is derived for conservative chemical transport in heterogeneous geological formations for single realizations and for ensemble averages of the domain the application of these transport equations is focused on accounting for the appearance of non fickian anomalous transport behavior the general ensemble averaged transport equation is shown to be equivalent to a continuous time random walk ctrw and reduces to the conventional forms of the advection dispersion equation ade under highly restrictive conditions fractional derivative formulations of the transport equations both temporal and spatial emerge as special cases of the ctrw in particular the use in this context of levy flights is critically examined in order to determine chemical transport in field scale situations the ctrw approach is generalized to nonstationary systems we outline a practical numerical scheme similar to those used with extended geological models to account for the often important effects of unresolved heterogeneities

continuous time random walks in periodic systems fluid limit and fractional differential equations on the circle in this paper the continuous time random walk on the circle is studied we derive the corresponding generalized master equation and discuss the effects of topology especially important when levy flights are allowed then we work out the fluid limit equation formulated in terms of the periodic version of the fractional riemann liouville operators for which we provide explicit expressions finally we compute the propagator in some simple cases the analysis presented herein should be relevant when investigating anomalous transport phenomena in systems with periodic dimensions

linear feedback shift registers and the minimal realization problem the first author is partially supported by grants mineco mtm2017 83624 p mtm2017 90682 redt and upv ehu giu16 42 the second author is partially supported by grants mineco mtm2017 83624 p and mtm2017 90682 redt

algebraic geometric codes and multidimensional cyclic codes a unified theory and algorithms for decoding using grobner bases it is proved that any algebraic geometric ag code can be expressed as a cross section of an extended multidimensional cyclic code both ag codes and multidimensional cyclic codes are described by a unified theory of linear block codes defined over point sets ag codes are defined over the points of an algebraic curve and an m dimensional cyclic code is defined over the points in m dimensional space the power of the unified theory is in its description of decoding techniques using grobner bases in order to fit an ag code into this theory a change of coordinates must be applied to the curve over which the code is defined so that the curve is in special position for curves in special position all computations can be performed with polynomials and this also makes it possible to use the theory of grobner bases next a transform is defined for ag codes which generalizes the discrete fourier transform the transform is also related to a grobner basis and is useful in setting up the decoding problem in the decoding problem a key step is finding a grobner basis for an error locator ideal for ag codes multidimensional cyclic codes and indeed any cross section of an extended multidimensional cyclic code sakata s algorithm can be used to find linear recursion relations which hold on the syndrome array in this general context the authors give a self contained and simplified presentation of sakata s algorithm and present a general framework for decoding algorithms for this family of codes in which the use of sakata s algorithm is supplemented by a procedure for extending the syndrome array

diffusion equations for a markovian jumping process we consider a markovian jumping process which is defined in terms of the jump size distribution and the waiting time distribution with a position dependent frequency in the diffusion limit we assume the power law form for the frequency for small steps we derive the fokker planck equation and show the presence of the normal diffusion subdiffusion and superdiffusion for the l evy distribution of the step size we construct a fractional equation which possesses a variable coefficient and solve it in the diffusion limit then we calculate fractional moments and define the fractional diffusion coefficient as a natural extension to the cases with the divergent variance we also solve the master equation numerically and demonstrate that there are deviations from the l evy stable distribution for large wave numbers

stable equilibrium based on levy statistics a linear boltzmann equation approach to obtain further insight on possible power law generalizations of boltzmann equilibrium concepts we consider stochastic collision models the models are a generalization of the rayleigh collision model for a heavy one dimensional particle m interacting with ideal gas particles with a mass m m similar to previous approaches we assume elastic uncorrelated and impulsive collisions we let the bath particle velocity distribution function to be of general form namely we do not postulate a specific form of power law equilibrium we show under certain conditions that the velocity distribution function of the heavy particle is levy stable the maxwellian distribution being a special case we demonstrate our results with numerical examples the relation of the power law equilibrium obtained here to thermodynamics is discussed in particular we compare between two models a thermodynamic and an energy scaling approaches these models yield insight into questions like the meaning of temperature for power law equilibrium and into the issue of the universality of the equilibrium i e is the width of the generalized maxwellian distribution functions obtained here independent of coupling constant to the bath

the art of signaling fifty years of coding theory in 1948 shannon developed fundamental limits on the efficiency of communication over noisy channels the coding theorem asserts that there are block codes with code rates arbitrarily close to channel capacity and probabilities of error arbitrarily close to zero fifty years later codes for the gaussian channel have been discovered that come close to these fundamental limits there is now a substantial algebraic theory of error correcting codes with as many connections to mathematics as to engineering practice and the last 20 years have seen the construction of algebraic geometry codes that can be encoded and decoded in polynomial time and that beat the gilbert varshamov bound given the size of coding theory as a subject this review is of necessity a personal perspective and the focus is reliable communication and not source coding or cryptography the emphasis is on connecting coding theories for hamming and euclidean space and on future challenges specifically in data networking wireless communication and quantum information theory

weak exactness for dual operator spaces we introduce a new tensor product circle times sigma lambda and study the weak condition c which is also called weak exactness for dual operator spaces our definition of weak condition c is equivalent to kirchberg s notion of weak exactness in the case of von neumann algebras we also study the connection of weak exact w tros with their linking von neumann algebras and study the structure of exact respectively nuclear w tros c 2007 elsevier inc all rights reserved

uncoupled continuous time random walks solution and limiting behavior of the master equation a detailed study is presented for a large class of uncoupled continuous time random walks ctrws the master equation is solved for the mittag leffler survival probability the properly scaled diffusive limit of the master equation is taken and its relation with the fractional diffusion equation is discussed finally some common objections found in the literature are thoroughly reviewed

on determining the independent point set for doubly periodic arrays and encoding two dimensional cyclic codes and their duals for the purpose of encoding two dimensional cyclic tdc codes an effective algorithm for finding the independent point set of an arbitrary module of doubly periodic dp arrays is proposed in addition a method for determining the characteristic ideal of a given set of dp arrays is exhibited with the aid of these methods it is possible to specify the structure of the generator and check ideals of tdc codes by applying this algorithm to nonsemisimple binary tdc codes with small areas several optimal linear codes have been found and their previously unknown tdc structures have been exhibited

stable equilibrium based on levy statistics stochastic collision models approach we investigate equilibrium properties of two very different stochastic collision models i the rayleigh particle and ii the driven maxwell gas for both models the equilibrium velocity distribution is a levy distribution the maxwell distribution being a special case we show how these models are related to fractional kinetic equations our work demonstrates that a stable power law equilibrium which is independent of details of the underlying models is a natural generalization of maxwell s velocity distribution

isomorphisms between c ternary algebras in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following generalized cauchy jensen additive mapping 2f j 1pxj2 j 1dyj j 1pf xj 2 j 1df yj this is applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the rassias stability theorem that appeared in his paper on the stability of the linear mapping in banach spaces see proc amr math soc 72 297 300 1978

rational approximation of 2 d linear discrete systems in this paper we present an efficient procedure to obtain a rational model for a 2 d linear shift invariant discrete system using first and second order data from it this procedure is a modification of the nonlinear least squares approximation and it generalizes the pade approximants and the spectral estimation modeling procedures the parameters of the approximating filter are obtained by solving a system of linear equations by means of an efficient recursive algorithm which is developed using the relation of the approximation problem with the theory of orthogonal polynomials on the unit bidisk we discuss some of the algebraic properties of the solution and apply them to define cases for which the bibo stability of the approximating filters is ensured the proposed procedure finds applications in the design and stabilization of 2 d recursive digital filters and in the autoregressive moving average arma modeling of stationary random fields

on injectivity and nuclearity for operator spaces an injective operator space v which is dual as a banach space has the form er 1 e where r is an injective von neumann algebra and where e is a projection in r this is used to show that an operator space v is nuclear if and only if it is locally reflexive and v ast ast is injective it is also shown that any exact operator space is locally reflexive

from the ehrenfest model to time fractional stochastic processes the ehrenfest model is considered as a good example of a markov chain i prove in this paper that the time fractional diffusion process with drift towards the origin is a natural generalization of the modified ehrenfest model the corresponding equation of evolution is a linear partial pseudo differential equation with fractional derivatives in time the orders lying between 0 and 1 i focus on finding a precise explicit analytical solution to this equation depending on the interval of the time the stationary solution of this model is also analytically and numerically calculated then i prove that the difference between the discrete approximate solution at time t n n 0 and the stationary solution obeys a power law with exponent between 0 and 1 the reversibility property is discussed for the ehrenfest model and its fractional version with a new observation

classification of contractively complemented hilbertian operator spaces abstract we construct some separable infinite dimensional homogeneous hilbertian operator spaces h m r and h m l which generalize the row and column spaces r and c the case m 0 we show that a separable infinite dimensional hilbertian jc triple is completely isometric to one of h m r h m l h m r h m l or the space spanned by creation operators on the full anti symmetric fock space in fact we show that h m l respectively h m r is completely isometric to the space of creation respectively annihilation operators on the m respectively m 1 anti symmetric tensors of the hilbert space together with the finite dimensional case studied in m neal b russo representation of contractively complemented hilbertian operator spaces on the fock space proc amer math soc 134 2006 475 485 this gives a full operator space classification of all rank one jc triples in terms of creation and annihilation operator spaces we use the above structural result for hilbertian jc triples to show that all contractive projections on a c algebra a with infinite dimensional hilbertian range are expansions which we define precisely of normal contractive projections from a onto a hilbertian space which is completely isometric to r c r c or this generalizes the well known result first proved for b h by robertson in a g robertson injective matricial hilbert spaces math proc cambridge philos soc 110 1991 183 190 that all hilbertian operator spaces that are completely contractively complemented in a c algebra are completely isometric to r or c we use the above representation on the fock space to compute various completely bounded banach mazur distances between these spaces or

decoding of hermitian codes the key equation and efficient error evaluation this paper presents a generalization of the key equation to hermitian codes the syndrome is interpreted as a power series and the product of this power series with a locator polynomial gives the error evaluator polynomial the computation of the evaluator polynomial may be done iteratively using a modified version of a previously published computationally efficient algorithm for computing locator polynomials

comment on approximate ternary jordan derivations on banach ternary algebras bavand savadkouhi et al j math phys 50 042303 2009 let a be a banach ternary algebra over c and x a ternary banach a module a c linear mapping d a a x x is called a ternary jordan derivation if d xxx a d x xx x xd x x x xxd x x for all x a bavand savadkouhi et al j math phys 50 042303 2009 investigated ternary jordan derivations on banach ternary algebras associated with the following functional equation f x y z 4 f 3x y 4z 4 f 4x 3z 4 2f x and proved the generalized ulam hyers stability of ternary jordan derivations on banach ternary algebras the mapping f in lemma 2 2 of bavand savadkouhi et al is identically zero and all of the results are trivial in this note we correct the statements of the results and the proofs

ordered c ast modules in this first part of a study of ordered operator spaces we develop the basic theory of ordered c bimodules a crucial role is played by open tripotents a jb triple variant of akemann s notion of open projection

impulse response arrays of discrete space systems over a finite field the main thrust of this paper is directed towards an analysis of the structure and properties of the impulse response array of two dimensional 2 d discrete space systems characterizable by rational functions having coefficients in a field z q it is shown that such an array exhibits a row column type of periodicity expressions for the period are derived arrays with a maximum of three levels in the auto correlation function are identified and explicit expressions for these levels are given

isomorphisms between c ternary algebras abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following cauchy jensen additive mappings 0 1 f x y 2 z f x y 2 z f x 2 f z 0 2 f x y 2 z f x y 2 z f y 0 3 2 f x y 2 z f x f y 2 f z these are applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

local properties of ternary rings of operators and their linking c algebras abstract we show that some local properties such as nuclearity exactness and local reflexivity of ternary rings of operators tros are closely related to the local properties of their linking c algebras we also show some equivalent conditions for nuclear tros and show that haagerup s decomposition property for completely bounded maps and pisier s norm can be naturally generalized to tros

continuous time random walks on moving fluids the scheme of the continuous time random walk ctrw is generalized to include the possibility of a moving background it is shown that this generalization reproduces in the macroscopic limit the usual diffusion advection equation and the properties of standard diffusion in a shear flow the new formalism is then used to derive the corresponding macroscopic equation for ctrw s with infinite mean squared step length and with infinite mean waiting time in a moving fluid for these two ctrw s we finally include an analysis of the dispersion in three different two dimensional linear shear flows

enveloping actions and takai duality for partial actions we show that any partial action on a topological space x is the restriction of a suitable global action called enveloping action that is essentially unique in the case of c algebras we prove that any partial action has a unique enveloping action up to morita equivalence and that the corresponding reduced crossed products are morita equivalent the study of the enveloping action up to morita equivalence reveals the form that takai duality takes for partial actions by applying our constructions we prove that the reduced crossed product of the reduced cross sectional algebra of a fell bundle by the dual coaction is liminal postliminal or nuclear if and only if so is the unit fiber of the bundle we also give a non commutative generalization of the well known fact that the integral curves of a vector field on a compact manifold are defined on all of r

contractive projections and operator spaces parallel to the study of finite dimensional banach spaces there is a growing interest in the corresponding local theory of operator spaces we define a family of hilbertian operator spaces h k n 1 k n generalizing the row and column hilbert spaces r n and c n and we show that an atomic subspace x c b h that is the range of a contractive projection on b h is isometrically completely contractive to an sum of the h k n and cartan factors of types 1 to 4 in particular for finite dimensional x this answers a question posed by oikhberg and rosenthal explicit in the proof is a classification up to complete isometry of atomic w closed jw triples without an infinite dimensional rank 1 w closed ideal

on the decoding of algebraic geometric codes this paper provides a survey of the existing literature on the decoding of algebraic geometric codes definitions theorems and cross references will be given we show what has been done discuss what still has to be done and pose some open problems

linear maps on c algebras which are derivations or triple derivations at a point abstract we prove new results about generalized derivations on c algebras by considering the triple product a b c 2 1 a b c c b a we introduce the study of linear maps which are triple derivations or triple homomorphisms at a point we prove that a continuous linear map t on a unital c algebra is a generalized derivation whenever it is a triple derivation at the unit element if we additionally assume t 1 0 then t is a derivation and a triple derivation furthermore a continuous linear map on a unital c algebra which is a triple derivation at the unit element is a triple derivation similar conclusions are obtained for continuous linear maps which are derivations or triple derivations at zero we also give an automatic continuity result that is we show that generalized derivations on a von neumann algebra and linear maps on a von neumann algebra which are derivations or triple derivations at zero are all continuous even if not assumed a priori to be so

approximate ternary jordan derivations on banach ternary algebras let a be a banach ternary algebra over a scalar field r or c and x be a ternary banach a module a linear mapping d a a x x is called a ternary jordan derivation if d xxx a d x xx x xd x x x xxd x x for all x a in this paper we investigate ternary jordan derivations on banach ternary algebras associated with the following functional equation f x y z 4 f 3x y 4z 4 f 4x 3z 4 2f x moreover we prove the generalized ulam hyers stability of ternary jordan derivations on banach ternary algebras

a characterization and a generalization of w modules we give a new banach module characterization of w modules also known as self dual hilbert c modules over a von neumann algebra this leads to a generalization of the notion and the theory of w modules to the setting where the operator algebras are weakly closed algebras of operators on a hilbert space that is we find the appropriate weak topology variant of our earlier notion of rigged modules and their theory which in turn generalizes the notions of a c module and a hilbert space successively our w rigged modules have canonical envelopes which are w modules indeed a w rigged module may be defined to be a subspace of a w module possessing certain properties

lattice parameter autoregressive modeling of two dimensional fields part i the quarter plane case quarter plane autoregressive lattice parameter modeling of two dimensional fields is developed as a natural extension of one dimensional lattice parameter theory starting with a given data field four prediction error fields are generated their linear combination is used to define and calculate 2 d lattice parameter reflection factors for successive lattice parameter model stages in addition to developing the basic theory the presentation includes the relationships between the quarter plane two dimensional transfer function and the lattice parameters the lattice parameter synthesis model for generating a two dimensional field from a random field input and lattice parameter stability conditions the theory has been confirmed by computer simulations the extension of this lattice parameter theory for the asymmetric half plane case is to be presented in a subsequent paper

finding a basis for the characteristic ideal of an n dimensional linear recurring sequence an n dimensional linear recurring sequence sigma of elements from a field f for n or 1 is considered an algorithm chi base which determines a basis for the ideal characteristic polynomials of sigma under certain reasonable conditions is presented this analysis applied to doubly periodic arrays in particular

twisted actions and regular fell bundles over inverse semigroups we introduce a new notion of twisted actions of inverse semigroups and show that they correspond b ectively to certain regular fell bundles over inverse semigroups yielding in this way a structure classication of such bun dles these include as special cases all the stable fell bundles our denition of twisted actions properly generalizes a pre vious one intro duced by sieben and corresponds to busby smith twisted actions in the group case as an application we describe twisted etale groupoid c algebras in terms of crossed products by twisted actions of inverse semigroups and show that sieben s twisted actions essentially correspond to twisted etale groupoids with topologically trivial twists

fractional dynamics of systems with long range space interaction and temporal memory abstract field equations with time and coordinate derivatives of noninteger order are derived from a stationary action principle for the cases of power law memory function and long range interaction in systems the method is applied to obtain a fractional generalization of the ginzburg landau and nonlinear schrodinger equations as another example dynamical equations for particle chains with power law interaction and memory are considered in the continuous limit the obtained fractional equations can be applied to complex media with without random parameters or processes

on semigroups generated by two consecutive integers and improved hermitian codes analysis of the berlekamp massey sakata algorithm for decoding one point codes leads to two methods for improving code rate one method due to feng and rao removes parity checks that may be recovered by their majority voting algorithm the second method is to design the code to correct only those error vectors of a given weight that are also geometrically generic in this work formulae are given for the redundancies of hermitian codes optimized with respect to these criteria as well as the formula for the order bound on the minimum distance the results proceed from an analysis of numerical semigroups generated by two consecutive integers

fractional calculus and continuous time finance ii the waiting time distribution we complement the theory of tick by tick dynamics of financial markets based on a continuous time random walk ctrw model recently proposed by scalas et al 4 and we point out its consistency with the behaviour observed in the waiting time distribution for bund future prices traded at liffe london

simplified understanding and efficient decoding of a class of algebraic geometric codes an efficient decoding algorithm for algebraic geometric codes is presented for codes from a large class of irreducible plane curves including hermitian curves it can correct up to d 1 2 errors where d is the designed minimum distance with it we also obtain a proof of d sub min spl ges d without directly using the riemann roch theorem the algorithm consists of gaussian elimination on a specially arranged syndrome matrix followed by a novel majority voting scheme a fast implementation incorporating block hankel matrix techniques is obtained whose worst case running time is o mn sup 2 where m is the degree of the curve applications of our techniques to decoding other algebraic geometric codes to decoding bch codes to actual minimum distance and to two dimensional shift register synthesis are also presented

on the zelmanovian classification of prime jb triples complex jb triples are complex banach spaces endowed with a triple product subjected to suitable conditions of algebraic and analytic nature see section 1 for the definition they were introduced by w kaup in order to provide an algebraic setting for the study of bounded symmetric domains in complex banach spaces the open unit ball of every complex jb triple is a bounded symmetric domain ka1 and every bounded symmetric domain in any complex banach space is bi holomorphically equivalent to the open unit ball of a suitable complex jb triple ka3 fundamental examples of complex jb triples are provided by complex c algebras with triple product defined by xyz x 1 2 xy z zy x 1

fast decoding of codes from algebraic plane curves improvement to an earlier decoding algorithm for codes from algebraic geometry is presented for codes from an arbitrary regular plane curve the authors correct up to d 2 m sup 2 8 m 4 9 8 errors where d is the designed distance of the code and m is the degree of the curve the complexity of finding the error locator is o n sup 7 3 where n is the length of the code for codes from hermitian curves the complexity of finding the error values given the error locator is o n sup 2 and the same complexity can be obtained in the general case if only d 2 m sup 2 2 errors are corrected