strongly self absorbing c algebras say that a separable unital c algebra v c is strongly self absorbing if there exists an isomorphism v such that lx ai e approximately unitarily equivalent homomorphisms we study this class of algebras which includes the cuntz algebras 2 ooo the uhf algebras of infinite type the jiang su algebra z and tensor products of 00 with uhf algebras of infinite type given a strongly self absorbing c algebra v we characterise when a separable c algebra absorbs v tensorially i e is p stable and prove closure properties for the class of separable testable c algebras finally we compute the possible if groups and prove a number of classification results which suggest that the examples listed above are the only strongly self absorbing c algebras

on anomalous diffusion and the fractional generalized langevin equation for a harmonic oscillator the fractional generalized langevin equation fgle is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two parameter mittag leffler noise the solution of this fgle is discussed by means of the laplace transform methodology and the kernels are presented in terms of the three parameter mittag leffler functions recent results associated with a generalized langevin equation are recovered

the characteristic square of a factor and the cocycle conjugacy of discrete group actions on factors this paper has three main purposes rst to associate to any separable factor m a canonical commuting exact square of groups called the characteristic square ofm secondly to formulate at least in a preliminary way a methodology for approaching non smooth classi cation problems in analysis and thirdly to use this approach in conjunction with the characteristic square to complete the cocycle conjugacy classi cation of actions of discrete amenable groups on injective factors of type iii1 this result and previous works on the cocyle conjugacy classi cation problem combine to produce a cocycle conjugacy classi cation theorem which applies simultaneously to all countable amenable groups and all injective separable factors and in which the characteristic square and our new methodology play a crucial role the cocycle conjugacy classi cation problem has by now a long and distinguished history beginning with connes ground breaking outer conjugacy classi cation of single automorphisms of the approximately nite dimensional or afd factor r0 of type ii1 c3 in the intervening 20 years enormous progress has been made the rst step was taken by v jones j who identi ed the true nature of the cocycle conjugacy invariants and completed the classi cation of actions of nite groups on r0 ocneanu o re ned this work and introduced new analytic techniques enabling him to extend the classi cation to countable amenable groups acting on the semi nite afd factor r0 1 and to some actions on afd factors of type iii also sutherland and takesaki using groupoid and duality techniques originating in jt extended the classi cation results to invent math 132 331 380 1998

the spatial rokhlin property for actions of compact quantum groups abstract we introduce the spatial rokhlin property for actions of coexact compact quantum groups on c algebras generalizing the rokhlin property for both actions of classical compact groups and finite quantum groups two key ingredients in our approach are the concept of sequentially split homomorphisms and the use of braided tensor products instead of ordinary tensor products we show that various structure results carry over from the classical theory to this more general setting in particular we show that a number of c algebraic properties relevant to the classification program pass from the underlying c algebra of a rokhlin action to both the crossed product and the fixed point algebra towards establishing a classification theory we show that rokhlin actions exhibit a rigidity property with respect to approximate unitary equivalence regarding duality theory we introduce the notion of spatial approximate representability for actions of discrete quantum groups the spatial rokhlin property for actions of a coexact compact quantum group is shown to be dual to spatial approximate representability for actions of its dual discrete quantum group and vice versa

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

generalized langevin equation with a three parameter mittag leffler noise abstract the relaxation functions for a given generalized langevin equation in the presence of a three parameter mittag leffler noise are studied analytically the results are represented by three parameter mittag leffler functions exact results for the velocity and displacement correlation functions of a diffusing particle are obtained by using the laplace transform method the asymptotic behavior of the particle in the short and long time limits are found by using the tauberian theorems it is shown that for large times the particle motion is subdiffusive for 1 and superdiffusive for many previously obtained results are recovered due to the many parameters contained in the noise term the model considered in this work may be used to improve the description of data and to model anomalous diffusive processes in complex media

fractional dynamics of populations abstract nature often presents complex dynamics which cannot be explained by means of ordinary models in this paper we establish an approach to certain fractional dynamic systems using only deterministic arguments the behavior of the trajectories of fractional non linear autonomous systems around the corresponding critical points in the phase space is studied in this work we arrive to several interesting conclusions for example we conclude that the order of fractional derivation is an excellent controller of the velocity how the mentioned trajectories approach to or away from the critical point such property could contribute to faithfully represent the anomalous reality of the competition among some species in cellular populations as cancer or hiv we use classical models which describe dynamics of certain populations in competition to give a justification of the possible interest of the corresponding fractional models in biological areas of research

existence and uniqueness of an inverse source problem for a fractional integrodifferential equation abstract we study an inverse source problem for a fractional integrodifferential equation this inverse problem aims to determine a time varying source term in the fractional integrodifferential equation from the measurement data at a fixed point x 0 by using the fixed point theorem in suitable sobolev space the existence and uniqueness of this inverse problem are obtained

weighted average finite difference methods for fractional diffusion equations a class of finite difference methods for solving fractional diffusion equations is considered these methods are an extension of the weighted average methods for ordinary non fractional diffusion equations their accuracy is of order x 2 and t except for the fractional version of the crank nicholson method where the accuracy with respect to the timestep is of order t 2 if a second order approximation to the fractional time derivative is used their stability is analyzed by means of a recently proposed procedure akin to the standard von neumann stability analysis a simple and accurate stability criterion valid for different discretization schemes of the fractional derivative arbitrary weight factor and arbitrary order of the fractional derivative is found and checked numerically some examples are provided in which the new methods numerical solutions are obtained and compared against exact solutions

decomposition rank and z stability we show that separable simple nonelementary unital c algebras with finite decomposition rank absorb the jiang su algebra mathcal z tensorially this has a number of consequences for elliott s program to classify nuclear c algebras by their k theory data in particular it completes the classification of c algebras associated to uniquely ergodic smooth minimal dynamical systems by their ordered k groups

fractional wave equation with a frictional memory kernel of mittag leffler type abstract in this paper we give an analytical treatment of a fractional wave equation with caputo time fractional derivative and frictional memory kernel of mittag leffler type this problem generalizes a recently solved problem 62 of a wave equation for a vibrating string in presence of a fractional friction with power law memory kernel such equations can be used in the context of modeling processes in complex and viscoelastic media

approximate solutions for boundary value problems of time fractional wave equation in this article we implement relatively a new analytical technique the adomian decomposition method for solving the boundary value problems of time fractional wave equation the fractional derivative is described in the caputo sense the decomposition method is used to construct analytical approximate solutions of time fractional wave equation subject to specified boundary conditions the solutions are calculated in the form of a convergent series with easily computable components some examples are given the results reveal that the adomian method is very effective and convenient

z stability of crossed products by strongly outer actions ii we consider a crossed product of a unital simple separable nuclear stably finite z stable c algebra a by a strongly outer cocycle action of a discrete countable amenable group under the assumption that a has finitely many extremal tracial states and is elementary amenable we show that the twisted crossed product c algebra is z stable as an application we also prove that all strongly outer cocycle actions of the klein bottle group on z are cocycle conjugate to each other this is the first classification result for actions of non abelian infinite groups on stably finite c algebras

the general time fractional wave equation for a vibrating string the solution of a general time fractional wave equation for a vibrating string is obtained in terms of the mittag leffler type functions and complete set of eigenfunctions of the sturm liouville problem the time fractional derivative used is taken in the caputo sense and the method of separation of variables and the laplace transform method are used to solve the equation some results for special cases of the initial and boundary conditions are obtained and it is shown that the corresponding solutions of the integer order equations are special cases of those of time fractional equations the proposed general equation may be used for modeling different processes in complex or viscoelastic media disordered materials etc

rohlin flows on the cuntz algebra o it is shown that certain quasi free flows on the cuntz algebra o have the rohlin property and therefore are cocycle conjugate with each other this in particular shows that any unital separable nuclear purely infinite simple c algebra has a rohlin flow

some aspects of fractional diffusion equations of single and distributed order abstract the time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative with a fractional derivative of order 0 1 the fundamental solution for the cauchy problem is interpreted as a probability density of a self similar non markovian stochastic process related to a phenomenon of sub diffusion the variance grows in time sub linearly a further generalization is obtained by considering a continuous or discrete distribution of fractional time derivatives of order less than one then the fundamental solution is still a probability density of a non markovian process that however is no longer self similar but exhibits a corresponding distribution of time scales

fractional extensions of the temperature field problems in oil strata we consider fractional extensions of the incomplete lumped formulation and the lumped formulation of the temperature field problems in oil strata laplace transform is used to solve the corresponding heat equations with an additional term representing the internal heat sources efros theorem a generalized form of the laplace convolution is used to obtain the analytic solutions special cases are mentioned

fractional calculus with an integral operator containing a generalized mittag leffler function in the kernel in this paper we introduce and investigate a fractional calculus with an integral operator which contains the following family of generalized mittag leffler functions e a b c k z email protected n 0 c k email protected email protected z nn z b email protected c r a max 0 r k 1 r k 0 in its kernel l n being the familiar pochhammer symbol a number of corollaries and consequences of the main results presented here are also considered

the rohlin property for shifts on uhf algebras and automorphisms of cuntz algebras abstract we show that the shift on the uhf algebra m n has the rohlin property for any odd n hence by brotteli et al the crossed product of a uhf algebra by a shift ergodic theory dynam systems 13 1993 615 626 for any n 2 3 and that any automorphism of the cuntz algebra o n n m is outer for any m 0

fractional fokker planck dynamics numerical algorithm and simulations anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional fokker planck dynamics via the underlying continuous time random walk an efficient numerical algorithm is developed which is applicable for an arbitrary potential this algorithm is then applied to investigate the fractional current and the corresponding nonlinear mobility in different washboard potentials normal and fractional diffusion are compared through their time evolution of the probability density in state space moreover we discuss the stationary probability density of the fractional current values

classification of outer actions of zn on o2 abstract we will show that any two outer actions of z n on o 2 are cocycle conjugate

low floor decoders for ldpc codes one of the most significant impediments to the use of ldpc codes in many communication and storage systems is the error rate floor phenomenon associated with their iterative decoders the error floor has been attributed to certain subgraphs of an ldpc code s tanner graph induced by so called trapping sets we show in this paper that once we identify the trapping sets of an ldpc code of interest a sum product algorithm spa decoder can be custom designed to yield floors that are orders of magnitude lower than floors of the the conventional spa decoder we present three classes of such decoders 1 a bi mode decoder 2 a bit pinning decoder which utilizes one or more outer algebraic codes and 3 three generalized ldpc decoders we demonstrate the effectiveness of these decoders for two codes the rate 1 2 2640 1320 margulis code which is notorious for its floors and a rate 0 3 640 192 quasi cyclic code which has been devised for this study although the paper focuses on these two codes the decoder design techniques presented are fully generalizable to any ldpc code

finite group actions on c algebras with the rohlin property i basic properties of finite group actions with the rohlin property on unital c algebras are investigated a characterization of finite group actions with the rohlin property on the cuntz algebra 02 is given in terms of central sequences which may be considered as an equivariant version of e kirchberg and n c phillips s characterization of 02 a large class of symmetries on 02 are classified in terms of the fixed point algebras for conjugacy and the crossed products for cocycle conjugacy model actions of symmetries of 02 are constructed for given k theoretical invariants

a fourier method for the fractional diffusion equation describing sub diffusion in this paper a fractional partial differential equation fpde describing sub diffusion is considered an implicit difference approximation scheme idas for solving a fpde is presented we propose a fourier method for analyzing the stability and convergence of the idas derive the global accuracy of the idas and discuss the solvability finally numerical examples are given to compare with the exact solution for the order of convergence and simulate the fractional dynamical systems

nonexistence of global solutions for a time fractional damped wave equation in a k times halved space abstract in this paper we study the time fractional damped wave equation c d 0 u u c d 0 u u p t 0 x d k where 1 2 0 1 c d 0 is the left sided caputo fractional derivative of order with respect to the variable time t p 1 and d k k 1 2 n is the k times halved space given by d k x x 1 x 2 x n r n x i 0 i 1 2 k using the nonlinear capacity method we prove that the problem admits no global weak solutions with suitable initial data when 1 p 1 2 n k 2 1

z2 actions on kirchberg algebras abstract we classify a large class of z 2 actions on the kirchberg algebras employing the kasparov group kk 1 as the space of classification invariants

classification of uniformly outer actions of z2 on uhf algebras we give a complete classification up to cocycle conjugacy of uniformly outer actions of on uhf algebras in particular it is shown that any two uniformly outer actions of on a uhf algebra of infinite type are cocycle conjugate we also classify them up to outer conjugacy

effects of a fractional friction with power law memory kernel on string vibrations in this paper we give an analytical treatment of a wave equation for a vibrating string in the presence of a fractional friction with power law memory kernel the exact solution is obtained in terms of the mittag leffler type functions and a generalized integral operator containing a four parameter mittag leffler function in the kernel the method of separation of the variables laplace transform method and sturm liouville problem are used to solve the equation analytically the asymptotic behaviors of the solution of a special case fractional differential equation are obtained directly from the analytical solution of the equation and by using the tauberian theorems the proposed model may be used for describing processes where the memory effects of complex media could not be neglected

mathbb z actions on ah algebras and mathbb z 2 actions on af algebras we consider mathbb z actions single automorphisms on a unital simple ah algebra with real rank zero and slow dimension growth and show that the uniform outerness implies the rohlin property under some technical assumptions moreover two mathbb z actions with the rohlin property on such a c algebra are shown to be cocycle conjugate if they are asymptotically unitarily equivalent we also prove that locally approximately inner and uniformly outer mathbb z 2 actions on a unital simple af algebra with a unique trace have the rohlin property and classify them up to cocycle conjugacy employing the orderext group as classification invariants

the wright functions as solutions of the time fractional diffusion equation we revisit the cauchy problem for the time fractional diffusion equation which is obtained from the standard diffusion equation by replacing the first order time derivative with a fractional derivative of order email protected 0 2 by using the fourier laplace transforms the fundamentals solutions green functions are shown to be high transcendental functions of the wright type that can be interpreted as spatial probability density functions evolving in time with similarity properties we provide a general representation of these functions in terms of mellin barnes integrals useful for numerical computation

the nuclear dimension of c algebras abstract we introduce the nuclear dimension of a c algebra this is a noncommutative version of topological covering dimension based on a modification of the earlier concept of decomposition rank our notion behaves well with respect to inductive limits tensor products hereditary subalgebras hence ideals quotients and even extensions it can be computed for many examples in particular it is finite for all uct kirchberg algebras in fact all classes of nuclear c algebras which have so far been successfully classified consist of examples with finite nuclear dimension and it turns out that finite nuclear dimension implies many properties relevant for the classification program surprisingly the concept is also linked to coarse geometry since for a discrete metric space of bounded geometry the nuclear dimension of the associated uniform roe algebra is dominated by the asymptotic dimension of the underlying space

equivariant homomorphisms rokhlin constraints and equivariant uhf absorption abstract we classify equivariant homomorphisms between c dynamical systems associated to actions of finite groups with the rokhlin property in addition the given actions are classified an obstruction is obtained for the cuntz semigroup of a c algebra allowing such an action we also obtain an equivariant uhf absorption result

regularity properties in the classification program for separable amenable c algebras we report on recent progress in the program to classify separable amenable c algebras our emphasis is on the newly apparent role of regularity properties such as finite decomposition rank strict comparison of positive elements and z stability and on the importance of the cuntz semigroup we include a brief history of the program s successes since 1989 a more detailed look at the villadsen type algebras which have so dramatically changed the landscape and a collection of announcements on the structure and properties of the cuntz semigroup

actions on uhf algebras of infinite type we prove that all strongly outer z actions on a uhf algebra of infinite type are strongly cocycle conjugate to each other we also prove that all strongly outer asymptotically representable z actions on a unital simple ah algebra with real rank zero slow dimension growth and finitely many extremal tracial states are cocycle conjugate to each other

the structure of the automorphism group of an injective factor and the cocycle conjugacy of discrete abelian group actions we complete classification of discrete abelian or finite group actions on injective type iii1 factors up to cocycle conjugacy we also give a proof for connes characterization of the ker mod and cnt m for an injective factor m of type iii 0 introduction the purpose of this paper is to give a proof of connes announcement on approximately inner automorphisms and centrally trivial automorphisms of an injective 1980 mathematics subject classification 1985 revision 46l40

fractional calculus and some intermediate physical processes one of the main applications of the fractional calculus integration and differentiation of arbitrary fractional order is the modeling of the intermediate processes j frac calculus 7 1995 89 int j theo phys 35 2 1996 311 r gorenflo r rutman fachbereich mathematik reprint no a 28 94 1994 f mainardi proc 14th imacs world congr vol 1 1994 p 329 chaos soliton fract 7 6 1996 1 j math phys 30 1989 134 in this work we use the fractional calculus to formulate the models which represent the two intermediate physical process convection diffusion and transport diffusion processes the existence and uniqueness of their solution will be proved and the continuation to the convection diffusion and transport processes are studied

unbounded derivations in at algebras letabe a simple unital at algebra of real rank zero such that it has a unique tracial state andk1 a is neither 0 norz for each hom k1 a r with dense range inrwe construct a closed derivation inawhich generates a one parameter automorphism group ofasuch that u u 2 i u for any unitaryu d furthermore we construct such an with the rohlin property which is defined in kishimoto comm math phys 179 1996 599 622 in this case the crossed producta ris a simple at algebra of real rank zero as an application we obtain that for such ac algebraathe kernel of the natural homomorphism of the groupinn a of approximately inner automorphisms intoext k1 a k0 a ext k0 a k1 a is the group hinn a of automorphisms homotopic to inner automorphisms combining with the result of kishimoto and kumjian trans amer math soc to appear inn a hinn a is isomorphic to the above direct sum as another application of the construction of derivations we show that ifais ac algebra of the above type and hinn a has the rohlin property and comes from hom k1 a r with dense range as in kishimoto and kumjian preprint then the crossed producta zis again of the same type in particulara zis an at algebra the other properties are known from kishimoto j operator theory40 1998

a rohlin property for one parameter automorphism groups we define a rohlin property for one parameter automorphism groups of unital simplec algebras and show that for such an automorphism group any cocycle is almost a coboundary we apply the same method to the single automorphism case and show that if an automorphism of a unital simplec algebra with a certain condition has a central sequence of approximate eigen unitaries for any complex number of modulus one then any cocycle is almost a coboundary or the automorphism has the stability we also show that if a one parameter automorphism group of a unital separable purely infinite simplec algebra has the rohlin property then the crossed product is simple and purely infinite

generalized distributed order diffusion equations with composite time fractional derivative abstract in this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the fourier laplace transform method we represent solutions in terms of infinite series in fox h functions the fractional and second moments are derived by using mittag leffler functions we observe decelerating anomalous subdiffusion in case of two composite time fractional derivatives generalized uniformly distributed order diffusion equation as a model for strong anomalous behavior is analyzed by using tauberian theorem some previously obtained results are special cases of those presented in this paper

fractional diffusion equation with a generalized riemann liouville time fractional derivative in this paper the solution of a fractional diffusion equation with a hilfer generalized riemann liouville time fractional derivative is obtained in terms of mittag leffler type functions and fox s h function the considered equation represents a quite general extension of the classical diffusion heat conduction equation the methods of separation of variables laplace transform and analysis of the sturm liouville problem are used to solve the fractional diffusion equation defined in a bounded domain by using the fourier laplace transform method it is shown that the fundamental solution of the fractional diffusion equation with a generalized riemann liouville time fractional derivative defined in the infinite domain can be expressed via fox s h function it is shown that the corresponding solutions of the diffusion equations with time fractional derivative in the caputo and riemann liouville sense are special cases of those diffusion equations with the hilfer generalized riemann liouville time fractional derivative the asymptotic behaviour of the solutions are found for large values of the spatial variable the fractional moments of the fundamental solution of the fractional diffusion equation are obtained the obtained results are relevant in the context of glass relaxation and aquifer problems

nonlinear reaction with fractional dynamics in this paper we consider a system of three fractional differential equations describing a nonlinear reaction our analysis includes both analytical technique and numerical simulation this allows us to control the efficiency of the numerical method we combine the numerical approximation of fractional integral with finding zeros of a function of one variable the variable gives a desired solution the solution has a peak its position in time depends on the order of fractional derivative the two other solutions of this system have a completely monotonic character

a reliable modification of the rectangular decomposition method abstract in this paper we present a powerful modification of the rectangular decomposition method that is used to solve fractional diffusion wave equations the new modification extends the application of the rectangular decomposition method to solve a wide class of space time fractional partial differential equations the proposed modification gives an analytical solution in the form of a convergent series with easily computable components some numerical examples are given to illustrate the efficiency and reliability of the method the new modification introduces a promising tool for many partial differential equations

generalized langevin equation with tempered memory kernel abstract we study a generalized langevin equation for a free particle in presence of a truncated power law and mittag leffler memory kernel it is shown that in presence of truncation the particle from subdiffusive behavior in the short time limit turns to normal diffusion in the long time limit the case of harmonic oscillator is considered as well and the relaxation functions and the normalized displacement correlation function are represented in an exact form by considering external time dependent periodic force we obtain resonant behavior even in case of a free particle due to the influence of the environment on the particle movement additionally the double peak phenomenon in the imaginary part of the complex susceptibility is observed it is obtained that the truncation parameter has a huge influence on the behavior of these quantities and it is shown how the truncation parameter changes the critical frequencies the normalized displacement correlation function for a fractional generalized langevin equation is investigated as well all the results are exact and given in terms of the three parameter mittag leffler function and the prabhakar generalized integral operator which in the kernel contains a three parameter mittag leffler function such kind of truncated langevin equation motion can be of high relevance for the description of lateral diffusion of lipids and proteins in cell membranes

finite group actions on c algebras with the rohlin property ii abstract we classify finite group actions on some classes of c algebras with the rohlin property in terms of the k groups a group cohomological obstruction is obtained for the k groups of a c algebra allowing such an action for example the tate cohomology groups with the k groups as the coefficient modules must vanish model actions with the rohlin property are constructed for given k theoretical invariants quasi free actions of finite cyclic groups on the cuntz algebras and their dual actions are investigated from the view point of the rohlin property

fractional langevin equation we investigate fractional brownian motion with a microscopic random matrix model and introduce a fractional langevin equation we use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath we further compare fractional brownian motion with the fractal time process the respective mean square displacements of these two forms of anomalous diffusion exhibit the same power law behavior here we show that their lowest moments are actually all identical except the second moment of the velocity this provides a simple criterion that enable us to distinguish these two non markovian processes

economic fluctuations and anomalous diffusion we quantify the relation between trading activity measured by the number of transactions n deltat and the price change g deltat for a given stock over a time interval t t deltat to this end we analyze a database documenting every transaction for 1000 u s stocks for the two year period 1994 1995 we find that price movements are equivalent to a complex variant of classic diffusion where the diffusion constant fluctuates drastically in time we relate the analog for stock price fluctuations of the diffusion constant known in economics as the volatility to two microscopic quantities i the number of transactions n deltat in deltat which is the analog of the number of collisions and ii the variance w 2 deltat of the price changes for all transactions in deltat which is the analog of the local mean square displacement between collisions our results are consistent with the interpretation that the power law tails of p g deltat are due to p w deltat and the long range correlations in g deltat are due to n deltat