anomalous continuous time random walk spectral diffusion in coherent third order optical response recursive relations are derived for nonlinear optical response functions of a two level chromophore with stochastic frequency fluctuations described by a continuous time random walk stationary ensembles are constructed and signatures of anomalous relaxation in the photon echo signal are discussed for a two state jump modulation with a power law waiting time density function psi t approximately t alpha 1 stretched exponential decay of the photon echo signal is predicted for 0 alpha 1 and power law asymptotics for 1 alpha 2

limit theorems for coupled continuous time random walks scaling limits of continuous time random walks are used in physics to model anomalous diffusion in which a cloud of particles spreads at a different rate than the classical brownian motion governing equations for these limit processes generalize the classical diffusion equation in this article we characterize scaling limits in the case where the particle jump sizes and the waiting time between jumps are dependent this leads to an efficient method of computing the limit and a surprising connection to fractional derivatives

linear preserver problems a brief introduction and some special techniques abstract linear preserver problems concern the characterization of linear operators on matrix spaces that leave certain functions subsets relations etc invariant the earliest papers on linear preserver problems date back to 1897 and a great deal of effort has been devoted to the study of this type of question since then we present a brief picture of the subject aiming at giving a gentle introduction to the reader then we describe some techniques used in our recent papers on this type of problem

levy walks and propagators in intermittent chaotic systems we study the propagator p r t for enhanced diffusion in intermittent chaotic systems represented by a class of iterated maps the analysis is based on the velocity model which is characterized by motion at a constant velocity with interruptions where sojourn times are chosen randomly but according to power law distributions the velocity model reproduces excellently the map generated motion the relationship to l evy walks and scaling properties is discussed

linear maps preserving the spectral radius abstract let x be a complex banach space if b x b x is a surjective linear map such that a and a have the same spectral radius for every a b x then c where is either an algebra automorphism or an antiautomorphism of b x and c is a complex constant such that c 1

asymptotic distributions of continuous time random walks a probabilistic approach we provide a systematic analysis of the possible asymptotic distributions o one dimensional continuous time random walks ctrws by applying the limit theorems of probability theory biased and unbiased walks of coupled and decoupled memory are considered in contrast to previous work concerning decoupled memory and levy walks we deal also with arbitrary coupled memory and with jump densities asymmetric about its mean obtaining asymmetric levy stable limits suprisingly it is found that in most cases coupled memory has no essential influence on the form of the limiting distribution we discuss interesting properties of walks with an infinite mean waiting time between successive jumps

additive maps preserving jordan zero products on nest algebras abstract let alg n and alg m be nest algebras associated with the nests n and m on banach spaces assume that n n and m m are complemented whenever n n and m m let alg n alg m be a unital additive surjection it is shown that preserves jordan zero products in both directions that is a b b a 0 ab ba 0 if and only if is either a ring isomorphism or a ring anti isomorphism particularly all unital additive surjective maps between hilbert space nest algebras which preserves jordan zero products are characterized completely

levy walks in dynamical systems abstract we investigate anomalous diffusion generated by iterated maps and analyze the motion in terms of the probabilistic levy walks we present expressions for the mean squared displacement and for the propagator which deviate from those for brownian motion the theoretical results are corroborated by numerical calculations

linear maps preserving zero products on nest subalgebras of von neumann algebras in this paper it is proved that every surjective linear map preserving identity and zero products in both directions between two nest subalgebras with non trivial nests of any factor von neumann algebra is an isomorphism and that every surjective weakly continuous linear map preserving identity and zero jordan products in both directions between two nest subalgebras with non trivial nests of any factor von neumann algebra is either an isomorphism or an anti isomorphism

asymptotic solutions of decoupled continuous time random walks with superheavy tailed waiting time and heavy tailed jump length distributions we study the long time behavior of decoupled continuous time random walks characterized by superheavy tailed distributions of waiting times and symmetric heavy tailed distributions of jump lengths our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time we show that the probability density of the scaled walker position converges in the long time limit to a nondegenerate one only if the scaling function behaves in a certain way this function as well as the limiting probability density are determined in explicit form also we express the limiting probability density which has heavy tails in terms of the fox h function and find its behavior for small and large distances

continuous time random walk with a superheavy tailed distribution of waiting times we study the long time behavior of the probability density associated with the decoupled continuous time random walk which is characterized by a superheavy tailed distribution of waiting times it is shown that if the random walk is unbiased biased and the jump distribution has a finite second moment then the properly scaled probability density converges in the long time limit to a symmetric two sided an asymmetric one sided exponential density the convergence occurs in such a way that all the moments of the probability density grow slower than any power of time as a consequence the reference random walk can be viewed as a generic model of superslow diffusion a few examples of superheavy tailed distributions of waiting times that give rise to qualitatively different laws of superslow diffusion are considered

similarity preserving linear maps on matrices abstract we determine all similarity preserving linear maps on the space of n x n complex matrices and all unitary equivalence preserving linear maps on the space of n x n hermitian matrices sub majorization preserving linear maps on hermitian matrices are also determined

p adic interpolation of square roots of central l values of modular forms we construct a meromorphic function on part of the eigencurve that interpolates a square root of a ratio of quadratic twists of the central modular l value

time evolution of the probability distribution in stochastic and chaotic systems with enhanced diffusion we perform a detailed study of the time evolution of the probability distribution for two processes displaying enhanced diffusion a stochastic process named the levy walk and a deterministic chaotic process the amplified climbing sine map the time evolution of the probability distribution differs in the two cases and carries information which is peculiar to the investigated process

semi markov approach to continuous time random walk limit processes continuous time random walks ctrws are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences their scaling limits are typically non markovian and the computation of their finite dimensional distributions is an important open problem this paper develops a general semi markov theory for ctrw limit processes in mathbb r d with infinitely many particle jumps renewals in finite time intervals the particle jumps and waiting times can be coupled and vary with space and time by augmenting the state space to include the scaling limits of renewal times a ctrw limit process can be embedded in a markov process explicit analytic expressions for the transition kernels of these markov processes are then derived which allow the computation of all finite dimensional distributions for ctrw limits two examples illustrate the proposed method

zero product preserving additive maps on symmetric operator spaces and self adjoint operator spaces in this note we characterize the additive maps on the space of symmetric operators and the space of self adjoint operators which preserve zero products in both directions and the additive maps on the space of self adjoint operators which preserve jordan zero products in both directions we also give a complete classification of additive maps on the von neumann algebra of all bounded linear operators acting on a hilbert space which preserve square zero in both directions or preserve operators annihilated by a polynomial in both directions

nest subalgebras of von neumann algebras abstract the structure of a certain class of separably acting reflexive operator algebras is investigated for which the nest algebras of j ringrose can be considered prototypes to a fixed von neumann algebra and a complete nest of projections contained therein one associates the algebra of all operators in the von neumann algebra which leave every member of the nest invariant a generalization of the ringrose criterion for inclusion in the jacobson radical of a nest algebra is given for this more general class of algebras further properties of the radical are studied

random walks with infinite spatial and temporal moments the continuous time random walk of montroll and weiss has been modified by scher and lax to include a coupled spatial temporal memory we treat novel cases for the random walk and the corresponding generalized master equation when combinations of both spatial and temporal moments of the memory are infinite the asymptotic properties of the probability distribution for being at any lattice site as a function of time and its variance are calculated the resulting behavior includes localized diffusive wavelike and levy s stable laws for the appropriate scaled variable we show that an infinite mean waiting time can lead to long time diffusive behavior while a finite mean waiting time is not sufficient to ensure the same

williams watts dielectric relaxation a fractal time stochastic process dielectric relaxation in amorphous materials is treated in a defect diffusion model where relaxation occurs when a mobile defect such as a vacancy reaches a frozen in dipole the random motion of the defect is assumed to be governed by a fractal time stochastic process where the mean duration between defect movements is infinite when there are many more defects than dipoles the williams watts decaying fractional exponential relaxation law is derived the argument of the exponential is related to the number of distinct sites visited by the random walk of the defect for the same reaction dynamics but with more traps than walkers an algebraically decaying relaxation is found

some general techniques on linear preserver problems abstract several general techniques on linear preserver problems are described the first one is based on a transfer principle in model theoretic algebra that allows one to extend linear preserver results on complex matrices to matrices over other algebraically closed fields of characteristic 0 the second one concerns the use of some simple geometric technique to reduce linear preserver problems to standard types so that known results can be applied the third one is about solving linear preserver problems on more general operator algebras by reducing the problems to idempotent preservers numerous examples will be given to demonstrate the proposed techniques