explicit representations for multiscale levy processes and asymptotics of multifractal conservation laws nonlinear conservation laws driven by levy processes have solutions which in the case of supercritical nonlinearities have an asymptotic behavior dictated by the solutions of the linearized equations thus the explicit representation of the latter is of interest in the nonlinear theory in this paper we concentrate on the case where the driving levy process is a multiscale stable anomalous diffusion which corresponds to the case of multifractal conservation laws considered in biler et al j differ equations 148 9 1998 stud math 135 231 1999 ann inst henri poincare anal nonlineaire 18 613 2001 and stud math 148 171 2001 the explicit representations building on the previous work on single scale problems see e g gorska and penson phys rev e 83 061125 2011 are developed in terms of the special functions such as meijer g functions and are amenable to direct numerical evaluations of relevant probabilities

on an integral type operator from the bloch space to mixed norm spaces let be a holomorphic self map of b and g h b such that g 0 0 where h b is the space of all holomorphic functions on the unit ball b of c n in this paper we investigate the following integral type operator d g f z 0 1 d f t z g t z d t t f h b where d f is the fractional derivative of f h b the boundedness and compactness of the operators d g between mixed norm spaces and bloch spaces in the unit ball are studied

modeling of waiting times and price changes in currency exchange data abstract a theory which describes the share price evolution at financial markets as a continuous time random walk physica a 287 2000 468 physica a 314 2002 749 eur phys j b 27 2002 273 physica a 376 2000 284 has been generalized in order to take into account the dependence of waiting times t on price returns x a joint probability density function pdf x t x t which uses the concept of a levy stable distribution is worked out the theory is fitted to high frequency us japanese yen exchange rate and low frequency 19th century irish stock data the theory has been fitted both to price return and to waiting time data and the adherence to data in terms of the 2 test statistic has been improved when compared to the old theory

relaxation functions in dipolar materials we compare two simple cartoons of relaxation processes in dipolar materials the first passage relaxation function introduced by k weron 1991 and the average relaxation function expressing the proportion of dipoles which did not change their imposed aligned orientation up to a certain time the latter providing a description closer to what is experimentally measured in some cases the two relaxation functions are proved to coincide

extended cesaro operators on bergman spaces we define an extended cesaro operator tg with holomorphic symbol g in the unit ball b of cn for a large class of weights w we characterize those g for which tg is bounded or compact from bergman space lpa w b to lqa w b 0 p q in addition we obtain some results about equivalent norms the norm of point evaluation functionals and the interpolation sequences on lpa w b

analyzing signal attenuation in pfg anomalous diffusion via a modified gaussian phase distribution approximation based on fractal derivative model abstract pulsed field gradient pfg technique is a noninvasive tool and has been increasingly employed to study anomalous diffusions in nuclear magnetic resonance nmr and magnetic resonance imaging mri however the analysis of pfg anomalous diffusion is much more complicated than normal diffusion in this paper a fractal derivative model based modified gaussian phase distribution method is proposed to describe pfg anomalous diffusion by using the phase distribution obtained from the effective phase shift diffusion method based on fractal derivatives and employing some of the traditional gaussian phase distribution approximation techniques a general signal attenuation expression for free fractional diffusion is derived this expression describes a stretched exponential function based attenuation which is distinct from both the exponential attenuation for normal diffusion obtained from conventional gaussian phase distribution approximation and the mittag leffler function based attenuation for anomalous diffusion obtained from fractional derivative the obtained signal attenuation expression can analyze the finite gradient pulse width fgpw effect additionally it can generally be applied to all three types of pfg fractional diffusions classified based on time derivative order and space derivative order these three types of fractional diffusions include time fractional diffusion with 0 2 2 space fractional diffusion with 1 0 2 and general fractional diffusion with 0 2 the results in this paper are consistent with reported results based on effective phase shift diffusion equation method and instantaneous signal attenuation method this method provides a new convenient approximation formalism for analyzing pfg anomalous diffusion experiments the expression that can simultaneously interpret general fractional diffusion and fgpw effect could be especially important in pfg mri where the narrow gradient pulse limit cannot be satisfied

boundedness and compactness of an integral type operator from bloch type spaces with normal weights to f p q s space abstract the boundedness and compactness of the integral type operator l g f z 0 1 r f tz g tz dt t z b where g is a holomorphic function on the open unit ball b in c n such that g 0 0 and is a holomorphic self map of b from bloch type spaces b and b 0 where is a normal weight to f p q s space on b are characterized solving a recent open problem

relaxation time distributions for an anomalously diffusing particle abstract as well known the generalized langevin equation with a memory kernel decreasing at large times as an inverse power law of time describes the motion of an anomalously diffusing particle here we focus attention on some new aspects of the dynamics successively considering the memory kernel the particle s mean velocity and the scattering function all these quantities are studied from a unique angle namely the discussion of the possible existence of a distribution of relaxation times characterizing their time decay although a very popular concept a relaxation time distribution cannot be associated with any time decreasing quantity from a mathematical point of view the decay has to be described by a completely monotonic function technically we use a memory kernel decaying as a mittag leffler function the mittag leffler functions interpolate between stretched or compressed exponential behaviour at short times and inverse power law behaviour at large times we show that in the case of a subdiffusive motion relaxation time distributions can be defined for the memory kernel and for the scattering function but not for the particle s mean velocity the situation is opposite in the superdiffusive case

on an integral type operator from logarithmic bloch type and mixed norm spaces to bloch type spaces abstract this paper studies the boundedness and compactness of the following integral type operator recently introduced by this author p g f z 0 1 f t z g t z d t t z b where is a holomorphic self map of the unit ball b in c n and g is a holomorphic function on b such that g 0 0 from logarithmic bloch type and mixed norm spaces to bloch type spaces

on a mathematical framework for the constitutive equations of anisotropic dielectric relaxation three classes of time domain non relativistic anisotropic dielectric constitutive equations of increasing generality are discussed in each class dissipativity is ensured by the choice of a class of convolution kernels in the d to e constitutive equation expressing the electric field e in terms of the electric displacement field d defining properties of the inverse e to d kernels and their fourier laplace transforms complex dielectric functions are determined by inversion of the d to e constitutive equation by this procedure it is shown that dielectric functions of the dipolar dielectrics are tensor valued bernstein functions while the dielectric functions of the drude lorentz type are tensor valued negative definite functions the properties of the complex dielectric permittivities are also determined for either class the theory is applied to an exhaustive review of empirical response functions of real dielectric materials encountered in the literature each class of convolution kernels is consistent with existence of a conserved energy but in one case a strictly dissipative energy can be constructed

iterated differentiation followed by composition from bloch type spaces to weighted bmoa spaces abstract let be a holomorphic self map of the open unit disk d and h d the class of holomorphic functions on d for n n 0 define an operator by c d n f f n f h d we characterize the boundedness and compactness of operator c d n from bloch type spaces to weighted bmoa spaces

on a product type operator from bloch spaces to weighted type spaces on the unit ball we characterize the boundedness and compactness of a product of radial derivative composition and multiplication operators from bloch spaces to weighted type spaces on the unit ball

on an integral type operator from ω bloch spaces to µ zygmund spaces let h b denote the space of all holomorphic functions on the unit ball b c n we study the boundedness and compactness of the following integral type operatorp g f z 0 1f tz g tz dtt f h b z b where g h b and g 0 0 from w bloch spaces to m zygmund spaces

on a product type operator from weighted bergman orlicz space to some weighted type spaces let d z c z 1 be the open unit disk an analytic self map of d and an analytic function on d let d be the differentiation operator and w the weighted composition operator the boundedness and compactness of the product type operator dw from the weighted bergman orlicz space to the bers type space weighted bloch space and weighted zygmund space on d are characterized

on 1 f noise and other distributions with long tails abstract it is shown following shockley shockley w 1957 proc ire 45 279 290 that when a population is engaged in tasks whose completion requires the successful conclusion of many independent subtasks the distribution function for successes in the primary task is log normal it is also shown that when the dispersion of the log normal distribution is large the distribution is mimicked by a 1 x distribution over a wide range of x this argument provides a generic set of processes that yields the much observed 1 x distribution and will also lead to a 1 f noise spectrum it is commonly found that distributions that seem to be log normal over a broad range say to the 95th percentile of a population change to an inverse fractional power pareto distribution for the last few percentile annual income distributions are examples with this structure the very wealthy generally achieve their superwealth through amplification processes that are not available to most we have introduced a simple amplification model to characterize the transition from a log normal distribution to an inverse power pareto tail

levy stable probability densities and mechanical relaxation in solid polymers early investigations by weber r and f kohlrausch maxwell and boltzmann of relaxation in viscoelastic solids are reviewed a two state model stress tensor describing strain coupling to internal conformations of a polymer chain is used to derive a linear response version of the boltzmann superposition principle for shear stress relaxation the relaxation function of kohlrausch t exp t is identical to the williams watts empirical dielectric relaxation function and in the model corresponds to the autocorrelation function of a segment s differential shape anisotropy tensor by analogy with the dielectric problem exp t is interpreted as the survival probability of a frozen segment in a swarm of hopping defects with a stable waiting time distributionat for defect motion the exponent a is the fractal dimension of a hierarchical scaling set of defect hopping times integral transforms of t needed for data analysis are evaluated the cosine and inverse laplace transforms are stable probability densities the reciprocal kernel for short time compliance is discussed

a relationship between asymmetric levy stable distributions and the dielectric susceptibility this paper as a complement to the work of montroll and bendler is concerned with the levy stable distributions and their connection to the dielectric response of dipolar materials in the frequency domain the necessary and sufficient condition for this connection is found the presented probabilistic analysis is based on the mathematically correct representation of the meaning of the relaxation function of a system of dipoles and shows why the same form of a distribution of relaxation rates namely the completely asymmetric levy stable distribution should apply in all different relaxing systems this is in contrast to the traditional definition of the relaxation function expressed as a weighted average of exponential relaxation functions which does not explain the universality of the dielectric relaxation law it also follows from the present considerations that not only is the imaginary part of the dielectric susceptibility directly related to the levy stable distribution as was found by montroll and bendler but so is the real part as a consequence the relation cot n 2 for p and 0 n 1 implied by experimental results is obtained

on blog to qlogp pullbacks abstract we characterize the boundedness and the compactness of composition operators acting on the weighted bloch space b log generalizing previous results and answering to a question of r yoneda

rectifiable sets and coarea formula for metric valued mappings we study lipschitz mappings defined on an hn rectifiable metric space with values in an arbitrary metric space we find necessary and sufficient conditions on the image and the preimage of a mapping for the validity of the coarea formula as a consequence we prove the coarea formula for some classes of mappings with hk finite image we also obtain a metric analog of the implicit function theorem all these results are extended to large classes of mappings with values in a metric space including sobolev mappings and bv mappings

essential norm of products of multiplication composition and differentiation operators on weighted bergman spaces abstract let be a holomorphic function on the open unit disk d and a holomorphic self map of d let c m and d denote the composition multiplication and differentiation operator respectively we find an asymptotic expression for the essential norm of products of these operators on weighted bergman spaces on the unit disk this paper is a continuation of our recent paper concerning the boundedness of these operators on weighted bergman spaces

generating functional approach to space and time dependent colored noise a stochastic model for time and space dependent colored noise is suggested based on the following assumptions 1 the noise field is generated by a random number of point events corresponding to a correlated point process 2 the contributions of the different events to the noise field are additive each contribution being a random function selected from the same probability density functional an analytical treatment of the noise field described by these assumptions is possible the generating functional of the noise field as well as the corresponding cumulants can be computed exactly all cumulants are explicitly evaluated when the contribution of an event is given by a diffusion equation a detailed analysis of the asymptotic behavior is made for time homogeneous and translationally invariant processes a gaussian random field colored in space and time emerges for very frequent independent events of very small intensities provided that the central moments of the contribution of an event to the noise field are finite and fast decreasing in space the correlations among events lead to corrections of the gauss limit law however the cumulants of the random fields are also finite if the central moments of an event are slowly decreasing in space a different type of asymptotic behavior occurs the cumulants of the noise field become infinite and the resulting field is described by a non gaussian stable law of the l evy type the theory may be applied to the study of stochastic gravitational fluctuations in galactic systems to the analysis of concentration fluctuations for diffusion processes in disordered systems and for the analysis of the influence of environmental fluctuations in continuum mechanics and electrodynamics

generalized product type operators from weighted bergman orlicz spaces to bloch orlicz spaces let d be the open unit disk in the complex plane an analytic self map of d and an analytic function on d let dn be the nth differentiation operator and w the weighted composition operator in this paper the boundedness and compactness of the generalized product type operators dnw and w dn from weighted bergman orlicz spaces to bloch orlicz spaces are characterized

the co area formula for sobolev mappings we extend federer s co area formula to mappings f belonging to the sobolev class w 1 p r n r m 1 m m and more generally to mappings with gradient in the lorentz space l m 1 r n this is accomplished by showing that the graph of f in r n m is a hausdorff n rectifiable set

extended cesaro operators between bloch type spaces in the unit ball of cn abstract in this paper we characterize those holomorphic symbols in the unit ball of c n for which the induced extended cesaro operator t b b respectively b 0 b 0 is bounded or compact where and are normal functions on 0 1 in addition we obtain some properties of those spaces b and b 0

response theory for random channel kinetics in complex systems application to lifetime distributions of active intermediates we present a response theory for random channel kinetics based on the method of characteristic functionals we assume that the uctuations of the rate coecients are generated by the contributions of a large number of reaction channels and can be described in terms of a set of grand canonical probability density functionals we consider linear as well as nonlinear responses for systems with static or dynamic disorder for all cases considered we derive analytical expressions for the ensemble average of the response of the system to an external perturbation the theory is applied for developing a new approach to the analysis of the kinetics in complex chemical systems based on a random channel approach we assume that the total transition rate from one state of the system to another is made up of the contributions of a large number of random reaction pathways which can be described in terms of a stochastic point process we study the response of such a system to an external perturbation and show that it can be expressed in terms of a set of lifetime distributions of reaction intermediates we examine the possibilities of applying the technique to the study of large chemical systems by means of tracer experiments and suggest methods for computing rate distributions from measured lifetime distributions we generalize the method of spectral kinetic analysis for the interpretation of measured lifetime distributions we investigate the relationships between spectral kinetics analysis and random channel statistics c 2000 published by elsevier science b v all rights reserved

composition operators from bloch type spaces into qk type spaces supposeis an analytic map of the unit disk d into itself x is a banach space of analytic functions on d define the composition operator c cf f for all f x in this paper the boundedness and compactness of the composition operators from bloch spaces into qk p q and qk 0 p q spaces are discussed where 0 keywords composition operator analytic function bspace k carleson measure compact k carleson measure

nonequilibrium fluctuation dissipation relations for independent random rate processes with dynamical disorder a class of rate processes with dynamical disorder is investigated based on the two following assumptions a the system is composed of a random number of particles or quasiparticles which decay according to a first order kinetic law b the rate coefficient of the process is a random function of time with known stochastic properties the formalism of characteristic functionals is used for the direct computation of the dynamical averages the suggested approach is more general than the other approaches used in the literature it is not limited to a particular type of stochastic process and can be applied to any type of random evolution of the rate coefficient we derive an infinity of exact fluctuation dissipation relations which establish connections among the moments of the survival function and the moments of the number of surviving particles the analysis of these fluctuation dissipation relations leads to the unexpected result that in the thermodynamic limit the fluctuations of the number of partic

compact composition operators on the bloch space necessary and sufficient conditions are given for a composition operator cof f o q to be compact on the bloch space w and on the little bloch space o weakly compact composition operators on o are shown to be compact if q e o is a conformal mapping of the unit disk d into itself whose image q d approaches the unit circle t only in a finite number of nontangential cusps then co is compact on 7o on the other hand if there is a point of t n q d at which q d does not have a cusp then co is not compact

products of volterra type operator and composition operator from h and bloch spaces to zygmund spaces the boundedness and compactness of the products of volterra type operators and composition operators from the space of bounded analytic functions and the bloch space to the zygmund space are discussed in this paper

products of integral type operators and composition operators between bloch type spaces a complete picture on the boundedness and compactness of the products of integral type operators and composition operators between bloch type spaces of holomorphic functions on the unit disk is given in this paper

relaxation in heterogeneous systems a rare events dominated phenomenon abstract we have derived a general two power law relaxation function for heterogeneous materials using the maximum entropy principle for nonextensive systems the power law exponents of the relaxation function are simply related to a global fractal parameter and for large time to the entropy nonextensivity parameter q for intermediate times the relaxation follows a stretched exponential behavior the asymptotic power law behaviors both in the time and the frequency domains coincide with those of the weron generalized dielectric function derived in the stochastic theory from an extension of the levy central limit theorem these results are in full agreement with the jonscher universality principle and trace the origin of the large t power law universality with system dependent exponent and q to the scaling behavior of the extreme value distribution function of the effective macroscopic waiting time and the fluctuation of the number of relaxing entities

cesaro operators on hardy spaces in the unit ball this article establishes the boundedness of the generalized cesaro operator on holomorphic hardy spaces in the unit ball the approach consists in writing the generalized cesaro operator as a composition of certain integral operators

integral type operators from iterated logarithmic bloch spaces to zygmund type spaces let h b denote the space of all holomorphic functions on the unit ball b of c n and rh z j 1 nz j h z j z the radial derivative of h in this paper we study the boundedness and compactness of the following integral operator t g f z 0 1f tz rg tz dtt f h b z b from iterated logarithmic bloch spaces to zygmund type spaces

products of composition and differentiation operators from zygmund spaces to bloch spaces and bers spaces abstract the boundedness and compactness of the products of differentiation and composition operators from zygmund spaces to bloch spaces and bers spaces are discussed in this paper

generalized composition operators on zygmund spaces and bloch type spaces the boundedness and compactness of the generalized composition operator on zygmund spaces and bloch type spaces are investigated in this paper

scaling in animal group size distributions an elementary model of animal aggregation is presented the group size distributions resulting from this model are truncated power laws the predictions of the model are found to be consistent with data that describe the group size distributions of tuna fish sardinellas and african buffaloes

integral type operators from bloch type spaces to zygmund type spaces let h b denote the space of all holomorphic functions on the unit ball email protected c n this paper investigates the following integral type operator with symbol email protected h b t g f z email protected 0 1f tz rg tz dtt email protected h b email protected b where rg z email protected j 1 nz email protected email protected z j z is the radial derivative of g the boundedness and compactness of the operator t g from bloch type spaces to zygmund type spaces are studied

weighted differentiation composition operators from h and bloch spaces to nth weighted type spaces on the unit disk we characterize the boundedness and compactness of weighted differentiation composition operators from the space of bounded analytic functions the bloch space and the little bloch space to nth weighted type spaces on the unit disk

on an integral type operator from logarithmic bloch type spaces to mixed norm spaces on the unit ball let h b denote the space of all holomorphic functions on the open unit ball b of c n and email protected h b we characterize the boundedness and compactness of the following integral type operator l gf z email protected 0 1rf tz g tz dtt email protected b where rf is the radial derivative of function f from logarithmic bloch type spaces to mixed norm spaces on the unit ball

on an integral type operator from iterated logarithmic bloch spaces into bloch type spaces let h b denote the space of all holomorphic functions on the open unit ball b of c n let f f 1 f n be a holomorphic self map of b and email protected h b such that g 0 0 in this paper we study the boundedness and compactness of the following integral type operator recently introduced by xiangling zhu and the second authori f gf z email protected 0 1rf f tz g tz dtt email protected b from the iterated logarithmic bloch spaces into the bloch type spaces for the case when f z z we also obtain a sufficient and necessary condition for the boundedness of this operator from the iterated logarithmic bloch space into the little bloch type space

closed form solutions for the levy stable distribution the levy stable distribution is the attractor of distributions which hold power laws with infinite variance this distribution has been used in a variety of research areas for example in economics it is used to model financial market fluctuations and in statistical mechanics it is used as a numerical solution of fractional kinetic equations of anomalous transport this function does not have an explicit expression and no uniform solution has been proposed yet this paper presents a uniform analytical approximation for the levy stable distribution based on matching power series expansions for this solution the trans stable function is defined as an auxiliary function which removes the numerical issues of the calculations of the levy stable distribution then the uniform solution is proposed as a result of an asymptotic matching between two types of approximations called the inner solution and the outer solution finally the results of analytical approximation are compared to the numerical results of the levy stable distribution function making this uniform solution valid to be applied as an analytical approximation

generalized weighted composition operators from zygmund spaces to bloch orlicz type spaces let d be the open unit disk in the complex plane c and h d the class of all analytic functions on d let be an analytic self map of d and h d in this paper the boundedness and compactness of the generalized weighted composition operator d n f f n from the zygmund space to the bloch orlicz space and the little bloch orlicz space are characterized

an integral type operator from qk p q spaces to zygmund type spaces abstract we study the boundedness and compactness of an integral type operator from q k p q and q k 0 p q spaces to zygmund type spaces in particular we use two families of functions to characterize the boundedness and compactness

extended cesaro operators between different hardy spaces abstract let h p denote the hardy space of holomorphic functions on the unit ball b this note gives some sufficient and necessary conditions for the boundedness and compactness of the following extended cesaro operators t g f z 0 1 f tz r g tz dt t and l g f z 0 1 r f tz g tz dt t where z b and g is a fixed holomorphic map on b acting from the space h p into the space h q for the case p q our results extend and simplify some one dimensional results

bounded superposition operators between bloch orlicz and α bloch spaces we characterize all entire functions that transform a bloch orlicz space into the bloch space by superposition

linearly coupled quantum oscillators with levy stable noise abstract the influence of an external noise on two linearly coupled quantum oscillators is investigated the noise is described by the probability measure corresponding to a symmetric levy stable distribution in calculations the path integral technique is used this paper is a continuation of investigations started by bose datta and feinsilver

diffusion in layered random flows polymers electrons in random potentials and spin depolarization in random fields several related models are studied in a common framework we first reconsider the model of matheron and de marsilly for anomalous tracer dispersion in a stratified porous medium in each horizontal layer the flow velocity is constant parallel to the layer and depends randomly on the vertical coordinate z this model is mapped onto ad 1 localization problem in a random potential and equivalently onto ad 1 polymer at larget theaveraged distribution of horizontal displacementsx takes the scaling form p x t z 0 at 5 4q bxt 3 4 whereq y is independent of the details of the model q y a andb are obtained exactly for a large class of models from the lifschitz tails of the localization problem we find in the regionx t3 4 i e y thatq y y exp c y 4 3 we also obtain exactly ind 1 the scaling functions for the local and total average magnetization of spins diffusing in a random magnetic field by mapping onto a polymer problem as well as the average local concentration for diffusion in the presence of random sources and sinks these mappings are then used to study higher dimensional extensions of these models

a bridge between dubovitskiĭ federer theorems and the coarea formula abstract the morse sard theorem requires that a mapping v r n r m is of class c k k max n m 0 in 1957 dubovitski generalized this result by proving that almost all level sets for a c k mapping have h s negligible intersection with its critical set where s max n m k 1 0 here the critical set or m critical set is defined as z v m x r n rank v x m another generalization was obtained independently by dubovitski and federer in 1966 namely for c k mappings v r n r d and integers m d they proved that the set of m critical values v z v m is h q negligible for q m 1 n m 1 k they also established the sharpness of these results within the c k category here we prove that dubovitski s theorem can be generalized to the case of continuous mappings of the sobolev lorentz class w p 1 k r n r d p n k this is the minimal integrability assumption that guarantees the continuity of mappings in this situation the mappings need not to be everywhere differentiable and in order to handle the set of nondifferentiability points we establish for such mappings an analog of the luzin n property with respect to lower dimensional hausdorff content finally we formulate and prove a bridge theorem that includes all the above results as particular cases as a limiting case in this bridge theorem we also establish a new coarea type formula if e x r n rank v x m then e j m v x d x r d h n m e v 1 y d h m y the mapping v is r d valued with arbitrary d and the formula is obtained without any restrictions on the image v r n such as m rectifiability or finiteness with respect to the m hausdorff measure these last results are new also for smooth mappings but are presented here in the general sobolev context the proofs of the results are based on our previous joint papers with j bourgain 2013 2015

levy noise levy flights levy fluctuations this paper is concerned with a levy noise characterized for t 0 by the functional with 0 2 then levy flights can be defined through a stochastic differential equations rather than the usual chapmann kolmogorov equation we have used this functional approach to solve a plane rotor in the presence of levy noise the linear damped stochastic process driven by levy noise is revisited and its non autonomous and non markovian generalizations have been solved in the context of our functional analysis

weighted composition operators from zygmund spaces into bloch spaces abstract let be an analytic self map and u be a fixed analytic function on the open unit disk d in the complex plane c the weighted composition operator is defined by uc f z u z f z z d f h d this paper studies the boundedness and compactness of weighted composition operators from zygmund spaces into bloch spaces

generating functional approach to multichannel parallel relaxation with application to the problem of direct energy transfer in fractal systems with dynamic disorder a model for multichannel parallel relaxation is suggested based on the following assumptions a an individual channel is characterized by a set of continuous state variables the corresponding relaxation rate is a function of the state variables as well as of the time interval for which the channel is open b the number of channels is a random variable described by a correlated point process defined in the space of state parameters of an individual channel analytical expressions for the generating functional of the overall relaxation rate and for the average survival function are derived in terms of the generating functional of the point process the general formalism is applied to the problem of direct energy transfer from excited donors to acceptors in fractal systems with dynamic disorder it is assumed that the number of acceptors obeys a poissonian distribution law with a constant average density in a df dimensional fractal structure embedded in a ds dimensional euclidean space ds 1 2 3 and th

universality classes for asymptotic behavior of relaxation processes in systems with dynamical disorder dynamical generalizations of stretched exponential the asymptotic behavior of multichannel parallel relaxation processes for systems with dynamical disorder is investigated in the limit of a very large number of channels an individual channel is characterized by a state vector x which due to dynamical disorder is a random function of time a limit of the thermodynamic type in the x space is introduced for which both the volume available and the average number of channels tend to infinity but the average volume density of channels remains constant scaling arguments combined with a stochastic renormalization group approach lead to the identification of two different types of universal behavior of the relaxation function corresponding to nonintermittent and intermittent fluctuations respectively for nonintermittent fluctuations a dynamical generalization of the static huber s relaxation equation is derived which depends only on the average functional density of channels w t d w t the channels being classified according to their different relaxation rates w w t which are random functions of time for intermittent fluctuations a more complicated relaxation equation is derived which in addition to the average density of channels w t d w t depends also on a positive fractal exponent h which characterizes the fluctuations of the density of channels the general theory is applied for constructing dynamical analogs of the stretched exponential relaxation function for nonintermittent fluctuations the type of relaxation is determined by the regression dynamics of the fluctuations of the relaxation rate if the regression process is fast and described by an exponential attenuation function then after an initial stretched exponential behavior the relaxation process slows down and it is not fully completed even in the limit of very large times for self similar regression obeying a negative power law the relaxation process is less sensitive to the influence of dynamical disorder both for small and large times the relaxation process is described by stretched exponentials with the same fractal exponent as for systems with static disorder for large times the efficiency of the relaxation process is also slowed down by fluctuations similar patterns are found for intermittent fluctuations with the difference that for very large times and a slow regression process a crossover from a stretched exponential to a self similar algebraic relaxation function occurs some implications of the results for the study of relaxation processes in

integral type operators acting between weighted type spaces on the unit ball let b denote the unit ball in c n and h b the space of all holomorphic functions on b we study the boundedness and compactness of the following integral type operatorsi f gf z email protected 0 1rf f tz g tz dtt email protected b where email protected h b g 0 0 f is a holomorphic self map of b and rf is the radial derivative of f between weighted type spaces on the unit ball

spin in contact with thermostat exact reduced dynamics abstract new aspects of exact reduced dynamics of a simple model of an open system spin 1 2 in a magnetic field and coupled to a bose reservoir are presented a relaxation problem final states of the system schrodinger like and heisenberg like representations of dynamics are considered a master equation for a statistical operator of the system and its solution are obtained and the related question of the construction of a semigroup for the time evolution is discussed

on levy or stable distributions and the williams watts model of dielectric relaxation this paper is concerned with the levy or stable distribution function defined by the fourier transform q alpha left z right frac 1 2 pi int infty infty exp left izu left u right alpha right du with 0 alpha leqslant 2 when 2 it becomes the gauss distribution function and when 1 the cauchy distribution when 2 the distribution has a long inverse power tail q alpha left z right sim frac gamma left 1 alpha right sin tfrac 1 2 pi alpha pi left z right 1 alpha in the regime of small if logz 1 the distribution is mimicked by a log normal distribution we have derived rapidly converging algorithms for the numerical calculation ofq z for various in the range 0 1 the functionq z appears naturally in the williams watts model of dielectric relaxation in that model one expresses the normalized dielectric parameter as in n left omega right equiv in n left omega right i in n left omega right int 0 infty e i omega t left d phi left t right mathord left vphantom d phi left t right dt right kern nulldelimiterspace dt right dt with phi left t right exp left t mathord left vphantom t tau right kern nulldelimiterspace tau right alpha it has been found empirically by various authors that observed dielectric parameters of a wide variety of materials of a broad range of frequencies are fitted remarkably accurately by using this form of t e n is shown to be directly related toq z it is also shown that if the williams watts exponential is expressed as a weighted average of exponential relaxation functions exp left t mathord left vphantom t tau right kern nulldelimiterspace tau right alpha int 0 infty g left lambda alpha right e lambda t dt the weight functiong is expressible as a stable distribution some suggestions are made about physical models that might lead to the williams watts form of t

on the equivalence of the parallel channel and the correlated cluster relaxation models the question of the origins of nonexponential relaxation is addressed in terms of the probabilistic approach to relaxation the interconnection between two differently rooted probabilistic models i e between the parallel channel and the correlated cluster models is presented we show that clearly different probabilistic origins yield in both approaches a well defined class of universally valid two power law responses with the stretched exponential and exponential decay laws as special cases the equivalence of both models indicates that variations in the local environment of the relaxing configurational units parallel channel relaxation can provide a basis for self similar relaxation dynamics without the need for hierarchically constrained dynamics correlated clusters relaxation

on some integral type operators between a general space and bloch type spaces abstract the boundedness and compactness of the next integral operators p g f z 0 1 f tz g tz dt t and l g f z 0 1 r f tz g tz dt t between f p q s spaces and bloch type spaces on the unit ball of c n are studied among other results we solve some open problems and considerably extend results in the paper li and stevic compactness of riemann stieltjes operators between f p q s and bloch spaces publ math debrecen 72 1 2 2008 111 128

composition operators on bloch orlicz type spaces abstract in this paper we use young s functions to define the bloch orlicz spaces as a generalization of bloch spaces we study continuity boundedness from below and compactness of composition operators on bloch orlicz spaces

characterizations of α bloch spaces on the unit ball abstract we obtain a characterization of the bloch space for any 0 in the unit ball of c n in terms of f z f w z w moreover a new characterization for the bloch space is given

reverse estimates in growth spaces let h b d denote the space of holomorphic functions on the unit ball b d of mathbb c d given a radial doubling weight w we construct functions f g in h b 1 such that f g is comparable to w also we obtain similar results for b d d 2 and for circular strictly convex domains with smooth boundary as an application we study weighted composition operators and related integral operators on growth spaces of holomorphic functions

on the iterated logarithmic bloch space on the unit ball abstract we introduce a new space of analytic functions on the unit ball the so called iterated logarithmic bloch space b log k and study some of its properties among other features we study the boundedness and compactness of weighted composition operators on the unit disk as well as of a recently introduced integral type operator on the unit ball with i domain the iterated logarithmic bloch space b log k or the little iterated logarithmic bloch space b log k 0 and ii range the bloch type space b or the little bloch type space b 0 or the weighted space h or the little weighted space h 0

a generalized cauchy process and its application to relaxation phenomena we study some of the basic properties of a generalized cauchy process indexed by two parameters the application of the lamperti transformation to the generalized cauchy process leads to a self similar process which preserves the long range dependence the asymptotic properties of spectral density of the process are derived possible application of this process to model relaxation phenomena is considered

on a new operator from the logarithmic bloch space to the bloch type space on the unit ball abstract we study the boundedness and compactness of a recently introduced operator denoted by p g which is a kind of the product of composition and integral operators on the unit ball b c n from the logarithmic bloch space b log and the little logarithmic bloch space b log 0 to the bloch type space b or the little bloch type space b 0

burr levy tsallis abstract the purpose of this short paper dedicated to prof constantin tsallis on his 60th anniversary is to show how the use of mathematical tools and physical concepts introduced by burr levy and tsallis open a new line of analysis of the old problem of non debye decay and universality of relaxation we also show how a finite characteristic time scale can be expressed in terms of a q expectation using the concept of q escort probability the comparison with the weron et al probabilistic theory of relaxation leads to a better understanding of the stochastic properties underlying the tsallis entropy concept

weighted composition operators between weighted bergman spaces and hardy spaces on the unit ball of cn abstract in this paper we study the weighted composition operators w f f between weighted bergman spaces and hardy spaces on the unit ball of c n we characterize the boundedness and the compactness of the weighted composition operators w a p a q 0 q p 1 and w h p b h q b 0 q p

characterizations of qt spaces abstract we introduce a new space qt space of analytic functions on the unit disk in terms of a nondecreasing function t the relation between qt and qp spaces which have attracted considerable attention is given by studying the growth order of t the counterpart q t of qt for the meromorphic case is also considered and investigated we note that some characterizations of q t and qt are different moreover our results answer a question raised by p wu 1998 complex variables35 157 170 in the negative

self organisation of random oscillators with levy stable distributions a novel possibility of self organized behaviour of stochastically driven oscillators is presented it is shown that synchronization by l e vy stable processes is significantly more efficient than that by oscillators with gaussian statistics the impact of outlier events from the tail of the distribution function was examined by artificially introducing a few additional oscillators with very strong coupling strengths and it is found that remarkably even one such rare and extreme event may govern the long term behaviour of the coupled system in addition to the multiplicative noise component we have investigated the impact of an external additive l e vy distributed noise component on the synchronisation properties of the oscillators

products of composition multiplication and radial derivative operators from logarithmic bloch spaces to weighted type spaces on the unit ball abstract let h b denote the space of all holomorphic functions on the unit ball b of c n h b and be a holomorphic self map of b let c m and r denote the composition multiplication and radial derivative operators respectively in this paper we characterize the boundedness and compactness of linear operators induced by products of these operators from logarithmic bloch spaces to weighted type spaces on the unit ball

products of multiplication composition and differentiation operators on weighted bergman spaces abstract let be a holomorphic function on the open unit disk d and a holomorphic self map of d let c m and d denote the composition multiplication and differentiation operator respectively we consider linear operators induced by products of these operators on weighted bergman spaces on d the boundedness is established by using carleson type measures