generalized weighted hardy cesaro operators and their commutators on weighted morrey spaces abstract let 0 1 0 s 0 1 r be measurable functions and be a parameter curve in r n given by t x 0 1 r n s t x s t x in this paper we study a new weighted hardy cesaro operator defined by u s f x 0 1 f s t x t d t for measurable complex valued functions f on r n under certain conditions on s t and on an absolutely homogeneous weight function we characterize the weight function such that u s is bounded on weighted morrey spaces l p and then compute the corresponding operator norm of u s we also give a necessary and sufficient condition on the function which ensures the boundedness of the commutator of the operator u s on l p with symbols in bmo

the stochastic rayleigh diffusion model statistical inference and computational aspects applications to modelling of real cases abstract in this paper we consider a stochastic system modelling by the stochastic rayleigh diffusion process and we discuss theoretical aspects of the latter and establish a statistical methodology to adjust it to real cases particulary in the field of biometry and related areas the rayleigh process according to the definition of c giorno a nobile l ricciardi l sacerdote some remarks on the rayleigh process journal of applied probability 23 1986 398 408 is examined from the perspective of the corresponding nonlinear stochastic differential equation and from its associated probability density function we obtain the corresponding mean functions trend function and conditional trend function which depend of kummer functions the drift parameters are estimated by maximum likelihood on the basis of continuous sampling of the process and they are calculated by computational methods we propose numerical approximations for the diffusion coefficient from an extension of the m chesney j elliot estimating the instantaneous volatility and covariance of risky assets applied stochastic models and data analysis 11 1995 51 58 procedure to the case of nonlinear stochastic differential equations and we establish also computational procedures and simulation algorithm that are applied to obtened simulated paths of the fitted process the proposed methodology is applied to two studies carried out in andalusia spain on females and males life expectancy at birth between 1944 and 2001

survival probability of a mobile particle in a fluctuating field we study the the survival probability p t upto time t of a test particle moving in a fluctuating external field the particle moves according to some prescribed deterministic or stochastic rules and survives as long as the external field that it sees at its own location does not change sign this is a natural generalization of the static persistence when the particle is at rest that has generated considerable recent interests two types of motions of the particle are considered in one case the particle adopts a strategy to live longer and in the other it just diffuses randomly three different external fields were considered i the solution of diffusion equation ii the colour profile of the q state potts model undergoing zero temperature coarsening dynamics and iii spatially uncorrelated brownian signals in most cases studied p t sim t theta m for large t the exponent theta m is calculated via numerically analytically by approximate methods and in some cases exactly it is shown in some special cases that the survival probability of the mobile particle is related to the persistence of special patterns present in the initial configuration of a phase ordering system

self diffusion and visited surface in the droplet condensation problem breath figures abstract we study experimentally and theoretically new aspects of condensation growth and coalescence of droplets on a substrate we address in particular the dynamics of a marked droplet which undergoes coalescences with neighbouring droplets we find that the number of coalescences of the droplet grows as log t t is time and that the traveled distance increases as r t the average radius of the droplets at time t the fraction of the surface which was never covered by any droplet an important quantity for applications such as drug spreading or surface decontamination decays as t showing that completion occurs only slowly heuristic arguments accurate numerical simulations on simplified models which neglect polydispersity and an exact solution reported elsewhere a bray b derrida and c godreche europhys lett 27 1994 175 strongly support these findings and show that this power law decay is a generic feature common to many different situations finally the contour of the ensemble of dry sites appears fractal with dimension d 1 22 an experimental result not reproduced by the simplified models

lp and bmo bounds of weighted hardy littlewood averages abstract this paper characterizes those nonnegative functions defined on 0 1 for which the weighted hardy littlewood average u f 0 1 f t t dt is bounded on either l p r n p 1 or bmo r n meanwhile the corresponding operator norms are worked out

the norm inequalities for the weighted cesaro mean operators this paper gives some necessary and sufficient conditions for the weighted cesaro mean operators to be bounded on herz spaces the corresponding new operator norm inequalities are obtained

universal distribution of masses in a one dimensional sticky gas abstract agglomeration of particles by perfectly inelastic collisions is studied in the case of a one dimensional gas particles move freely between collisions both mass and momentum are conserved at binary encounters it is shown that under a weak mean field like hypothesis admitting the existence of correlations between the velocities of colliding particles the dynamics drives the system towards a scaling regime with a universal exponential distribution of masses

dependence of eigenvalues of sturm liouville problems with eigenparameter dependent boundary conditions abstract this paper is concerned with regular sturm liouville problems with eigenparameter dependent boundary conditions we obtain that the eigenvalues are not only continuously but also smoothly dependent on the parameters of the problem in particular eigenparameter dependent boundary condition matrix moreover the differential expression of the eigenvalues with respect to the data is given the dependence of the nth eigenvalue as a function of the parameters of the problem is also investigated by pr u fer transformation and the inequalities of eigenvalues

dependence of eigenvalues on the boundary conditions of sturm liouville problems with one singular endpoint abstract this paper is concerned with continuous and differentiable dependence of isolated eigenvalues on the boundary conditions of self adjoint sturm liouville problems with one singular endpoint locally continuous dependence of eigenvalues on the boundary conditions is proved especially in the limit point case the continuous dependence of isolated eigenvalues is shown by the relationships between weyl titchmarsh m function and the spectrum of the singular problems then continuous eigenvalue branches through each isolated eigenvalue over the space of boundary conditions are formed it is rigorously shown that the eigenfunctions for the eigenvalues along a continuous simple eigenvalue branch can be continuously chosen with uniform bound in l w 2 norm its proof is different from that in the regular sturm liouville problems the derivative formulas of the continuous simple eigenvalue branch with respect to all the parameters in the boundary conditions are given and thus its monotonicity with respect to some parameters is derived

reaction diffusion models in one dimension with disorder we study a large class of one dimensional reaction diffusion models with quenched disorder using a real space renormalization group method rsrg which yields exact results at large time particles e g of several species undergo diffusion with random local bias sinai model and may react upon meeting we obtain a detailed description of the asymptotic states i e attractive fixed points of the rsrg such as the large time decay of the density of each specie their associated universal amplitudes and the spatial distribution of particles we also derive the spectrum of nontrivial exponents which characterize the convergence towards the asymptotic states for reactions which lead to several possible asymptotic states separated by unstable fixed points we analyze the dynamical phase diagram and obtain the critical exponents characterizing the transitions we also obtain a detailed characterization of the persistence properties for single particles as well as more complex patterns we compute the decay exponents for the probability of no crossing of a given point by respectively the single particle trajectories ensuremath theta or the thermally averaged packets overline ensuremath theta the generalized persistence exponents associated to n crossings are also obtained specifying to the process a stackrel ensuremath rightarrow a ensuremath emptyset or a with probabilities r 1 ensuremath r we compute exactly the exponents ensuremath delta r and ensuremath psi r characterizing the survival up to time t of a domain without any merging or with mergings respectively and the exponents ensuremath delta a r and ensuremath psi a r characterizing the survival up to time t of a particle a without any coalescence or with coalescences respectively overline ensuremath theta ensuremath psi and ensuremath delta obey hypergeometric equations and are numerically surprisingly close to pure system exponents though associated to a completely different diffusion length the effect of additional disorder in the reaction rates as well as some open questions are also discussed

stable distributions in stochastic fragmentation we investigate a class of stochastic fragmentation processes involving stable and unstable fragments we solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small size tail furthermore the entire range of acceptable values of decay exponent consistent with length conservation can be realized we show that the stochastic fragmentation process is non self averaging as moments exhibit significant sample to sample fluctuations additionally we find that the distributions of the moments and of extremal characteristics possess an infinite set of progressively weaker singularities

escape rates in periodically driven markov processes we present an approximate analytical expression for the escape rate of time dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrateand fire model for neural spiking the novel approximation i s based on a discrete state markovian modeling of the full long time dynamics with time dependent rates it is valid in a wide parameter regime beyond the restraining limits of weak driving linear response and or weak noise the scheme is carefully tested and yields excellent agreement with three different numerical methods based on the langevin equation the fokker planck equation and an integral equation

dynamical critical behaviours of the ising spin chain swendsen wang and wolff algorithms we study the zero temperature ising chain evolving according to the swendsen wang dynamics we determine analytically the domain length distribution and various historical characteristics e g the density of unreacted domains is shown to scale with the average domain length as l with 3 2 for the q state potts model 1 q 1 we also compute the domain length distribution for the ising chain endowed with the zero temperature wolff dynamics

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

dependence of eigenvalues of sturm liouville problems with interface conditions this paper investigates sturm liouville problems with interface conditions we obtain that the eigen values depend not only continuously but also smoothly on the coefficient functions boundary conditions and interface conditions moreover the derivative of the eigenvalues with respect to each of these parameters is given

left definite sturm liouville problems abstract left definite regular self adjoint sturm liouville problems with either separated or coupled boundary conditions are studied we give an elementary proof of the existence of eigenvalues for these problems for any fixed equation we establish a sequence of inequalities among the eigenvalues for different boundary conditions and estimate the range of each eigenvalue as a function on the space of boundary conditions some of our results here yield an algorithm for numerically computing the eigenvalues of a left definite problem with an arbitrary coupled boundary condition our inequalities imply that the well known asymptotic formula for the eigenvalues in the separated case also holds in the coupled case moreover we study the continuous and differentiable dependence of the eigenvalues of the general left definite problem on all the parameters in its differential equation and boundary condition

continuity of hardy type operators on rectangularly defined spaces abstract we introduce a generalization of rectangular herz spaces defined in 3 and prove boundedness of a version of the n dimensional hardy operator on them we also study the action of the hausdorff operator on some subspaces of bmo

aggregation kinetics for a one dimensional zero degree kelvin model of spinodal decomposition we study analytically the approach to equilibrium in a simple zero temperature model for phase separation in a binary alloy in which nearest neighbor interchange can occur only if the portion of ab bonds is thereby decreased the approach to equilibrium is found analytically because of the existence of infinitely many possible stationary states the asymptotic distribution of ab pairs depends on the details of the initial state and must be obtained by a recursion method

the study of jacobi and cyclic jacobi matrix eigenvalue problems using sturm liouville theory abstract we study the eigenvalues of matrix problems involving jacobi and cyclic jacobi matrices as functions of certain entries of particular interest are the limits of the eigenvalues as these entries approach infinity our approach is to use the recently discovered equivalence between these problems and a class of sturm liouville problems and then to apply the sturm liouville theory

analytical results for generalized persistence properties of smooth processes we present a general scheme to calculate within the independent interval approximation generalized level dependent persistence properties for processes having a finite density of zero crossings our results are especially relevant for the diffusion equation evolving from random initial conditions one of the simplest coarsening systems exact results are obtained in certain limits and rely on a new method to deal with constrained multiplicative processes an excellent agreement of our analytical predictions with direct numerical simulations of the diffusion equation is found

domain number distribution in the nonequilibrium ising model we study domain distributions in the one dimensional ising model subject to zero temperature glauber and kawasaki dynamics the survival probability of a domain s t t and an unreacted domain q1 t t are characterized by two independent nontrivial exponents we develop an independent interval approximation that provides close estimates for many characteristics of the domain length and number distributions including the scaling exponents

two interval sturm liouville operators in modified hilbert spaces abstract by modifying the inner product in the direct sum of the hilbert spaces associated with each of two underlying intervals on which the sturm liouville equation is defined we generate self adjoint realizations for boundary conditions with any real coupling matrix whose determinant is positive this contrasts with the usual theory which requires the coupling matrix to have determinant one

equivalence of inverse sturm liouville problems with boundary conditions rationally dependent on the eigenparameter abstract three inverse problems for a sturm liouville boundary value problem y qy y y 0 cos y 0 sin and y 1 f y 1 are considered for rational f it is shown that the weyl m function uniquely determines f and q and is in turn uniquely determined by either two spectra from different values of or by the prufer angle for this it is necessary to produce direct results of independent interest on asymptotics and oscillation

statistical description of contact interacting brownian walkers on the line the distribution of interval lengths between brownian walkers on the line is investigated the walkers are independent until collision at collision the left walker disappears and the right walker survives with probability p this problem arises in the context of diffusion limited reactions and also in the scaling limit of the voter model a systematic expansion in correlation between neighbor intervals gives a series of approximations of increasing accuracy for the probability density functions of interval lengths the first approximation beyond mere statistical independence between successive intervals already gives excellent results as established by comparison with direct numerical simulations

dependence of the nth sturm liouville eigenvalue on the problem abstract we consider the nth eigenvalue as a function on the space of self adjoint regular sturm liouville problems with positive leading coefficient and weight functions the discontinuity of the nth eigenvalue is completely characterized

experimental measurement of the persistence exponent of the planar ising model using a twisted nematic liquid crystal system exhibiting planar ising model dynamics we have measured the scaling exponent ensuremath theta which characterizes the time evolution p t ensuremath sim t ensuremath ensuremath theta of the probability p t that the local order parameter has not switched its state by the time t for 0 4 sec 200 sec following the phase quench the system exhibits scaling behavior and measured over this interval ensuremath theta 0 19 ifmmode pm else textpm fi 0 03 in good agreement with theoretical analysis and numerical simulations

sturm liouville problems and discontinuous eigenvalues if a sturm liouville problem is given in an open interval of the real line then regular boundary value problems can be considered on compact sub intervals for these regular problems all with necessarily discrete spectra the eigenvalues depend on both the end points of the compact intervals and upon the choice of the real separated boundary conditions at these end points these eigenvalues are not in general continuous functionsof the end points and boundary conditions the paper shows the surprising form of these discontinuities the results have applications to the approximations of singular sturm liouville problems by regular problems and to the theoretical aspects of the sleign2 computer program

boundary conditions for stochastic solutions of the convection diffusion equation stochastic methods offer an attractively simple solution to complex transport controlled problems and have a wide range of physical chemical and biological applications stochastic methods do not suffer from the numerical diffusion that plagues grid based methods but they typically lose accuracy in the vicinity of interfacial boundaries in this work we introduce some ideas and algorithms that can be used to implement boundary conditions in stochastic simulations of the convection diffusion equation with accuracies comparable to the bulk phase the algorithms have been tested in two dimensional channel flows over a range of peclet numbers and compared with independent finite difference calculations

eigenvalues of sturm liouville problems with discontinuity conditions inside a finite interval abstract in this work we use the regularized sampling method to compute the eigenvalues of sturm liouville problems with discontinuity conditions inside a finite interval we work out an example by computing a few eigenvalues and their corresponding eigenfunctions

eigenvalues of limit point sturm liouville problems abstract the dependence of the eigenvalues of self adjoint sturm liouville problems on the boundary conditions when each endpoint is regular or in the limit circle case is now due to some surprisingly recent results well understood here we study this dependence for singular problems with one endpoint in the limit point case

dependence of eigenvalues of sturm liouville problems on the boundary abstract the eigenvalues of sturm liouville sl problems depend not only continuously but smoothly on boundary points the derivative of the n th eigenvalue as a function of an endpoint satisfies a first order differential equation this for arbitrary separated or coupled self adjoint regular boundary conditions in addition as the length of the interval shrinks to zero all higher eigenvalues march off to plus infinity this is also true for the first i e lowest dirichlet eigenvalue but not for the lowest neumann eigenvalue the latter has a finite limit

deterministic soluble model of coarsening we investigate a three phase deterministic one dimensional phase ordering model in which interfaces move ballistically and annihilate upon colliding we determine analytically the autocorrelation function a t this is done by computing generalized first passage type probabilities mathrm p mathrm n t which measure the fraction of space crossed by exactly n interfaces during the time interval 0 t and then expressing the autocorrelation function via mathrm p mathrm n s we further reveal the spatial structure of the system by analyzing the domain size distribution

on the area under a continuous time brownian motion till its first passage time the area swept out under a one dimensional brownian motion till its first passage time is analysed using a fokker planck technique we obtain an exact expression for the area distribution for the zero drift case and provide various asymptotic results for the nonzero drift case emphasizing the critical nature of the behaviour in the limit of vanishing drift the results offer important insights into the asymptotic behaviour of a number of discrete models we also provide a succinct derivation for the distribution of the maximum displacement observed during a first passage

eigenvalues of regular sturm liouville problems abstract the eigenvalues of sturm liouville sl problems depend not only continuously but smoothly on the problem an expression for the derivative of an eigenvalue with respect to a given parameter an endpoint a boundary condition a coefficient or the weight function is found

the p adic weighted hardy cesaro operator and an application to discrete hardy inequalities abstract this paper aims to investigate the boundedness of the p adic analog of the weighted hardy cesaro operator u s f z p f s t t d t on weighted lebesgue spaces and weighted bmo spaces in each case we obtain the corresponding operator norms u s in particular these results have a surprising relevance to discrete hardy inequalities on the real field we prove a reverse bmo hardy inequality and give a necessary condition on so that the commutator of u s is bounded on l r q p n with symbols in bmo q p n

statistics of the occupation time of renewal processes we present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time according to the nature of the distribution of time intervals the probability density functions of these random variables have very different scalings in time we analyze successively the cases where this distribution is narrow where it is broad with index 1 and finally where it is broad with index 1 2 the methods introduced in this work provide a basis for the investigation of the statistics of the occupation time of more complex stochastic processes see joint paper by g de smedt c godreche and j m luck 26

dynamics of the formation of two dimensional ordered structures the growth of ordered domains in lattice gas models which occurs after the system is quenched from infinite temperature to a state below the critical temperaturet c is studied by monte carlo simulation for a square lattice with repulsion between nearest and next nearest neighbors which in equilibrium exhibits fourfold degenerate 2 1 superstructures the time dependent energy e t domain size l t and structure functions q t are obtained both for glauber dynamics no conservation law and the case with conserved density kawasaki dynamics at late times the energy excess and halfwidth of the structure factor decrease proportional tot x whilel t t x where the exponent x 1 2 for glauber dynamics and x 1 3 for kawasaki dynamics in addition the structure factor satisfies a scaling laws k t t 2xs ktx the smaller exponent for the conserved density case is traced back to the excess density contained in the walls between ordered domains which must be redistributed during growth quenches tot t c t tc where we estimate dynamic critical exponents andt 0 are also considered in the latter case the system becomes frozen in a glasslike domain pattern far from equilibrium when using kawasaki dynamics the generalization of our results to other lattices and structures also is briefly discussed

the distribution of the area under a bessel excursion and its moments a bessel excursion is a bessel process that begins at the origin and first returns there at some given time t we study the distribution of the area under such an excursion which recently found application in the context of laser cooling the area a scales with the time as a sim t 3 2 independent of the dimension d but the functional form of the distribution does depend on d we demonstrate that for d 1 the distribution reduces as expected to the distribution for the area under a brownian excursion known as the airy distribution deriving a new expression for the airy distribution in the process we show that the distribution is symmetric in d 2 with nonanalytic behavior at d 2 we calculate the first and second moments of the distribution as well as a particular fractional moment we also analyze the analytic continuation from d 2 in the limit where d rightarrow 4 from below this analytically continued distribution is described by a one sided levy alpha stable distribution with index 2 3 and a scale factor proportional to 4 d t 3 2

power laws and stretched exponentials in a noisy finite time singularity model we discuss the influence of white noise on a generic dynamical finite time singularity model for a single degree of freedom we find that the noise effectively resolves the finite time singularity and replaces it by a first passage time or absorbing state distribution with a peak at the singularity and a long time tail exhibiting power law or stretched exponential behavior the study might be of relevance in the context of hydrodynamics on a nanometer scale in material physics and in biophysics

floquet theory for left definite sturm liouville problems abstract we determine the essential spectrum of left definite sturm liouville problems with periodic coefficients and a weight function which changes sign

hardy type theorems on fourier transforms revised abstract we obtain new conditions on periodic integrable functions so that their transformed fourier series belong to l p this improves the classical hardy and bellman results a counterpart for the fourier transforms is also established our main tool is a new extension of the hausdorff young paley inequality for fourier transforms

a class of fokker planck equations with logarithmic factors in diffusion and drift terms the x2 ln x dependence of the diffusion coefficient in the fokker planck equation is retrieved by means of symmetry arguments exact solutions of the equation with logarithmic factors in coefficients are presented algebraic and log algebraic solutions are found for some values of exponents they seem to be analogues on an interval of log normal distributions

low and high dimension limits of a phase separation model we study a simple zero temperature model for phase separation of a binary alloy in which nearest neighbor interchange can occur if the fraction of ab pairs is not thereby increased we present analytic results for the one dimensional case and numerical results for the infinite dimensionality limit on a cayley tree in neither limit does the final fraction of ab pairs agree with the dimension independent result found previously ind 3 4 5

damped finite time singularity driven by noise we consider the combined influence of linear damping and noise on a dynamical finite time singularity model for a single degree of freedom we find that the noise effectively resolves the finite time singularity and replaces it by a first passage time distribution or absorbing state distribution with a peak at the singularity and a long time tail the damping introduces a characteristic cross over time in the early time regime the probability distribution and first passage time distribution show a power law behavior with scaling exponent depending on the ratio of the nonlinear coupling strength to the noise strength in the late time regime the behavior is controlled by the damping the study might be of relevance in the context of hydrodynamics on a nanometer scale in material physics and in biophysics

emergence of fractals in aggregation with stochastic self replication we propose and investigate a simple model which describes the kinetics of aggregation of brownian particles with stochastic self replication an exact solution and the scaling theory are presented alongside numerical simulation which fully support all theoretical findings in particular we show analytically that the particle size distribution function exhibits dynamic scaling and we verify it numerically using the idea of data collapse furthermore the conditions under which the resulting system emerges as a fractal are found the fractal dimension of the system is given and the relationship between this fractal dimension and a conserved quantity is pointed out

dependence of eigenvalues of fourth order differential equations with discontinuous boundary conditions on the problem abstract fourth order boundary value problems with discontinuous boundary conditions are studied we prove that the eigenvalues depend not only continuously but smoothly on the coefficients and on the boundary conditions and find formulas for the derivatives with respect to each of these parameters

persistence and dynamics in the annni chain we investigate both the local and global persistence behaviour in the annni axial next nearest neighbour ising model we find that when the ratio of the second neighbour interaction to the first neighbour interaction is less than 1 p t the probability of a spin to remain in its original state up to time t shows a stretched exponential decay for 1 p t has an algebraic decay but the exponent is different from that of the nearest neighbour ising model the global persistence behaviour shows similar features we also conduct some deeper investigations in the dynamics of the annni model and conclude that it has a different dynamical behaviour compared to the nearest neighbour ising model

statistical behavior of domain systems we study the statistical behavior of two out of equilibrium systems the first one is a quasi one dimensional gas with two species of particles under the action of an external field which drives each species in opposite directions the second one is a one dimensional spin system with nearest neighbor interactions also under the influence of an external driving force both systems show a dynamical scaling with domain formation the statistical behavior of these domains is compared with models based on the coalescing random walk and the interacting random walk we find that the scaling domain size distribution of the gas and the spin systems is well fitted by the wigner surmise which lead us to explore a possible connection between these systems and the circular orthogonal ensemble of random matrices however the study of the correlation function of the domain edges shows that the statistical behavior of the domains in both gas and spin systems is not completely well described by a circular orthogonal ensemble nor it is by other models proposed such as the coalescing random walk and the interacting random walk nevertheless we find that a simple model of independent intervals describes more closely the statistical behavior of the domains formed in these systems

dependence of eigenvalues of a class of fourth order sturm liouville problems on the boundary in this paper we consider the dependence of eigenvalues of a class of fourth order sturm liouville problems on the boundary we show that the eigenvalues depend not only continuously but smoothly on boundary points and that the derivative of the nth eigenvalue as a function of an endpoint satisfies a first order differential equation in addition we prove that as the length of the interval shrinks to zero all higher fourth order dirichlet eigenvalues march off to plus infinity this is also true for the first i e lowest eigenvalue

regular third order boundary value problems abstract in this paper we consider some boundary value problems generated by third order formally symmetric self adjoint regular differential expression and separated real coupled and complex coupled boundary conditions it is shown that these problems generate self adjoint operators moreover the dependence of eigenvalues of these problems on the data are studied and some derivatives of the eigenvalues with respect to some elements of data are introduced

existence of multiple positive solutions for sturm liouville like four point boundary value problem with p laplacian abstract in this paper we consider the sturm liouville like four point boundary value problem with p laplacian p u t f t u t 0 t 0 1 u 0 u 0 u 1 u 0 where p s s p 2 s p 1 by means of a fixed point theorem for operators on a cone the existence of multiple at least three positive solutions to the above boundary value problem is obtained

hardy space estimates of hausdorff operators on the heisenberg group abstract this is a continuation of a series of works about hausdorff operator on hardy spaces in the setting of the heisenberg group in this paper we obtain the boundedness from lebesgue spaces to hardy spaces for fractional hausdorff operators and their compositions with riesz transforms we also establish the boundedness for two kinds of special hausdorff operators the hausdorff poisson operator and the hausdorff gauss operator on hardy spaces

domain statistics in coarsening systems we study the domain number and size distributions in the one dimensional ising and q state potts models subject to zero temperature glauber dynamics the survival probability of a domain s t t 2c and an unreacted domain q1 t t 2d are characterized by two independent nontrivial exponents for the ising case we find c50 126 and d51 27 using numerical simulations we develop an independent interval approximation that predicts the qualitative behavior of the domain distribution and provides good estimates for the exponents exact results for the domain distribution are also obtained in several solvable cases s1063 651x 97 00110 4

dynamics of the condensate in zero range processes for stochastic processes leading to condensation the condensate once it is formed performs an ergodic stationary state motion over the system we analyse this motion and especially its characteristic time for zero range processes the characteristic time is found to grow with the system size much faster than the diffusive time scale but not exponentially fast this holds both in the mean field geometry and on finite dimensional lattices in the generic situation where the critical mass distribution follows a power law the characteristic time grows as a power of the system size

aggregation with multiple conservation laws aggregation processes with an arbitrary number of conserved quantities are investigated on the mean field level an exact solution for the size distribution is obtained the asymptotic form of this solution exhibits nontrivial double scaling while processes with one conserved quantity are governed by a single scale processes with multiple conservation laws exhibit an additional diffusion like scale the theory is applied to ballistic aggregation with mass and momentum conserving collisions and to diffusive aggregation with multiple species

superaging correlation function and ergodicity breaking for brownian motion in logarithmic potentials we consider an overdamped brownian particle moving in a confining asymptotically logarithmic potential which supports a normalized boltzmann equilibrium density we derive analytical expressions for the two time correlation function and the fluctuations of the time averaged position of the particle for large but finite times we characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential and we support our predictions with extensive langevin simulations while the boltzmann measure is used to obtain stationary correlation functions we show how the non normalizable infinite covariant density is related to the superaging behavior

symmetry classification and exact solutions of the one dimensional fokker planck equation with arbitrary coefficients of drift and diffusion symmetry properties of the one dimensional fokker planck equations with arbitrary coefficients of drift and diffusion are investigated it is proved that the group symmetry of these equations can be one two four or six parametric and corresponding criteria are obtained the changes of the variables reducing fokker planck equations to the heat equation and schrodinger equation with certain potentials are determined using the substructure of the invariance algebra of the rayleigh process equation we obtain the differential invariants and construct some classes of the exact solutions of this equation

stochastic aggregation scaling properties we study the scaling properties of stochastic aggregation processes in one dimension numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent non trivial exponents corresponding to the survival probability of particles and monomers the overall behaviour agrees qualitatively with the mean field theory this theory also provides a useful approximation for the decay exponents as well as the limiting mass distribution

generalized poincare embeddings and weighted hardy operator on qpα q spaces abstract the poincare embeddings w 1 n r n bmo r n and the john nirenberg inequality in bmo r n are classical results in modern analysis and partial differential equations this paper studies the generalized poincare embeddings and the john nirenberg inequality in q p q r n spaces furthermore for the weighted hardy operator u and its adjoint v this paper gives sufficient and necessary conditions on weight function to ensure the boundedness of them on q p q r n spaces

stochastic calculus for uncoupled continuous time random walks the continuous time random walk ctrw is a pure jump stochastic process with several applications not only in physics but also in insurance finance and economics a definition is given for a class of stochastic integrals driven by a ctrw which includes the it and stratonovich cases an uncoupled ctrw with zero mean jumps is a martingale it is proved that as a consequence of the martingale transform theorem if the ctrw is a martingale the it integral is a martingale too it is shown how the definition of the stochastic integrals can be used to easily compute them by monte carlo simulation the relations between a ctrw its quadratic variation its stratonovich integral and its it integral are highlighted by numerical calculations when the jumps in space of the ctrw have a symmetric levy alpha stable distribution and its waiting times have a one parameter mittag leffler distribution remarkably these distributions have fat tails and an unbounded quadratic variation in the diffusive limit of vanishing scale parameters the probability density of this kind of ctrw satisfies the space time fractional diffusion equation fde or more in general the fractional fokker planck equation which generalizes the standard diffusion equation solved by the probability density of the wiener process and thus provides a phenomenologic model of anomalous diffusion we also provide an analytic expression for the quadratic variation of the stochastic process described by the fde and check it by monte carlo

regular approximation of singular sturm liouville problems with transmission conditions in this paper we study regular approximation of singular sturm liouville problems with transmission conditions we construct all self adjoint extensions of the minimal operators and the induced restriction operators using the abstract operator theory in the hilbert space we obtain that the spectrum of singular sturm liouville problems with transmission conditions can be approximated by eigenvalues of a sequence of regular sturm liouville problems with transmission conditions

power law tail distributions and nonergodicity we establish an explicit correspondence between ergodicity breaking in a system described by power law tail distributions and the divergence of the moments of these distributions

sturm liouville problems with boundary conditions rationally dependent on the eigenparameter ii necessary and sufficient conditions are given for two sequences n and n to be the eigenvalues and norming constants of a sturm liouville boundary value problem y qy y y 0 cos y 0 sin and y 1 f y 1 where f is a rational function of herglotz nevanlinna type it is also proved that q and f are uniquely determined by the sequences n and n

error estimate of eigenvalues of perturbed second order discrete sturm liouville problems abstract this paper is concerned with eigenvalues of perturbed second order vector discrete sturm liouville problems by some variational properties of eigenvalues of discrete sturm liouville problems error estimates of eigenvalues of perturbed problems sufficiently close to a given sturm liouville problem are given under a certain non singularity condition perturbations of the coefficient functions of the difference equation the weight function and the coefficients of the boundary condition are all considered this together with higher dimension involved results in a certain complexity of the problem and difficulty of study as a direct consequence continuous dependence of eigenvalues on problems is obtained under the non singularity condition in addition an example is presented to illustrate the necessity of the non singularity condition

distribution of domain sizes in the zero temperature glauber dynamics of the one dimensional potts model for the zero temperature glauber dynamics of the q state potts model we calculate the exact distribution of domain sizes by mapping the problem on an exactly soluble one species coagulation model a1a a in the long time limit this distribution is universal and from its complicated exact expression we extract its behavior in various regimes our results are tested in a simulation and compared to the predictions of a simple approximation proposed recently considering the dynamics of domain walls as a reaction diffusion model a1a a with probability q22 q21 and a1a f with probability 1 q21 we calculate the pair correlation function in the long time regime s1063 651x 96 12809 9

on the boundary conditions in self adjoint multi interval sturm liouville problems abstract in this paper we completely solve a problem whose two interval case has been studied recently by wang et al in a wang j sun a zettl two interval sturm liouville operators in modified hilbert spaces j math anal appl 328 2007 390 399 the problem is to give an explicit description of all boundary conditions defining the self adjoint differential operators associated with several sturm liouville equations together i e the so called multi interval sturm liouville problems the explicit description obtained in this paper only uses hermitian matrices as an application we then show that a generic self adjoint boundary condition can not come from any direct sum of self adjoint operators associated with the individual sturm liouville equations and it depends non trivially on the multiples used in the definition of the so called maximum operator

random walkers in one dimensional random environments exact renormalization group analysis sinai s model of diffusion in one dimension with random local bias is studied by a real space renormalization group which yields exact results at long times the effects of an additional small uniform bias force are also studied we obtain analytically the scaling form of the distribution of the position x t of a particle the probability of it not returning to the origin and the distributions of first passage times in an infinite sample as well as in the presence of a boundary and in a finite but large sample we compute the distribution of the meeting time of two particles in the same environment we also obtain a detailed analytic description of the thermally averaged trajectories by computing quantities such as the joint distribution of the number of returns and of the number of jumps forward these quantities obey multifractal scaling characterized by generalized persistence exponents ensuremath theta g which we compute in the presence of a small bias the number of returns to the origin becomes finite characterized by a universal scaling function which we obtain the full statistics of the distribution of successive times of return of thermally averaged trajectories is obtained as well as detailed analytical information about correlations between directions and times of successive jumps the two time distribution of the positions of a particle x t and x t ensuremath with tg t ensuremath is also computed exactly it is found to exhibit aging with several time regimes characterized by different behaviors in the unbiased case for t ensuremath t ensuremath ensuremath sim t ensuremath ensuremath alpha with ensuremath alpha g1 it exhibits a mathrm ln t mathrm ln t ensuremath scaling with a singularity at coinciding rescaled positions x t x t ensuremath this singularity is a novel feature and corresponds to particles that remain in a renormalized valley for closer times ensuremath alpha l1 the two time diffusion front exhibits a quasiequilibrium regime with a mathrm ln t ensuremath t ensuremath mathrm ln t ensuremath behavior which we compute the crossover to a t t ensuremath aging form in the presence of a small bias is also obtained analytically rare events corresponding to intermittent splitting of the thermal packet between separated wells which dominate some averaged observables are also characterized in detail connections with the green function of a one dimensional schr odinger problem and quantum spin chains are discussed

reaction kinetics of cluster impurities we study the density of clustered immobile reactants in the diffusion controlled single species annihilation an initial state in which these impurities occupy a subspace of codimension d leads to a substantial enhancement of their survival probability the smoluchowski rate theory suggests that the codimensionality plays a crucial role in determining the long time behavior the system undergoes a transition at d 2 for d 2 above this critical codimension d 2 the subspace decays indefinitely at the critical codimension inverse logarithmic decay occurs ni t log t a d d above the critical codimension the decay is algebraic ni t t a d d in general the exponents governing the long time behavior depend on the dimension as well as the codimension

coarsening and persistence in the voter model the voter model is a simple model for coarsening with a nonconserved scalar order parameter we investigate coarsening and persistence in the voter model by introducing the quantity pn t defined as the fraction of voters who changed their opinion n times up to time t we show that pn t exhibits scaling behavior that strongly depends on the dimension as well as on the initial opinion concentrations exact results are obtained for the average number of opinion changes n and the autocorrelation function a t 21 n pn t 2d 2 in arbitrary dimension d these exact results are complemented by a mean field theory heuristic arguments and numerical simulations for dimensions d 2 the system does not coarsen and the opinion changes follow a nearly poissonian distribution in agreement with mean field theory for dimensions d 2 the distribution is given by a different scaling form which is characterized by nontrivial scaling exponents for unequal opinion concentrations an unusual situation occurs where different scaling functions correspond to the majority and the minority as well as for even and odd n

non trivial exponents in the zero temperature dynamics of the 1d ising and potts models we consider the glauber dynamics of the q state potts model in one dimension at zero temperature starting with a random initial configuration we measure the density r t of spins which have never flipped from the beginning of the simulation until time t we find that for large t the density r t has a power law decay left r t sim t theta right where the exponent theta varies with q our simulations lead to theta simeq 37 for q 2 theta simeq 53 for q 3 and theta longrightarrow 1 as q longrightarrow infty

self similar gaussian processes for modeling anomalous diffusion we study some gaussian models for anomalous diffusion which include the time rescaled brownian motion two types of fractional brownian motion and models associated with fractional brownian motion based on the generalized langevin equation gaussian processes associated with these models satisfy the anomalous diffusion relation which requires the mean square displacement to vary with t ensuremath alpha 0l ensuremath alpha l2 however these processes have different properties thus indicating that the anomalous diffusion relation with a single parameter is insufficient to characterize the underlying mechanism although the two versions of fractional brownian motion and time rescaled brownian motion all have the same probability distribution function the slepian theorem can be used to compare their first passage time distributions which are different finally in order to model anomalous diffusion with a variable exponent ensuremath alpha t it is necessary to consider the multifractional extensions of these gaussian processes

estimates of weighted hardy littlewood averages on the p adic vector space abstract in the p adic vector space q p n we characterize those non negative functions defined on z p w q p 0 w p 1 for which the weighted hardy littlewood average u f z p f t t d t is bounded on l r q p n 1 r and on bmo q p n also in each case we find the corresponding operator norm u

first passage and first exit times of a bessel like stochastic process we study a stochastic process x t which is a particular case of the rayleigh process and whose square is the bessel process with various applications in physics chemistry biology economics finance and other fields the stochastic differential equation is dx t nd x t dt 2d dw t where w t is the wiener process the drift term can arise from a logarithmic potential or from taking x t as the norm of a multidimensional random walk due to the singularity of the drift term for x t 0 different natures of boundary at the origin arise depending on the real parameter n entrance exit and regular for each of them we calculate analytically and numerically the probability density functions of first passage times or first exit times nontrivial behavior is observed in the case of a regular boundary