on james and jordan von neumann constants of lorentz sequence spaces the nonsquare or james constant j x and the jordan von neumann constant cnj x are computed for two dimensional lorentz sequence spaces d 2 w q in the case where 2 q the jordan von neumann constant is also calculated in the case where 1 q 2

on the blockwise bootstrap for empirical processes for stationary sequences in this paper we study the weak convergence to an appropriate gaussian process of the empirical process of the block based bootstrap estimator proposed by k unsch for stationary sequences the classes of processes investigated are weak dependent and associated sequences we also prove that differently from the independent situation the bootstrapped estimator of the mean of certain dependent sequences satisfies the central limit theorem while the mean of the original sequence does not

the weighted hardy s inequality for nonincreasing functions the purpose of this paper is to give an alternative proof of recent results of m arino and b muckenhoupt 1 and e sawyer 8 concerning hardy s inequality for nonincreasing functions and related applications to the boundedness of some classical operators on general lorentz spaces our approach will extend the results of 1 8 to the values of the parameters which are inaccessible by the methods of these papers

dynamics of complex interfaces complex interfacial dynamics is studied in an oscillatory medium described by a deterministic coupled map lattice this dynamical system supports only stable periodic attractors the interfaces that separate the stable homogeneous phases exhibit different types of behavior ranging from simple planar fronts with low periodicity to highly irregular fronts with complex spatiotemporal transients a dynamical analysis of the system is carried out for a small interface length l in which the probabilities of occurrence of given periodic orbits the velocities of the corresponding interfaces and lyapunov exponents are calculated the importance of transient dynamics for large l is demonstrated in the large l regime the interfacial evolution and structure are characterized in statistical terms and the simulation results are compared with phenomenological stochastic models such as edwards wilkinson and kardar parisi zhang equations in some parameter regions the deterministic transient interfacial dynamics of the coupled map model is described well by such models if finite size effects are taken into account nucleation and growth dynamics are also investigated the system provides a framework in which to study complex interfacial structures

a lattice renorming theorem and applications to vector valued processes a norm 11 11 on a banach space e is said to be locally uniformly convex if iixnii lxii and iix xli 211xii implies that xn x in norm it is shown that a banach lattice has an order equivalent locally uniformly convex norm if and only if the lattice is order continuous this result is used to reduce convergence theorems for lattice valued positive martingales and submartingales to the scalar case 0 introduction a norm j on a banach space e is said to have the kadec klee property sometimes property h if whenever xn x weakly and llx ll lix ll then x0 x strongly the aim of this paper is to show that if e has an equivalent kadec klee norm then one may obtain convergence theorems for e valued random processes xj whenever j ixjj is a well known real valued convergent process and whenever the limit can be identified in the banach space for instance the classical kadec renorming theorem for separable banach spaces gives the convergence of vector valued martingales uniform amarts and additive processes ergodic theorem since their norms are real valued submartingales amarts and subadditive processes respectively while the identification of the limit requires the radonnikodym property on the space for the first two processes the limit of the third process exists in any banach space if now we consider positive submartingales and subadditive processes valued in a banach lattice one needs that the equivalent kadec klee norm be also a lattice norm in order to conclude that the norms of these processes are real valued submartingales and subadditive processes respectively 1 deals with the existence of such a lattice renorming while in 1i we show how this leads to a unified approach for proving the almost sure convergence of the processes mentioned above i renorming order continuous lattices a norm jj 1 on a banach space e is said to be locally uniformly convex if jjx jj i jjxii and iix xnjj 2j1xii imply that xn x strongly this notion is clearly stronger than the kadec klee property received by the editors october 15 1979 and in revised form february 11 1980 presented to the society san antonio january 1980 ams mos subject classifications 1970 primary 46b99 60g99

isomorphic copies in the lattice e and its symmetrization e with applications to orlicz lorentz spaces the paper is devoted to the isomorphic structure of symmetrizations of quasi banach ideal function or sequence lattices the symmetrization e of a quasi banach ideal lattice e of measurable functions on i 0 a 0 a or i n consists of all functions with decreasing rearrangement belonging to e for an order continuous e we show that every subsymmetric basic sequence in e which converges to zero in measure is equivalent to another one in the cone of positive decreasing elements in e and conversely among several consequences we show that provided e is order continuous with fatou property e contains an order isomorphic copy of lp if and only if either e contains a normalized lp basic sequence which converges to zero in measure or e contains the function t 1 p we apply these results to the family of two weighted orlicz lorentz spaces w v i defined on i n or i 0 a 0 a this family contains usual orlicz lorentz spaces w i when v 1 and orlicz marcinkiewicz spaces m w i when v 1 w we show that for a large class of weights w v it is equivalent for the space w v 0 1 and for the non weighted orlicz space l 0 1 to contain a given sequential orlicz space h isomorphically as a sublattice in their respective order continuous parts we provide a complete characterization of order isomorphic copies of lp in these spaces over 0 1 or n exclusively in terms of the indices of if i 0 we show that the set of exponents p for which lp lattice embeds in the order continuous part of w v i is the union of three intervals determined respectively by the indices of and by the condition that the function t 1 p belongs to the space

uniform k monotonicity and k order continuity in symmetric spaces with application to approximation theory abstract we investigate k order continuity in a symmetric space e using the fundamental function of e we also show a connection between reflexivity and k order continuity in symmetric spaces next we present several results devoted to a characterization of uniform k monotonicity and decreasing increasing uniform k monotonicity in symmetric spaces we also discuss a relationship between decreasing resp increasing uniform monotonicity and decreasing resp increasing uniform k monotonicity next we deliberate a correlation between uniform k monotonicity and uniform rotundity in symmetric spaces finally employing k monotonicity properties and k order continuity we provide solvability and stability of the best approximation problem in the sense of the hardy littlewood polya relation in symmetric spaces

points of monotonicity in orlicz lorentz function spaces abstract in orlicz lorentz function space m 0 points of upper monotonicity lower monotonicity upper local uniform monotonicity and lower local uniform monotonicity are characterized as the corollary we can easily obtain the criteria for strict monotonicity upper local uniform monotonicity and lower local uniform monotonicity of m 0

relationships between k monotonicity and rotundity properties with application abstract in this paper we investigate a relationship between fully k rotundity properties uniform k monotonicity properties reflexivity and k order continuity in symmetric spaces e we also answer a crucial question whether fully k rotundity properties might be restricted in definition to e d the positive cone of all nonnegative and decreasing elements of e we present a complete characterization of decreasing uniform k monotonicity and k order continuity in e it is worth mentioning that we also establish several auxiliary results describing reflexivity in lorentz spaces p w and k order continuity in orlicz spaces l finally we show an application of discussed geometric properties to the approximation theory

association and random measures our point of departure is the result due to burton and waymire that every infinitely divisible random measure has the property variously known as association positive correlations or the fkg property this leads into a study of stationary associated random measures onrd we establish simple necessary and sufficient conditions for ergodicity and mixing when second moments are present we also study the second moment condition that is usually referrent to as finite susceptibility as one consequence of these results we can easily rederive some central limit theorems of burton and waymire using association techniques we obtain a law of the iterated logarithm for infinitely divisible random measures under simple moment hypotheses finally we apply these results to a class of stationary random measures related to measure valued markov branching processes

fractional laplacian in bounded domains the fractional laplacian operator ensuremath ensuremath ensuremath delta ensuremath alpha 2 appears in a wide class of physical systems including l evy flights and stochastic interfaces in this paper we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval the implementation of boundary conditions is justified by appealing to two physical models namely hopping particles and elastic springs the eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions some analytical results concerning the structure of the eigenvalue spectrum are also obtained

on some geometric properties of generalized orlicz lorentz function spaces in this article we continue investigations concerning generalized orlicz lorentz function spaces initiated in the papers foralewski 2011 29 30 cf also foralewski 2008 27 28 first it is shown that modular is orthogonally subadditive next monotonicity properties are considered in order to get sufficient conditions for uniform monotonicity of the space a strong condition of 2 type and the notion of regularity of the generated musielak orlicz function are introduced finally criteria for non squareness of are presented

symmetry based determination of space time functions in nonequilibrium growth processes we study the space time correlation and response functions in nonequilibrium growth processes described by linear stochastic langevin equations exploiting exclusively the existence of space and time dependent symmetries of the noiseless part of these equations we derive expressions for the universal scaling functions of two time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion the usefulness of the space time functions is illustrated through the investigation of two atomistic growth models the family model and the restricted family model which are shown to belong to a unique universality class in 1 1 and 2 1 space dimensions this corrects earlier studies which claimed that in 2 1 dimensions the two models belong to different universality classes

characterizations of kadec klee properties in symmetric spaces of measurable functions we present several characterizations of kadec klee properties in symmetric function spaces on the half line based on the k functional of j peetre in addition to the usual kadec klee property we study those symmetric spaces for which sequential convergence in measure respectively local convergence in measure on the unit sphere coincides with norm convergence

property β of rolewicz and orthogonal convexities of calderon lozanovskiĭ spaces abstract we find criteria for property of rolewicz and orthogonal convexities in calderon lozanovski spaces in order to present characterization for property in the sequence case we introduce a new respective monotonicity property the particular case of orlicz lorentz spaces will also be discussed

on the convergence rate in the central limit theorem for associated processes on donne des taux de convergence uniforme dans le theoreme central limite pour des processus associes au troisieme moment fini la stationarite n etant pas requise

local monotonicity structure of symmetric spaces with applications abstract in this paper we discuss several monotonicity properties in banach lattices we start with several general results on local structure of symmetric banach function spaces discussing in particular whether a point x e has some local property if and only if its nonincreasing rearrangement x has the same property section 2 in that section we also prove some general facts for nonincreasing rearrangements which may be of independent interest next we apply these results to find complete criteria for local monotonicity structure of lorentz spaces p and orlicz lorentz spaces sections 3 local structure of lorentz spaces 4 1 local structure of orlicz lorentz spaces 4 2 local uniform structure of lorentz spaces we conclude with the description of global monotonicity structure of lorentz spaces p section 4 3 we finish with the applications of upper monotonicity and lower monotonicity points to local best dominated approximation problems in banach lattices section 5

a strong invariance principle for associated random fields in this paper we generalize yu s ann probab 24 1996 2079 2097 strong invariance principle for associated sequences to the multi parameter case under the assumption that the covariance coefficient u n decays exponentially as n the main tools that we use are the following the berkes and morrow

deconvolving multivariate kernel density estimates from contaminated associated observations we consider the estimation of the multivariate probability density function f x sub 1 x sub p of x sub 1 x sub p of a stationary positively or negatively associated pa or na random process x sub i sub i 1 sup spl infin from noisy observations both ordinary smooth and super smooth noise are considered quadratic mean and asymptotic normality results are established

weak convergence for weighted empirical processes of dependent sequences in this paper we establish weak convergence theorems for weighted empirical processes of strong mixing p mixing and associated sequences we apply these results to obtain weak convergence of integral functionals of empirical processes and of mean residual life processes in reliability theory to carry out the proofs we develop two rosenthal type inequalities for strong mixing and associated sequences

local approach to kadec klee properties in symmetric function spaces abstract we prove several results concerning local approach to kadec klee properties with respect to global local convergence in measure in symmetric banach function spaces which may be of independent interest moreover we prove characterizations of these properties in the lorentz spaces finally we show applications of h g and h l points to the local best dominated approximation problems in banach lattices

local δ2e x condition as a crucial tool for local structure of calderon lozanovskiĭ spaces abstract we shall give a full criterion for a point x e to be a point of order continuity of calderon lozanovski spaces e in order to get that result we introduce the new local 2 e x condition which appears to be necessary and sufficient for this goal next we study the structure of points of lower local uniform monotonicity llum for short we give a result concerning general kothe sequence spaces and we present a characterization for llum points in calderon lozanovski spaces

rotundity structure of local nature for generalized orlicz lorentz function spaces abstract criteria for extreme points and rotund points in generalized orlicz lorentz function spaces which were introduced in foralewski 2011 27 are given some examples show that in these spaces the notion of rotund point is essentially stronger than the notion of extreme point finally the criteria obtained in this paper are interpreted in the case of classical orlicz lorentz spaces results of this paper are related to the results from carothers et al 1992 9 kaminska 1990 4 foralewski et al 2008 26

monotonicity and rotundity of lorentz spaces γp w abstract criteria for rotundity strict monotonicity and lower local uniform monotonicity of the lorentz spaces p w of maximal functions are given under arbitrary nonnegative weight function w necessary conditions are also established for uniform monotonicity of the spaces p w for 1 p moreover the spaces 1 w that are uniformly monotone are characterized

local rotundity structure of generalized orlicz lorentz sequence spaces abstract we give some criteria for extreme points and strong u points in generalized orlicz lorentz sequence spaces which were introduced in p foralewski h hudzik l szymaszkiewicz on some geometric and topological properties of generalized orlicz lorentz sequence spaces math nachr in press cf g g lorentz an inequality for rearrangements amer math monthly 60 1953 176 179 m nawrocki the mackey topology of some f spaces ph d dissertation adam mickiewicz university poznan 1984 in polish some examples show that in these spaces the notion of the strong u point is essentially stronger than the notion of the extreme point this paper is related to the results from a kaminska extreme points in orlicz lorentz spaces arch math 55 1990 173 180 see remark 1

a strong approximation theorem for positively dependent gaussian sequences and its applications abstract under the polynomial decay rates and finite second moment a strong approximation theorem for partial sums of linear positive quadrant dependent gaussian sequences is derived as applications the law of the iterated logarithm the chung type law of the iterated logarithm and the almost sure central limit theorem are obtained with minimal conditions

continuum model for radial interface growth abstract a stochastic partial differential equation along the lines of the kardar parisi zhang equation is introduced for the evolution of a growing interface in a radial geometry regular polygon solutions as well as radially symmetric solutions are identified in the deterministic limit the polygon solutions of relevance to on lattice eden growth from a seed in the zero noise limit are unstable in the continuum in favour of the symmetric solutions the asymptotic surface width scaling for stochastic radial interface growth is investigated through numerical simulations and found to be characterized by the same scaling exponent as that for stochastic growth on a substrate

nonlocal kardar parisi zhang equation to model interface growth the dynamics of the growth of interfaces in the presence of noise and when the normal velocity is constant in the weakly nonlinear limit are described by the kardar parisi zhang kpz equation in many applications however the growth is controlled by nonlocal transport which is not contained in the original kpz equation for these problems we are proposing an extension of the kpz model where the nonlocal contribution is expressed through a hilbert transform and can act to either stabilize or destabilize the interface the model is illustrated with a specific example from reactive infiltration the properties of the solution of the resulting equation are studied in one spatial dimension in the linear and the nonlinear limits for both stable and unstable growth we find that the early time behavior has a power law scaling similar to that of the kpz equation however in the case of stable growth the scaling of the saturation width is logarithmic which differs from the power law in the kpz equation this dependence reflects the stabilizing effect of nonlocal transport in the unstable case we obtain results similar to those of olami et al phys rev e 55 2649 1997

on geometric structure of symmetric spaces abstract in this article we discuss local approach to strict k monotonicity and local uniform rotundity in symmetric spaces we prove several general results on local structure of symmetric spaces e showing relation between strict monotonicity and strict k monotonicity and the kadec klee property for global convergence in measure we also present the full criteria for points of upper k monotonicity in lorentz spaces p w for degenerated weight function w next we characterize local uniform rotundity in symmetric spaces e proving several correspondences between x e a point of local uniform rotundity and its decreasing rearrangement x and absolute value x finally we apply these results to find complete criteria for local uniform rotundity of lorentz spaces p w

on the strong convergence rate for positively associated random variables abstract for sequences of the positively associated random variables which are strictly weaker than the classical associated random ones introduced by esary et al 1967 7 strong convergence rate n 1 2 log n 1 2 is obtained which reaches the available one for independent random variables in terms of berstein type inequality further we give the corresponding precise asymptotics with respect to the rate mentioned above which extend and improve the relevant results in fu 2009 8

pointwise products of some banach function spaces and factorization abstract the well known factorization theorem of lozanovski may be written in the form l 1 e e where means the pointwise product of banach ideal spaces a natural generalization of this problem would be the question when one can factorize f through e i e when f e m e f where m e f is the space of pointwise multipliers from e to f properties of m e f were investigated in our earlier paper 41 and here we collect and prove some properties of the construction e f the formulas for pointwise product of calderon lozanovski e spaces lorentz spaces and marcinkiewicz spaces are proved these results are then used to prove factorization theorems for such spaces finally it is proved in theorem 11 that under some natural assumptions a rearrangement invariant banach function space may be factorized through a marcinkiewicz space

local approach to order continuity in cesaro function spaces abstract the goal of this paper is to present a complete characterization of points of order continuity in abstract cesaro function spaces cx for x being a symmetric function space under some additional assumptions mentioned result takes the form c x a c x a we also find simple equivalent condition for this equality which in the case of i 0 1 comes to x l furthermore we prove that x is order continuous if and only if cx is under assumption that the cesaro operator is bounded on x this result is applied to particular spaces namely cesaro orlicz function spaces cesaro lorentz function spaces and cesaro marcinkiewicz function spaces to get criteria for oc points

the law of the iterated logarithm for positively dependent random variables the levy s type maximal inequality is a key to establish the law of the iterated logarithm for associated random variables unfortunately this type inequality cannot be obtained for a generalization of association i e linear positive quadrant dependence because of their special dependence structure the purpose of this paper is to provide a different approach to obtain a law of the iterated logarithm for a sequence of linear positive quadrant dependent random variables

exact rates in log law for positively associated random variables abstract let x n n 1 be a strictly stationary sequence of positively associated random variables with mean zero and finite variance set s n k 1 n x k m n max k n s k n 1 suppose 2 e x 1 2 2 k 2 e x 1 x k in this paper we study the exact convergence rates of a kind of weighted infinite series of p m n e n log n p s n e n log n and i s n e n log n as e 0 respectively

uniformly nonsquare banach spaces have the fixed point property for nonexpansive mappings abstract it is shown that if the modulus x of nearly uniform smoothness of a reflexive banach space satisfies x 0 1 then every bounded closed convex subset of x has the fixed point property for nonexpansive mappings in particular uniformly nonsquare banach spaces have this property since they are properly included in this class of spaces this answers a long standing question in the theory

on the james constant and b convexity of cesaro and cesaro orlicz sequence spaces abstract the classical james constant and the nth james constants which are measure of b convexity for the cesaro sequence spaces ces p and the cesaro orlicz sequence spaces ces m are calculated these investigations show that ces p ces m are not uniformly non square and even they are not b convex therefore the classical cesaro sequence spaces ces p are natural examples of reflexive spaces which are not b convex moreover the james constant for the two dimensional cesaro space ces 2 2 is calculated

symmetrization factorization and arithmetic of quasi banach function spaces abstract we investigate relations between symmetrizations of quasi banach function spaces and constructions such as calderon lozanovski spaces pointwise product spaces and pointwise multipliers we show that under reasonable assumptions the symmetrization commutates with these operations we determine also the spaces of pointwise multipliers between lorentz spaces and cesaro spaces the methods that we develop may be regarded as an arithmetic of quasi banach function spaces and proofs of theorem 3 theorem 4 theorem 6 give a kind of tutorial for these methods finally the above results will be used in proofs of some factorization results

equidistributed random variables in lp q abstract we consider linear combinations of independent identically distributed random variables in l p q in fact we provide several norm inequalities for sums from a larger class of equidistributed random variables

convexity and concavity constants in lorentz and marcinkiewicz spaces abstract we provide here the formulas for the q convexity and q concavity constants for function and sequence lorentz spaces associated to either decreasing or increasing weights it yields also the formula for the q convexity constants in function and sequence marcinkiewicz spaces in this paper we extent and enhance the results from g j o jameson the q concavity constants of lorentz sequence spaces and related inequalities math z 227 1998 129 142 and a kaminska a m parrish the q concavity and q convexity constants in lorentz spaces in banach spaces and their applications in analysis conference in honor of nigel kalton may 2006 walter de gruyter berlin 2007 pp 357 373

local structure of symmetrizations e with applications abstract we study the local structure of the separated point x in the space e with respect to properties of its nonincreasing rearrangement x in the space e in particular we get the characterizations of local structure in the lorentz and marcinkiewicz spaces it is worth to mention that the local structure of a separated point can be applicable to the local best dominated approximation problems in banach lattices

correlations in a generalized elastic model fractional langevin equation approach the generalized elastic model gem provides the evolution equation which governs the stochastic motion of several many body systems in nature such as polymers membranes and growing interfaces on the other hand a probe tracer particle in these systems performs a fractional brownian motion due to the spatial interactions with the other system s components the tracer s anomalous dynamics can be described by a fractional langevin equation fle with a space time correlated noise we demonstrate that the description given in terms of gem coincides with that furnished by the relative fle by showing that the correlation functions of the stochastic field obtained within the fle framework agree with the corresponding quantities calculated from the gem furthermore we show that the fox h function formalism appears to be very convenient to describe the correlation properties within the fle approach

dual spaces of weak orlicz hardy spaces for vector valued martingales abstract the dual spaces of weak orlicz hardy spaces for b valued martingales which are defined by quasi concave functions are identified to obtain the results the so called weak type generalized campanato spaces are introduced and the classical technique of atomic decompositions is employed the results obtained here extend the corresponding known results in the literature from real valued setting to vector valued setting and from strong type spaces to weak type spaces

normal approximation for associated point processes via stein s method with applications to determinantal point processes abstract we use stein s method to provide non asymptotic l 1 bounds also known as wasserstein bounds to the normal for functionals of associated point processes as for supporting tools we use the connection between association and mixing properties that was recently uncovered by 29 we apply our main results to determinantal point processes which are known to be negatively associated a potential application to determinantal point processes in the laguerre gaussian family is also presented

non local fractional growing surfaces planar and radial geometries the fractional langevin equation has been used to describe the evolution of the location of a stochastically growing interface in both planar and radial geometries the interface dynamics can be driven by both local and non local effects since the fractional derivative is non local in terms of h unless is an even nonnegative integer in this paper we consider a general two term langevin equation and calculate the interface location in planar and radial geometries we study the dynamics of the system for the stabilizing and destabilizing cases and for different time limits the analytical results are confirmed by numerically solving the fractional stochastic equations

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

on isometric copies of l and james constants in cesaro orlicz sequence spaces abstract for a wide class of orlicz functions not satisfying the growth condition 2 we show that the cesaro orlicz sequence spaces ces equipped with the luxemburg norm contain an order linearly isometric copy of l we also compute the n th james constant in these spaces for any orlicz function under either the luxemburg or orlicz norm showing that they are equal to n for any natural n 2 in particular we prove that the non trivial spaces ces are not b convex for any orlicz function