weighted estimates for the helmholtz equation and some applications we characterize the radial functionsvin rnfor which the a priori inequality u1 2 2 k uv1 2 2 c v 1 2 k2 u 2holds with constant independent ofk the condition is forvto have the x rays transform everywhere bounded we apply these estimates to the well posedness of evolution schrodinger equations with time dependent drift terms and to the restriction of the fourier transform to euclidean spheres

violation of the fluctuation dissipation theorem in glassy systems basic notions and the numerical evidence this review reports on the research done during past years on violations of the fluctuation dissipation theorem fdt in glassy systems it is focused on the existence of a quasi fluctuation dissipation theorem qfdt in glassy systems and the current supporting knowledge gained from numerical simulation studies it covers a broad range of non stationary aging and stationary driven systems such as structural glasses spin glasses coarsening systems ferromagnetic models at criticality trap models models with entropy barriers kinetically constrained models sheared systems and granular media the review is divided into four main parts 1 an introductory section explaining basic notions related to the existence of the fdt in equilibrium and its possible extension to the glassy regime qfdt 2 a description of the basic analytical tools and results derived in the framework of some exactly solvable models 3 a detailed report of the current evidence in favour of the qfdt and 4 a brief digression on the experimental evidence in its favour this review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the qfdt as well as for the more expert readers who may be interested in more specific results

parabolic muckenhoupt weights in the euclidean space abstract we introduce a parabolic analogue of muckenhoupt s a p class we show that these weights satisfy a reverse holder type inequality and also prove a john nirenberg inequality for a related bmo type class both results are multidimensional generalizations of known one dimensional results as an application of our methods we extend a two dimensional weighted norm inequality of a lerner and s ombrosi to dimensions n 3

maximum principles extension problem and inversion for nonlocal one sided equations abstract we study one sided nonlocal equations of the form x 0 u x u x 0 x x 0 1 d x f x 0 on the real line notice that to compute this nonlocal operator of order 0 1 at a point x 0 we need to know the values of u x to the right of x 0 that is for x x 0 we show that the operator above corresponds to a fractional power of a one sided first order derivative maximum principles and a characterization with an extension problem in the spirit of caffarelli silvestre and stinga torrea are proved it is also shown that these fractional equations can be solved in the general setting of weighted one sided spaces in this regard we present suitable inversion results along the way we are able to unify and clarify several notions of fractional derivatives found in the literature

toeplitz operators on herglotz wave functions abstract the space of herglotz wave functions in r 2 consists of all the solutions of the helmholtz equation that can be represented as the fourier transform in r 2 of a measure supported in the circle and with density in l 2 s 1 this space has a structure of a hilbert space with reproducing kernel the purpose of this article is to study toeplitz operators with nonnegative radial symbols defined on this space we study the symbols defining bounded and compact toeplitz operators as well as the toeplitz operators belonging to the schatten classes s p

weighted norm inequalities for oscillatory integrals with finite type phases on the line abstract we obtain two weighted l 2 norm inequalities for oscillatory integral operators of convolution type on the line whose phases are of finite type the conditions imposed on the weights involve geometrically defined maximal functions and the inequalities are best possible in the sense that they imply the full l p r l q r mapping properties of the oscillatory integrals our results build on work of carbery soria vargas and the first author

some comments on fourier analysis uncertainty and modeling investigation of the problem of simultaneously concentrating a function and its fourier transform has led to some interesting special functions that have widespread applications in engineering they provide a means of proving a rigorous version of an engineering folk theorem called the 2wt theorem many generalizations of these ideas seem to possess a similar elegant mathematical structure a brief descriptive review is given of these developments

generalized strichartz estimates and scattering for 3d zakharov system we obtain scattering for the 3d zakharov system with non radial small data in the energy space with angular regularity of degree one the main ingredient is a generalized strichartz estimate for the schrodinger equation in the space of l2 angular integrability

weighted inequalities for one sided maximal functions let m be the maximal operator defined by g mb f x sup f t lg t dt f g t dt where g is a positive locally integrable function on r we characterize the pairs of nonnegative functions u v for which mb applies lp v in lp u or in weaklp u our results generalize sawyer s case g 1 but our proofs are different and we do not use hardy s inequalities which makes the proofs of the inequalities self contained

two weight weak and extra weak type inequalities for the one sided maximal operator let be the one sided maximal operator and let be a convex non decreasing function on 0 0 0 we present necessary and sufficient conditions on a couple of weight functions such that the integral inqualities of weak type and of extra weak type hold our proofs do not refer to the theory of orlicz spaces

granular contact force density of states and entropy in a modified edwards ensemble a method has been found to analyze edwards granular contact force probability functional for a special case as a result the granular contact force probability density functions are obtained from first principles for this case the results are in excellent agreement with the experimental and simulation data the derivation assumes edwards flat measure a density of states dos that is uniform within the metastable regions of phase space the enabling assumption supported by physical arguments and empirical evidence is that correlating information is not significantly recursive through loops in the packing maximizing a state counting entropy results in a transport equation that can be solved numerically for the present this has been done using the mean structure approximation projecting the dos across all angular coordinates to more clearly identify its predominant nonuniformities these features are 1 the grain factor psi related to grain stability and strong correlation between the contact forces on the same grain and 2 the structure factor upsilon related to newton s third law and strong correlation between neighboring grains

an approach to the analysis of repeated measurements summary a linear model for repeated measurements is proposed in which the correlation structure within each time sequence of measurements includes parameters for measurement error variation between experimental units and serial correlation within units an approach to data analysis is presented which involves preliminary analysis by ordinary least squares use of the empirical semi variogram of residuals to suggest a suitable correlation structure and formal inference using likelihood based methods applications to two biological data sets are described

on the coifman type inequality for the oscillation of one sided averages abstract in this paper we study the coifman type estimate for an oscillation operator related to the one sided discrete square function s we prove that for any a weight w the l p w norm of this operator and therefore the l p w norm of s is dominated by a constant times the l p w norm of the one sided hardy littlewood maximal function iterated two times for the k th commutator with a bmo function we show that k 2 iterates of the one sided hardy littlewood maximal function are sufficient

the spherical maximal operator on radial functions abstract we use simple one dimensional operators to bound pointwise the spherical maximal operator acting on radial functions with this bounds we obtain weighted inequalities which are sharp for power weights we also discuss boundedness results on morrey spaces and give a fefferman stein type inequality the bounds of the two dimensional case can be use for the universal maximal operator as well

weighted inequalities for maximal functions associated with general measures for certain positive borel measures u on r and for th any of three naturally associated maximal function operators of hardy littlewood type the weight pairs u v for which th is of weak type p p 1 p oo and of strong type p p 1 p oo are characterized only minimal assumptions are placed on u in particular u need not satisfy a doubling condition nor need it be continuous

band limited functions lp convergence we consider the set bp q functions of lp tl whose fourier spectrum lies in i2 i2 we prove that the prolate spheroidal wave func tions constitute a basis of this space if and only if 4 3 p 4 the result is obtained as a consequence of the analogous problem for the spherical bessel functions the proof rely on a weighted inequality for the hubert transform

mixed norm estimates for the cesaro means associated with dunkl hermite expansions our main goal in this article is to study mixed norm estimates for the cesaro means associated with dunkl hermite expansions on r d these expansions arise when one considers the dunkl hermite operator or dunkl harmonic oscillator h kappa delta kappa vertical bar x vertical bar 2 where delta kappa stands for the dunkl laplacian it is shown that the desired mixed norm estimates are equivalent to vector valued inequalities for a sequence of cesaro means for laguerre expansions with shifted parameter in order to obtain such vector valued inequalities we develop an argument to extend these laguerre operators for complex values of the parameters involved and apply a version of the three lines lemma

d optimal cohort designs for linear mixed effects models the d optimality criterion is used to construct optimal designs for different numbers of independent cohorts which constitute a number of repeated measurements per subject over time a cost function for longitudinal data is proposed and the optimality criterion is optimized taking into account the cost of the study first an optimal number of design points for a given number of cohorts and cost was identified then an optimal number of cohorts is identified by comparing the relative efficiencies res a numerical study shows that for models describing the trend of a continuous outcome over time by polynomials the most efficient number of repeated measurements is equal to the sum of the total number of cohorts and the degree of the polynomial in the model res of a purely longitudinal cohort design with only one cohort and mixed longitudinal and cross sectional cohort designs with more cohorts are compared the results show that a purely longitudinal cohort design with only one cohort of subjects measured at the optimal time points is the most efficient design the findings in this paper show that one can obtain a highly efficient design for parameter estimation with only a few repeated measurements the results of this study will reduce the cost of data collection and ease the logistical burdens in cohort studies

measuring explained variation in linear mixed effects models we generalize the well known r2 measure for linear regression to linear mixed effects models our work was motivated by a cluster randomized study conducted by the eastern cooperative oncology group to compare two different versions of informed consent document we quantify the variation in the response that is explained by the covariates under the linear mixed model and study three types of measures to estimate such quantities the first type of measures make direct use of the estimated variances the second type of measures use residual sums of squares in analogy to the linear regression the third type of measures are based on the kullback leibler information gain all the measures can be easily obtained from software programs that fit linear mixed models we study the performance of the measures through monte carlo simulations and illustrate the usefulness of the measures on data sets copyright 2003 john wiley sons ltd

general multilevel linear modeling for group analysis in fmri this article discusses general modeling of multisubject and or multisession fmri data in particular we show that a two level mixed effects model where parameters of interest at the group level are estimated from parameter and variance estimates from the single session level can be made equivalent to a single complete mixed effects model where parameters of interest at the group level are estimated directly from all of the original single sessions time series data if the co variance at the second level is set equal to the sum of the co variances in the single level form using the blue with known covariances this result has significant implications for group studies in fmri since it shows that the group analysis requires only values of the parameter estimates and their co variance from the first level generalizing the well established summary statistics approach in fmri the simple and generalized framework allows different prewhitening and different first level regressors to be used for each subject the framework incorporates multiple levels and cases such as repeated measures paired or unpaired t tests and f tests at the group level explicit examples of such models are given in the article using numerical simulations based on typical first level covariance structures from real fmri data we demonstrate that by taking into account lower level covariances and heterogeneity a substantial increase in higher level z score is possible

radial weights and mixed norm inequalities for the disc multiplier in this paper we show that the l2 weighted inequalities with radial weights of the multiplier for the ball are controlled by the maximal function defined by averages on arbitrary rectangles this solves the case of radial weights of a problem proposed by e stein in 1978 it also gives an elegant and simple proof of the boundedness of the multiplier for the ball on the spaces of mixed norm lradp lang2 for 2n n 1 p 2n n 1 obtained by a cordoba and by g mockenhaupt additional work is presented in order to extend these mixed norm estimates to the end points 2n n 1 and 2n n 1 in the sharp form of restricted weak type inequalities

mean and weak convergence of fourier bessel series abstract we study the uniform boundedness on some weighted lp spaces of the partial sum operators associated to fourier bessel series obtaining necessary and sufficient conditions for this boundedness in terms of the weights on the other hand we study the weak and restricted weak type of the partial sum operators in the end points of the interval of strong boundedness

singular integrals maximal functions and fourier restriction to spheres the disk multiplier revisited abstract several estimates for singular integrals maximal functions and spherical summation operator are given in the spaces l rad p l ang 2 r n n 2

a mixed effects model for the analysis of repeated measures cross over studies a mixed effects model is developed for cross over trials in which the response is measured repeatedly within each time period relative to previous work on repeated measures cross overs the methodology synthesizes two important features first our procedure eliminates preliminary testing for carry over defined loosely as the component of a response that is due to treatment in the preceding period this is achieved by generalizing the methodology to cross over designs in which preliminary testing for carry over is unnecessary we focus largely on simple carry over that is carry over that lasts for exactly one period and is independent of the treatment administered in the period in which the carry over occurs however we also illustrate a modification of the procedure for a repeated measures cross over design which uses a more complicated model of carry over second the model allows both the between and within subject variance to differ among treatments conditions are described wherein closed form cf solutions to the variance components as well as closed form hypothesis tests of the treatment differences exist flexibility in the model is illustrated with an example in which inference based on the cf likelihood based estimates of the variance and estimates formed using an iterative routine proc mixed are compared

one sided extrapolation at infinity and singular integrals in this paper we prove on one hand extrapolation from infinity for the one sided classes ap a p q a p q and on the other hand the bmo boundedness for one sided singular integrals we also provide several applications of our results

theory of powders starting from the observations that powders have a large number of particles and reproducible properties we show how statistical mechanics applies to powders the volume of the powder plays the role of the energy in conventional statistical mechanics with the hypothesis that all states of a specified volume are equally probable we introduce a variable x the compactivity which is analogous to the temperature in thermodynamics some simple models are considered which demonstrate how the problems involved can be tackled using the concept of compactivity there is an increasing interest in applying the methods of statistical mechanics and of transport theory to systems which are neither atomistic nor in equilibrium but which still fulfil a remaining tenet of statistical physics which is that systems can be completely defined by a very small number of parameters and can be constructed in a reproducible way powders fall into this category if a powder consists for example of uniform cubes of salt and is poured into a container falling at low density uniformly from a great height one expects a salt powder of a certain density repeating the preparation reproduces the same density a treatment such as shaking the powder by a definite routine produces a new density and the identical routine applied to another sample of the initial powder will result in the same final density clearly a maxwell demon could arrange the little cubes of nacl to make a material of different properties to that of our experiment but if such demonics are ignored and we restrict ourselves to extensive operations such as stirring shaking compressing all actions which do not act on grains individually then well defined states of the powder result in this paper we will set up a framework for describing the state of the powder basing our development on anologies with statistical mechanics some attempts have been made to apply information theory ideas directly to powders

one sided fractional derivatives fractional laplacians and weighted sobolev spaces abstract we characterize one sided weighted sobolev spaces w 1 p r where is a one sided sawyer weight in terms of a e and weighted l p limits as 1 of marchaud fractional derivatives of order similar results for weighted sobolev spaces w 2 p r n where is an a p muckenhoupt weight are proved in terms of limits as s 1 of fractional laplacians s these are bourgain brezis mironescu type characterizations for weighted sobolev spaces we also complement their work by studying a e and weighted l p limits as s 0

the multiplier for the ball and radial functions abstract it is shown that the multiplier for the ball is restricted weak type on radial functions in l p r n when p 2n n 1 interpolation then yields a theorem of herz

mean convergence of prolate spheroidal series and their extensions abstract the aim of this paper is to establish the range of p s for which the expansion of a function f l p in a generalized prolate spheroidal wave function pswfs basis converges to f in l p two generalizations of pswfs are considered here the circular pswfs introduced by d slepian and the weighted pswfs introduced by wang and zhang both cases cover the classical pswfs for which the corresponding results have been previously established by barcelo and cordoba to establish those results we prove a general result that allows to extend mean convergence in a given basis e g jacobi polynomials or bessel basis to mean convergence in a second basis here the generalized pswfs

subdyadic square functions and applications to weighted harmonic analysis abstract through the study of novel variants of the classical littlewood paley stein g functions we obtain pointwise estimates for broad classes of highly singular fourier multipliers on r d satisfying regularity hypotheses adapted to fine subdyadic scales in particular this allows us to efficiently bound such multipliers by geometrically defined maximal operators via general weighted l 2 inequalities in the spirit of a well known conjecture of stein our framework applies to solution operators for dispersive pde such as the time dependent free schrodinger equation and other highly oscillatory convolution operators that fall well beyond the scope of the calderon zygmund theory

on edwards theory of powders abstract we briefly review a statistical mechanics approach for the description of granular materials following the original ideas developed by edwards we show that edwards assumptions works very well for a class of lattice models and we discuss some recent analytic results obtained in such a framework on their phase diagram jamming transition and mixing segregation properties

mean and almost everywhere convergence of fourier neumann series abstract let j denote the bessel function of order the functions x 2 2 1 2j 2n 1 x1 2 n 0 1 2 form an orthogonal system in l2 0 x dx when 1 in this paper we analyze the range of p and for which the fourier series with respect to this system converges in the lp 0 x dx norm also we describe the space in which the span of the system is dense and we show some of its properties finally we study the almost everywhere convergence of the fourier series for functions in such spaces

a stein conjecture for the circle we discuss the manner in which one might expect directional maximal functions to control the fourier extension operator via l 2 weighted inequalities we prove a general inequality of this type for the extension operator restricted to circles in the plane

fundamental problems in statistical physics of jammed packings abstract for packed i e jammed hard and rough objects kinetic energy is a minor and ignorable quantity as is elastic strain hence in the static case the stress equations need supplementing by missing equations depending solely on configurations a different pathway of analysis is the calculation of the probability distribution of interparticle forces this paper presents the mini review of recently obtained results in this field and poses a number of fundamental problems which are yet to be solved

regression calibration for models with two predictor variables measured with error and their interaction using instrumental variables and longitudinal data regression calibration provides a way to obtain unbiased estimators of fixed effects in regression models when one or more predictors are measured with error recent development of measurement error methods has focused on models that include interaction terms between measured with error predictors and separately methods for estimation in models that account for correlated data in this work explicit and novel forms of regression calibration estimators and associated asymptotic variances are derived for longitudinal models that include interaction terms when data from instrumental and unbiased surrogate variables are available but not the actual predictors of interest the longitudinal data are fit using linear mixed models that contain random intercepts and account for serial correlation and unequally spaced observations the motivating application involves a longitudinal study of exposure to two pollutants predictors outdoor fine particulate matter and cigarette smoke and their association in interactive form with levels of a biomarker of inflammation leukotriene e4 lte4 outcome in asthmatic children since the exposure concentrations could not be directly observed measurements from a fixed outdoor monitor and urinary cotinine concentrations were used as instrumental variables and concentrations of fine ambient particulate matter and cigarette smoke measured with error by personal monitors were used as unbiased surrogate variables the derived regression calibration methods were applied to estimate coefficients of the unobserved predictors and their interaction allowing for direct comparison of toxicity of the different pollutants simulations were used to verify accuracy of inferential methods based on asymptotic theory

on weights satisfying parabolic muckenhoupt conditions abstract this note collects results related to parabolic muckenhoupt a p weights for a doubly nonlinear parabolic partial differential equation a general approach is proposed which extends the theory beyond the quadratic growth case in particular the natural parabolic geometry for the equation and the unavoidable time lag are incorporated in the definitions and results the limiting muckenhoupt conditions of a type are also discussed and several open questions are posed

weighted norm inequalities for the riemann liouville and weyl fractional integral operators caracterisation des fonctions poids pour lesquelles l operateur integral fractionnaire de riemann liouville d ordre 0 est borne

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

a weighted inequality for the maximal bochner riesz operator on r2 for e r2 let 7 1 2 2 i it is a well known theorem of carleson and sjolin that t defines a bounded operator on z 4 if a 0 in this paper we obtain an explicit weighted inequality of the form sup t f x 2w x dxti f 2paw x dx 0 0 this strengthens the above theorem of carleson and sjolin the method gives information on the maximal operator associated to general suitably smooth radial fourier multipliers of r2

equiconvergence theorems for fourier bessel expansions with applications to the harmonic analysis of radial functions in euclidean and non euclidean spaces we shall prove an equiconvergence theorem between fourier bessel expansions of functions in certain weighted lebesgue spaces and the classical cosine fourier expansions of suitable related functions these weighted lebesgue spaces arise naturally in the harmonic analysis of radial functions on euclidean spaces and we shall use the equiconvergence result to deduce shag results for the pointwise almost everywhere convergence of fourier integrals of radial functions in the lorentz spaces l p q r n also we shall briefly apply the above approach to the study of the harmonic analysis of radial functions on noneuclidean hyperbolic spaces

edwards measures for powders and glasses can one construct a thermodynamics for compact slowly moving powders and grains a few years ago edwards proposed a possible step in this direction raising the fascinating perspective that such systems have a statistical mechanics of their own different from that of maxwell boltzmann and gibbs allowing us to have some information while still ignoring dynamic details recent developments in the theory of glasses have come to confirm these ideas within mean field in order to go beyond we explicitly generate edwards measure in a 3d model comparison of the results with the irreversible compaction data shows very good agreement the present framework immediately suggests new experimental checks

why not routinely use best linear unbiased predictors blups as estimates of cholesterol per cent fat from kcal and physical activity measures of biologic and behavioural variables on a patient often estimate longer term latent values with the two connected by a simple response error model for example a subject s measured total cholesterol is an estimate equal to the best linear unbiased estimate blue of a subject s latent total cholesterol with known or estimated variances an alternative estimate is the best linear unbiased predictor blup we illustrate and discuss when the blue or blup will be a better estimate of a subject s latent value given a single measure on a subject concluding that the blup estimator should be routinely used for total cholesterol and per cent kcal from fat with a modified blup estimator used for large observed values of leisure time activity data from a large longitudinal study of seasonal variation in serum cholesterol forms the backdrop for the illustrations simulations which mimic the empirical and response error distributions are used to guide choice of an estimator we use the simulations to describe criteria for estimator choice to identify parameter ranges where blue or blup estimates are superior and discuss key ideas that underlie the results

weak type estimates for bochner riesz spherical summation multipliers we consider the bochner riesz multiplier tofw 1 1 12 tjw 8 0 where denotes the fourier transform it is shown that the multiplier operator to is weak type po po acting on lpo rn radial functions where po is the critical value 2n n 1 28

on radial weights for the spherical summation operator abstract in this paper we give a sufficient condition for radial weights such that the spherical summation operator is bounded on l 2 r n x dx n 2 when applied to power weights x x x these conditions are also necessary moreover in the general case we shall show that our condition is almost necessary furthermore we give an example which shows that the conjecture in anderson proc amer math soc 83 no 2 1981 269 275 fails to hold

weighted inequalities for the one sided hardy littlewood maximal functions let m f x suph 0 l h jx h t 1 idt denote the one sided maximal function of hardy and littlewood for w x 0 on r and 1 0 and a v ll p then m is bounded from lp v to lp w if and only if m x a w 0 the corresponding weak type inequality is also characterized further properties of a weights such as a a e and a p a a1 p are established

modelling covariance structure in the analysis of repeated measures data the term repeated measures refers to data with multiple observations on the same sampling unit in most cases the multiple observations are taken over time but they could be over space it is usually plausible to assume that observations on the same unit are correlated hence statistical analysis of repeated measures data must address the issue of covariation between measures on the same unit until recently analysis techniques available in computer software only offered the user limited and inadequate choices one choice was to ignore covariance structure and make invalid assumptions another was to avoid the covariance structure issue by analysing transformed data or making adjustments to otherwise inadequate analyses ignoring covariance structure may result in erroneous inference and avoiding it may result in inefficient inference recently available mixed model methodology permits the covariance structure to be incorporated into the statistical model the mixed procedure of the sas r system provides a rich selection of covariance structures through the random and repeated statements modelling the covariance structure is a major hurdle in the use of proc mixed however once the covariance structure is modelled inference about fixed effects proceeds essentially as when using proc glm an example from the pharmaceutical industry is used to illustrate how to choose a covariance structure the example also illustrates the effects of choice of covariance structure on tests and estimates of fixed effects in many situations estimates of linear combinations are invariant with respect to covariance structure yet standard errors of the estimates may still depend on the covariance structure

linear adjoint restriction estimates for paraboloid we prove a class of modified paraboloid restriction estimates with a loss of angular derivatives for the full set of paraboloid restriction conjecture indices this result generalizes the paraboloid restriction estimate in radial case from shao rev mat iberoam 25 2009 1127 1168 as well as the result from miao et al proc ams 140 2012 2091 2102 as an application we show a local smoothing estimate for a solution of the linear schrodinger equation under the assumption that the initial datum has additional angular regularity

some weighted estimates for littlewood paley functions and radial multipliers abstract we prove some weighted estimates for certain littlewood paley operators on the weighted hardy spaces h w p 0 p 1 and on the weighted l p spaces we also prove some weighted estimates for the bochner riesz operators and the spherical means

applications of the statistical mechanics of inherent states to granular media abstract we review the results of a statistical mechanics approach to granular materials and its extension to non thermal systems in their inherent states we introduce a tapping dynamics based on a dynamics used for real granular matter which allows to visit the space of the inherent states it is assumed that under stationarity or quasi stationarity the distribution among the inherent states satisfies the principle of maximum entropy this leads to a distribution characterised by a configurational temperature related to edwards compactivity the prediction from such an approach are checked on a standard hamiltonian lattice model and in the present unifying framework it is possible to explain a variety of properties of granular materials ranging from their logarithmic compaction to typical memory phenomena

on the weak behaviour of partial sums of legendre series sn j x denotes the nth partial sum of the legendre expansion of f x it was proved by h pollard in 4 that if f e lp 1 1 where 4 3 4 however j newman and w rudin in 3 showed that the inequality iisnv j ilp cp iifiip is false atp 4 orp 4 3 the aim of this paper is to examine the weak behaviour atp 4 much in the spirit of the hilbert transform at l 0 2wt we now need some notations to state our main results the lebesgue measure of any set e c 1 1 will be denoted as m e xe x will as usual denote the characteristic function of a set e we then have

a statistical mechanics approach to the inherent states of granular media abstract we consider a statistical mechanics approach to granular systems by following the original ideas developed by edwards we use the concept of inherent states defined as the stable configurations in the potential energy landscape introduced in the context of glasses under simplifying assumptions the equilibrium inherent states can be characterized by a configurational temperature 1 we link to edwards compactivity and address the problem of its experimental measure we also discuss the possibility to describe the time dependent distribution probability in the inherent states with an appropriate master equation

fractional integrals on compact riemannian symmetric spaces of rank one abstract in this paper we study mixed norm boundedness for fractional integrals related to laplace beltrami operators on compact riemannian symmetric spaces of rank one the key point is the analysis of weighted inequalities for fractional integral operators associated to trigonometric jacobi polynomials expansions in particular we find a novel sharp estimate for the jacobi fractional integral kernel with explicit dependence on the type parameters

generalized hormander s conditions commutators and weights we present a general framework to deal with commutators of singular integral operators with bmo functions hormander type conditions associated with young functions are assumed on the kernels coifman type estimates weighted norm inequalities and two weight estimates are considered we give applications to homogeneous singular integrals fourier multipliers and one sided operators

using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data the general linear mixed model provides a useful approach for analysing a wide variety of data structures which practising statisticians often encounter two such data structures which can be problematic to analyse are unbalanced repeated measures data and longitudinal data owing to recent advances in methods and software the mixed model analysis is now readily available to data analysts the model is similar in many respects to ordinary multiple regression but because it allows correlation between the observations it requires additional work to specify models and to assess goodness of fit the extra complexity involved is compensated for by the additional flexibility it provides in model fitting the purpose of this tutorial is to provide readers with a sufficient introduction to the theory to understand the method and a more extensive discussion of model fitting and checking in order to provide guidelines for its use we provide two detailed case studies one a clinical trial with repeated measures and dropouts and one an epidemiological survey with longitudinal follow up

the surprising almost everywhere convergence of fourier neumann series for most orthogonal systems and their corresponding fourier series the study of the almost everywhere convergence for functions in l p requires very complicated research harder than in the case of the mean convergence for instance for trigonometric series the almost everywhere convergence for functions in l 2 is the celebrated carleson theorem proved in 1966 and extended to l p by hunt in 1967 in this paper we take the system j n a x 2 a 2n 1 j a 2 n 1 x x a 1 n 0 1 2 with j m being the bessel function of the first kind and of the order m which is orthonormal in l 2 0 x 2 a 1dx and whose fourier series are the so called fourier neumann series we study the almost everywhere convergence of fourier neumann series for functions in l p 0 x 2 a 1dx and we show that surprisingly the proof is relatively simple inasmuch as the mean convergence has already been established

stationary probability distribution in granular media abstract we discuss recent developments in the formulation of a statistical mechanics approach to non thermal systems such as granular media we review a few important numerical results on the assessment of edwards theory and in particular we apply these ideas to study a mean field model of a hard sphere binary mixture under gravity which can be fully analytically investigated as a consequence we derive the rich phase diagram and predict the features of segregation patterns of the mixture

quasi equilibrium interpretation of ageing dynamics we develop an interpretation of the off equilibrium dynamical solution of mean field glassy models in terms of quasi equilibrium concepts we show that the relaxation of the thermo remanent magnetization follows a generalized version of the onsager regression postulate of induced fluctuations we then find the rationale for the equality between the fluctuation dissipation ratio and the rate of growth of the configurational entropy close to the asymptotic state found empirically in mean field solutions

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

radial multipliers and restriction to surfaces of the fourier transform in mixed norm spaces in this article we revisit some classical conjectures in harmonic analysis in the setting of mixed norm spaces l rad p l ang 2 left mathbb r n right we produce sharp bounds for the restriction of the fourier transform to compact hypersurfaces of revolution in the mixed norm setting and study an extension of the disc multiplier we also present some results for the discrete restriction conjecture and state an intriguing open problem