best constants in rosenthal type inequalities and the kruglov operator let x be a symmetric banach function space on 0 1 with the kruglov property and let f f k n k 1 n 1 be an arbitrary sequence of independent random variables in x this paper presents sharp estimates in the deterministic characterization of the quantities

non squareness properties of orlicz lorentz sequence spaces abstract in this paper criteria for non squareness properties non squareness local uniform non squareness and uniform non squareness of orlicz lorentz sequence spaces and of their n dimensional subspaces n n 2 as well as of the subspaces a of all order continuous elements in are given since degenerate orlicz functions and degenerate weight sequences are also admitted these investigations concern the most possible wide class of orlicz lorentz sequence spaces finally as immediate consequences criteria for all non squareness properties of orlicz sequence spaces which complete the results of sundaresan 1966 53 hudzik 1985 23 hudzik 1985 24 are deduced it is worth recalling that uniform non squareness is an important property because it implies super reflexivity as well as the fixed point property see james 1964 31 james 1972 33 and garcia falset et al 2006 19

embeddings of operator ideals into lp spaces on finite von neumann algebras abstract let l h be the algebra of all bounded operators on an infinite dimensional hilbert space h and let i i be an ideal in l h equipped with a banach norm which is distinct from the schatten von neumann ideal l p h 1 p 2 we prove that i isomorphically embeds into an l p space l p r 1 p 2 here r is the hyperfinite ii1 factor if its commutative core that is calkin space for i isomorphically embeds into l p 0 1 furthermore we prove that an orlicz ideal l m h l p h isomorphically embeds into l p r 1 p 2 if and only if it is an interpolation space for the banach couple l p h l 2 h finally we consider isomorphic embeddings of i i into l p spaces associated with arbitrary finite von neumann algebras

extrapolation with weights rearrangement invariant function spaces modular inequalities and applications to singular integrals abstract we present an extrapolation theory that allows us to obtain from weighted l p inequalities on pairs of functions for p fixed and all a weights estimates for the same pairs on very general rearrangement invariant quasi banach function spaces with a weights and also modular inequalities with a weights vector valued inequalities are obtained automatically without the need of a banach valued theory this provides a method to prove very fine estimates for a variety of operators which include singular and fractional integrals and their commutators in particular we obtain weighted and vector valued extensions of the classical theorems of boyd and lorentz shimogaki the key is to develop appropriate versions of rubio de francia s algorithm

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

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

banach saks property in marcinkiewicz spaces abstract we catalogue all marcinkiewicz function and sequence spaces with the banach saks property and present necessary and sufficient conditions for a wide subclass of spaces to possess the p banach saks property 1 p we apply our results to several open problems

the banach saks p property we obtain general theorems which enable the calculation of the banach saks index set for rearrangement invariant function spaces in terms of their boyd indices for many important classes of rearrangement invariant spaces the index set is non trivial if and only if the boyd indices of the underlying space are non trivial although the latter equivalence does not hold in full generality we also study banach saks index sets defined for weakly null sequences of identically distributed independent random variables and their connections with the classical banach saks index set

φ moment inequalities for independent and freely independent random variables abstract this paper is devoted to the study of moments of sums of independent freely independent random variables more precisely let f k k 1 n be a sequence of positive symmetrically distributed independent random variables and let be an orlicz function with 2 condition we provide an equivalent expression for the quantity e k 1 n f k in term of the sum of disjoint copies of the sequence f k k 1 n we also prove an analogous result in the setting of free probability furthermore we provide an equivalent characterization of sup 1 k n x k for positive freely independent random variables and also present some new results on free johnson schechtman inequalities in the quasi banach symmetric operator space

incremental learning of 3d dct compact representations for robust visual tracking visual tracking usually requires an object appearance model that is robust to changing illumination pose and other factors encountered in video many recent trackers utilize appearance samples in previous frames to form the bases upon which the object appearance model is built this approach has the following limitations 1 the bases are data driven so they can be easily corrupted and 2 it is difficult to robustly update the bases in challenging situations in this paper we construct an appearance model using the 3d discrete cosine transform 3d dct the 3d dct is based on a set of cosine basis functions which are determined by the dimensions of the 3d signal and thus independent of the input video data in addition the 3d dct can generate a compact energy spectrum whose high frequency coefficients are sparse if the appearance samples are similar by discarding these high frequency coefficients we simultaneously obtain a compact 3d dct based object representation and a signal reconstruction based similarity measure reflecting the information loss from signal reconstruction to efficiently update the object representation we propose an incremental 3d dct algorithm which decomposes the 3d dct into successive operations of the 2d discrete cosine transform 2d dct and 1d discrete cosine transform 1d dct on the input video data as a result the incremental 3d dct algorithm only needs to compute the 2d dct for newly added frames as well as the 1d dct along the third dimension which significantly reduces the computational complexity based on this incremental 3d dct algorithm we design a discriminative criterion to evaluate the likelihood of a test sample belonging to the foreground object we then embed the discriminative criterion into a particle filtering framework for object state inference over time experimental results demonstrate the effectiveness and robustness of the proposed tracker

the classification problem for nonatomic weak lp spaces abstract the aim of the paper is to study the isomorphic structure of the weak l p space l p when is a purely nonatomic measure space using maharam s classification of measure algebras it is shown that every such l p is isomorphic to a weak l p space defined on a weighted direct sum of product measure spaces of the type 2 several isomorphic invariants are then obtained in particular it is found that there is a notable difference between the case 1 p 2 and the case where 2 p applying the methods developed we obtain an isomorphic classification of the purely nonatomic weak l p spaces in a special case

on the nonlinear axisymmetric dynamic buckling behavior of clamped functionally graded spherical caps abstract here the dynamic thermal buckling behavior of functionally graded spherical caps is studied considering geometric nonlinearity based on von karman s assumptions the formulation is based on first order shear deformation theory and it includes the in plane and rotary inertia effects the material properties are graded in the thickness direction according to the power law distribution in terms of volume fractions of the material constituents the effective material properties are evaluated using homogenization method the governing equations obtained using finite element approach are solved employing the newmark s integration technique coupled with a modified newton raphson iteration scheme the pressure load corresponding to a sudden jump in the maximum average displacement in the time history of the shell structure is taken as the dynamic buckling load the present model is validated against the available isotropic case a detailed numerical study is carried out to highlight the influences of shell geometries power law index of functional graded material and boundary conditions on the dynamic buckling load of shallow spherical shells

measuring the magnitude of sums of independent random variables this paper considers how to measure the magnitude of the sum of independent random variables in several ways we give a formula for the tail distribution for sequences that satisfy the so called levy property we then give a connection between the tail distribution and the pth moment and between the pth moment and the rearrangement invariant norms

martingale inequalities in noncommutative symmetric spaces abstract we provide generalizations of burkholder s inequalities involving conditioned square functions of martingales to the general context of martingales in noncommutative symmetric spaces more precisely we prove that burkholder s inequalities are valid for any martingale in noncommutative space constructed from a symmetric space defined on the interval 0 with the fatou property and whose boyd indices are strictly between 1 and 2 this answers positively a question raised by jiao and may be viewed as a conditioned version of similar inequalities for square functions of noncommutative martingales using duality we also recover the previously known case where the boyd indices are finite and are strictly larger than 2

johnson schechtman inequalities in the free probability theory abstract we introduce and study a free kruglov operator as an application of this study we prove an analogue of the johnson schechtman inequalities in the setting of free probability theory and an arbitrary symmetric operator space this extends and complements earlier l p results of junge et al 2007 12

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

orlicz sequence spaces spanned by identically distributed independent random variables in lp spaces abstract let 1 p 2 and let l p l p 0 1 be the classical l p space of all classes of p integrable functions on 0 1 it is known that any subspace in l p spanned by a sequence of independent copies of a mean zero random variable f l p is isomorphic to some orlicz sequence space l n we employ methods from interpolation theory to fully describe the class of orlicz functions n which can be obtained by this procedure and to identify the precise connection between n and the distribution of f our methods strengthen and complement classical results of m i kadec as well as those of j bretagnolle and d dacunha castelle

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

dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading abstract in this paper a formulation for the dynamic stability analysis of functionally graded shells under harmonic axial loading is presented a profile for the volume fraction is assumed and a normal mode expansion of the equations of motion yields a system of mathieu hill equations the stability of which is analyzed by the bolotin s method the present study examines the effects of the volume fraction of the material constituents and their distribution on the parametric response in particular the positions and sizes of the instability regions

isomorphic classification of lp q spaces abstract we prove that for all 1 p q p q p 1 p 2 and p 2 q 2 the banach space l p q does not isomorphically embed into the space l p q 0 1 we also prove under the same conditions that the space l p q 0 does not isomorphically embed into the space l p q 0 1 l p q

approximation of zonoids by zonotopes on etudie une propriete d approximation des corps convexes de r n qui sont des limites de sommes de segments

some remarks on multilinear maps and interpolation a multilinear version of the boyd interpolation theorem is proved in the context of quasi normed rearrangement invariant spaces a multilinear marcinkiewicz interpolation theorem is obtained as a corollary several applications are given including estimates for bilinear fractional integrals

robust tracking via locally structured representation representation method is critical to visual tracking a robust representation describes the target accurately leading to good tracking performance in this work a novel representation is proposed which is designed to be simultaneously low rank and joint sparse for the local patches within a target region in this representation the subspace structure is exploited by the low rank constraint to reflect the global information of all the patches and the sparsity structure is captured by the joint sparsity restriction to describe the locally intimate relationship between the neighboring patches importantly to make the representation computationally applicable to visual tracking a novel fast algorithm based on greedy strategy is proposed and the performance analysis of this algorithm is also presented thus the tracking in this work is formulated as a locally low rank and joint sparse matching problem within particle filtering framework a large number of experimental results show that the tracking drift problem is effectively alleviated in various challenging situations by using the proposed representation method both qualitative and quantitative evaluations demonstrate that the proposed tracker performs favorably against many other state of the art trackers benefitting from the good adaptive capability of the representation all the parameters of the proposed tracking algorithm are fixed in all the experiments

central limit theorems and weak laws of large numbers in certain banach spaces for b a type 2 banach lattice we obtain a relationship between the central limit theorem in b and the weak law of large numbers for the sum of the squares of the random vectors in another banach lattice b 2 we then obtain some two sided estimates for e sn pwhich in lpspaces 1 p give n a s c for the weak law of large numbers as a consequence of these estimates we also solve the domain of attraction problem in lp p 2 several examples and counterexamples are provided

independent sums of hn1 t and hn1 δ abstract we construct a new idempotent fourier multiplier on the hardy space on the bidisc which could not be obtained by applying known one dimensional results the main tool is a new l 1 equivalent of the stein martingale inequality which holds for a special filtration of periodic subsets of t with some restrictions on the functions involved we also identify the isomorphic type of the range of the associated operator as the independent sum of dyadic h n 1 which is known to be a complemented and invariant subspace of dyadic h 1

rosenthal inequalities in noncommutative symmetric spaces abstract we give a direct proof of the upper khintchine inequality for a noncommutative symmetric quasi banach function space with nontrivial upper boyd index this settles an open question of c le merdy and the fourth named author le merdy and sukochev 2008 24 we apply this result to derive a version of rosenthal s theorem for sums of independent random variables in a noncommutative symmetric space as a result we obtain a new proof of rosenthal s theorem for haagerup l p spaces

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

self expressive tracking target representation is critical to visual tracking a good representation usually exploits some inherent relationship and structures among the observed targets the candidates or both in this work we observe that the candidates are strongly correlated to each other and exhibit obvious clustering structure when they are densely sampled around possible target locations thus we propose a self expressive tracking set algorithm based on an accurate representation with good discriminative performance the interrelationship and the clustering structure among the observed targets and the candidates are exploited by using a self expressive scheme with a low rank constraint further we design a discriminative criterion of the likelihood for target location which simultaneously considers the target background and representation errors to appropriately capture the appearance changes of the target we develop an update strategy that adaptively switches different update rates during tracking extensive experiments demonstrate that our tracking algorithm outperforms many other state of the art methods highlightsan observation of the inherent relationship and structure among the candidates a structured representation with naturally discriminative power for target description an evaluation criterion of the likelihood of the candidates belonging to the target an update strategy with adaptive update rates for appearance model maintenance

robust visual tracking with discriminative sparse learning recently sparse representation in the task of visual tracking has been obtained increasing attention and many algorithms are proposed based on it in these algorithms for visual tracking each candidate target is sparsely represented by a set of target templates however these algorithms fail to consider the structural information of the space of the target templates i e target template set in this paper we propose an algorithm named non local self similarity nlss based sparse coding algorithm nlssc to learn the sparse representations which considers the geometrical structure of the set of target candidates by using non local self similarity nlss as a smooth operator the proposed method can turn the tracking into sparse representations problems in which the information of the set of target candidates is exploited extensive experimental results on visual tracking have demonstrated the effectiveness of the proposed algorithm

the nonlinear dynamic buckling response of functionally graded truncated conical shells abstract in this study the nonlinear dynamic buckling of functionally graded fg truncated conical shells subjected to axial compressive load varying as a linear function of time is investigated the material properties of the fg truncated shell are assumed to vary continuously through the thickness of the shell the nonlinear pre buckling deformations of the fg truncated conical shell are taken into account the fundamental relations and modified donnell type nonlinear dynamic stability and compatibility equations of the fg truncated conical shell are derived and solved by using the superposition principle galerkin and runge kutta methods the values of the dimensionless nonlinear critical time parameter have been found numerically finally carrying out some computations the effects of the compositional profiles the variation of the truncated conical shell geometric parameters and the axial loading speed on the dimensionless linear and nonlinear critical time parameters have been studied comparing the results of this study with those in the literature validates the present analysis

dynamic behavior of a cylindrical crack in a functionally graded interlayer under torsional loading in this paper the problem of a cylindrical crack located in a functionally graded material fgm interlayer between two coaxial elastic dissimilar homogeneous cylinders and subjected to a torsional impact loading is considered the shear modulus and the mass density of the fgm interlayer are assumed to vary continuously between those of the two coaxial cylinders this mixed boundary value problem is first reduced to a singular integral equation with a cauchy type kernel in the laplace domain by applying laplace and fourier integral transforms the singular integral equation is then solved numerically and the dynamic stress intensity factor dsif is also obtained by a numerical laplace inversion technique the dsif is found to rise rapidly to a peak and then reduce and tend to the static value almost without oscillation the influences of the crack location the fgm interlayer thickness and the relative magnitudes of the adjoining material properties are examined it is found among others that by increasing the fgm gradient the dsif can be greatly reduced