on flows associated to sobolev vector fields in wiener spaces an approach a la diperna lions in this paper we extend the diperna lions theory of flows associated to sobolev vector fields to the case of cameron martin valued vector fields in wiener spaces e having a sobolev regularity the proof is based on the analysis of the continuity equation in e and on uniform gaussian commutator estimates in finite dimensional spaces

one dimensional transport equations with discontinuous coefficients we consider one dimensional linear transport equations with bounded but possibly discontinuous coefficient a the cauchy problem is studied from two different points of view in the first case we assume that a is piecewise continuous we give an existence result and a precise description of the solutions on the lines of discontinuity in the second case we assume that a satisfies a one sided lipschitz condition we give existence uniqueness and general stability results for backward lipschitz solutions and forward measure solutions by using a duality method we prove that the flux associated to these measure solutions is a product by some canonical representative of a key words linear transport equations discontinuous coefficients weak stability duality product of a measure by a discontinuous function nonnegative solutions 1991 mathematics subject classification primary 35f10 35b35 34a12 to appear in nonlinear analysis tma departement de mathematiques et applications umr cnrs 8553 ecole normale superieure et cnrs 45 rue d ulm 75230 paris cedex 05 france francois bouchut ens fr mathematiques applications et physique mathematique d orleans umr cnrs 6628 universite d orleans 45067 orleans cedex 2 france james math cnrs fr

generalized mixed variational principles and solutions of ill conditioned problems in computational mechanics part ii shear locking abstract although the finite element method fem has been extensively applied to various areas of engineering the ill conditioned problems occurring in many situations are still thorny to deal with this study attempts to provide a high performing and simple approach to the solutions of ill conditioned problems the theoretical foundation of it is the parametrized variational principles called the generalized mixed variational principles gmvps initiated by rong in 1981 gmvps can solve many kinds of ill conditioned problems in computational mechanics among them four cases are investigated in detail the volumetric locking the shear locking the inhomogeneousness and the membrane locking problems composing four parts of the study part i part iv respectively this paper is part ii wherein a gmvp specially suited to the reissner plate theory and timoshenko beam theory is constructed providing a mathematical foundation for establishing fem formulations which can automatically unlock the shear locking and produce no spurious zero energy modes

convergence of numerical approximations to non linear continuity equations with rough force fields we prove quantitative regularity estimates for the solutions to non linear continuity equations and their discretized numerical approximations on cartesian grids when advected by a rough force field this allows us to not only recover the known optimal regularity for linear transport equations but also to obtain the convergence of a wide range of numerical schemes our proof is based on novel commutator estimates quantifying and extending to the non linear case the classical commutator approach of the theory of renormalized solutions

on the uniqueness of solutions to continuity equations abstract we obtain sufficient conditions for the uniqueness of solutions to the cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous

compactness for nonlinear continuity equations abstract we prove compactness and hence existence for solutions to a class of nonlinear transport equations the corresponding models combine the features of linear transport equations and scalar conservation laws we introduce a new method which gives quantitative compactness estimates compatible with both frameworks

on the control of pressure oscillation in bilinear displacement constant pressure element abstract due to the singularity in the global pressure matrix equation the bilinear displacement constant pressure element produces an uncontrollable checkerboard pattern in the pressure solution although the well known penalty treatment in the pressure equation overcomes the singularity problem it still produces oscillatory pressure under certain conditions the proposed method employs a rank one filtering operator in the pressure equation to filter out the checkerboard mode without affecting the non checkerboarding pressure field the numerical results suggest that the pressure oscillation in the penalty method and the rank one filtering method is a result of the absence of the checkerboard mode a pressure recovery procedure is then suggested to recover the appropriate checkerboard mode numerical results for both solid and fluid mechanics problems are included

the rank transform method in some two factor designs abstract the use of the rank transform for testing problems in some two factor designs is considered the rank transform procedure consists of replacing the observations by their ranks in the combined sample and performing one of the standard analysis of variance anova procedures on these ranks the asymptotic version of the rank transform is introduced and its usefulness as a means for understanding the nature of the rank transform is examined it is demonstrated that the asymptotic version of the transformation helps identify the testing problems where the rank transform method works and helps suggest which anova procedure should be used on the ranks this approach is applied on the balanced and unbalanced nested model and the balanced and unbalanced two way layout with and without interaction the extension of the rank transform method to some of these models is new the proposed procedures do not share the known simplicity of existing rank transform statistics but they do allow heteroscedasticity

vanishing viscosity with short wave long wave interactions for systems of conservation laws motivated by benney s general theory we propose new models for short wave long wave interactions when the long waves are described by nonlinear systems of conservation laws we prove the strong convergence of the solutions of the vanishing viscosity and short wave long wave interactions systems by using compactness results from compensated compactness theory and new energy estimates obtained for the coupled systems we analyze several of the representative examples such as scalar conservation laws general symmetric systems nonlinear elasticity and nonlinear electromagnetism

on rank transformation techniques for balanced incomplete repeated measures designs abstract asymptotic properties of statistics designed to detect general alternatives in compound symmetric balanced incomplete repeated measures designs with fixed treatment effects are investigated included in this study are the analysis of variance anova f statistic its rank transform durbin s statistic by making asymptotic relative efficiency comparisions among these statistics when they have been computed with and without mean alignment valuable new insight into their large sample performance characteristics is gained evidence is presented corroborating recent empirical studies that suggest that mean alignment can improve the performance of rank transformation statistics finally it is noted that the rank transform of the anova f statistic when it is computed using mean aligned data is generally the most efficient among the statistics studied here

solvability of one non newtonian fluid dynamics model with memory abstract in the present paper we establish the existence of weak solutions to the initial boundary value problem for one viscoelastic model of oldroyd s type fluid with memory along trajectories of the velocity field previously such problem has been studied for corresponding regularized models the reason of the regularization was the lack of results on the solvability of the cauchy problem with not sufficiently smooth velocity field however recent results about regular lagrangian flows generalization of classical solutions of a cauchy problem allow to establish the existence theorem for the original problem we use topological approximation method which involves the approximation of the original problem by regularized operator equations with consequent application of topological degree theory for its solvability this allows to establish the existence of weak solutions of considered problem on the base of a priori estimates and passing to the limit

optimal mixing and optimal stirring for fixed energy fixed power or fixed palenstrophy flows we consider passive scalar mixing by a prescribed divergence free velocity vector field in a periodic box and address the following question starting from a given initial inhomogeneous distribution of passive tracers and given a certain energy budget power budget or finite palenstrophy budget what incompressible flow field best mixes the scalar quantity we focus on the optimal stirring strategy recently proposed by lin et al optimal stirring strategies for passive scalar mixing j fluid mech 675 465 2011 10 1017 s0022112011000292 that determines the flow field that instantaneously maximizes the depletion of the h 1 mix norm in this work we bridge some of the gap between the best available a priori analysis and simulation results after recalling some previous analysis we present an explicit example demonstrating finite time perfect mixing with a finite energy constraint on the stirring flow on the other hand using a recent result by wirosoetisno et al long time stability of a classi

transport equation extension of classical results for div b bmo we investigate the transport equation ut b u 0 our result improves the criteria on uniqueness of weak solutions replacing the classical condition divb l by divb bmo

efficacies of rank transform statistics in two way models with no interaction abstract to test for treatment effects in a two way model when the classical assumptions of normality of errors and constancy of variance cannot be verified hora and conover 1984 proposed a rank test in which the entire data set is ranked the ranks are scored and then the classical analysis of variance f statistic is applied to the scored ranks they showed that the limiting null distribution of this test statistic is a chi squared distribution divided by its degrees of freedom simulation results suggest that this procedure called the rank transform procedure has good power properties this article determines the asymptotic relative efficiency of the rank transform procedure relative to the classical f statistic to do this vectors of linear rank statistics are shown to have a limiting multivariate normal distribution under a sequence of pitman alternatives this work is based on the results of hajek 1968 the rank transform statistic is then expressed as a quadratic form in the vectors divide

global existence of weak solutions for compresssible navier stokes equations thermodynamically unstable pressure and anisotropic viscous stress tensor we prove global existence of appropriate weak solutions for the compressible navier stokes equations for more general stress tensor than those covered by p l lions and e feireisl s theory more precisely we focus on more general pressure laws which are not thermodynamically stable we are also able to handle some anisotropy in the viscous stress tensor to give answers to these two longstanding problems we revisit the classical compactness theory on the density by obtaining precise quantitative regularity estimates this requires a more precise analysis of the structure of the equations combined to a novel approach to the compactness of the continuity equation these two cases open the theory to important physical applications for instance to describe solar events virial pressure law geophysical flows eddy viscosity or biological situations anisotropy

nonparametric methods for detecting treatment effects in repeated measures designs abstract sufficient conditions are given that guarantee the limiting distribution of a test proposed by agresti and pendergast 1986 to detect treatment effects in repeated measures designs the test which is appropriate for either the original or aligned data is related to one proposed by koch 1969 and to the rank transformation statistic using pitman asymptotic relative efficiency comparisons situations are presented where these tests are more efficient than their standard parametric and nonparametric competitors the problem of detecting ordered alternatives in repeated measures designs is also considered a rank transformation analog of page s 1963 l is shown to be generally more efficient in the pitman sense than the standard competitors when the number of treatments is not too large

a unified nonparametric approach for unbalanced factorial designs motivated by questions arising from the field of statistical genetics we consider the problem of testing main nested and interaction effects in unbalanced factorial designs based on the concept of composite linear rank statistics a new notion of weighted rank is proposed asymptotic normality of weighted linear rank statistics is established under mild conditions and consistent estimators are developed for the corresponding limiting covariance structure a unified framework to use weighted rank to construct test statistics for main nested and interaction effects in unbalanced factorial designs is established the proposed tests statistics are applicable to unbalanced designs with arbitrary cell replicates greater than one per cell the limiting distributions under both the null hypotheses and pitman alternatives are derived monte carlo simulations are conducted to confirm the validity and power of the proposed tests genetic datasets from a simulated backcross study are analyzed to demonstrate th

the f statistic in the two way layout with rank score transformed data abstract the limiting null distribution of the usual f statistic for main effects in the two way layout is shown to have the same limiting distribution when applied to ranks and scores based on ranks as when applied to normal data the limit is taken as the cell size n increases without bound the denominator of the f statistic times j 1 j is shown to provide an unbiased and consistent estimator of the limit as n of n 1 times the variance of the treatment sum of scores when the null hypothesis is true the test based on the scores statistic is demonstrated to be consistent for a wide class of fixed alternative hypotheses

strong solutions to stochastic differential equations with rough coefficients we study strong existence and pathwise uniqueness for stochastic dierential equations in r d with rough coecients

a large deviations principle for stochastic flows of viscous fluids abstract we study the well posedness of a stochastic differential equation on the two dimensional torus t 2 driven by an infinite dimensional wiener process with drift in the sobolev space l 2 0 t h 1 t 2 the solution corresponds to a stochastic lagrangian flow in the sense of diperna lions by taking into account that the motion of a viscous incompressible fluid on the torus can be described through a suitable stochastic differential equation of the previous type we study the inviscid limit by establishing a large deviations principle we show that as the viscosity goes to zero the lagrangian stochastic navier stokes flow approaches the euler deterministic lagrangian flow with an exponential rate function

rank procedures for the two factor mixed model abstract the test problem of fixed treatment effects is considered in the two factor mixed model with interaction and unequal cell frequencies when the classical assumptions of normality do not hold an explicit form of a test statistic is derived using a partial rank transform ranking all observations within each block and the asymptotic distribution of the statistic is determined under the assumption that the number of blocks tends to infinity and the cell frequencies are bounded the statistic reduces to friedman s statistic if no interactions are involved in the model and all cell frequencies are equal hence the proposed test can be regarded as a generalization of friedman s test for repeated observations when the cell frequencies are not equal the test is compared to a corresponding test that can be used under the assumption of normality by the criterion of asymptotic relative efficiency in the case of two treatments the exact conditional distribution is determined and estimators and confidenc

renormalized solutions of the 2d euler equations in this paper we prove that solutions of the 2d euler equations in vorticity formulation obtained via vanishing viscosity approximation are renormalized

a paradigm for higher order polygonal elements in finite elasticity using a gradient correction scheme abstract recent studies have demonstrated that polygonal elements possess great potential in the study of nonlinear elastic materials under finite deformations on the one hand these elements are well suited to model complex microstructures e g particulate microstructures and microstructures involving different length scales and incorporating periodic boundary conditions on the other hand polygonal elements are found to be more tolerant to large localized deformations than the standard finite elements and to produce more accurate results in bending and shear with mixed formulations lower order mixed polygonal elements are also shown to be numerically stable on voronoi type meshes without any additional stabilization treatment however polygonal elements generally suffer from persistent consistency errors under mesh refinement with the commonly used numerical integration schemes as a result non convergent finite element results typically occur which severely limit their applications in this work a general gradient correction scheme is adopted that restores the polynomial consistency by adding a minimal perturbation to the gradient of the displacement field with the correction scheme the recovery of optimal convergence for solutions of displacement based and mixed formulations with both linear and quadratic displacement interpolants is confirmed by numerical studies of several boundary value problems in finite elasticity in addition for mixed polygonal elements the various choices of the pressure field approximations are discussed and their performance on stability and accuracy are numerically investigated we present applications of those elements in physically based examples including a study of filled elastomers with interphasial effect and a qualitative comparison with cavitation experiments for fiber reinforced elastomers

dimension prints and the avoidance of sets for flow solutions of non autonomous ordinary differential equations we provide a criterion for a generalised flow solution of a non autonomous ordinary differential equation to avoid a subset of the phase space this improves on that established by aizenman for the autonomous case where avoidance is guaranteed if the underlying vector field is sufficiently regular and the subset has sufficiently small box counting dimension we define the r codimension print of a subset s rn 0 t which is a subset of 0 2 that encodes the dimension of s in a way that distinguishes spatial and temporal detail we prove that the subset s is avoided by a generalised flow solution with underlying vector field in lp 0 t lq rn with 1 p q if the holder conjugates q p are in the r codimension print of s

a posteriori error estimation in large strain elasticity using equilibrated local neumann problems abstract a method to obtain a posteriori an accurate measure of the error in finite element computations is to solve a neumann problem with equilibrated tractions for each finite element we extend this approach to large strain elasticity and mixed finite elements which are well suited for nearly incompressible rubber like materials for an l2 projection of the error in the first piola kirchhoff stress tensor we prove that the estimator provides a guaranteed upper bound without multiplicative constants numerical examples confirm the effectiveness for both linear and ogden material

a note on the rank transform for interactions summary the asymptotic properties of the rank transform statistic for testing for interaction in a balanced two way classification are studied necessary and sufficient conditions are obtained for the asymptotic distribution of this rank transform statistic to be chi squared under the null hypothesis of no interaction it is shown that the rank transform test statistic for interaction is asymptotically chi squared divided by its degrees of freedom when there are exactly two levels of both main effects or when there is only one main effect in the latter case the test detects a nested effect instead of an interaction in all other two way layouts there exist values for the main effects such that under the null hypothesis of no interaction the expected value of the rank transform test statistic goes to infinity as the sample size increases

on the lagrangian structure of transport equations the vlasov poisson system the vlasov poisson system is an important nonlinear transport equation used to describe the evolution of particles under their self consistent electric or gravitational field the existence of classical solutions is limited to dimensions d 3 under strong assumptions on the initial data whereas weak solutions are known to exist under milder conditions however in the setting of weak solutions it is unclear whether the eulerian description provided by the equation physically corresponds to a lagrangian evolution of the particles in this article we develop several general tools concerning the lagrangian structure of transport equations with nonsmooth vector fields and we apply these results to show that weak renormalized solutions of vlasov poisson are lagrangian and actually that the concepts of renormalized and lagrangian solutions are equivalent as a corollary we prove that finite energy solutions in dimension d 4 are transported by a global flow in particular they preserve all the natural casimir invariants and we obtain the global existence of weak solutions in any dimension under minimal assumptions on the initial data

flows for non smooth vector fields with subexponentially integrable divergence abstract in this paper we study flows associated to sobolev vector fields with subexponentially integrable divergence our approach is based on the transport equation following diperna lions 17 a key ingredient is to use a quantitative estimate of solutions to the cauchy problem of transport equation to obtain the regularity of density functions

steady nearly incompressible vector fields in two dimension chain rule and renormalization given bounded vector field b mathbb r d to mathbb r d scalar field u mathbb r d to mathbb r and a smooth function beta mathbb r to mathbb r we study the characterization of the distribution rm div beta u b in terms of div b and div ub in the case of bv vector fields b and under some further assumptions such characterization was obtained by l ambrosio c de lellis and j mal up to an error term which is a measure concentrated on the so called tangential set of b we answer some questions posed in their paper concerning the properties of this term in particular we construct a nearly incompressible bv vector field b and a bounded function u for which this term is nonzero for steady nearly incompressible vector fields b and under some further assumptions in the case when d 2 we provide complete characterization of div beta u b in terms of div b and div ub our approach relies on the structure of level sets of lipschitz functions on mathbb r 2 obtained by g alberti s bianchini and g crippa extending our technique we obtain new sufficient conditions when any bounded weak solution u of partial t u b cdot nabla u 0 is renormalized that is when it also solves partial t beta u b cdot nabla beta u 0 for any smooth function beta colon mathbb r to mathbb r as a consequence we obtain new a uniqueness result for this equation

critical non sobolev regularity for continuity equations with rough velocity fields abstract we present a divergence free vector field in the sobolev space h 1 such that the flow associated to the field does not belong to any sobolev space the vector field is deterministic but constructed as the realization of a random field combining simple elements this construction illustrates the optimality of recent quantitative regularity estimates as it gives a straightforward example of a well posed flow which has nevertheless only very weak regularity

well posedness of the transport equation by stochastic perturbation we consider the linear transport equation with a globally holder continuous and bounded vector field with an integrability condition on the divergence while uniqueness may fail for the deterministic pde we prove that a multiplicative stochastic perturbation of brownian type is enough to render the equation well posed this seems to be the first explicit example of a pde of fluid dynamics that becomes well posed under the influence of a multiplicative noise the key tool is a differentiable stochastic flow constructed and analyzed by means of a special transformation of the drift of ito tanaka type

existence and uniqueness of maximal regular flows for non smooth vector fields in this paper we provide a complete analogy between the cauchy lipschitz and the diperna lions theories for ode s by developing a local version of the diperna lions theory more precisely we prove the existence and uniqueness of a maximal regular flow for the diperna lions theory using only local regularity and summability assumptions on the vector field in analogy with the classical theory which uses only local regularity assumptions we also study the behaviour of the ode trajectories before the maximal existence time unlike the cauchy lipschitz theory this behaviour crucially depends on the nature of the bounds imposed on the spatial divergence of the vector field in particular a global assumption on the divergence is needed to obtain a proper blow up of the trajectories

lagrangian flows and the one dimensional peano phenomenon for odes we consider the one dimensional ordinary differential equation with a vector field which is merely continuous and nonnegative and satisfies a condition on the amount of zeros although it is classically known that this problem lacks uniqueness of classical trajectories we show that there is uniqueness for the so called regular lagrangian flow by now usual notion of flow in nonsmooth situations as well as uniqueness of distributional solutions for the associated continuity equation the proof relies on a space reparametrization argument around the zeros of the vector field

analysis finite element computation and error estimation in transversely isotropic nearly incompressible finite elasticity abstract in this paper we present constitutive models for nearly incompressible transversely isotropic materials in finite hyperelasticity particularly for reinforced rubber like materials which are of essential engineering interest the theory is developed using a convected curvilinear coordinate system based on a mixed two field displacement pressure energy functional furthermore an a posteriori error estimator without multiplicative constants is derived for non linear anisotropic problems which measures the discretization error in the first piola kirchhoff stresses in the l 2 norm by solving local neumann problems with equilibrated tractions illustrative numerical examples demonstrate the anisotropic material behaviour of reinforced materials and the efficiency of using adaptive finite element methods

an improved reproducing kernel particle method for nearly incompressible finite elasticity the previously developed reproducing kernel particle method rkpm employs a high order quadrature rule for desired domain integration accuracy this leads to an over constrained condition in the limit of incompressibility and volumetric locking and pressure oscillation were encountered the employment of a large support size in the reproducing kernel shape function increases the dependency in the discrete constraint equations at quadrature points and thereby relieves locking however this approach consumes high cpu and it cannot effectively resolve pressure oscillation difficulty in this paper a pressure projection method is introduced by locally projecting the pressure onto a lower order space to reduce the number of independent discrete constraint equations this approach relieves the over constrained condition and thus eliminates volumetric locking and pressure oscillation without the expense of employing large support size in rkpm the method is developed in a general framework of nearly incompressible finite elasticity and therefore linear problems are also applicable to further reduce the computational cost a stabilized reduced integration method based on an assumed strain approach on the gradient matrix associated with the deformation gradient is also introduced the resulting stiffness matrix and force vector of rkpm are obtained explicitly without numerical integration

nonparametric methods for stratified two sample designs with application to multiclinic trials abstract motivated by some problems arising from multiclinic trials we consider stratified two sample designs nonparametric effects are defined and nonparametric hypotheses are formulated in a design where treatment centers strata and interactions are assumed to be fixed factors the interpretation of the nonparametric effects and hypotheses is analyzed in two classes of semiparametric models the linear models and models with lehmann alternatives the case where centers and interactions are assumed to be random factors the so called mixed model is also considered nonparametric effects and hypotheses are defined for general models and their properties are analyzed in corresponding linear models and in models with lehmann alternatives the nonparametric effects are estimated by linear rank statistics where the ranks over all centers are used the mixed model for repeated baseline and endpoint observations is briefly considered and rank procedures are also proposed for this model all procedure

degenerate sdes with singular drift and applications to heisenberg groups abstract by using the ultracontractivity of a reference diffusion semigroup krylov s estimate is established for a class of degenerate sdes with singular drifts which leads to existence and pathwise uniqueness by means of zvonkin s transformation the main result is applied to singular sdes on generalized heisenberg groups

a uniform strain hexahedron and quadrilateral with orthogonal hourglass control the treatment of zero energy modes which arise due to one point integration of first order isoparametric finite elements is addressed a method for precisely isolating these modes for arbitrary geometry is developed two hourglass control schemes viscous and elastic are presented and examined in addition a convenient one point integration scheme which analytically integrates the element volume and uniform strain modes is presented

stable mixing estimates in the infinite peclet number limit abstract we consider a passive scalar f advected by a strictly monotone shear flow and with a diffusivity parameter 1 we prove an estimate on the homogeneous h 1 norm of f that combines both the l 2 enhanced diffusion effect at a sharp rate proportional to 1 3 and the sharp mixing decay proportional to t 1 of the h 1 norm of f when 0 in particular the estimate is stable in the infinite peclet number limit as 0 to the best of our knowledge this is the first result of this kind since the work of kelvin in 1887 on the couette flow the two key ingredients in the proof are an adaptation of the hypocoercivity method and the use of a vector field j that commutes with the transport part of the equation the l 2 norm of jf together with the l 2 norm of f produces a suitable upper bound for the h 1 norm of the solution that gives the extra decay factor of t 1

lagrangian solutions to the vlasov poisson system with l1 density the recently developed theory of lagrangian flows for transport equations with low regularity coefficients enables to consider non bv vector fields we apply this theory to prove existence and stability of global lagrangian solutions to the repulsive vlasov poisson system with only integrable initial distribution function with finite energy these solutions have a well defined lagrangian flow an a priori estimate on the smallness of the superlevels of the flow in three dimensions is established in order to control the characteristics

limitations of the rank transform procedure a study of repeated measures designs part i abstract the applicability of the rank transform procedure to two way repeated measures designs with equicorrelated errors is examined all of the common testing problems with these models are examined it is demonstrated that with the exception of one testing problem the rank transform procedure is not generally applicable this complements the findings in akritas 1990 for models with independent errors the one valid rank transform statistic presented here does have the interesting feature that it allows the covariance of the equicorrelated errors to depend on the column treatment this is due to the robustness of the corresponding f statistic to this kind of departure from the assumption of a common covariance matrix it is shown however that the efficacy of this rank transform procedure has the undesirable property of depending on the model parameters

on empirical likelihood for a semiparametric mixture model summary plant and animal studies of quantitative trait loci provide data which arise from mixtures of distributions with known mixing proportions previous approaches to estimation involve modelling the distributions parametrically we propose a semiparametric alternative which assumes that the log ratio of the component densities satisfies a linear model with the baseline density unspecified it is demonstrated that a constrained empirical likelihood has an irregularity under the null hypothesis that the two densities are equal a factorisation of the likelihood suggests a partial empirical likelihood which permits unconstrained estimation of the parameters and which is shown to give consistent and asymptotically normal estimators regardless of the null the asymptotic null distribution of the log partial likelihood ratio is chi squared theoretical calculations show that the procedure may be as efficient as the full empirical likelihood in the regular set up the usefulness of the robust methodology is illustrated with a rat study of breast cancer resistance genes

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

analysis of the implicit upwind finite volume scheme with rough coefficients we study the implicit upwind finite volume scheme for numerically approximating the linear continuity equation in the low regularity diperna lions setting that is we are concerned with advecting velocity fields that are spatially sobolev regular and data that are merely integrable we prove that on unstructured regular meshes the rate of convergence of approximate solutions generated by the upwind scheme towards the unique distributional solution of the continuous model is at hbox least 1 2 the numerical error is estimated in terms of logarithmic kantorovich rubinstein distances and provides thus a bound on the rate of weak convergence

sobolev estimates for solutions of the transport equation and ode flows associated to non lipschitz drifts it is known after jabin j differ equ 260 5 4739 4757 2016 and alberti et al ann pde 5 1 9 2019 that ode flows and solutions of the transport equation associated to sobolev vector fields do not propagate sobolev regularity even of fractional order in this paper we improve the result at clop and jylha j differ equ 266 8 4544 4567 2019 and show that some kind of propagation of sobolev regularity happens as soon as the gradient of the drift is exponentially integrable we provide sharp sobolev estimates and new examples as an application of our main theorem we generalize a regularity result for the 2d euler equation obtained by bahouri and chemin in bahouri and chemin arch ration mech anal 127 2 159 181 1994

continuity equations and ode flows with non smooth velocity in this paper we review many aspects of the well posedness theory for the cauchy problem for the continuity and transport equations and for the ordinary differential equation ode in this framework we deal with velocity fields that are not smooth but enjoy suitable weak differentiability assumptions we first explore the connection between the partial differential equation pde and the ode in a very general non smooth setting then we address the renormalization property for the pde and prove that such a property holds for sobolev velocity fields and for bounded variation velocity fields finally we present an approach to the ode theory based on quantitative estimates

stochastic lagrangian particle approach to fractal navier stokes equations in this article we study the fractal navier stokes equations by using the stochastic lagrangian particle path approach in constantin and iyer comm pure appl math lxi 330 345 2008 more precisely a stochastic representation for the fractal navier stokes equations is given in terms of stochastic differential equations driven by levy processes based on this representation a self contained proof for the existence of a local unique solution for the fractal navier stokes equation with initial data in mathbb w 1 p is provided and in the case of two dimensions or large viscosity the existence of global solutions is also obtained in order to obtain the global existence in any dimensions for large viscosity the gradient estimates for levy processes with time dependent and discontinuous drifts are proved

a unified approach to rank tests for multivariate and repeated measures designs abstract a unified approach to asymptotic rank tests is presented for a wide class of univariate and multivariate models including repeated measures designs without compound symmetry the models are assumed to be balanced and complete with more than one replication per cell the proposed rank tests are constructed by ranking all of the observations together regardless of row column or component membership this method of ranking offers increased power over the method of n rankings the resulting test statistic is a quadratic form in linear rank statistics asymptotic distributions are determined under pitman alternatives that allow for both scale and location alternatives the resulting statistics include tests for factor effects both scale and location differences in one two and higher way layouts with repeated measures on one or several factors without assuming equicorrelation also included are tests for the multivariate two and k sample problem as well as multivariate versions of the tests

asymptotic relative efficiencies of the rank transformation procedure in randomized complete block designs abstract this article provides insight into the powers of alternative tests for experimental effects in the presence of a blocking factor three rank tests and the usual f test are compared using asymptotic relative efficiencies are s rank tests provide a useful alternative method of analysis when the assumptions of the f test are not met further rank tests are usually more powerful than the f test when outliers are present or when the distribution of the data possesses heavy tails the rank tests studied are friedman s test the aligned ranks test and the rank transformation procedure the rank transformation test consists of ranking all of the data as one sample and then applying the usual f test to the ranks two main themes form the body of the article the first theme is the development of the limiting noncentrality parameter of the rank transformation statistic the development uses the methods popularized by hajek and sidak 1967 a lemma is given that establishes the joint limiting distribu

global existence of weak solutions to the fene dumbbell model of polymeric flows systems coupling fluids and polymers are of great interest in many branches of sciences one of the most classical models to describe them is the fene finite extensible nonlinear elastic dumbbell model we prove global existence of weak solutions to the fene dumbbell model of polymeric flows the main difficulty is the passage to the limit in a nonlinear term that has no obvious compactness properties the proof uses many weak convergence techniques in particular it is based on the control of the propagation of strong convergence of some well chosen quantity by studying a transport equation for its defect measure in addition this quantity controls a rescaled defect measure of the gradient of the velocity

on the perturbed lagrangian formulation for nearly incompressible and incompressible hyperelasticity a perturbed lagrangian formulation for nearly incompressible and incompressible hyperelasticity is developed by performing a conjugate transformation on the volumetric energy function the formulation is developed without reference to any specific material models or volumetric energy functions solution existence conditions for general nearly incompressible hyperelasticity problems and their discrete counterparts are described a discussion on the convergence of nearly incompressible solutions to an incompressible solution of continuous as well as discrete hyperelasticity problems is given the rate of convergence with respect to the compressibility parameter is shown to be one in several numerical examples

nonparametric hypotheses and rank statistics for unbalanced factorial designs abstract factorial designs are studied with independent observations fixed number of levels and possibly unequal number of observations per factor level combination in this context the nonparametric null hypotheses introduced by akritas and arnold are considered new rank statistics are derived for testing the nonparametric hypotheses of no main effects no interaction and no factor effects in unbalanced crossed classifications the formulation of all results includes tied observations extensions of these procedures to higher way layouts are given and the efficacies of the test statistics against nonparametric alternatives are derived a modification of the test statistics and approximations to their finite sample distributions are also given the small sample performance of the procedures for two factors is examined in a simulation study as an illustration a real dataset with ordinal data is analyzed

hourglass control in linear and nonlinear problems abstract mesh stabilization techniques for controlling the hourglass modes in under integrated hexahedral and quadrilateral elements are described it is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly it is also shown that this leads to an hourglass control that satisfies the patch test the nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed finally effective means of implementing these hourglass procedure in computer codes are described applications to both the laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered

exponential self similar mixing by incompressible flows we study the problem of the optimal mixing of a passive scalar under the action of an incompressible flow in two space dimensions the scalar solves the continuity equation with a divergence free velocity field which satisfies a bound in the sobolev space ws p where s 0 and 1 p the mixing properties are given in terms of a characteristic length scale called the mixing scale we consider two notions of mixing scale one functional expressed in terms of the homogeneous sobolev norm h 1 the other geometric related to rearrangements of sets we study rates of decay in time of both scales under self similar mixing for the case s 1 and 1 p including the case of lipschitz continuous velocities and the case of physical interest of enstrophy constrained flows we present examples of velocity fields and initial configurations for the scalar that saturate the exponential lower bound established in previous works on the time decay of both scales we also present several consequences for the geometry of regular lagrangian flows associated to sobolev velocity fields

lagrangian flows driven by bv fields in wiener spaces we establish the renormalization property for essentially bounded solutions of the continuity equation associated to bounded variation bv fields in wiener spaces with values in the associated cameron martin space thus obtaining by standard arguments new uniqueness and stability results for correspondent lagrangian flows

hyperbolicity of the nonlinear models of maxwell s equations we consider the class of nonlinear models of electromagnetism that has been described by coleman dill 7 a model is completely determined by its energy density w b d viewing the electromagnetic field b d as a 3 2 matrix we show that polyconvexity of w implies the local well posedness of the cauchy problem within smooth functions of class hs with s 1 d 2

on the use of a friedman type statistic in balanced and unbalanced block designs distribution free tests and multiple comparison procedures are considered for randomized block designs a general friedman type statistic is defined that is usable in almost any block design with arbitrary missing data structure for balanced incomplete block designs a multiple comparison procedure and exact tables are given for a statistic equivalent to one proposed by durbin 1951 finally for designs with missing observations on only one treatment we present exact tables for the test statistic and we consider a multiple comparison procedure

finite element methods for constrained problems in elasticity several different variational formulations of boundary value problems with constraints are discussed with particular reference to constrained problems in elasticity special attention is given to exterior penalty methods a discussion of the conditions necessary for penalty methods to provide a basis for stable and convergent finite element methods is given in particular the use of reduced integration is discussed and criteria on the order of reduced integration rules sufficient to produce stable and convergent schemes are described applications of reduced integration penalty methods to incompressible elasticity problems and contact problems are described

stochastic differential equations with coefficients in sobolev spaces abstract we consider the ito stochastic differential equation d x t j 1 m a j x t d w t j a 0 x t d t on r d the diffusion coefficients a 1 a m are supposed to be in the sobolev space w loc 1 p r d with p d and to have linear growth for the drift coefficient a 0 we distinguish two cases i a 0 is a continuous vector field whose distributional divergence a 0 with respect to the gaussian measure d exists ii a 0 has sobolev regularity w loc 1 p for some p 1 assume r d exp 0 a 0 j 1 m a j 2 a j 2 d d for some 0 0 in case i if the pathwise uniqueness of solutions holds then the push forward x t d admits a density with respect to d in particular if the coefficients are bounded lipschitz continuous then x t leaves the lebesgue measure leb d quasi invariant in case ii we develop a method used by g crippa and c de lellis for ode and implemented by x zhang for sde to establish existence and uniqueness of stochastic flow of maps

polynomial mixing under a certain stationary euler flow abstract we study the mixing properties of a scalar on the unit disk advected by a certain incompressible velocity field u which is a stationary radial solution of the euler equation the scalar solves the continuity equation with the velocity field u and we can measure the degree of mixedness of with two different scales commonly used in this setting namely the geometric and the functional mixing scale we develop a physical space approach well adapted to the quantitative analysis of the decay in time of the geometric mixing scale which turns out to be polynomial for a large class of initial data this extends previous results for the functional mixing scale based on the explicit expression for the solution in fourier variable results that are also partially recovered by our approach

the resolution of the yang mills plateau problem in super critical dimensions abstract we study the minimization problem for the yang mills energy under fixed boundary connection in supercritical dimension n 5 we define the natural function space a g in which to formulate this problem in analogy to the space of integral currents used for the classical plateau problem the space a g can be also interpreted as a space of weak connections on a real measure theoretic version of reflexive sheaves from complex geometry we prove the existence of weak solutions to the yang mills plateau problem in the space a g we then prove the optimal regularity result for solutions of this plateau problem on the way to prove this result we establish a coulomb gauge extraction theorem for weak curvatures with small yang mills density this generalizes to the general framework of weak l 2 curvatures previous works of meyer riviere and tao tian in which respectively a strong approximability property and an admissibility property were assumed in addition

rank tests for main and interaction effects in analysis of variance abstract a class of rank tests for analysis of variance based on linear functions of the wilcoxon mann whitney statistics between cells is studied this class includes many popular procedures assuming a location family model a condition for optimal pitman efficacy of tests of main effects in this class is given tests for main effects in two way layouts that achieve this optimality are shown to improve on previous proposals when the sample sizes are unbalanced nested orthogonal contrasts are introduced that can be used to decompose the overall test statistics into independent components to assess the contribution of individual contrasts a new definition of interaction appropriate for rank based analysis of variance is suggested and test procedures are proposed

universal mixers in all dimensions abstract we construct universal mixers incompressible flows that mix arbitrarily well general solutions to the corresponding transport equation in all dimensions this mixing is exponential in time i e essentially optimal for any initial condition with at least some regularity and we also show that a uniform mixing rate for all initial conditions cannot be achieved the flows are time periodic and uniformly in time bounded in spaces w s p for a range of s p that includes points with s 1 and p 2

lagrangian solutions to the 2d euler system with l1 vorticity and infinite energy we consider solutions to the two dimensional incompressible euler system with only integrable vorticity thus with possibly locally infinite energy with such regularity we use the recently developed theory of lagrangian flows associated to vector fields with gradient given by a singular integral in order to define lagrangian solutions for which the vorticity is transported by the flow we prove strong stability of these solutions via strong convergence of the flow under the only assumption of l1 weak convergence of the initial vorticity the existence of lagrangian solutions to the euler system follows for arbitrary l1 vorticity relations with previously known notions of solutions are established

friedman type statistics and consistent multiple comparisons for unbalanced designs with missing data abstract a generalization of the friedman test using the marginal likelihood principle kalbfleisch and prentice 1973 is presented and its asymptotic power given it allows use of a variety of score functions and handles ties and unbalanced designs some well known statistics including the tests of kruskal and wallis 1952 prentice 1979 and rinaman 1983 are proven to be special cases whereas others e g klotz 1980 groggel and skillings 1986 rai 1987 skillings and mack 1981 are shown to be less appropriate multiple comparisons are considered under both the global hypothesis and alternatives evaluating non centrality parameters under local shift alternatives the procedures of klotz 1980 and for a special case skillings and mack 1981 can be either anticonservative showing differences that do not exist or insensitive ignoring differences that do exist depending on the distribution of missing data a new scheffe type procedure for arbitrarily missing data is presented and recomme

estimates and regularity results for the diperna lions flow in this paper we derive new simple estimates for ordinary differential equations with sobolev coefficients these estimates not only allow to recover some old and recent results in a simple direct way but they also have some new interesting corollaries

comparison of asymptotically distribution free procedures for the analysis of complete blocks abstract the friedman test or sign test when k 2 depends entirely on within block rankings in a recent paper quade 1979 attempted to provide a test with more power than the friedman test by considering a k sample extension of the wilcoxon signed ranks test this is done by taking advantage of the between block information a third way to approach the problem and still retain both the within and between block information is first to transform all the observations to ranks from 1 to bk b blocks and k treatments and then to apply the parametric f test to the ranks this approach is shown to be asymptotically distribution free under suitable conditions computer simulation results indicate that this procedure is both robust and powerful for small sample sizes

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

plane waves in nonlinear electromagnetism on enonce un theoreme d existence globale pour le probleme de cauchy des ondes planes les donnees initiales sont supposees mesurables et bornees mais pas necessairement petites

a displacement based finite element formulation for incompressible and nearly incompressible cardiac mechanics the lagrange multiplier lm and penalty methods are commonly used to enforce incompressibility and compressibility in models of cardiac mechanics in this paper we show how both formulations may be equivalently thought of as a weakly penalized system derived from the statically condensed perturbed lagrangian formulation which may be directly discretized maintaining the simplicity of penalty formulations with the convergence characteristics of lm techniques a modified shamanskii newton raphson scheme is introduced to enhance the nonlinear convergence of the weakly penalized system and exploiting its equivalence modifications are developed for the penalty form focusing on accuracy we proceed to study the convergence behavior of these approaches using different interpolation schemes for both a simple test problem and more complex models of cardiac mechanics our results illustrate the well known influence of locking phenomena on the penalty approach particularly for lower order schemes and its effect on accuracy for whole cycle mechanics additionally we verify that direct discretization of the weakly penalized form produces similar convergence behavior to mixed formulations while avoiding the use of an additional variable combining a simple structure which allows the solution of computationally challenging problems with good convergence characteristics the weakly penalized form provides an accurate and efficient alternative to incompressibility and compressibility in cardiac mechanics