weak strong uniqueness of dissipative measure valued solutions for polyconvex elastodynamics for the equations of elastodynamics with polyconvex stored energy and some related simpler systems we define a notion of a dissipative measure valued solution and show that such a solution agrees with a classical solution with the same initial data when such a classical solution exists as an application of the method we give a short proof of strong convergence in the continuum limit of a lattice approximation of one dimensional elastodynamics in the presence of a classical solution also for a system of conservation laws endowed with a positive and convex entropy we show that dissipative measure valued solutions attain their initial data in a strong sense after time averaging

vanishing viscosity solutions of nonlinear hyperbolic systems we consider the cauchy problem for a strictly hyperbolic n n system in one space dimension ut a u ux 0 assuming that the initial data have small total variation we show that the solutions of the viscous approximations ut a u ux euxx are defined globally in time and satisfy uniform bv estimates independent of e moreover they depend continuously on the initial data in the l 1 distance with a lipschitz constant independent of t e letting e 0 these viscous solutions converge to a unique limit depending lipschitz continuously on the initial data in the conservative case where a df is the jacobian

global ill posedness of the isentropic system of gas dynamics we consider the isentropic compressible euler system in 2 space dimensions with pressure law p 2 and we show the existence of classical riemann data i e pure jump discontinuities across a line for which there are infinitely many admissible bounded weak solutions bounded away from the void we also show that some of these riemann data are generated by a 1 dimensional compression wave our theorem leads therefore to lipschitz initial data for which there are infinitely many global bounded admissible weak solutions c 2015 wiley periodicals inc

the euler equations as a differential inclusion we propose a new point of view on weak solutions of the euler equations describing the motion of an ideal incompressible fluid in r n with n 2 we give a reformulation of the euler equations as a differential inclusion and in this way we obtain transparent proofs of several celebrated results of v scheffer and a shnirelman concerning the non uniqueness of weak solutions and the existence of energy decreasing solutions our results are stronger because they work in any dimension and yield bounded velocity and pressure

convexity and absolute continuity of the laplace beltrami operator on montre que l existence de bonnes fonctions convexes implique l absolue continuite par rapport a la mesure de lebesgue des mesures spectrales de l extension auto adjointe du laplacien c 0 m dans l 2 m

the vanishing viscosity limit of statistical solutions of the navier stokes equations ii the general case abstract we study problems of vanishing viscosity limit of statistical solutions of the navier stokes equation in 3 d and general boundary conditions in 2 d in this case due to lack of sufficiently strong estimate besides energy type one we can have only weak convergence in the limit by a statistical extension of the generalized young measure theorem of r diperna and a majda we show that a weak limit is a measure valued solution of the euler equation as another corollary of the extended young measure theorem we show that any statistical solution generates measure valued solutions in a canonical fashion

oscillations and concentrations in weak solutions of the incompressible fluid equations the authors introduce a new concept of measure valued solution for the 3 d incompressible euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations one application of the concepts developed here is the following important result a sequence of leray hopf weak solutions of the navier stokes equations converges in the high reynolds number limit to a measure valued solution of 3 d euler defined for all positive times the authors present several explicit examples of solution sequences for 3 d incompressible euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations an extensions of the concept of young measure is developed to incorporate these complex phenomena in the measure valued solutions constructed here

em and beyond the basic theme of the em algorithm to repeatedly use complete data methods to solve incomplete data problems is also a theme of several more recent statistical techniques these techniques multiple imputation data augmentation stochastic relaxation and sampling importance resampling combine simulation techniques with complete data methods to attack problems that are difficult or impossible for em

imputation of missing categorical data by maximizing internal consistency this paper suggests a method to supplant missing categorical data by reasonable replacements these replacements will maximize the consistency of the completed data as measured by guttman s squared correlation ratio the text outlines a solution of the optimization problem describes relationships with the relevant psychometric theory and studies some properties of the method in detail the main result is that the average correlation should be at least 0 50 before the method becomes practical at that point the technique gives reasonable results up to 10 15 missing data

kahler parabolicity and the euler number of compact manifolds of non positive sectional curvature let m 2n be a compact riemannian manifold of non positive sectional curvature it is shown that if m 2n is homeomorphic to a kahler manifold then its euler number satisfies the inequality 1 n chi m 2n geq 0

on the spectrum of a finite volume negatively curved manifold we show that a noncompact manifold with bounded sectional curvature whose ends are sufficiently gromov hausdorff close to rays has a finite dimensional space of square integrable harmonic forms in the special case of a finite volume manifold with pinched negative sectional curvature we show that the essential spectrum of the p iorm laplacian is the union of the essential spectra of a collection of ordinary differential operators associated to the ends we give examples of such manifolds with curvature pinched arbitrarily close to 1 and with an infinite number of gaps in the spectrum of the function laplacian 1 introduction in this paper we consider riemannian manifolds of finite volume and pinched negative sectional curvature we give results about the kernel of the differential form laplacian and about its essential spectrum our first result is the finite dimensionality of the space of square integrable harmonic forms for a more general class of riemannian manifolds which can be roughly characterized as those with bounded sectional curvature and with ends that are sufficiently gromov hausdorff close to rays let m be a complete connected rc dimensional riemannian manifold with a basepoint m let br m denote the distance ball around m and let sr m dbr m be the distance sphere around m put

gleaning in the field of dual scaling some historical background and preliminary technical information are first presented and then a number of hidden but important methodological aspects of dual scaling are illustrated and discussed normed versus projected weights the amount of information accounted for by each solution a perfect solution to the problem of multidimensional unfolding multidimensional quantification space graphical display number of option problems option standardization versus item standardization and asymmetry of symmetric dual scaling contrary to the common perception that dual scaling and similar quantification methods are now mathematically transparent the present study demonstrates how much more needs to be clarified for routine use of the method to arrive at valid conclusions data analysis must be carried out in such a way that common sense intuition and sound logic will prevail

the vanishing viscosity limit of statistical solutions of the navier stokes equations i 2 d periodic case in this paper we present a result on the vanishing viscosity limit of the statistical solutions of the navier stokes equations in the 2 d periodic domain in this case the enstrophy type estimate combined with the strengthened energy estimate lead to the strong compactness for the family of statistical solutions thus by choosing a subsequence we can have a statistical solution of the euler equation as the vanishing viscosity limit of the sequence this provides us the global existence in time of statistical solution of the 2 d euler equation in the periodic domain with the initial data of finite mean enstrophy the uniqueness remains open

gaussianization based quasi imputation and expansion strategies for incomplete correlated binary responses new quasi imputation and expansion strategies for correlated binary responses are proposed by borrowing ideas from random number generation the core idea is to convert correlated binary outcomes to multivariate normal outcomes in a sensible way so that re conversion to the binary scale after performing multiple imputation yields the original specified marginal expectations and correlations this conversion process ensures that the correlations are transformed reasonably which in turn allows us to take advantage of well developed imputation techniques for gaussian outcomes we use the phrase quasi because the original observations are not guaranteed to be preserved we argue that if the inferential goals are well defined it is not necessary to strictly adhere to the established definition of multiple imputation our expansion scheme employs a similar strategy where imputation is used as an intermediate step it leads to proportionally inflated observed patterns forcing the data set to a complete rectangular format the plausibility of the proposed methodology is examined by applying it to a wide range of simulated data sets that reflect alternative assumptions on complete data populations and missing data mechanisms we also present an application using a data set from obesity research we conclude that the proposed method is a promising tool for handling incomplete longitudinal or clustered binary outcomes under ignorable non response mechanisms

morse novikov cohomology of almost nonnegatively curved manifolds abstract let m n be a closed manifold of almost nonnegative sectional curvature and nonzero first de rham cohomology group using a topological argument we show that the morse novikov cohomology group h p m n vanishes for any p and h d r 1 m n 0 based on a new integral formula we also show that a similar result holds for a closed manifold of almost nonnegative ricci curvature under the additional assumption that its curvature operator is uniformly bounded from below

a quantitative analysis of oka s lemma in this paper we will examine a strong form of oka s lemma which provides sufficient conditions for compact and subelliptic estimates for the overline partial neumann operator on lipschitz domains on smooth domains the condition for subellipticity is equivalent to d angelo finite type and the condition for compactness is equivalent to catlin s condition p as an application we will prove regularity for the overline partial neumann operator in the sobolev space ws 0 leq s frac 1 2 on c2 domains

sur la l 2 cohomologie des varietes a courbure negative we give a topological interpretation of the space of l2 harmonic forms on finite volume manifolds with sufficiently pinched negative curvature we give examples showing that this interpretation fails if the curvature is not sufficiently pinched and that our result is sharp with respect to the pinching constants the method consists first in comparing l2 cohomology with weighted l2 cohomology thanks to previuos works done by t ohsawa and then in identifying these weighted spaces

on statistical and measure valued solutions of differential equations abstract we discuss the relation between statistical measure valued and weak solutions for typical cases of nonuniquely solvable systems of ordinary differential equations and for the case of hyperbolic conservation laws

the inviscid burgers equation with brownian initial velocity the law of the hopf cole solution of the inviscid burgers equation with brownian initial velocity is made explicit as examples of applications we investigate the smoothness of the solution the statistical distribution of the shocks we determine the exact hausdorff function of the lagrangian regular points and investigate the existence of lagrangian regular points in a fixed borel set

clustering n objects into k groups under optimal scaling of variables we propose a method to reduce many categorical variables to one variable withk categories or stated otherwise to classifyn objects intok groups objects are measured on a set of nominal ordinal or numerical variables or any mix of these and they are represented asn points inp dimensional euclidean space starting from homogeneity analysis also called multiple correspondence analysis the essential feature of our approach is that these object points are restricted to lie at only one ofk locations it follows that thesek locations must be equal to the centroids of all objects belonging to the same group which corresponds to a sum of squared distances clustering criterion the problem is not only to estimate the group allocation but also to obtain an optimal transformation of the data matrix an alternating least squares algorithm and an example are given

statistical solutions of hyperbolic conservation laws foundations we seek to define statistical solutions of hyperbolic systems of conservation laws as time parametrized probability measures on p integrable functions to do so we prove the equivalence between probability measures on l p spaces and infinite families of correlation measures each member of this family termed a correlation marginal is a young measure on a finite dimensional tensor product domain and provides information about multi point correlations of the underlying integrable functions we also prove that any probability measure on a l p space is uniquely determined by certain moments correlation functions of the equivalent correlation measure we utilize this equivalence to define statistical solutions of multi dimensional conservation laws in terms of an infinite set of equations each evolving a moment of the correlation marginal these evolution equations can be interpreted as augmenting entropy measure valued solutions with additional information about the evolution of all possible multi point correlation functions our concept of statistical solutions can accommodate uncertain initial data as well as possibly non atomic solutions even for atomic initial data for multi dimensional scalar conservation laws we impose additional entropy conditions and prove that the resulting entropy statistical solutions exist are unique and are stable with respect to the 1 wasserstein metric on probability measures on l 1

an imputation strategy for incomplete longitudinal ordinal data a new quasi imputation strategy for correlated ordinal responses is proposed by borrowing ideas from random number generation the essential idea is collapsing ordinal levels to binary ones and converting correlated binary outcomes to multivariate normal outcomes in a sensible way so that re conversion to the binary and then ordinal scale after conducting multiple imputation yields the original marginal distributions and correlations this conversion process ensures that the correlations are transformed reasonably which in turn allows us to take advantage of well developed imputation techniques for gaussian outcomes we use the phrase quasi because the original observations are not guaranteed to be preserved we present an application using a data set from psychiatric research we conclude that the proposed method may be a promising tool for handling incomplete longitudinal or clustered ordinal outcomes

the hodge cohomology of a conformally compact metric on etudie le laplacien de hogde agissant sur des k formes differentielles pour une classe de varietes de riemann completes a courbure sectionnelle negative proche de l infini ces varietes ont des compactifications c sur lesquelles la metrique est conforme a une metrique lisse jusqu au bord avec un facteur conforme 2 une fonction definissante pour le bord

statistical solutions and onsager s conjecture abstract we prove a version of onsager s conjecture on the conservation of energy for the incompressible euler equations in the context of statistical solutions as introduced recently by fjordholm et al 2017 as a byproduct we also obtain an alternative proof for the conservative direction of onsager s conjecture for weak solutions under a weaker besov type regularity assumption than previously known

the first l2 betti number of certain homogeneous spaces including classifying spaces for variations of hodge structures in this paper we prove the vanishing of the first l betti number for certain complex homogeneous spaces d g v where g is a semi simple lie group and v is a compact subgroup l cohomology is the appropriate extension of hodge theory for harmonic forms to the case of a noncompact complete manifold x inasmuch as here every l cohomology class can be represented by an l harmonic form see 1 in particular non existence of non trivial l harmonic p forms means that the p th l betti number vanishes besides offering the possibility to extend hodge theory to the noncompact case it can be used to obtain topological information about compact quotients of x by the lindex theorem of atiyah 1 based on this theorem dodziuk singer 4 12 suggested to use l cohomology to approach the hopf conjecture concerning the euler characteristic of riemannian manifolds of non positive curvature which has been verified in several special but important cases 2 3

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea