traveling waves for conservation laws with cubic nonlinearity and bbm type dispersion abstract scalar conservation laws with non convex fluxes have shock wave solutions that violate the lax entropy condition in this paper such solutions are selected by showing that some of them have corresponding traveling waves for the equation supplemented with dissipative and dispersive higher order terms for a cubic flux traveling waves can be calculated explicitly for linear dissipative and dispersive terms information about their existence can be used to solve the riemann problem in which we find solutions for some data that are different from the classical lax oleinik construction we consider dispersive terms of a bbm type and show that the calculation of traveling waves is somewhat more intricate than for a kdv type dispersion the explicit calculation is based upon the calculation of parabolic invariant manifolds for the associated ode describing traveling waves the results extend to the p system of one dimensional elasticity with a cubic stress strain law

a sharp interface model for the propagation of martensitic phase boundaries a model for the quasistatic evolution of martensitic phase boundaries is presented the model is essentially the gradient flow of an energy that can contain elastic energy due to the underlying change in crystal structure in the course of the phase transformation and surface energy penalizing the area of the phase boundary this leads to a free boundary problem with a nonlocal velocity that arises from a coupling to the elasticity equation we show existence of solutions under a technical convergence condition using an implicit time discretization

fully discrete entropy conservative schemes of arbitrary order we consider weak solutions of hyperbolic or hyperbolic elliptic systems of conservation laws in one space dimension and their approximation by finite difference schemes in conservative form the systems under consideration are endowed with an entropy entropy flux pair we introduce a general approach to construct second and third order accurate fully discrete in both space and time entropy conservative schemes in general these schemes are fully nonlinear implicit but in some important cases can be explicit or linear implicit furthermore semidiscrete entropy conservative schemes of arbitrary order are presented the entropy conservative schemes are used to construct a numerical method for the computation of weak solutions containing nonclassical regularization sensitive shock waves finally specific examples are investigated and tested numerically our approach extends the results and techniques by tadmor in numerical methods for compressible flows finite difference element and volume techniques asme new york 1986 pp 149 158 lefloch and rohde siam j numer anal 37 2000 pp 2023 2060

the riemann problem for reversible reactive flows with metastability a hyperbolic model for dynamic phase transitions is studied the model involves three phases liquid vapor and a mixture of them metastable regions are present both in the liquid and in the vapor phase results on the behavior of traveling wave profiles of the model involving viscosity species diffusion and relaxation are obtained these behaviors are consistent with physical intuitions admissibility criteria kinetic relations that mimic the behavior of traveling wave profiles are then proposed admissible basic waves of the model are liquefaction evaporation and isobaric waves in addition to lax shock and rarefaction waves based on these waves solutions of the riemann problem for the model are constructed for general riemann initial data most of the physical phenomena are embodied in the solver for some riemann initial data solutions are expected to be nonunique which solutions actually appear depends on whether nucleation already occurred or not the model admits both solutions as it sh

linear stability of propagating phase boundaries in capillary fluids abstract dynamical phase changes occurring along planar traveling waves in capillary fluids are considered their multi dimensional stability which is encoded in the spectrum of a third order variational differential operator is addressed by two approaches on one hand an original energy method is used to show that these diffuse interfaces are weakly stable more precisely the spectrum of the involved operator is found to coincide with the imaginary axis on the other hand an evans function technique reveals a bifurcation phenomenon about zero the interpretation of which still needs some clarification it is the counterpart of the surface waves exhibited in an earlier work for the corresponding sharp interfaces

a kinetic decomposition for singular limits of non local conservation laws abstract we consider a non local regularization of nonlinear hyperbolic conservation laws in several space variables the regularization is motivated by the theory of phase dynamics and is based on a convolution operator we formulate the initial value problem and begin by deriving a priori estimates which are independent of the regularization parameter following hwang and tzavaras we establish a kinetic decomposition associated with the problem under consideration and we conclude that the sequence of solutions generated by the non local model converges to a weak solution of the corresponding hyperbolic problem depending on the scaling introduced in the non local dispersive term this weak limit is either a classical kruzkov solution satisfying all entropy inequalities or more interestingly a nonclassical entropy solution in the sense defined by lefloch that is a weak solution satisfying a single entropy inequality and containing undercompressive shock waves possibly selected by a kinetic relation finally we illustrate our analytical conclusions with numerical experiments in one spatial variable

kinetic relations and the propagation of phase boundaries in solids this paper treats the dynamics of phase transformations in elastic bars the specific issue studied is the compatibility of the field equations and jump conditions of the one dimensional theory of such bars with two additional constitutive requirements a kinetic relation controlling the rate at which the phase transition takes place and a nucleation criterion for the initiation of the phase transition a special elastic material with a piecewise linear non monotonic stress strain relation is considered and the riemann problem for this material is analyzed for a large class of initial data it is found that the kinetic relation and the nucleation criterion together single out a unique solution to this problem from among the infinitely many solutions that satisfy the entropy jump condition at all strain discontinuities

response models for mixed binary and quantitative variables summary a number of special representations are considered for the joint distribution of qualitative mostly binary and quantitative variables in addition to the conditional gaussian models and to conditional gaussian regression chain models some emphasis is placed on models derived from an underlying multivariate normal distribution and on models in which discrete probabilities are specified linearly in terms of unknown parameters the possibilities for choosing between the models empirically are examined as well as the testing of independence and conditional independence and the estimation of parameters often the testing of independence is exactly or nearly the same for a number of different models

the relaxation of non quasiconvex variational integrals we show that the steepest descent algorithm in connection with wiggly energies yields minimizing sequences that converge to a global minimum of the associated non quasiconvex variational integrals we introduce a multi level infinite dimensional variant of the steepest descent algorithm designed to compute complex microstructures by forming non smooth minimizers from the smooth initial guesses we apply this multi level method to the minimization of the variational problems associated with martensitic branching

perturbation analysis for the projection of a point to an affine set abstract we present a perturbation analysis for the projection of a point to an affine set in r n the matrix involved is not assumed to be full rank and the perturbation is arbitrary error bounds for the solution under the rank preserving and rank nondecreasing perturbations are obtained the results given here appear to be the most general up to now

coupling of general lagrangian systems this work is devoted to the coupling of two fluid models such a s two euler systems in lagrangian coordinates at a fixed interface we define coupling conditi ons which can be expressed in terms of continuity of some well chosen variables and then solve the coupled riemann problem in the present setting where the interface is characteristic a particula r choice of dependent variables which are transmitted ensures the overall conservativity

the riemann problem for thermoelastic materials with phase change abstract we consider the riemann problem for a system of conservation laws related to a phase transition problem the system is nonisentropic and we treat the case where the latent heat is not zero we study the cases where the initial data are given in the same phase and in the different phases the role of the entropy condition is studied as well as the kinetic relation and the entropy rate admissibility criterion we confine our attention to the case where the speeds of phase boundaries are close to zero this is one interesting case in physics we discuss the number of phase boundaries consistent with the above criteria and the uniqueness and nonuniqueness issue of the solution to the riemann problem

general existence theorems for hamilton jacobi equations in the scalar and vectorial cases keywords dirichlet problem hamilton jacobi equation existence of solutions reference caa article 1997 002doi 10 1007 bf02392708view record in web of science record created on 2008 11 25 modified on 2017 05 12

strong collapsibility of association measures in linear models a measure of association in linear models is strongly collapsible over a discrete background variable if it remains unchanged no matter how the background variable is partially pooled and if it also coincides with the corresponding marginal measure of association strong collapsibility implies that the measure of association can be studied no matter how the background variable is categorized and no matter whether or not it is recorded in this paper necessary and sufficient conditions are given for strong collapsibility of the measure of association in linear models

fast relaxation solvers for hyperbolic elliptic phase transition problems phase transition problems in compressible media can be modelled by mixed hyperbolic elliptic systems of conservation laws within this approach phase boundaries are understood as shock waves that satisfy additional constraints sometimes called kinetic relations for numerical approximation tracking type algorithms have been suggested the core piece of these algorithms is the usage of exact riemann solvers incorporating the kinetic relation however exact riemann solvers are computationally expensive or even not available in this paper we present a class of approximate riemann solvers for hyperbolic elliptic models that relies on a generalized relaxation procedure it preserves in particular the kinetic relation for phase boundaries exactly and gives for isolated phase transitions the correct solutions in combination with a novel subiteration procedure the approximate riemann solvers are used in the tracking algorithms the efficiency of the approach is validated on a barotropic system with linear kin

kinetic stabilization of a nonlinear sonic phase boundary we consider a system arising in the study of phase transitions in elastodynamics a system of two conservation laws in a single space dimension the system has two hyperbolic regions with an elliptic zone in between a phase boundary is a strong discontinuity in a solution with left and right states belonging to different hyperbolic regions we call such a solution a phase wave

the buckley leverett equation with dynamic capillary pressure the buckley leverett equation for two phase flow in a porous medium is modified by including dependence of the capillary pressure on the rate of change of saturation this model due to hassanizadeh and gray results in a nonlinear pseudoparabolic partial differential equation phase plane analysis including a separation function to measure the distance between invariant manifolds is used to determine when the equation supports traveling waves corresponding to undercompressive shocks the riemann problem for the underlying conservation law is solved and the structures of the various solutions are confirmed with numerical simulations of the partial differential equation

hierarchical interaction models lauritzen and wermuth have proposed a class of models for mixed qualitative and continuous data defined by two properties that the continuous variables are normally distributed given the qualitative variables and that a set of conditional independence relations hold between specified pairs of variables the present paper examines an extension to this class called hierarchical interaction models a compact form for model representation is described and an estimation algorithm is given some properties of the models a compact form for model representation is described and an estimation algorithm is given some properties of the models concerning marginalization and conditioning are examined the class includes and generalizes hierarchical log linear models standard fixed effect anova multivariate anova and multivariate regression models

propagating phase boundaries formulation of the problem and existence via the glimm method this paper treats the hyperbolic elliptic system of two conservation laws which describes the dynamics of an elastic material having a non monotone strain stress function followingabeyaratne knowles we propose a notion of admissible weak solution for this system in the class of functions of bounded variation the formulation includes an entropy inequality a kinetic relation imposed along any subsonic phase boundary and an initiation criterion for the appearance of new phase boundaries we prove thel1 continuous dependence of the solution to the riemann problem our main result yields the existence and the stability of propagating phase boundaries the proofs are based onglimm s scheme and in particular on the techniques ofglimm andlax in order to deal with the kinetic relation we prove a result of pointwise convergence of the phase boundary

on beams made of a phase transforming material this paper presents a theory for the mechanics of beams made of single crystals of shape memory alloys the behavior of such beams can be quite unexpected and complicated due to the presence and propagation of phase boundaries it is shown that the usual laws of mechanics do not fully determine the propagation of phase boundaries and that there is a need for additional constitutive information in the form of a kinetic relation a simple experiment to measure this kinetic relation is proposed finally a strategy to use such beams for propulsion at small scales is presented

collapsibility of logistic regression coefficients summary in this paper we discuss collapsibility of logistic regression coefficients over a background variable and present necessary and sufficient conditions for collapsibility

on the łojasiewicz simon gradient inequality on submanifolds abstract we provide sufficient conditions for the ojasiewicz simon gradient inequality to hold on a submanifold of a banach space and discuss the optimality of our assumptions our result provides a tool to study asymptotic properties of quasilinear parabolic equations with nonlinear constraints

relative entropy in multi phase models of 1d elastodynamics convergence of a non local to a local model abstract in this paper we study a local and a non local regularization of the system of nonlinear elastodynamics with a non convex energy we show that solutions of the non local model converge to those of the local model in a certain regime the arguments are based on the relative entropy framework and provide an example of how local and non local regularizations may compensate for non convexity of the energy and enable the use of the relative entropy stability theory even if the energy is not quasi or poly convex

on spatial and material covariant balance laws in elasticity this paper presents some developments related to the idea of covariance in elasticity the geometric point of view in continuum mechanics is briefly reviewed building on this regarding the reference configuration and the ambient space as riemannian manifolds with their own metrics a lagrangian field theory of elastic bodies with evolving reference configurations is developed it is shown that even in this general setting the euler lagrange equations resulting from horizontal referential variations are equivalent to those resulting from vertical spatial variations the classical green naghdi rivilin theorem is revisited and a material version of it is discussed it is shown that energy balance in general cannot be invariant under isometries of the reference configuration which in this case is identified with a subset of r 3 transformation properties of balance of energy under rigid translations and rotations of the reference configuration is obtained the spatial covariant theory of elasticity is also revisited the transformation of balance of energy under an arbitrary diffeomorphism of the reference configuration is obtained and it is shown that some nonstandard terms appear in the transformed balance of energy then conditions under which energy balance is materially covariant are obtained it is seen that material covariance of energy balance is equivalent to conservation of mass isotropy material doyle ericksen formula and an extra condition that we call configurational inviscidity in the last part of the paper the connection between noether s theorem and covariance is investigated it is shown that the doyleericksen formula can be obtained as a consequence of spatial covariance of lagrangian density similarly it is shown that the material doyle ericksen formula can be obtained from material covariance of lagrangian density 2006 american institute of physics doi 10 1063 1 2190827

collapsibility of relative risk in contingency tables with a response variable we consider the collapsibility of relative risks in contingency tables with a polytomous response variable simple collapsibility of relative risks means that they are consistent over all levels of a collapsed variable and also coincide with the corresponding marginal relative risk strong collapsibility of relative risks means that they retain simple collapsibility no matter how the variable is partially collapsed we present necessary and sufficient conditions for simple and strong collapsibilities of relative risks

non classical riemann solvers with nucleation we introduce a new nonclassical riemann solver for scalar conservation laws with concave convex flux function this solver is based on both a kinetic relation which determines the propagation speed of undercompressive nonclassical shock waves and a nucleation crite rion which makes a choice between a classical riemann solution and a nonclassical one we establish the existence of nonclassical entropy solutions of the cauchy problem and discuss several examples of wave interactions we also show the existence of a class of solutions called splitting merging solutions which are made of two large shocks and small bv bounded variation perturbations the nucleation solvers as we call them are applied to and actually motivated by the theory of thin film flows they help explain numerical results observed for such flows

why many theories of shock waves are necessary kinetic functions equivalent equations and fourth order models we consider several systems of nonlinear hyperbolic conservation laws describing the dynamics of nonlinear waves in presence of phase transition phenomena these models admit under compressive shock waves which are not uniquely determined by a standard entropy criterion but must be characterized by a kinetic relation building on earlier work by lefloch and collaborators we investigate the numerical approximation of these models by high order finite difference schemes and uncover several new features of the kinetic function associated with physically motivated second and third order regularization terms especially viscosity and capillarity terms on one hand the role of the equivalent equation associated with a finite difference scheme is discussed we conjecture here and demonstrate numerically that the numerical kinetic function associated with a scheme approaches the analytic kinetic function associated with the given model especially since its equivalent equation approaches the regularized model at a higher order on the other hand we demonstrate numerically that a kinetic function can be associated with the thin liquid film model and the generalized camassa holm model finally we investigate to what extent a kinetic function can be associated with the equations of van der waals fluids whose flux function admits two inflection points

the riemann problem for a van der waals fluid with entropy rate admissibility criterion nonisothermal case where a and b are the characteristic constants of the fluid thus when the temperature is sufficiently low p v is positive and thus the system i 1 is elliptic on a certain interval c fl while p v is negative on b liquid phase as well as on oo vapor phase on which 1 1 is hyperbolic the riemann problem for i 1 is a special initial value problem in which the initial data are of the form

on the error estimate for the projection of a point onto a linear manifold abstract suppose that the linear system a h x b is consistent the problem of finding the solution x to min a h x b 1 2 x p 2 2 is studied where a c n m b c m x p c n and a b p are given when a b and p are perturbed an error bound for the solution x is obtained roundoff error bounds for the singular value decomposition method the column pivoting method and the rank revealing method are obtained the results in this paper extend those of arioli laratta and menchi to the case when a is not of full rank and either m n or m n

moderating effects of subgroups in linear models summary possibilities for moderating effects of a subgrouping variable on strength or direction of an association have been much discussed by social scientists but have not been given satisfactory statistical formulations the results concern directed measures of associations in linear models containing just three variables some key words analysis of covariance analysis of variance cg distribution conditional independence graphical chain model parallel regressions yule simpson paradox 1 introduction linear models are commonly used as a framework to estimate and test how a continuous response variable depends on potential influencing variables this paper is concerned with the situation in which two influences are random variables as well which may be discrete or continuous the continuous random variables are to stand for quantitative properties of observational units while the discrete variables either capture qualitative properties or they represent subgroups of the population to which the observational units belong to think of all variables as random variables is usually appropriate for data obtained from observational studies where one cannot control which levels or values of the influencing variables are to be observed the linear model permits an analysis conditional on fixed levels and values of the influences but frequently the association structure among the influences is in social science applications of interest itself and as it will turn out it is important for a correct interpretation of how the response depends on the influences awareness of such problems in interpretation is widespread among social scientists as is documented by extensive discussions of moderating effects see for example saunders 1956 zedeck 1971 and baron kenny 1986 there a variable is called a moderator if its presence changes the strength or direction of an association however methods recommended to social scientists for identifying moderating effects given in the above literature or by cohen cohen 1983 pp 310 4 have been shown to be seriously deficient wermuth 1988 thus there is need for clarification we treat the case of a potential discrete moderator variable and call its categories or levels the subgroups in the linear model a moderating effect is closely tied to the notion of consistent results on an association wermuth 1987 in the present context results are said to be weakly consistent if the associations within subgroups coincide in direction and strongly consistent if the associ ations within subgroups coincide in direction and strength this notion depends typically on the chosen measure of association in linear models we look at directed measures of

numerical integrations of systems of conservation laws of mixed type the systems of conservation laws have been used to model dynamic phase transitions in for example the propagating phase boundaries in solids and the van der waals fluid when integrating such mixed hyperbolic elliptic systems the lax friedrichs scheme is known to give the correct solutions selected by a viscosity capillarity criterion except for a spike at the phase boundary which does not go away even with a refined mesh 15 we identify the source of this spike as an inconsistency between the lax friedrichs discretization and the viscosity capillarity equations and show a simple change of variable that can eliminate this spike we then implement a high resolution scheme for the mixed type problems that select the same viscosity capillarity solutions as the lax friedrichs scheme with higher resolutions furthermore a flexibility in the first order scheme is used to obtain solutions for a wide range of the viscosity capillarity equations

convergence of solutions to the equation of quasi static approximation of viscoelasticity with capillarity the long time behavior of solutions to the quasi steady approximation of the equation of viscoelasticity with capillarity is investigated we consider the equation with a number of boundary conditions including such that the set of equilibria is necessarily at least one dimensional we prove that any solution converges to an equilibrium point we admit some kind of initial data with infinite energy we use tools based on the assumption that the nonlinear term is real analytic

a model numerical scheme for the propagation of phase transitions in solids in this paper we devise a simple finite difference scheme that produces approximations to the viscosity capillarity solutions of the equations that govern the propagation of phase transitions in solids or to the equations of van der waals fluids for all positive values of the dimensionless parameter that characterizes the viscosity capillarity solution numerical experiments showing the convergence properties of the method are presented

kinetic relations for a lattice model of phase transitions the aim of this article is to analyse travelling waves for a lattice model of phase transitions specifically the fermi pasta ulam chain with piecewise quadratic interaction potential first for fixed sufficiently large subsonic wave speeds we rigorously prove the existence of a family of travelling wave solutions second it is shown that this family of solutions gives rise to a kinetic relation which depends on the jump in the oscillatory energy in the solution tails third our constructive approach provides a very good approximate travelling wave solution

global existence of diffusive dispersive traveling waves for general flux functions abstract we establish a global existence of traveling waves for diffusive dispersive conservation laws for locally lipschitz flux functions using lyapunov stability techniques we reduce the global problem of finding traveling waves to considering local behaviors of a stable trajectory of the saddle point

convergence analysis and numerical simulation for a hyperbolic system abstract in this paper we develop and analyze a finite volume element method for the approximation of the hyperbolic type equations arising in mathematical physics in one space dimension in recent years there has been increasing attention in the literatures to the development analysis and implementation of the solution of hyperbolic equations in this work we construct the discrete finite volume element schemes and give the optimal error estimates between the finite volume element solution and the exact solution moreover numerical experiments are also provided to demonstrate the behavior of the methods and confirm the efficiency and robustness of the presented approach and method finally some conclusions are obtained and our further research work is proposed

convergence asymptotic periodicity and finite point blow up in one dimensional semilinear heat equations abstract we consider the initial value problem for the semilinear heat equation u t u xx f u t 0 x l t 0 under the dirichlet the neumann or the periodic boundary conditions we show that each solution whether it exists globally for t 0 or blows up in a finite time possesses an asymptotic profile in a certain sense and tends to this profile as time increases in the special case where f u t t f u t for some t 0 among other things the above statement is interpreted as saying that any bounded global solution converges as t to a time t periodic solution having some specific spatial structure in the case where the solution blows up in a finite time say at t t 0 assuming simply that f is a smooth function satisfying some growth conditions and that the initial data is a nonconstant bounded function we prove that the blow up set is a finite set and that lim t t 0 u x t x exists with being a smooth function having at most finitely many singular points

modelling evaporation fronts with reactive riemann solvers this work deals with the modelling of permeable fronts and the building of a numerical method allowing the multi dimensional propagation of such fronts a particular attention is given to evaporation waves that appear in cavitating systems these ones are considered as discontinuities through which a non equilibrium liquid turns to a liquid vapor mixture at thermodynamic equilibrium such transformation occurs at finite rate in order to determine this kinetics the evaporation front is assumed to propagate at the maximum admissible speed corresponding to the chapman jouguet deflagration point j r simoes moreira j e shepherd evaporation waves in superheated dodecane j fluid mech 382 1999 63 86 using this particular kinetic relation rankine hugoniot relations are closed at such fronts then it is possible to solve the associated reactive riemann problem however another difficulty is present to solve the multi dimensional propagation of permeable fronts this kind of front is subsonic and a conventional averaging scheme such as godunov scheme is inappropriate to overcome this difficulty the reactive riemann problem solution is embedded into the discrete equations method dem r abgrall r saurel discrete equations for physical and numerical compressible multiphase mixtures j comp phys 186 2003 361 396 r saurel s gavrilyuk f renaud a multiphase model with internal degrees of freedom application to shock bubble interaction j fluid mech 495 2003 283 321 this numerical method necessitates deep extensions that are detailed herein numerical results are shown and validated over experimental data some examples show that the same method may be applied to the propagation of detonation fronts

dynamics as a mechanism preventing the formation of finer and finer microstructure we study the dynamics of pattern formation in the one dimensional partial differential equation u u w u x x u xxt u 0 text u u x t text x in 0 1 text t 0 proposed recently by ball holmes james pego swart bhjps as a mathematical cartoon for the dynamic formation of microstructures observed in various crystalline solids here w is a double well potential like 1 4 ux 2 1 2 what makes this equation interesting and unusual is that it possesses as a lyapunov function a free energy consisting of kinetic energy plus a nonconvex elastic energy but no interfacial energy contribution which does not attain a minimum but favours the formation of finer and finer phase mixtures e u u t int limits 0 1 frac u t 2 2 w u x frac u 2 2 dx our analysis of the dynamics confirms the following surprising and striking difference between statics and dynamics conjectured in bhjps on the basis of numerical simulations of swart holmes sh while minimizing the above energy predicts infinitely fine patterns mathematically weak but not strong convergence of all minimizing sequences unvn of e u v in the sobolev space w1p 0 1 l2 0 1 solutions to the evolution equation of ball et al typically develop patterns of small but finite length scale mathematically strong convergence in w1p 0 1 l2 0 1 of all solutions u t ut t with low initial energy as time t

error analysis of algorithms for computing the projection of a point onto a linear manifold the accumulation of rounding errors in methods used to compute the projection of a point onto a linear manifold is studied the methods are based on modified gram schmidt householder and givens orthogonal factorizations

normal modes and nonlinear stability behaviour of dynamic phase boundaries in elastic materials this paper considers an ideal nonthermal elastic medium described by a stored energy function w it studies time dependent configurations with subsonically moving phase boundaries across which in addition to the jump relations of rankine hugoniot type expressing conservation some kinetic rule g acts as a two sided boundary condition the paper establishes a concise version of a normal modes determinant that characterizes the local in time linear and nonlinear in stability of such patterns specific attention is given to the case where w has two local minimizers ua ub which can coexist via a static planar phase boundary being dynamic perturbations of such interesting configurations this paper shows that the stability behaviour of corresponding almost static phase boundaries is uniformly controlled by an explicit expression that can be determined from derivatives of w and g at ua and ub

finding the orthogonal projection of a point onto an affine subspace a simple method is proposed to find the orthogonal projection of a given point to the solution set of a system of linear equations this is also a direct method for solving systems of linear equations the output of the method is either the projection or inconsistency of the system moreover in the process also linearly dependent equations are recognized this paper is constrained for giving theoretical foundations computational complexity and some numerical experiments with dense matrices although the method allows to employ sparsity the raw method could not compete with best software packages in solving linear equations for general matrices but it was competitive in finding projections for matrices with small number of rows relative to the number of columns

on substantive research hypotheses conditional independence graphs and graphical chain models summary graphs consisting of points and lines or arrows as connections between selected pairs of points are used to formulate hypotheses about relations between variables points stand for variables connections represent associations when a missing connection is interpreted as a conditional independence the graph characterizes a conditional independence structure as well statistical models called graphical chain models correspond to special types of graphs which are interpreted in this fashion examples are used to illustrate how conditional independences are reflected in summary statistics derived from the models and how the graphs help to identify analogies and equivalences between different models graphical chain models are shown to provide a unifying concept for many statistical techniques that in the past have proven to be useful in analyses of data they also provide tools for new types of analysis

long time behavior for a nonlinear plate equation with thermal memory abstract we consider a nonlinear plate equation with thermal memory effects due to non fourier heat flux laws first we prove the existence and uniqueness of global solutions as well as the existence of a global attractor then we use a suitable ojasiewicz simon type inequality to show the convergence of global solutions to single steady states as time goes to infinity under the assumption that the nonlinear term f is real analytic moreover we provide an estimate on the convergence rate

kinetics and nucleation for driven thin film flow abstract the lubrication theory of thin liquid films driven by a constant surface stress opposing gravity is described by a scalar fourth order pde for the film height h h t h 2 h 3 x h 3 h x x x x in which is a positive constant related to surface tension in this paper the wave structure of solutions observed in numerical simulations with 0 is related to the recent hyperbolic theory of the underlying scalar conservation law in which 0 this theory involves a kinetic relation describing possible undercompressive shocks and a nucleation condition governing the transition from classical to non classical solution of the riemann problem the kinetic relation and nucleation condition are derived from consideration of traveling wave solutions with 0 the kinetic relation is identified with a codimension one bifurcation of the corresponding vector field for which there is a traveling wave approximating an undercompressive shock the nucleation condition is identified as a transition in the vector field at which there is no traveling wave connecting upstream and downstream heights the thresholds defined by these conditions are incorporated into a riemann solver map which is tested for initial value problems for the full pde it is found that the parameter determines a limit to the applicability of the hyperbolic theory in which the fourth order diffusion can dominate short time transients resulting in long time convergence to the classical solution when the hyperbolic theory would predict a non classical solution

an existence result for a class of second order evolution equations of mixed type we give an existence and uniqueness result for a linear abstract evolution equation of second order with some coefficient in front of the second temporal derivative which may degenerate to zero and change sign

a simple unified approach to some convergence theorems of l simon abstract we give a new and easier proof for the convergences result of l simon 15 concerning global and bounded solutions of a heat equation with analytic nonlinearity by constructing a new liapunov functional for the elliptic equation we are able to prove the second convergence theorem of 15 in the same way as the first theorem the results are more general and can be applied to other problems such as fourth order equation and vector valued systems of gradient type

convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity abstract we prove convergence of global bounded and smooth solutions of the wave equation with linear dissipation and analytic nonlinearity a generalization and examples of applications are given at the end of the paper

computation of nonclassical solutions to hamilton jacobi problems this paper is devoted to the construction of numerical methods for the approximation of nonclassical solutions to multidimensional hamilton jacobi equations for both scalar and vectorial problems recent theoretical results have yielded existence of solutions in many cases for which the usual viscosity approach was ill suited or not applicable the selection criterion used here is based on a viscoelasticity capillarity approach common in solid mechanics numerical methods adapted to this framework are built consistency of the model equation with the given selection criterion is essential it is achieved here through the use of high order finite difference schemes by considering applications to potential well problems the convergence of the methods are investigated