existence of uncountably many bounded nonoscillatory solutions and their iterative approximations for second order nonlinear neutral delay difference equations in this paper the banach fixed point theorem is employed to establish several existence results of uncountably many bounded nonoscillatory solutions for the second order nonlinear neutral delay difference email protected n dx n b n x email protected email protected n x h 1 n x h 2 n x h k n f n x f 1 n x f 2 n x f k n c n n n 0 where t email protected n n email protected n 0 a b c n n 0 r with a n 0 for email protected n n 0 h f n n 0xr k r and h l f l n n 0 z withlimn h l n limn f l n email protected 1 2 k a few mann type iterative approximation schemes with errors are suggested and the errors estimates between the iterative approximations and the nonoscillatory solutions are discussed seven nontrivial examples are given to illustrate the advantages of our results

closed solution for the spatially homogeneous kac s model of the nonlinear boltzmann equation finds a closed spatially homogeneous solution of the nonlinear kac s model 1956 in 1 1 dimensions velocity v and time t choosing for the even velocity part of the distribution function the bobylev krook wu mode 1975 6 the author adds an odd velocity part the author finds the possibility of the existence of the tjon relaxation effect when the time t is increasing this depends on both the initial condition and the cross section

fluid dynamic limit for the ruijgrok wu model of the boltzmann equation abstract in this paper we consider the fluid dynamic limit for the ruijgrok wu model derived from the boltzmann equation we use new technique developed in s hwang a e tzavaras kinetic decomposition of approximate solutions to conservation laws applications to relaxation and diffusion dispersion approximations comm partial differential equations 27 2002 1229 1254 in order to get the convergence first we obtain the approximate transport equation for the given kinetic model then using the averaging lemma we obtain the convergence this paper shows how to relate the given kinetic model with the averaging lemma to get the convergence

bi solitons for a class of non linear equations with quadratic non linearity ii abstract we consider the class of non integrable non linear equations l q k k 2 l q 1 i j q aij i x i j t j 0 in 1 1 dimensions we seek rational solutions k 1 2 which we call bi solitons with exponential type variables i exp ix it in this paper we restrict to q 2 and 3 and investigate the general q case in the following paper we find that these bi solitons exist when the operator lq with can be factorized as the product of smaller order differential operators besides the trivial factorized bi solitons we show that there exist non trivial ones whenever k may be written as lmaxx l2fl z 1 2 in order to understand the origin of the factorization property to any polynomial k l2fl z we associate a linear transformation such that lqk has only the power l2 of k2 for q 2 and 3 we find that there exist particular polynomials of this type restraining lq to be a product of smallr order operators for the full non linear equations we verify that all the bi solitons can be obtained from these particular polynomials

a discrete time event history approach to informative drop out in mixed latent markov models with covariates summary mixed latent markov mlm models represent an important tool of analysis of longitudinal data when response variables are affected by time fixed and time varying unobserved heterogeneity in which the latter is accounted for by a hidden markov chain in order to avoid bias when using a model of this type in the presence of informative drop out we propose an event history eh extension of the latent markov approach that may be used with multivariate longitudinal data in which one or more outcomes of a different nature are observed at each time occasion the eh component of the resulting model is referred to the interval censored drop out and bias in mlm modeling is avoided by correlated random effects included in the different model components which follow common latent distributions in order to perform maximum likelihood estimation of the proposed model by the expectation maximization algorithm we extend the usual forward backward recursions of baum and welch the algorithm has the same complexity as the one adopted in cases of non informative drop out we illustrate the proposed approach through simulations and an application based on data coming from a medical study about primary biliary cirrhosis in which there are two outcomes of interest one continuous and the other binary

a bidimensional finite mixture model for longitudinal data subject to dropout in longitudinal studies subjects may be lost to follow up and thus present incomplete response sequences when the mechanism underlying the dropout is nonignorable we need to account for dependence between the longitudinal and the dropout process we propose to model such a dependence through discrete latent effects which are outcome specific and account for heterogeneity in the univariate profiles dependence between profiles is introduced by using a probability matrix to describe the corresponding joint distribution in this way we separately model dependence within each outcome and dependence between outcomes the major feature of this proposal when compared with standard finite mixture models is that it allows the nonignorable dropout model to properly nest its ignorable counterpart we also discuss the use of an index of local sensitivity to nonignorability to investigate the effects that assumptions about the dropout process may have on model parameter estimates the proposal is illustrated via the analysis of data from a longitudinal study on the dynamics of cognitive functioning in the elderly

shared parameter models under random effects misspecification summary a common objective in longitudinal studies is the investigation of the association structure between a longitudinal response process and the time to an event of interest an attractive paradigm for the joint modelling of longitudinal and survival processes is the shared parameter framework where a set of random effects is assumed to induce their interdependence in this work we propose an alternative parameterization for shared parameter models and investigate the effect of misspecifying the random effects distribution in the parameter estimates and their standard errors

estimation and comparison of changes in the presence of information right censoring by modeling the censoring process abstract in estimating and comparing the rates of change of a continuous variable between two groups the unweighted averages of individual simple least squares estimates from each group are often used under a linear random effects model when all individuals have completed observations at identical time points these statistics are maximum likelihood estimates for the expected rates of change however with censored of missing data these estimates are no longer efficient when compared to generalized least squares estimates when in addition the right censoring process is dependent upon the individual rates of change i e informative right censoring the generalized least squares estimates will be biased likelihood ratio test for informativeness of the censoring process and maximum likelihood estimates for the expected rates of change and the parameters of the right censoring process are developed under a linear random effect models with a probit model for the right censoring process in realistic situations we illustrate that the bias in estimating group rate of change and the reduction of power in comparing group difference could be substantial when strong dependency of the right censoring process on individual rates of change is ignored author

model for the analysis of binary longitudinal pain data subject to informative dropout through remedication abstract we address the problem of accounting for informative dropout in the form of rescue medication when comparing pain relievers with respect to longitudinal binary pain relief outcomes we present a selection model approach for binary longitudinal data that accommodates informative dropout the relationship between dropout or remedication and the binary pain relief response is assumed to be characterized by a random effect that is conditional on this random effect response and dropout are independent unlike previous approaches to this problem which rely on numerical or approximation methods we obtain a closed form expression for the marginal log likelihood of response and dropout by specifying a complementary log log link function for both components and a conjugate log gamma random effect distribution a data analysis supported by simulation results suggest that the model fits reasonably well results are compared to those obtained from conventional but somewhat inappropriate analyses

existence of uncountably many bounded positive solutions for a third order nonlinear neutral delay difference equation this paper deals with the solvability of the third order nonlinear neutral delay difference equation d 2 a n d x n b nx n t d 2f n x n b 1 n x n b 2 n x n b k n dg n x n c 1 n x n c 2 n x n c k n h n x n d 1 n x n d 2 n x n d k n n n 0 relative to the sequence b n n n n 0 r using the krasnoselskii s fixed point theorem and schauder s fixed point theorem a few sufficient conditions of the existence of uncountably many bounded positive solutions for the equation are presented seven examples are included to demonstrate the advantages and effectiveness of the results presented in this paper

an approximate generalized linear model with random effects for informative missing data this paper develops a class of models to deal with missing data from longitudinal studies we assume that separate models for the primary response and missingness e g number of missed visits are linked by a common random parameter such models have been developed in the econometrics heckman 1979 econometrica 47 153 161 and biostatistics wu and carroll 1988 biometrics 44 175 188 literature for a gaussian primary response we allow the primary response conditional on the random parameter to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness the resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects an example is given to illustrate the approximate approach and simulations are performed to critique the adequacy of the approximation for repeated binary data

a bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time to event motivated by a real data example on renal graft failure we propose a new semiparametric multivariate joint model that relates multiple longitudinal outcomes to a time to event to allow for greater flexibility key components of the model are modelled nonparametrically in particular for the subject specific longitudinal evolutions we use a spline based approach the baseline risk function is assumed piecewise constant and the distribution of the latent terms is modelled using a dirichlet process prior formulation additionally we discuss the choice of a suitable parameterization from a practitioner s point of view to relate the longitudinal process to the survival outcome specifically we present three main families of parameterizations discuss their features and present tools to choose between them

linearized oscillation of first order nonlinear neutral delay differential equations abstract in this paper we establish a equivalence of oscillation for the first order nonlinear neutral delay differential equation x t px t i 1 m q i f i x t i 0 and its corresponding linear equation x t px t i 1 m q i x t i 0 under a weaker condition on fi

exact solution for the spatially homogeneous nonlinear kac model of the boltzmann equation with an external force term the author studies the spatially homogeneous kac model of the nonlinear boltzmann equation in 1 1 dimensions velocity v and time t when an external force term is present the author finds a closed solution the force term decreases exponentially with time like constant1 exp constant2 t where both constants depend explicitly on the moments of the cross section the author finds for the relaxation to equilibrium that the tjon overpopulation effect depends on both the initial condition and the microscopic model of cross section for the existence of this effect the author establishes a criterion which is a well defined linear combination of the moments of the author cross section

modelling progression of cd4 lymphocyte count and its relationship to survival time the purpose of this article is to model the progression of cd4 lymphocyte count and the relationship between different features of this progression and survival time the complicating factors in this analysis are that the cd4 lymphocyte count is observed only at certain fixed times and with a high degree of measurement error and that the length of the vector of observations is determined in part by the length of survival if probability of death depends on the true unobserved cd4 lymphocyte count then the survival process must be modelled wu and carroll 1988 biometrics 44 175 188 proposed a random effects model for two sample longitudinal data in the presence of informative censoring in which the individual effects included only slopes and intercepts we propose methods for fitting a broad class of models of this type in which both the repeated cd4 lymphocyte counts and the survival time are modelled using random effects these methods permit us to estimate parameters describing the progression of cd4 lymphocyte count as well as the effect of differences in the cd4 trajectory on survival we apply these methods to results of aids clinical trials

similarity solutions of 2 velocity models of the extended boltzmann equation abstract we analyse in the frame of the extended kinetic theory travelling wave solutions for the 2 velocity discrete models of the boltzmann equation the extended formalism allows for absorption creation due to scattering with a background as well as for the existence of external sources of test particles as a preliminary step existence uniqueness and stability of equilibrium states are investigated we find new soliton like solutions and analyse their dependence of the physical parameters of the model

exact solutions in 1 1 dimensions of the general two velocity discrete illner model the illner model is the most general two velocity discrete model of a boltzmann equation in one spatial dimension which satisfies an h theorem it includes as particular cases both the carleman and the mckean models solitons one dimensional solutions and bisolitons two dimensional space plus time solutions which are defined as rational fractions and solutions with one or two exponential variables are determined the model is treated as a nonintegrable nonlinear one and from the solitons the possible class of bisolitons is guessed two classes of physically acceptable bisolitons are found the first class is distributions positive only along one semiaxis and identically zero outside these are interpreted physically by introducing elastic walls plus source or sink terms which become negligible at infinite time the second class is periodic solutions which can be seen as damped sound waves essentially the same tools are used as in a companion paper for the six velocity broadwell model where the two bisoliton classes mentioned above also exist this suggests that general methods for obtaining nontrivial exact solutions could exist for the hyperbolic semilinear discrete boltzmann models

semi inhomogeneous solutions of the kac model of boltzmann equations constructs semi inhomogeneous solutions of the kac model for which the spatial dependence is only present in the odd velocity part of the distribution at the macroscopic level the local density the local energy and the associated current components are determined and discussed while at the microscopic level there exist two different classes of distributions as an illustration the author gives two solutions explicitly for one class the distributions relax towards a maxwellian equilibrium solution and they correspond either to a contraction or an expansion while for the other they go to zero when the time increases to infinity the space variable appears linearly and in order to maintain the positivity stays inside a finite interval assuming that the distributions are zero outside such intervals a physical interpretation can be obtained for the whole space axis provided appropriate elastic walls sinks and sources are introduced these boundary conditions seem more natural for the class of distributions with maxwellian relaxation

global solvability for a second order nonlinear neutral delay difference equation this paper studies the global existence of solutions of the second order nonlinear neutral delay difference equation d a email protected x n bx n t f n x n d 1 n x n d 2 n x n d k n c n n n 0 with respect to all email protected r a few results on global existence of uncountably many bounded nonoscillatory solutions are established for the above difference equation several nontrivial examples which dwell upon the importance of the results obtained in this paper are also included

closed similarity solutions for a class of stationary nonlinear boltzmann like equations the authors look for closed stationary solutions of nonlinear transport equations of the stochastic boltzmann type in 1 1 dimensions velocity v and position x these solutions mainly written as the product of an exponential by a polynomial in z xlambda v2 have the quasi similarity property as a consequence of their polynomial character they violate the positivity requirement however the authors think that they are the dominant term of infinite series solutions which might have the desired positivity property calculations are greatly simplified by using sum rules analogous to conservation of mass and energy

convergence of a splitting scheme applied to the ruijgrok wu model of the boltzmann equation this paper deals with upwind splitting schemes for the ruijgrok wu model physica a 113 1982 401 416 of the kinetic theory of rare7ed gases in the 8uid dynamic scaling we prove the stability and the convergence for these schemes the relaxation limit is also investigated and the limit equation is proved to be a 7rst order quasi linear conservation law the loss of quasi monotonicity of the present model makes it necessary to give a more careful analysis of its structure we also obtain global error estimates in the spaces w s p for 16s61 p 16p6 and pointwise error estimates for the approximate solution the proof naturally uses the framework introduced by nessyahu and tadmor siam j numer anal 29 1992 1505 1519 due to the convexity of the 8ux function c

the geometry of mixture likelihoods a general theory in this paper certain fundamental properties of the maximum likelihood estimator of a mixing distribution are shown to be geometric properties of the likelihood set the existence support size likelihood equations and uniqueness of the estimator are revealed to be directly related to the properties of the convex hull of the likelihood set and the support hyperplanes of that hull it is shown using geometric techniques that the estimator exists under quite general conditions with a support size no larger than the number of distinct observations analysis of the convex dual of the likelihood set leads to a dual maximization problem a convergent algorithm is described the defining equations for the estimator are compared with the usual parametric likelihood equations for finite mixtures sufficient conditions for uniqueness are given part ii will deal with a special theory for exponential family mixtures

multiscale analysis for interacting particles relaxation systems and scalar conservation laws we investigate the derivation of semilinear relaxation systems and scalar conservation laws from a class of stochastic interacting particle systems these systems are markov jump processes set on a lattice they satisfy detailed mass balance but not detailed balance of momentum and are equipped with multiple scalings using a combination of correlation function methods with compactness and convergence properties of semidiscrete relaxation schemes we prove that at a mesoscopic scale the interacting particle system gives rise to a semilinear hyperbolic system of relaxation type while at a macroscopic scale it yields a scalar conservation law rates of convergence are obtained in both scalings

numerical schemes for hyperbolic systems of conservation laws with stiff diffusive relaxation hyperbolic systems of conservation laws often have diffusive relaxation terms that lead to a small relaxation limit governed by reduced systems of a parabolic or hyperbolic type in such systems the understanding of basic wave pattern is difficult to achieve and standard high resolution methods fail to describe the right asymptotic behavior unless the small relaxation rate is numerically resolved we develop high resolution underresolved numerical schemes that possess the discrete analogue of the continuous asymptotic limit which are thus able to approximate the equilibrium system with high order accuracy even if the limiting equations may change type

lie transformations similarity reduction and solutions for the nonlinear madelung fluid equations with external potential the application of lie group methods to a system of coupled nonlinear partial differential equations representing what is usually called a madelung fluid is shown the generating operators of the transformation group that depends on five arbitrary group constants will be constructed and all subclasses of systems of ordinary differential equations derived by similarity reduction will be presented in tabular form two subclasses of physical interest are investigated in detail and the similarity solutions are compared with solutions found earlier by the application of inverse scattering transform techniques to the cubic nonlinear schrodinger equation similarity solutions for the madelung equations with linear external potential x f0x are presented

temperature overshoots for a 4 velocity unidimensional discrete boltzmann model we propose a 4 velocity unidimensional discrete boltzmann model with two different speeds 2 1 and two different masses 1 2 with the three conservation laws of mass momentum and energy satisfied we can introduce a nontrivial temperature first we determine the similarity shock waves satisfying physical properties positivity shock stability inequalities of the subsonic and supersonic flows increase or decrease of both mass and temperature across the shock it results that either the speed of the shock front is higher than the speed 1 of the slow particles and the shocks are compressive or less than 1 and the shocks are rarefactive we observe overshoots of the temperature across the shock with bumps higher and higher as the shock front speed increases second we study the 1 1 dimensional shock waves they represent the superposition and collision of two compressive shocks traveling in opposite directions and we observe temperature overshoots for not too large times

moment equations for the diffusion of the particles of a mixture via the scattering kernel formulation of the nonlinear boltzmann equation abstract there are two goals in this paper essentially devoted to the application of the scattering kernel formulation of the nonlinear boltzmann equation to the case of a mixture the first goal is to show the equivalence between the scattering kernel representation of the collision term and the two other representations usually adopted for it in the literature namely the kinetic and the transition probability representation respectively the second goal is to derive instead the general scalar nonlinear boltzmann equation that is the equation governing an isotropic distribution function for the mixture considered and to establish then the moment equations associated with it

joint modeling of survival and longitudinal data likelihood approach revisited the maximum likelihood approach to jointly model the survival time and its longitudinal covariates has been successful to model both processes in longitudinal studies random effects in the longitudinal process are often used to model the survival times through a proportional hazards model and this invokes an em algorithm to search for the maximum likelihood estimates mles several intriguing issues are examined here including the robustness of the mles against departure from the normal random effects assumption and difficulties with the profile likelihood approach to provide reliable estimates for the standard error of the mles we provide insights into the robustness property and suggest to overcome the difficulty of reliable estimates for the standard errors by using bootstrap procedures numerical studies and data analysis illustrate our points

a latent class mixture model for incomplete longitudinal gaussian data in the analyses of incomplete longitudinal clinical trial data there has been a shift away from simple methods that are valid only if the data are missing completely at random to more principled ignorable analyses which are valid under the less restrictive missing at random assumption the availability of the necessary standard statistical software nowadays allows for such analyses in practice while the possibility of data missing not at random mnar cannot be ruled out it is argued that analyses valid under mnar are not well suited for the primary analysis in clinical trials rather than either forgetting about or blindly shifting to an mnar framework the optimal place for mnar analyses is within a sensitivity analysis context one such route for sensitivity analysis is to consider next to selection models pattern mixture models or shared parameter models the latter can also be extended to a latent class mixture model the approach taken in this article the performance of the so obtained flexible model is assessed through simulations and the model is applied to data from a depression trial

mixed effects logistic regression models for longitudinal binary response data with informative drop out a shared parameter model with logistic link is presented for longitudinal binary response data to accommodate informative drop out the model consists of observed longitudinal and missing response components that share random effects parameters to our knowledge this is the first presentation of such a model for longitudinal binary response data comparisons are made to an approximate conditional logit model in terms of a clinical trial dataset and simulations the naive mixed effects logit model that does not account for informative drop out is also compared the simulation based differences among the models with respect to coverage of confidence intervals bias and mean squared error mse depend on at least two factors whether an effect is a between or within subject effect and the amount of between subject variation as exhibited by variance components of the random effects distributions when the shared parameter model holds the approximate conditional model provides confidence intervals with good coverage for within cluster factors but not for between cluster factors the converse is true for the naive model under a different drop out mechanism when the probability of drop out is dependent only on the current unobserved observation all three models behave similarly by providing between subject confidence intervals with good coverage and comparable mse and bias but poor within subject confidence intervals mse and bias the naive model does more poorly with respect to the within subject effects than do the shared parameter and approximate conditional models the data analysis which entails a comparison of two pain relievers and a placebo with respect to pain relief conforms to the simulation results based on the shared parameter model but not on the simulation based on the outcome driven drop out process this comparison between the data analysis and simulation results may provide evidence that the shared parameter model holds for the pain data

discrete velocity models of the boltzmann equation a survey on the mathematical aspects of the theory discrete velocity models of the boltzmann equation are of considerable conceptual interest in the kinetic theory of gases and at the same time a fascinating mathematical subject the last decade has seen a lot of work on this subject which is reviewed here we put an emphasis on mathematical aspects in particular the global existence question qualitative properties of solutions explicit solutions and the fluid dynamical limit the mechanical background is discussed more concisely in part i numerous contributions concerning other questions are outlined we try to give a complete reference list up to and including 1985

a semi parametric shared parameter model to handle nonmonotone nonignorable missingness longitudinal studies often generate incomplete response patterns according to a missing not at random mechanism shared parameter models provide an appealing framework for the joint modelling of the measurement and missingness processes especially in the nonmonotone missingness case and assume a set of random effects to induce the interdependence parametric assumptions are typically made for the random effects distribution violation of which leads to model misspecification with a potential effect on the parameter estimates and standard errors in this article we avoid any parametric assumption for the random effects distribution and leave it completely unspecified the estimation of the model is then made using a semi parametric maximum likelihood method our proposal is illustrated on a randomized longitudinal study on patients with rheumatoid arthritis exhibiting nonmonotone missingness

bounded oscillation of second order delay difference equations of unstable type abstract a series of sufficient conditions are obtained for the bounded oscillation of second order delay difference equations of unstable type some of them are sharp

linearized oscillations of first order nonlinear neutral delay difference equations abstract in this paper we establish an equivalence of oscillation for the first order nonlinear neutral delay difference equation x n px n r i 1 m q i f i x n i 0 and its corresponding linear equation x n px n r i 1 m q i x n i 0 under weaker conditions on f i

a completely solvable model of the nonlinear boltzmann equation abstract in one space and one time dimension a model of the nonlinear boltzmann equation is presented that is exactly solvable for all initial conditions furthermore this model has the following desirable properties i conservation of the number of particles ii energy conservation iii nonlinearity iv positivity of distribution functions and v unique equilibrium state for any given density which is approached as t for most physically interesting initial conditions some of the simple properties of this model are studied

existence of bounded positive solutions for a system of difference equations abstract this paper deals with the second order nonlinear neutral delay system of difference equations a n x n b n x n f n x h 1 n x h kn y w 1 n y w kn c n n n 0 p n y n q n y n g n x s 1 n x s kn y t 1 n y t kn r n n n 0 by virtue of the banach fixed point theorem and some natural modifications of the techniques in the literature we prove the existence results of uncountably many bounded positive solutions for the system of difference equations seven examples are constructed to explain the main results presented in this paper

joint analysis of bivariate longitudinal ordinal outcomes and competing risks survival times with nonparametric distributions for random effects we propose a semiparametric joint model for bivariate longitudinal ordinal outcomes and competing risks failure time data the association between the longitudinal and survival endpoints is captured by latent random effects this approach generalizes previous joint analysis that considers only one response variable at the longitudinal endpoint one unique feature of the proposed model is that we relax the commonly used normality assumption for random effects and leave the distribution completely unspecified we use a modified version of the vertex exchange method in conjunction with an expectation maximization algorithm to estimate the random effects distribution and model parameters we show via simulations that robust parameter estimates are obtained from the proposed method under various scenarios we illustrate the approach using cough severity and frequency data from a scleroderma lung study

exact solutions of the broadwell model in 1 1 dimensions the author studies the one spatial dimensional 6 velocity broadwell model with four identical densities and three independent ones the author determines solitons one dimensional shock wave solutions and bisolitons two dimensional space plus time solutions which are rational fractions with one or two exponential variables the author obtains three classes of positive exact solutions in 1 1 dimensions space x time t the first one is periodic in the space variable and for large time the solutions correspond to propagating damped linear waves the second is positive only along one semi x axis while the third positive along the whole x axis represents non planar damped shock waves using the same tools in a companion paper for the discrete 2 velocity models the author obtains in a two dimensional space the first two classes of solutions mentioned above this suggests that for the discrete boltzmann models general methods exist for the determination of non trivial exact solutions

solution to the nonlinear boltzmann equation for maxwell models for nonisotropic initial conditions the known solution to the spatially homogeneous nonlinear boltzmann equation for maxwell models in a series of laguerre polynomials is extended to include nonisotropic initial conditions existence proofs for a class of solutions are supplied the equations for the generalized nonisotropic laguerre moments are derived in explicit form for two and three dimensional models further it is shown that the ordinary moments satisfy the same set of equations as the hermite polynomial moments

connection between the existence of bisolitons for quadratic nonlinearities and a factorization of the associate linear operator in a first part we investigate the exponential type bisolitons of the class of equations e lq k e i j 1i j q aij xitji j k x k2 e 0 0 or e 0 which are rational solutions and we assume that their denominators have no coupling between the solitons we have found that their existence requires a factorization property of either the operator e lq for e 0 0 q 3 or lq for e 0 q 3 with the exception of the burgers equation we find three kinds of nontrivial bisolitons either those associated with the mixed nonlinearity x k2 alone or those common to the mixed nonlinearity and kkx or those belonging to kkx alone in the second part we look at the two last types of bisolitons for q 3 and give a constructive method leading both to factorized linear operators and to the explicit determination of the bisolitons we consider mainly lq 2 t a t b x c xx g xg 2 k gx with the linear operator factorizing the linear part of the burgers equation lq 2 t is a differential operato

existence of uncountably many bounded positive solutions for second order nonlinear neutral delay difference equations this paper deals with the second order nonlinear neutral delay difference equation d a n d x n b n x n t c n f n x f 1 n x f 2 n x f k n d n n n 0 by using krasnoselskii s fix

space localization and well balanced schemes for discrete kinetic models in diffusive regimes we derive and study well balanced schemes for quasi monotone discrete kinetic models by means of a rigorous localization procedure we reformulate the collision terms as nonconservative products and solve the resulting riemann problem whose solution is self similar the construction of an asymptotic preserving ap godunov scheme is straightforward and various compactness properties are established within different scalings finally some computational results are supplied to show that this approach is realizable and efficient on concrete 2 2 models

a conjecture on the possible exact 1 1 dimensional solutions to the discrete boltzmann models i the exact multidimensional exponential type solutions to the discrete boltzmann models which have been found are sums of unidimensional similarity waves our goal is to obtain at a linear level a physical signature of the class of possible exact rational solutions in the discrete kinetic theory contrary to the continuous theory the macroscopic conservation laws are included into the set of nonlinear equations for the densities these conservation laws being linear differential relations underline the above recalled result for a class of l l dimensional rational solutions with two exponential variables satisfying at least two conservation laws we prove that the possible solutions are sums of similarity waves we first consider the class of models with three independent densities and two conservation laws second we investigate what happens when the two conservation laws of mass and momentum exist third we sketch briefly results for five densities and three conservation laws finally we conjecture that all exact bounded l l dimensional solutions are sums of similarity waves

implicit explicit runge kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit we consider implicit explicit imex runge kutta r k schemes for hyperbolic systems with stiff relaxation in the so called diffusion limit in such a regime the system relaxes towards a convection diffusion equation the first objective of this paper is to show that traditional partitioned imex r k schemes will relax to an explicit scheme for the limit equation with no need of modification of the original system of course the explicit scheme obtained in the limit suffers from the classical parabolic stability restriction on the time step the main goal of this paper is to present an approach based on imex r k schemes that in the diffusion limit relaxes to an imex r k scheme for the convection diffusion equation in which the diffusion is treated implicitly this is achieved by a novel reformulation of the problem and subsequent application of imex r k schemes to it an analysis of such schemes to the reformulated problem shows that the schemes reduce to imex r k schemes for the limit equation unde

new classes of similarity solutions for the nonlinear carleman boltzmann equation abstract we apply the lie group based similarity method to the carleman model and calculate the generators of the group depending on four group constants heretofore undiscovered classes of similarity solutions will be presented and already discovered solutions by ernst and wick will be rediscovered and classified by specifying the group constants

exact solution for the spatially inhomogeneous nonlinear kac model of the boltzmann equation we study the spatially inhomogeneous kac model of the nonlinear boltzmann equation in 1 1 1 dimensions velocity v time t position x we obtain an exact solution which is the product of a maxwellian with a time dependent width by a second order polynomial in the velocity variable the solution satisfies a specular reflection condition at the boundary x x0 the position x0 x appears linearly and only in the odd part of the velocity distribution the range of x0 x being arbitrarily large but finite in order to maintain the positivity of the distribution the local density is spatially homogeneous further a particular linear relation between the moments of the cross section must be satisfied the most general maxwellian width has two relaxation times and their ratio is a function of the moments of the cross sections depending on whether this ratio is larger than or smaller than 1 we find contraction or expansion the solution relaxes towards a maxwellian equilibrium solution studying the tjon overpopu

on a class of nonintegrable equations in 1 1 dimensions with factorized associated linear operators we consider a class of nonintegrable nonlinear equations with powerlike nonlinearities kn xkn k being the solutions and n 2 n integer building explicitly their exponential type bisolitons the denominators of the bisolitons have no soliton couplings and the linear differential operators of the linear part of the equations are factorized operators we extend our study to a larger class of nonlinearities polynomial nonlinearities which are linear combinations of powerlike nonlinearities we study the two extreme possibilities either the bisoliton is specific of a mixed nonlinearity not being a solution of any component nonlinearity or the bisoliton is common to all components different properties occur depending whether the components are kn or xkn for kn nonlinearities in order to understand the origin of the factorization of the linear operators we give a criterion which is easily checked at an almost entirely linear level of constraints we conjecture that all possible bisolitons are of th

powerlike decreasing solutions of the boltzmann equation for a maxwell gas we study the homogeneous isotropic nonlinear boltzmann equation for a maxwellian interaction we show that solutions decreasing like inverse powers of the energy are physically acceptable both in the linearized and the quadratic problem because all moments may not exist we introduce a generalized generating function and a finite differential system for generalized sonine moments is derived these new solutions may lead to small relaxation rates and justify in most cases the linear approximation

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

efficient maximum likelihood estimation in semiparametric mixture models we consider maximum likelihood estimation in several examples of semiparametric mixture models including the exponential frailty model and the errors in variables model the observations consist of a sample of size n from the mixture density int p theta x z d eta z the mixing distribution is completely unknown we show that the first component hat theta n of the joint maximum likelihood estimator hat theta n hat eta n is asymptotically normal and asymptotically efficient in the semiparametric sense

on shock wave solutions in extended discrete kinetic theory exact traveling wave solutions joining asymptotic maxwellians in the frame of discrete velocity models of the boltzmann equation are investigated and discussed in an extended formulation which also allows for removal creation and scattering collisions with the particles of a given background it is shown that the classical broadwell shock wave structure does not carry over to any extended problem on the other hand families of exact shock wave solutions do exist for extended two velocity models for which such waves are lacking in the classical i e unextended case

nonignorable models for intermittently missing categorical longitudinal responses a class of nonignorable models is presented for handling nonmonotone missingness in categorical longitudinal responses this class of models includes the traditional selection models and shared parameter models this allows us to perform a broader than usual sensitivity analysis in particular instead of considering variations to a chosen nonignorable model we study sensitivity between different missing data frameworks an appealing feature of the developed class is that parameters with a marginal interpretation are obtained while algebraically simple models are considered specifically marginalized mixed effects models heagerty 1999 biometrics 55 688 698 are used for the longitudinal process that model separately the marginal mean and the correlation structure for the correlation structure random effects are introduced and their distribution is modeled either parametrically or non parametrically to avoid potential misspecifications

on group invariant solutions of the boltzmann equation after reviewing the complete lie group for the full boltzmann equation it is shown that projective transformations play a special role in the general case and the class of invariant solutions giving rise to homoenergetic affine flows is presented homoenergetic affine flows in the two dimensional case potential u r r 2 are considered in detail it is shown that the general solution of this problem can be essentially simplified by projective transformations

exact 2 1 dimensional solutions for two discrete velocity boltzmann models with four independent densities for the square discrete velocity boltzmann model the authors obtain exact 2 1 dimensional space x y time t solutions these are rational solutions with three exponential variables relaxing towards non uniform maxwellian equilibrium states with two exponential variables these are also solutions of another model with four independent densities and eight velocities oriented towards the eight corners of a cube the positivity problem for the densities is non trivial

high order asymptotic preserving dg imex schemes for discrete velocity kinetic equations in a diffusive scaling in this paper we develop a family of high order asymptotic preserving schemes for some discrete velocity kinetic equations under a diffusive scaling that in the asymptotic limit lead to macroscopic models such as the heat equation the porous media equation the advection diffusion equation and the viscous burgers equation our approach is based on the micro macro reformulation of the kinetic equation which involves a natural decomposition of the equation to the equilibrium and non equilibrium parts to achieve high order accuracy and uniform stability as well as to capture the correct asymptotic limit two new ingredients are employed in the proposed methods discontinuous galerkin dg spatial discretization of arbitrary order of accuracy with suitable numerical fluxes high order globally stiffly accurate implicit explicit imex runge kutta scheme in time equipped with a properly chosen implicit explicit strategy formal asymptotic analysis shows that the proposed scheme in the limit of e 0 is a consistent high order discretization for the limiting equation numerical results are presented to demonstrate the stability and high order accuracy of the proposed schemes together with their performance in the limit our methods are also tested for the continuous velocity one group transport equation in slab geometry and for several examples with spatially varying parameters

discrete boltzmann like equations a dynamical formulation abstract this investigation presents a dynamical formulation of boltzmann like discrete kinetic equations the central concept of such a formulation is based on the idea that a dissipative system is equipped with a functional poisson bracket and a dissipative bracket and with two functionals generating the dynamical evolution we present non canonical brackets and the generating functionals we also discuss their basic properties and investigate dynamical invariants as well as the production of entropy generated by the entropy functional via the dissipative part of the bracket when collisions are the only sources of dissipation we are coming up with a consistent up to now unknown version of the discrete boltzmann vlasov kinetic equation

bounded oscillation for second order nonlinear neutral difference equations in critical and non critical states the sufficient and necessary conditions for the bounded oscillation of the second order nonlinear neutral delay difference email protected 2 x n px email protected email protected i 1mq ix email protected i f n x email protected 1 n x email protected l n are obtained in critical and non critical cases

exact solutions of a hierarchy of mixing speeds models this paper presents several new aspects of discrete kinetic theory dkt first a hierarchy of d dimensional d 1 2 3 models is proposed with 2d 3 velocities and three moduli speeds 0 2 and a third one that can be arbitrary it is assumed that the particles at rest have an internal energy which for microscopic collisions supplies for the loss of the kinetic energy in a more general way than usual collisions are allowed that mix particles with different speeds second for the 1 1 dimensional restriction of the systems of pde for these models which have two independent quadratic collision terms we construct different exact solutions the usual types of exact solutions are studied periodic solutions and shock wave solutions obtained from the standard linearization of the scalar riccati equations called riccatian shock waves then other types of solutions of the coupled riccati equations are found called non riccatian shock waves and they are compared with the previous ones the main new result