uniform l1 stability estimate of the boltzmann equation near a local maxwellian abstract we consider the boltzmann equation describing the spacial temporal evolution of the velocity distribution function in a near exponential local maxwellian regime we present two robust nonlinear functionals measuring possible future collisions and l 1 distance between two mild solutions through the explicit local cancellation of the collision mechanism due to the special structure of an exponential local maxwellian solution we show that the nonlinear functionals in s y ha nonlinear functionals of the boltzmann equation and uniform stability estimates j differential equations 215 2005 178 205 satisfy uniform stability estimates these functionals can be employed to the study of l 1 scattering and uniform l 1 stability estimate of mild solutions for the boltzmann equation with inverse power intermolecular potentials

an application of single term haar wavelet series in the solution of nonlinear oscillator equations in this paper a novel single term haar wavelet series sthws method is implemented for the solution of the duffing equation and painleve s transcendents pi and pii the results in the form of a block pulse and a discrete solution are presented unlike classical numerical schemes the sthws method has no restrictions on the coefficients of the duffing equation as regards its solution pi and pii are analysed as regards their solutions up to nearest singularities poles using the sthws also an efficient computational implementation shows the remarkable features of wavelet based techniques

global existence to boltzmann equation with external force in infinite vacuum in this paper we give a condition on the bicharacteristic which guarantees the global existence of the mild solution to the boltzmann equation with an external force for the hard sphere model and potentials with angular cutoff in infinite vacuum this generalizes the previous results to the case when the force can have arbitrary strength the constructive condition on the bicharacteristic is used to obtain the pointwise estimates on the collision operator so that the global existence comes from the contraction mapping theorem

a higher order local linearization method for solving ordinary differential equations the local linearization ll method for the integration of ordinary differential equations is an explicit one step method that has a number of suitable dynamical properties however a major drawback of the ll integrator is that its order of convergence is only two the present paper overcomes this limitation by introducing a new class of numerical integrators called the llt method that is based on the addition of a correction term to the ll approximation in this way an arbitrary order of convergence can be achieved while retaining the dynamic properties of the ll method in particular it is proved that the llt method reproduces correctly the phase portrait of a dynamical system near hyperbolic stationary points to the order of convergence the performance of the introduced method is further illustrated through computer simulations

on the trend to global equilibrium for spatially inhomogeneous kinetic systems the boltzmann equation as part of our study of convergence to equilibrium for spatially inhomogeneous kinetic equations started in 21 we derive estimates on the rate of convergence to equilibrium for solutions of the boltzmann equation like o t our results hold conditionally to some strong but natural estimates of smoothness decay at large velocities and strict positivity which at the moment have only been established in certain particular cases among the most important steps in our proof are 1 quantitative variants of boltzmann s h theorem as proven in 52 60 based on symmetry features hypercontractivity and information theoretical tools 2 a new quantitative version of the instability of the hydrodynamic description for non small knudsen number 3 some functional inequalities with geometrical content in particular the korn type inequality which we established in 22 and 4 the study of a system of coupled differential inequalities of second order by a treatment inspired from 21 we also briefly point out the particular role of conformal velocity fields when they are allowed by the geometry of the problem

analyzing survival curves at a fixed point in time a common problem encountered in many medical applications is the comparison of survival curves often rather than comparison of the entire survival curves interest is focused on the comparison at a fixed point in time in most cases the naive test based on a difference in the estimates of survival is used for this comparison in this note we examine the performance of alternatives to the naive test these include tests based on a number of transformations of the survival function and a test based on a generalized linear model for pseudo observations the type i errors and power of these tests for a variety of sample sizes are compared by a monte carlo study we also discuss how these tests may be extended to situations where the data are stratified the pseudo value approach is also applicable in more detailed regression analysis of the survival probability at a fixed point in time the methods are illustrated on a study comparing survival for autologous and allogeneic bone marrow transplants

on the asymptotic equivalence between the enskog and the boltzmann equations an asymptotic equivalence theorem is proven between the solutions of the initial value problem in all space for the boltzmann and enskog equations for initial data which assure global existence for the solutions to the initial value problem for one of the two equations the proof is given starting from the solution of the boltzmann equation then the proof line is simply indicated when one starts from the enskog equation the proof holds for knudsen numbers of the order of unity and equivalence is proven when the scale of the dimensions of the gas particles characterizing the enskog equation tends to zero

uniform stability of the solutions to the relativistic enskog equation abstract we present the uniform stability of classical solutions to the relativistic enskog equation under the locally lipschitz assumption of the collision factors given by polewczak this stability is an extension of the result given by ha and xiao for the relativistic boltzmann equation and it is very useful for the study of the cauchy problem for the relativistic enskog equation

a matricial exponentially fitted scheme for the numerical solution of stiff initial value problems abstract we present an exponentially fitted scheme for the numerical integration of stiff systems of initial value problems the basic algorithm consists of an explicit one step method which requires the computation of the exponential of a matrix this task is achieved using ward s scaling and squaring algorithm 1 the results of some numerical experiments are presented which allow an appraisal of the proposed approach with other methods

local h theorem for a kinetic variational theory a localh theorem is derived for a recently proposed extension of enskog kinetic theory to a dense model fluid composed of particles with interactions extending beyond a hard core

on the cauchy problem for the nonlinear boltzmann equation global existence uniqueness and asymptotic stability the analysis of the initial value problem for the nonlinear boltzmann equation is considered in this paper a theorem defining global existence and uniqueness for initial data which decay at infinity with an inverse power law is the main result of this work and is obtained by suitable application of fixed point theorems in banach spaces the theorem also defines the asymptotic stability of the solutions

on the boltzmann equation in unbounded space far from equilibrium and the limit of zero mean free path this paper studies loeb solutions of the boltzmann equation in unbounded space under natural initial conditions of finite mass energy and entropy an existence theory for large initial data is presented maxwellian behaviour is obtained in the limits of zero mean free path and of infinite time in the standard space homogeneous hard potential case the infinite time limit is of strongl 1 type

density functional approach to quantum lattice systems for quantum lattice systems we consider the problem of characterizing the set of single particle densities which come from the ground state eigenspace of somen particle hamiltonian of the form h 0 sum nolimits i 1 n v x i whereh0 is a fixed bounded operator representing the kinetic and interaction energies we show that the conditions on are that it be strictly positive properly normalized and consistent with the pauli principle our results are valid for both finite and infinite lattices and for either bosons or fermions the coulomb interaction may be included inh0 if the lattice dimension is 2 we also characterize those single particle densities which come from the gibbs states of such hamiltonians at finite temperature in addition to the conditions stated above must satisfy a finite entropy condition

asymptotic behaviour of the boltzmann equation with infinite range forces we have previously obtained existence results for the space homogeneous non linear boltzmann equation for a class of encounters with infinite range including inversek th power molecules withk 3 in the present paper those solutions are proved to converge in weakl 1 sense fork 5 to maxwellian distributions whent also the higher moments converge to those of the relevant maxwellian the method of proof relies on non standard techniques

on the limit of the nonlinear enskog equation corresponding with fluid dynamics we prove that if a scale of the diameter of particles is not greater than a scale of the mean free path to a high enough power if the scale of the mean free path is sufficiently small and if the non hydrodynamic part of the initial data satisfies an assumption of smallness then a solution of the initial value problem exists for the enskog equation on a macroscopic time interval as long as a smooth solution of the euler equations for compressible fluids exists this enskog solution is approximated both by the corresponding solution of the boltzmann equation and by the solution of the euler equations

well posedness and scattering for the boltzmann equations soft potential with cut off we prove the global existence of the unique mild solution for the cauchy problem of the cut off boltzmann equation for soft potential model gamma 2 n with initial data small in l n x v where n 2 3 is the dimension the proof relies on the existing inhomogeneous strichartz estimates for the kinetic equation by ovcharov siam j math anal 43 3 1282 1310 2011 and convolution like estimates for the gain term of the boltzmann collision operator by alonso et al commun math phys 298 293 322 2010 the global dynamics of the solution is also characterized by showing that the small global solution scatters with respect to the kinetic transport operator in l n x v also the connection between function spaces and cut off soft potential model n gamma 2 n is characterized in the local well posedness result for the cauchy problem with large initial data

nonlinear functionals of the boltzmann equation and uniform stability estimates abstract we present nonlinear functionals measuring physical space variation and l 1 distance between two classical solutions for the boltzmann equation with a cut off inverse power potential in the case that initial datum is a small smooth perturbation of vacuum and decays fast enough in the phase space we show that these functionals satisfy stability estimates which lead to bv type estimates and a uniform l 1 stability

uniform stability estimates for solutions and their gradients to the boltzmann equation a unified approach abstract as to the cauchy problem for the spatially inhomogeneous boltzmann equation with cut off we prove uniform stability estimates for solutions and their gradients in a unified and elementary way

the inelastic enskog equation with external force in this paper the cauchy problem for the inelastic enskog equation with external force is considered for near vacuum data under the assumptions on the bi characteristic we proved the global existence of mild solution

the bayesian inversion problem for thermal average sampling of quantum systems abstract in this article we propose a novel method for sampling potential functions based on noisy observation data of a finite number of observables in quantum canonical ensembles which leads to the accurate sampling of a wide class of test observables the method is based on the bayesian inversion framework which provides a platform for analyzing the posterior distribution and naturally leads to an efficient numerical sampling algorithm we highlight that the stability estimate is obtained by treating the potential functions as intermediate variables in the following way the discrepancy between two sets of observation data of training observables can bound the distance between corresponding posterior distributions of potential functions while the latter naturally leads to a bound of the discrepancies between corresponding thermal averages of test observables besides the training observables can be more flexible than finite samples of the local density function which are mostly used in previous researches the method also applies to the multi level quantum systems in the non adiabatic regime in addition we provide extensive numerical tests to verify the accuracy and efficiency of the proposed algorithm

global boundedness of moments of solutions of the boltzmann equation for forces of infinite range this paper proves the global boundedness in time of higher moments to a weak solution of the non linear space homogeneous boltzmann equation for inverse kth power forces with k 5 in the course of the proof a new collisional estimate of v s v s v s v s is obtained where v v are the velocities before and v v are the velocities after a binary collision

global existence in l1 for the enskog equation and convergence of the solutions to solutions of the boltzmann equation for the enskog equation in a box an existence theorem is proved for initial data with finite mass energy and entropy then by letting the diameter of the molecules go to zero the weak convergence of solutions of the enskog equation to solutions of the boltzmann equation is proved

l1 and bv type stability of the boltzmann equation with external forces abstract based on the existence theory on the boltzmann equation with external forces in infinite vacuum in this paper we will study the l 1 and bv type stability of the classical solutions for small initial data the stability results generalize those for the boltzmann equation without force to the case with external force in particular we show that the stability can be established for the soft potentials directly while the stability for the hard potentials and hard sphere model is obtained through the construction of some nonlinear functionals the functionals thus constructed generalize those constructed in s y ha nonlinear functionals of the boltzmann equation and uniform stability estimates j differential equations 215 2005 178 205 for the case without force to capture the effect of the force term on the time evolution of the solutions

the enskog boltzmann equation in the whole space r3 some global existence uniqueness and stability results abstract the enskog boltzmann equation a partial differential integral equation of the hyperbolic type is a model which generalizes the classical boltzmann equation to high gas densities and is here considered with an analysis of the well posedness of the initial value problem in unbounded domains some new global existence and uniqueness results for the solutions of the initial value problem and a discussion on the asymptotic stability are provided under suitable assumptions about the size of the norm of the initial data and about the rate of decay to zero at infinity in the phase space

the inverse problem in classical statistical mechanics we address the problem of whether there exists an external potential corresponding to a given equilibrium single particle density of a classical system results are established for both the canonical and grand canonical distributions it is shown that for essentially all systems without hard core interactions there is a unique external potential which produces any given density the external potential is shown to be a continuous function of the density and in certain cases it is shown to be differentiable as a consequence of the differentiability of the inverse map which is established without reference to the hard core structure in the grand canonical ensemble we prove the existence of the ornstein zernike direct correlation function a set of necessary but not sufficient conditions for the solution of the inverse problem in systems with hard core interactions is derived

the density functional theory of classical fluids revisited we reconsider the density functional theory of nonuniform classical fluids from the point of view of convex analysis from the observation that the logarithm of the grand partition function log xi phi is a convex functional of the external potential phi it is shown that the kohn sham free energy cal a rho is a convex functional of the density rho log xi phi and cal a rho constitute a pair of legendre transforms and each of these functionals can therefore be obtained as the solution of a variational principle the convexity ensures the unicity of the solution in both cases the variational principle which gives log xi phi as the maximum of a functional of rho is precisely that considered in the density functional theory while the dual principle which gives cal a rho as the maximum of a functional of phi seems to be a new result

recommended tests for association in 2 2 tables summary the asymptotic pearson s chi squared test and fisher s exact test have long been the most used for testing association in 2 2 tables unconditional tests preserve the significance level and generally are more powerful than fisher s exact test for moderate to small samples but previously were disadvantaged by being computationally demanding this disadvantage is now moot as software to facilitate unconditional tests has been available for years moreover fisher s exact test with mid p adjustment gives about the same results as an unconditional test consequently several better tests are available and the choice of a test should depend only on its merits for the application involved unconditional tests and the mid p approach ought to be used more than they now are the traditional fisher s exact test should practically never be used copyright q 2009 john wiley sons ltd

the kinetic theory of simple reacting spheres i global existence result in a dilute gas case existence of global in time spatially inhomogeneous and l 1 renormalized solutions is proven for the model of simple reacting spheres under the assumptions that initially the system has a finite total mass energy and entropy

a stochastic system of particles modelling the euler equations we consider a system of n spheres interacting through elastic collisions at a stochastic distance in the limit n for a suitable rescaling of the interaction parameters we prove that the one particle distribution function converges to a local maxwellian whose gross density velocity and temperature satisfy the euler equation

small data existence for the enskog equation in l 1 an existence theorem for the enskog equation with small initial data is proved in anl1 setting this type of result is not available for the boltzmann equation

solving stiff differential equations with the method of patches we introduce a new method for solving very stiff sets of ordinary differential equations the basic idea is to replace the original nonlinear equations with a set of equally stiff equations that are piecewise linear and therefore can be solved exactly we demonstrate the value of the method on small systems of equations for which some other methods are inefficient or produce spurious solutions estimate error bounds and discuss extensions of the method to larger systems of equations and to partial differential equations

the grad limit for a system of soft spheres a model describing the dynamics of a system of soft spheres is introduced the model contains a random mechanism which mollifies the deterministic model of hard sphere molecules it allows a rigorous deduction of the corresponding boltzmann equation for a wide class of initial data and arbitrarily long times

global existence and asymptotic behavior for the discrete velocity models of the boltzmann equation by using fixed point techniques some theorems which supply local and global existence uniqueness and asymptotic behavior of the solution of a general discrete velocity model of the boltzmann equation in three dimensions are given

analysis of some krylov subspace approximations to the matrix exponential operator in this note a theoretical analysis of some krylov subspace approximations to the matrix exponential operation exp a v is presented and a priori and a posteriors error estimates are established several such approximations are considered the main idea of these techniquesis to approximately project the exponential operator onto a small krylov subspace and to carry out the resulting small exponential matrix computation accurately this general approach which has been used with success in several applications provides a systematic way of defining high order explicit type schemes for solving systems of ordinary differential equations or time dependent partial differential equations

global weak solutions and uniform lp stability of the boltzmann enskog equation abstract we present the regularity theory of renormalized solutions and uniform l p stability estimates of the boltzmann enskog model we use a multi dimensional bony type functional to control the time phase space integral of a truncated collision operator we employ cercignani s arguments and a bony type functional to show that the renormalized solutions to the boltzmann enskog model are weak solutions in usual distributional sense for the uniform l p stability estimate we use lu s trick together with the holder inequality

the boltzmann equation global existence for a rare gas in an infinite vacuum solutions of the boltzmann equation are proved to exist globally in time under conditions that include the case of a finite volume of gas in an infinite vacuum when the mean free path of the gas is large enough it is also proved as might be expected in this case that the density of the gas at each point in space goes to zero as time goes to infinity

a comparison of reflected versus test based confidence intervals for the median survival time based on censored data the small sample performance of some recently proposed nonparametric methods of constructing confidence intervals for the median survival time based on randomly right censored data is compared with that of two new methods most of these methods are equivalent for large samples all proposed intervals are either test based or reflected intervals in the sense defined in the paper coverage probabilities for the interval estimates were obtained by exact calculation for uncensored data and by stimulation for three life distributions and four censoring patterns in the range of situations studied test based methods often have less than nominal coverage while the coverage of the new reflected confidence intervals is closer to nominal although somewhat conservative and these intervals are easy to compute

l p estimates of the boltzmann equation around a traveling local maxwellian in this paper we are interested in the lp estimates of the boltzmann equation in the case that the distribution function stays around a traveling local maxwellian for this we divide both sides of the boltzmann equation by the velocity distribution function with a fractional exponent and reformulate the boltzmann equation into a regularized one this amounts to endowing additional integrability on the collision kernel which in turn enables us to apply simple holder type inequalities our results cover the whole range of lebesgue exponents 0 p

sine gordon theory for the equation of state of classical hard core coulomb systems iii loopwise expansion we present an exact field theoretical representation of an ionic solution made of charged hard spheres the action of the field theory is obtained by performing a hubbard stratonovich transform of the configurational boltzmann factor it is shown that the stillinger lovett sum rules are satisfied if and only if all the field correlation functions are short range functions the mean field gaussian and two loops approximations of the theory are derived and discussed the mean field approximation for the free energy constitutes an exact lower bound for the exact free energy while the mean field pressure is an exact upper bound the one loop order approximation is shown to be identical with the random phase approximation of the theory of liquids finally at the two loop order and in the pecular case of the restricted primitive model one recovers results obtained in the framework of the mode expansion theory

regularity of the moments of the solution of a transport equation let u u x v satisfy the transport equation u v xu f x rn v rnwhere f belongs to some space of type lp dx d v where is a positive bounded measure on rn we study the resulting regularity of the moment u x v d v in terms of fractional sobolev spaces for example counter examples are given in order to test the optimality of our results

global existence in l 1 for the modified nonlinear enskog equation in ℝ 3 a global existence theorem with large initial data inl1 is given for the modified enskog equation in 3 the method which is based on the existence of a liapunov functional analog of theh boltzmann theorem utilizes a weak compactness argument inl1 in a similar way to the diperna lions proof for the boltzmann equation the existence theorem is obtained under certain condition on the behavior of the geometric factory the condition ony amounts to the fact that thel1 norm of the collision term grows linearly when the local density tends to infinity

combining one sample confidence procedures for inference in the two sample case we present a simple general method for combining two one sample confidence procedures to obtain inferences in the two sample problem some applications give striking connections to established methods for example combining exact binomial confidence procedures gives new confidence intervals on the difference or ratio of proportions that match inferences using fisher s exact test and numeric studies show the associated confidence intervals bound the type i error rate combining exact one sample poisson confidence procedures recreates standard confidence intervals on the ratio and introduces new ones for the difference combining confidence procedures associated with one sample t tests recreates the behrens fisher intervals other applications provide new confidence intervals with fewer assumptions than previously needed for example the method creates new confidence intervals on the difference in medians that do not require shift and continuity assumptions we create a new confidence interval for the difference between two survival distributions at a fixed time point when there is independent censoring by combining the recently developed beta product confidence procedure for each single sample the resulting interval is designed to guarantee coverage regardless of sample size or censoring distribution and produces equivalent inferences to fisher s exact test when there is no censoring we show theoretically that when combining intervals asymptotically equivalent to normal intervals our method has asymptotically accurate coverage importantly all situations studied suggest guaranteed nominal coverage for our new interval whenever the original confidence procedures themselves guarantee coverage

inferential models a framework for prior free posterior probabilistic inference posterior probabilistic statistical inference without priors is an important but so far elusive goal fisher s fiducial inference dempster shafer theory of belief functions and bayesian inference with default priors are attempts to achieve this goal but to date none has given a completely satisfactory picture this article presents a new framework for probabilistic inference based on inferential models ims which not only provides data dependent probabilistic measures of uncertainty about the unknown parameter but also does so with an automatic long run frequency calibration property the key to this new approach is the identification of an unobservable auxiliary variable associated with observable data and unknown parameter and the prediction of this auxiliary variable with a random set before conditioning on data here we present a three step im construction and prove a frequency calibration property of the im s belief function under mild conditions a corresponding optimality theory is develo

on the trend to global equilibrium in spatially inhomogeneous entropy dissipating systems the linear fokker planck equation we study the long time behavior of kinetic equations in which transport and spatial confinement in an exterior potential or in a box are associated with a degenerate collision operator acting only in the velocity variable we expose a general method based on logarithmic sobolev inequalities and the entropy to overcome the well known problem due to the degeneracy in the position variable of the existence of infinitely many local equilibria this method requires that the solution be somewhat smooth in this paper we apply it to the linear fokker planck equation and prove decay to equilibrium faster than o t 1 for all 0 2001 john wiley sons inc

stability of global solution for the relativistic enskog equation near vacuum the cauchy problem of the relativistic enskog equation with near vacuum data is considered in this paper under the same assumption as that in jiang j stat phys 127 805 812 2007 for the relativistic enskog equation we obtain the uniform l stability of the solution what s more important is that for two new types of the scattering cross section we give the global existence and l1 x v stability for mild solution when the initial data lies in the space l1 x v as a corollary we have a bv type estimate it is worth mentioning that the stability results in this paper can be applied to the case in jiang j stat phys 127 805 812 2007

classical solution of the nonlinear boltzmann equation in all r 3 asymptotic behavior of solutions proof is given of the existence of a classical solution to the nonlinear boltzmann equation in allr3 the solution which is global in time exists if the initial data go to zero fast enough at infinity and the mean free path is sufficiently large the solution is smooth in the space variable if the initial value is smooth the asymptotic behavior of solutions is also given it is shown that ast the solution to the boltzmann equation can be approximated by the solution to the free motion problem

new properties of a class of generalized kinetic equations we give some properties of a new class of hard sphere kinetic equations of great generality introduced earlier by polewczak the assumptions used to obtain the general class are very weak and the equations include not only the standard and revised enskog equations but also generalizations thereof that can be expected to yield essentially exact transport coefficients in particular there is a natural two particle realization that is obtained from maximizing the information entropy subject to prescribed two particle and one particle probability distribution functions k particle analogs fork 2 also naturally follow we obtain liapunov functionals for the whole class of equations under consideration and discuss the question of which of these functionals can be expected to play the role ofh functions we also obtain several more special results that include new lower bounds on the potential part of theh function for the revised enskog equation the bounds are instrumental in obtaining global existence theorems and also imply that the necessary condition for invertibility of the nonequilibrium extension of local activity as a functional of local density is satisfied

on the classical solutions of the boltzmann equation on etudie le probleme aux valeurs initiales pour l equation de boltzmann on montre que des solutions au sens classique existent pour tout temps si la donnee initiale est assez proche de l equilibre on se restreint a un domaine cubique et on considere seulement la condition aux limites periodique

weighted l bounds and uniqueness for the boltzmann bgk model we prove rather general l bounds for hydrodynamical fields in terms of weighted l norms of the kinetic density we use these estimates to prove l bounds and uniqueness for the solution of the bgk equation which is a simple relaxation model introduced by bhatnagar gross krook to mimic boltzmann flows

second derivative extended backward differentiation formulas for the numerical integration of stiff systems a class of second derivative extended backward differentiation formulas suitable for the approximate numerical integration of stiff systems of first order ordinary differential equations is examine

on the validity of the inverse conjecture in classical density functional theory it is shown that the basic assumptions of the classical density functional approach are rigorously correct forh stable systems in the grand canonical ensemble moreover it is established that the set of all single particle densities is convex these results are derived by providing necessary and sufficient conditions for the solution of the classical inverse problem for single particle densities analogous results are obtained for the solution of the higher order correlation inverse problem and the ramifications of these results for the validity of two body decomposition of forces are discussed

a stochastic model associated with enskog equation and its kinetic limit we examine a system of particles in which the particles travel deterministically in between stochastic collisions the collisions are elastic and occur with probability d when two particles are at a distance when the number of particles n goes to infinity and n d goes to a nonzero constant we show that the particle density converges to a solution of the enskog equation

on the fokker planck boltzmann equation we consider the boltzmann equation perturbed by fokker planck type operator to overcome the lack of strong a priori estimates and to define a meaningful collision operator we introduce a notion of renormalized solution which enables us to establish stability results for sequences of solutions and global existence for the cauchy problem with large data the proof of stability and existence combines renormalization with an analysis of a defect measure

on the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids it is shown that the variational principle for the grand potential of a nonuniform fluid as a functional of the singlet density yields the potential distribution theory for the equilibrium density we derive the explicit form that the functional takes for a system of hard rods and propose an approximate one for hard spheres attractive interactions are also considered in mean field approximation in all cases the pair direct correlation function of the nonuniform system is obtained and the density gradient expansion of the free energy is investigated

numerical analysis of a shock wave solution of the enskog equation obtained via a monte carlo method in this paper a planar stationary shock wave like solution of the enskog equation obtained via a monte carlo technique is studied both the algorithm used to obtain the solution and the qualitative behavior of the macroscopic quantities are discussed in comparison with the corresponding solution of the boltzmann equation

on the cauchy problem for the inelastic boltzmann equation with external force in this paper the cauchy problem for the inelastic boltzmann equation with external force is considered for near vacuum data under the assumptions on the bicharacteristic generated by external force which can be arbitrarily large we prove the global existence of mild solution for initial data small enough with respect to the sup norm with exponential weight by using the contraction mapping theorem furthermore we prove the uniform l1 stability of the mild solution following from the exponential decay estimate and the gronwall s inequality for the case of soft potentials

interacting squares in arbitrary external field a model of a many body system composed of squares with contact pair interactions in an arbitrary external field is presented the formulation uses a mapping of the system onto polydisperse hard core mixtures on the polydisperse level then a simplified hamiltonian function is specified this assumption together with a further one about the global free energy functional for the pure hard core part of the idealized mixture make the model solvable it is expected to hold for high temperatures low densities or low temperatures the validity of the method of construction in the latter case is illustrated by a further application to a corresponding lattice system for which exact results to compare with are readily available when the temperature is sufficiently low

on the cauchy problem for boltzmann equations global existence and weak stability we study the large data cauchy problem for boltzmann equations with general collision kernels we prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in l to a solution from this stability result we deduce global existence of a solution to the cauchy problem our method relies upon recent compactness results for velocity averages a new formulation of the boltzmann equation which involves nonlinear normalization and an analysis of subsolutions and supersolutions it allows us to overcome the lack of strong a priori estimates and define a meaningful collision operator for general configurations

loeb solutions of the boltzmann equation existence problems for the boltzmann equation constitute a main area of research within the kinetic theory of gases and transport theory the present paper considers the spatially periodic case with l1 initial data the main result is that the loeb subsolutions obtained in a preceding paper are shown to be true solutions the proof relies on the observation that monotone entropy and finite energy imply loeb integrability of non standard approximate solutions and uses estimates from the proof of the h theorem two aspects of the continuity of the solutions are also considered

on a time and space discretized approximation of the boltzmann equation in the whole space abstract in this paper convergence results on the solutions of a time and space discrete model approximation of the boltzmann equation for a gas of maxwellian particles in a bounded domain obtained by babovsky and illner 1989 are extended to approximate the solutions of the boltzmann equation in the whole physical space this is done for a class of particle interactions including maxwell and soft cut off potentials in the sense of grad the main result shows that the solutions of the discrete model converge in l 1 to the solutions of the boltzmann equation when the discretization parameters go simultaneously to zero the convergence is uniform with respect to the discretization parameters in addition a sufficient condition for the implementation of the main result is provided the techniques detailed in this paper may be also applied in other contexts

on the inelastic enskog equation near vacuum the cauchy problem for the inelastic enskog equation is considered for near vacuum data the global existence of mild and classical solutions of the inelastic enskog equation is obtained then based on some new functionals we give the uniform l1 x v stability of solutions for the inelastic enskog equation

l 1 stability of the boltzmann equation for the hard sphere model we study the l1 stability of classical solutions to the boltzmann equation for a hard sphere model when initial datum is a small perturbation of a vacuum and tends to zero exponentially fast at infinity in the phase space for this we introduce nonlinear functionals measuring potential interactions between particles with different velocities and l1 distance between classical solutions we use pointwise estimates for a solution and the gain term of a collision operator to control the time evolution of nonlinear functionals

global existence inl1 for the generalized enskog equation various existence theorems are given for the generalized enskog equation inr3 and in a bounded spatial domain with periodic boundary conditions a very general form of the geometric factory is allowed including an explicit space velocity and time dependence the method is based on the existence of a liapunov functional an analog of theh function in the boltzmann equation and utilizes a weak compactness argument inl1

test based exact confidence intervals for the difference of two binomial proportions summary confidence intervals are often provided to estimate a treatment difference when the sample size is small as is typical in early phases of clinical trials confidence intervals based on large sample approximations may not be reliable in this report we propose test based methods of constructing exact confidence intervals for the difference in two binomial proportions these exact confidence intervals are obtained from the unconditional distribution of two binomial responses and they guarantee the level of coverage we compare the performance of these confidence intervals to ones based on the observed difference alone we show that a large improvement can be achieved by using the standardized z test with a constrained maximum likelihood estimate of the variance

global existence of classical solutions to the inelastic vlasov poisson boltzmann system we study the global existence and uniqueness of classical solutions to the inelastic vlasov poisson boltzmann system for a soft potential in the near vacuum regime for the global existence of classical solutions we assume reasonable conditions on the restitution coefficient which represents the character of inelastic collisions we use the smallness of initial data and an algebraically decaying weight function in the spatial variable to control the self consistence force and collision operator

well posedness of the iterative boltzmann inversion the iterative boltzmann inversion is a fixed point iteration to determine an effective pair potential for an ensemble of identical particles in thermal equilibrium from the corresponding radial distribution function although the method is reported to work reasonably well in practice it still lacks a rigorous convergence analysis in this paper we provide some first steps towards such an analysis and we show under quite general assumptions that the associated fixed point operator is lipschitz continuous in fact differentiable in a suitable neighborhood of the true pair potential assuming that such a potential exists in other words the iterative boltzmann inversion is well defined in the sense that if the kth iterate of the scheme is sufficiently close to the true pair potential then the k 1 st iterate is an admissible pair potential which again belongs to the domain of the fixed point operator on our way we establish important properties of the cavity distribution function and provide a proof of a statement formulated by groeneveld concerning the rate of decay at infinity of the ursell function associated with a lennard jones type potential

on the initial boundary value problems for the enskog equation in irregular domains the paper is concerned with the enskog equation with a constant high density factor for large initial data in l1 rn the initial boundary value problem is investigated for bounded domains with irregular boundaries the proof of an h theorem for the case of general domains and boundary conditions is given the main result guarantees the existence of global solutions of boundary value problems for large initial data with all v moments initially finite and domains having boundary with finite hausdorff measure and satisfying a cone condition existence and uniqueness are first proved for the case of bounded velocities the solution has finite norm int sup 0 leqslant t leqslant t f t 0 t x vt sqrt 1 v 2 dq text dv where q t0 x is taken on all possible n dimensional planes q v in rn l intersecting a fixed point and orthogonal to vectors 1 v v rn

solutions of the boltzmann equation with infinite energy existence stability and long time behavior this paper is devoted to studying a class of solutions to the nonlinear boltzmann equation having infinite kinetic energy these solutions have an upper maxwellian bound with infinite kinetic energy firstly the existence and stability of this kind of solutions are established near vacuum secondly it is proved that this kind of solutions are stable for any initial data as a consequence the boltzmann equation has at most one solution with infinite kinetic energy finally the long time behavior of the solutions is also established

overcomplete free energy functional for d 1 particle systems with next neighbor interactions we deduce an overcomplete free energy functional for d 1 particle systems with next neighbor interactions where the set of redundant variables are the local block densities i of i interacting particles the idea is to analyze the decomposition of a given pure system into blocks of i interacting particles by means of a mapping onto a hard rod mixture this mapping uses the local activity of component i of the mixture to control the local association of i particles of the pure system thus it identifies the local particle density of component i of the mixture with the local block density i of the given system consequently our overcomplete free energy functional takes on the hard rod mixture form with the set of block densities i representing the sequence of partition functions of the local aggregates of particle numbers i the system of equations for the local particle density of the original system is closed via a subsidiary condition for the block densities in terms of analoguous to the uniform isothermal isobaric technique all our results are expressible in terms of effective pressures we illustrate the theory with two standard examples the adhesive interaction and the square well potential for the uniform case our proof of such an overcomplete format is based on the exponential boundedness of the number of partitions of a positive integer hardy ramanujan formula and on varadhan s theorem on the asymptotics of a class of integrals

the inverse conjecture for the revised enskog equation it is shown that the pair correlation function which is by definition the high density factor in the revised enskog theory is not always a well defined functional of the local density moreover for a finite system with periodic boundary conditions and in the space homogeneous case this function computed at the contact value is bounded at the maximum allowed density i e a densitynmax such that in one dimension 1 a 1 l nmax 1 a equality sign which corresponds to the usual close packing density for whichl a is an integer being included as a particular case at least for the one dimensional gas model this finite value is shown to approach infinity in the thermodynamic and in the hydrodynamic limits a new form for the revised enskog equation which does not depend on the inverse conjecture is finally given

global existence and asymptotic behavior for the nonlinear enskog equation the existence of a classical solution to the nonlinear enskog equation in all mathbb r 3 is proved the solution which is global in time exists if the initial data go to zero fast enough at infinity and the mean path is sufficiently large the solution is smooth in space variable if the initial value is smooth the asymptoticbehavior of solutions is also given it is shown that as t to infty the solution to the enskog equation can be approximated by the solution to the free motion problem key words partial differential equations nonlinear integral equation asymptotic behavior kinetic theory boltzmann equation

on the inverse problem in statistical mechanics for quantum spin systems it is known that for a suitable space of potentials the equilibrium states arew dense in the set of all translation invariant states the problem discussed in this paper is how to recognize such equilibrium states and how to find the corresponding potential a necessary and sufficient condition for a state to be an equilibrium state for some potential is given in sect 3

on the cauchy problem for the discrete boltzmann equation with initial values inl1 ℝ we prove a global existence theorem for a discrete velocity model of the boltzmann equation when the initial values i x have finite entropy and for some constant 0 1 x i x el1

hohenberg kohn theorem and non v representable densities abstract in the density functional formalism of hohenberg and kohn1 the variation is only allowed over the one particle densities which are pure state v representable ps v representable levy2 and lieb3 proved that not every ensemble v representable e v representable density is ps v representable since we show that the hohenberg kohn formalism can be extended to a variation over e v representable densities for degenerated ground states levy s and lieb s result is not a counterexample to the universality of the hohenberg kohn theorem the question whether every n representable density is e v representable has remained open so far presenting examples of non e v representable densities we answer this question in the negative thus the value of levy s functional4 for the calculation of ground state energies is obvious since this functional only requires the n representability of the densities therefore we transfer two approaches for the calculation of excited state energies into the framework of levy s formalism

nonparametric estimation for the difference or ratio of median failure times a simple and purely nonparametric confidence interval procedure for the difference or ratio of two median failure times is proposed with censored observations the new proposal does not involve unstable and complicated nonparametric density estimates and is valid asymptotically even when the two underlying distribution functions differ in shape extensive numerical studies are carried out to examine the appropriateness of the new procedure for practical sample sizes

a note on the uniqueness result for the inverse henderson problem the inverse henderson problem of statistical mechanics is the theoretical foundation for many bottom up coarse graining techniques for the numerical simulation of complex soft matter physics this inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles roughly stated it asks for the interaction potential given the equilibrium pair correlation function of the system in 1974 henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system here we provide a rigorous proof of a slightly more general version of the latter statement using georgii s variant of the gibbs variational principle the inverse henderson problem of statistical mechanics is the theoretical foundation for many bottom up coarse graining techniques for the numerical simulation of complex soft matter physics this inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles roughly stated it asks for the interaction potential given the equilibrium pair correlation function of the system in 1974 henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system here we provide a rigorous proof of a slightly more general version of the latter statement using georgii s variant of the gibbs variational principle

equations de type de boltzmann spatialement homogenes we study the construction of a nonhomogeneous n valued markov process whose laws at fixed times evolve according to a boltzmann type equation spatially homogeneous we then consider the problem of the asymptotic propagation of chaos for a system of a large number of interacting particles

two sample quantile tests under general conditions summary a simple nonparametric two sample test for equality of a given collection of quantiles is developed which can be applied to a variety of empirical distribution functions including the kaplan meier estimator a self consistent estimator for doubly censored data and an estimator for repeated measures data the null hypothesis tested is that the quantiles are equal but other aspects of the distributions may diver between the two samples this procedure can also be applied to quantile testing in group sequential clinical trials with staggered patient entry a simple simulation study demonstrates that the moderate sample size properties of this procedure are reasonable