about the regularizing properties of the non cut off kac equation we prove in this work that under suitable assumptions the solution of the spatially homogeneous non cut off kac equation or of the spatially homogeneous non cut off 2d boltzmann equation with maxwellian molecules in the radial case becomes very regular with respect to the velocity variable as soon as the time is strictly positive

entropy dissipation and long range interactions we study boltzmann s collision operator for long range interactions i e without grad s angular cut off assumption we establish a functional inequality showing that the entropy dissipation controls smoothness of the distribution function in a precise sense our estimate is optimal and gives a unified treatment of both the linear and the nonlinear cases we also give simple and self contained proofs of several useful results that were scattered in previous works as an application we obtain several helpful estimates for the cauchy problem and for the landau approximation in plasma physics

the cauchy problem for the radially symmetric homogeneous boltzmann equation with shubin class initial datum and gelfand shilov smoothing effect abstract in this paper we study the cauchy problem for the radially symmetric homogeneous non cutoff boltzmann equation with maxwellian molecules the initial datum belongs to shubin space of the negative index which can be characterized by spectral decomposition of the harmonic oscillator and it is a small perturbation of maxwellian distribution the shubin space of the negative index contains the probability measures based on this spectral decomposition we construct the weak solution with shubin class initial datum we also prove that the cauchy problem enjoys gelfand shilov smoothing effect meaning that the smoothing properties are the same as the cauchy problem defined by the evolution equation associated to a fractional harmonic oscillator

on the closest string and substring problems the problem of finding a center string that is close to everygiven string arises in computational molecular biology and codingtheory this problem has two versions the closest string problemand the closest substring problem given a set of strings s s1 s2 sn each of length m the closest stringproblem is to find the smallest d and a string s of lengthm which is within hamming distance d to eachsi e s this problem comes fromcoding theory when we are looking for a code not too far away froma given set of codes closest substring problem with an additionalinput integer l asks for the smallest d and a strings of length l which is within hamming distance daway from a substring of length l of each si this problemis much more elusive than the closest string problem the closestsubstring problem is formulated from applications in findingconserved regions identifying genetic drug targets and generatinggenetic probes in molecular biology whether there are efficientapproximation algorithms for both problems are major open questionsin this area we present two polynomial time approximationalgorithms with approximation ratio 1 e for any smalle to settle both questions

global solutions and time decay of the non cutoff vlasov maxwell boltzmann system in the whole space the global in time classical solutions to the cauchy problem of the vlasov maxwell boltzmann system near maxwellians are obtained under the lower regularity index assumption and the weaker smallness condition on the initial perturbation in comparison with the work duan et al in kinet relat models 6 1 159 204 2013 in particular we show the relation between time decay rates and spatial derivatives of solutions our analysis relies on a refined energy estimates and the interpolation techniques between negative sobolev norms and positive sobolev norms without linear decay analysis

combinatorial n fold integer programming and applications many fundamental mathsf np hard problems can be formulated as integer linear programs ilps a famous algorithm by lenstra solves ilps in time that is exponential only in the dimension of the program and polynomial in the size of the ilp that algorithm became a ubiquitous tool in the design of fixed parameter algorithms for mathsf np hard problems where one wishes to isolate the hardness of a problem by some parameter however in many cases using lenstra s algorithm has two drawbacks first the run time of the resulting algorithms is often double exponential in the parameter and second an ilp formulation in small dimension cannot easily express problems involving many different costs inspired by the work of hemmecke et al math program 137 1 2 ser a 325 341 2013 we develop a single exponential algorithm for so called combinatorialn fold integer programs which are remarkably similar to prior ilp formulations for various problems but unlike them also allow variable dimension we then apply our algorithm to many relevant problems problems like closest string swap bribery weighted set multicover and several others and obtain exponential speedups in the dependence on the respective parameters the input size or both unlike lenstra s algorithm which is essentially a bounded search tree algorithm our result uses the technique of augmenting steps at its heart is a deep result stating that in combinatorial n fold ips existence of an augmenting step implies existence of a local augmenting step which can be found using dynamic programming our results provide an important insight into many problems by showing that they exhibit this phenomenon and highlights the importance of augmentation techniques

gelfand shilov smoothing properties of the radially symmetric spatially homogeneous boltzmann equation without angular cutoff we prove that the cauchy problem associated to the radially symmetric spatially homogeneous non cutoff boltzmann equation with maxwellian molecules enjoys the same gelfand shilov regularizing effect as the cauchy problem defined by the evolution equation associated to a fractional harmonic oscillator

smoothing effect and cauchy problem for radially symmetric homogeneous boltzmann equation with debye yukawa potential of shubin class initial datum abstract in this paper we study the cauchy problem for the radially symmetric homogeneous non cutoff boltzmann equation with debye yukawa potential the initial datum belongs to shubin type space of the negative index which can be characterized by spectral decomposition of the harmonic oscillator and it is a small perturbation of maxwellian distribution the shubin type space of negative index contains the probability measures based on the spectral decomposition we construct the weak solution with shubin type class initial datum and prove the smoothing effect for the solution to this cauchy problem

a class of k sample tests for comparing the cumulative incidence of a competing risk in this paper for right censored competing risks data a class of tests developed for comparing the cumulative incidence of a particular type of failure among different groups the tests are based on comparing weighted averages of the hazards of the subdistribution for the failure type of interest asymptotic results are derived by expressing the statistics in terms of counting processes and using martingale central limit theory it is proposed that weight functions very similar to those for the g p tests from ordinary survival analysis be used simulation results indicate that the asymptotic distributions provide adequate approximations in moderate sized samples

a comparison of goodness of fit tests for the logistic gee model generalized estimating equations have become a popular regression method for analysing clustered binary data methods to assess the goodness of fit of the fitted models have recently been developed however evaluations and comparisons of these methods are limited we discuss these methods and develop two additional statistics to evaluate goodness of fit we evaluate the performance of each of the statistics with respect to type i error rates and power in a simulation study guidance is provided regarding appropriate use of the statistics under various scenarios

the uncertainty principle on considere l existence et la regularite des solutions d equations aux derivees partielles la construction de solutions fondamentales explicites et les valeurs propres d operateurs de schrodinger

analysing competing risks data with transformation models we present a flexible class of marginal models for the cumulative incidence function the semiparametric transformation model is utilized in a decomposition for the marginal failure probabilities which extends previous work on farewell s cure model novel estimation inference and prediction procedures are developed with large sample properties derived from the theory of martingales and u statistics a small simulation study demonstrates that the methods are appropriate for practical use the methods are illustrated with a thorough analysis of a prostate cancer clinical trial simple graphical displays are used to check for the goodness of fit

smoothing estimates for boltzmann equation with full range interactions spatially homogeneous case in this work we are concerned with the regularities of the solutions to the boltzmann equation with physical collision kernels for the full range of intermolecular repulsive potentials r p 1 with p 2 we give new and constructive upper and lower bounds for the collision operator in terms of standard weighted fractional sobolev norms as an application we get the global entropy dissipation estimate which is a little stronger than that described by alexandre et al arch rational mech anal 152 4 327 355 2000 as another application we prove the smoothing effects for the strong solutions constructed by desvillettes and mouhot arch rational mech anal 193 2 227 253 2009 of the spatially homogeneous boltzmann equation with true hard potential and true moderately soft potential

regularizing effect and local existence for the non cutoff boltzmann equation the boltzmann equation without grad s angular cutoff assumption is believed to have a regularizing effect on the solutions because of the non integrable angular singularity of the cross section however even though this has been justified satisfactorily for the spatially homogeneous boltzmann equation it is still basically unsolved for the spatially inhomogeneous boltzmann equation in this paper by sharpening the coercivity and upper bound estimates for the collision operator establishing the hypo ellipticity of the boltzmann operator based on a generalized version of the uncertainty principle and analyzing the commutators between the collision operator and some weighted pseudo differential operators we prove the regularizing effect in all time space and velocity variables on the solutions when some mild regularity is imposed on these solutions for completeness we also show that when the initial data has this mild regularity and a maxwellian type decay in the velocity variable there exists a unique local solution with the same regularity so that this solution acquires the c regularity for any positive time

the landau equation in a periodic box the landau equation which was proposed by landau in 1936 is a fundamental equation to describe collisions among charged particles interacting with their coulombic force in this article global in time classical solutions near maxwellians are constructed for the landau equation in a periodic box our result also covers a class of generalized landau equations which describes grazing collisions in a dilute gas

generalised linear models for correlated pseudo observations with applications to multi state models will be in a given state at some time is a complex nonlinear function of the intensity regression coefficients we present a technique which models the state probabilities directly this method is based on the pseudo values from a jackknife statistic constructed from simple summary statistic estimates of the state probabilities these pseudo values are then used in a generalised estimating equation to obtain estimates of the model parameters we illustrate how this technique works by studying examples of common regression problems we apply the technique to model acute graft versus host disease in bone marrow transplants

phase space analysis of semilinear parabolic equations abstract we present a wave packet analysis of a class of possibly degenerate parabolic equations with variable coefficients as a consequence we prove local wellposedness of the corresponding cauchy problem in spaces of low regularity namely the modulation spaces assuming a nonlinearity of analytic type as another application we deduce that the corresponding phase space flow decreases the global wave front set we also consider the action on spaces of analytic functions provided the coefficients are analytic themselves

some solutions of the boltzmann equation without angular cutoff we show the existence of local or global in time solutions for the non homogeneous boltzmann equation this is done under the assumptions that initial data are smaller than a suitable maxwellian and that collisional cross sections do not satisfy grad s angular cutoff partial regularity in space velocity of the solutions constructed herein is also proved

on approximating string selection problems with outliers many problems in bioinformatics are about finding strings that approximately represent a collection of given strings we look at more general problems where some input strings can be classified as outliers the close to most strings problem is given a set s of the same length strings and a parameter d find a string x that maximizes the number of non outliers within hamming distance d of x we prove that this problem has no polynomial time approximation scheme ptas unless np has randomized polynomial time algorithms correcting a decade old erroneous proof made previously in the literature the most strings with few bad columns problem is to find a maximum size subset of input strings so that the number of non identical positions is at most k we show it has no ptas unless p np we also observe closest to k strings has no efficient ptas eptas unless a parameterized complexity hierarchy collapses in sum outliers help model problems associated with using biological data but we show the problem of finding an approximate solution is computationally difficult

prediction of cumulative incidence function under the proportional hazards model in the presence of dependent competing risks in survival analysis the cox model can be utilized to examine the covariate effects on the cause specific hazard function for the failure type of interest for this situation the cumulative incidence function provides an intuitively appealing summary curve for marginal probabilities of this particular event in this paper we show how to construct confidence intervals and bands for such a function under the cox model for future patients with certain covariates our proposals are illustrated with data from a prostate cancer trial

asymptotic analysis of the spatially homogeneous boltzmann equation grazing collisions limit in the present work we consider the asymptotic problem of the spatially homogeneous boltzmann equation when almost all collisions are grazing that is the deviation angle theta of the collision is limited near zero i e theta le epsilon we show that by taking the proper scaling to the cross section which was used in 37 that is assuming begin aligned b epsilon v v sigma 2 1 s v v gamma epsilon 3 sin 1 theta left frac theta epsilon right 1 2s mathrm 1 theta le epsilon end aligned where theta langle theta frac upsilon upsilon upsilon upsilon sigma rangle the solution f epsilon of the boltzmann equation with initial data f 0 can be globally or locally expanded in some weighted sobolev space as begin aligned f epsilon f o epsilon end aligned where the function f is the solution of landau equation which is associated with the grazing collisions limit of boltzmann equation with the same initial data f 0 this gives the rigorous justification of the landau approximation in the spatially homogeneous case in particular if taking gamma 3 and s 1 epsilon in the cross section b epsilon we show that the above asymptotic formula still holds and in this case f is the solution of landau equation with the coulomb potential going further we revisit the well posedness problem of the boltzmann equation in the limiting process we show there exists a common lifespan such that the uniform estimates of high regularities hold for each solution f epsilon thanks to the weak convergence results on the grazing collisions limit in 37 in other words we establish a unified framework to establish the well posedness results for both boltzmann and landau equations

ultra analytic effect of cauchy problem for a class of kinetic equations abstract the smoothing effect of the cauchy problem for a class of kinetic equations is studied we firstly consider the spatially homogeneous nonlinear landau equation with maxwellian molecules and inhomogeneous linear fokker planck equation to show the ultra analytic effects of the cauchy problem those smoothing effect results are optimal and similar to heat equation in the second part we study a model of spatially inhomogeneous linear landau equation with maxwellian molecules and show the analytic effect of the cauchy problem

global solutions in the critical besov space for the non cutoff boltzmann equation abstract the boltzmann equation is studied without the cutoff assumption under a perturbative setting a unique global solution of the cauchy problem of the equation is established in a critical chemin lerner space in order to analyze the collisional term of the equation a chemin lerner norm is combined with a non isotropic norm with respect to a velocity variable which yields an a priori estimate for an energy estimate together with local existence following from commutator estimates and the hahn banach extension theorem the desired solution is obtained

gevrey regularity of spatially homogeneous boltzmann equation without cutoff abstract in this paper we study the gevrey regularity of spatially homogeneous boltzmann equation without angular cutoff we prove the propagation of gevrey regularity for c solutions with the maxwellian decay to the cauchy problem of spatially homogeneous boltzmann equation the idea we use here is based on the framework of morimoto ukai s recent paper see y morimoto s ukai gevrey smoothing effect of solutions for spatially homogeneous nonlinear boltzmann equation without angular cutoff j pseudo differ oper appl 1 2010 139 159 but we extend the range of the index satisfying 2 s 1 1 s 0 1 2 and in this case we consider the kinetic factor in the form of v v instead of v as morimoto and ukai did before

the vlasov poisson boltzmann system without angular cutoff this paper is concerned with the vlasov poisson boltzmann system for plasma particles of two species in three space dimensions the boltzmann collision kernel is assumed to be angular non cutoff with 3 2s and 1 2 s 1 where s are two parameters describing the kinetic and angular singularities respectively we establish the global existence and convergence rates of classical solutions to the cauchy problem when initial data is near maxwellians this extends the results in duan et al j diff eqs 252 12 6356 6386 2012 math models methods appl sci 23 6 927 2013 for the cutoff kernel with 2 1 to the case 3 2 as long as the angular singularity exists instead and is strong enough i e s is close to 1 the proof is based on the time weighted energy method building also upon the recent studies of the non cutoff boltzmann equation in gressman and strain j amer math soc 24 3 771 847 2011 and the vlasov poisson landau system in guo j amer math soc 25 759 812 2012

regression modeling of competing risks data based on pseudovalues of the cumulative incidence function typically regression models for competing risks outcomes are based on proportional hazards models for the crude hazard rates these estimates often do not agree with impressions drawn from plots of cumulative incidence functions for each level of a risk factor we present a technique which models the cumulative incidence functions directly the method is based on the pseudovalues from a jackknife statistic constructed from the cumulative incidence curve these pseudovalues are used in a generalized estimating equation to obtain estimates of model parameters we study the properties of this estimator and apply the technique to a study of the effect of alternative donors on relapse for patients given a bone marrow transplant for leukemia

on the complexity of finding common approximate substrings problems associated with finding strings that are within a specified hamming distance of a given set of strings occur in several disciplines in this paper we use techniques from parameterized complexity to assess non polynomial time algorithmic options and complexity for the common approximate substring cas problem our analyses indicate under which parameter restrictions useful algorithms are possible and include both class membership and parameterized reductions to prove class hardness in order to achieve fixed parameter tractability either a fixed string length or both a fixed size alphabet and fixed substring length are sufficient fixing either the string length or the alphabet size and hamming distance is shown to be necessary unless w 1 fpt an assortment of parameterized class membership and hardness results cover all other parameterized variants showing in particular the effect of fixing the number of strings

the cauchy problem for the inhomogeneous non cutoff kac equation in critical besov space abstract in this work we investigate the cauchy problem for the spatially inhomogeneous non cutoff kac equation if the initial datum belongs to the spatially critical besov space we can prove the well posedness of weak solution under a perturbation framework furthermore it is shown that the solution enjoys gelfand shilov regularizing properties with respect to the velocity variable and gevrey regularizing properties with respect to the position variable in comparison with the recent result in 18 the gelfand shilov regularity index is improved to be optimal to the best of our knowledge our work is the first one that exhibits smoothing effect for the kinetic equation in besov spaces

predicting cumulative incidence probability by direct binomial regression we suggest a new simple approach for estimation and assessment of covariate effects for the cumulative incidence curve in the competing risks model we consider a semiparametric regression model where some effects may be time varying and some may be constant over time our estimator can be implemented by standard software our simulation study shows that the estimator works well and has finite sample properties comparable with the subdistribution approach we apply the method to bone marrow transplant data and estimate the cumulative incidence of death in complete remission following a bone marrow transplantation here death in complete remission and relapse are two competing events

uncertainty principle and kinetic equations abstract a large number of mathematical studies on the boltzmann equation are based on the grad s angular cutoff assumption however for particle interaction with inverse power law potentials the associated cross sections have a non integrable singularity corresponding to the grazing collisions smoothing properties of solutions are then expected on the other hand the uncertainty principle established by heisenberg in 1927 has been developed so far in various situations and it has been applied to the study of the existence and smoothness of solutions to partial differential equations this paper is the first one to apply this celebrated principle to the study of the singularity in the cross sections for kinetic equations precisely we will first prove a generalized version of the uncertainty principle and then apply it to justify rigorously the smoothing properties of solutions to some kinetic equations in particular we give some estimates on the regularity of solutions in sobolev spaces w r t all variables for both linearized and nonlinear space inhomogeneous boltzmann equations without angular cutoff as well as the linearized space inhomogeneous landau equation

regularizing effects for the classical solutions to the landau equation in the whole space abstract the landau equation describes the binary collisional effects through long range coulombian interaction in a plasma in this paper we prove that the known classical solutions to the landau equation near maxwellian in the whole space have a regularizing effect in all time space and velocity variables that is become immediately smooth with respect to all variables

wave packet analysis of schrodinger equations in analytic function spaces abstract we consider a class of linear schrodinger equations in r d with analytic symbols we prove a global in time integral representation for the corresponding propagator as a generalized gabor multiplier with a window analytic and decaying exponentially at infinity which is transported by the hamiltonian flow we then provide three applications of the above result the exponential sparsity in phase space of the corresponding propagator with respect to gabor wave packets a wave packet characterization of fourier integral operators with analytic phases and symbols and the propagation of analytic singularities

propagation of gevrey regularity for solutions of the boltzmann equation for maxwellian molecules we prove that gevrey regularity is propagated by the boltzmann equation with maxwellian molecules with or without angular cut off the proof relies on the wild expansion of the solution to the equation and on the characterization of gevrey regularity by the fourier transform

more efficient algorithms for closest string and substring problems the closest string problem and the closest substring problem are all natural theoretical computer science problems and find important applications in computational biology given n input strings the closest string substring problem finds a new string within distance d to a substring of each input string and such that d is minimized both problems are np complete in this paper we propose new algorithms for these two problems for the closest string problem we developed an exact algorithm with time complexity o n sigma o d where sigma is the alphabet this improves the previously best known result o nd o d and results into a polynomial time algorithm when d o log n by using this algorithm a polynomial time approximation scheme ptas for the closest string problem is also given with time complexity o n o epsilon 2 improving the previously best known o n o epsilon 2 log frac 1 epsilon ptas a new algorithm for the closest substring problem is also proposed finally we prove that a restricted version of the closest substring problem has the same parameterized complexity as the closest substring answering an open question in the literature

parameterized complexity analysis for the closest string with wildcards problem the closest string problem asks to find a string s which is not too far from each string in a set of m input strings where the distance is taken as the hamming distance this well studied problem has various applications in computational biology and drug design in this paper we introduce a new variant of closest string where the input strings can contain wildcards that can match any letter in the alphabet and the goal is to find a solution string without wildcards we call this problem the closest string with wildcards problem and we analyze it in the framework of parameterized complexity our study determines for each natural parameterization whether this parameterization yields a fixed parameter algorithm or whether such an algorithm is highly unlikely to exist

the geometry of binary collisions and generalized radon transforms elastic collisions are characterized by the conservation of momentum and energy we consider some geometrical aspects of such collisions when the energy of one particle can be expressed in terms of the moments as the geometry of elastic collisions is essential for the regularizing property of the gain term in the boltzmann equation which was proved by p l lions we show how such results can be deduced from a regularity theorem for generalized radon transforms by sogge stein this is possible for and for we also show that the same technique cannot be used with other choices of

the boltzmann equation without angular cutoff in the whole space qualitative properties of solutions this is a continuation of our series of works for the inhomogeneous boltzmann equation we study qualitative properties of classical solutions the full regularization in all variables uniqueness non negativity and convergence rate to the equilibrium to be precise together with the results of parts i and ii about the well posedness of the cauchy problem around the maxwellian we conclude this series with a satisfactory mathematical theory for the boltzmann equation without angular cutoff

on the string consensus problem and the manhattan sequence consensus problem abstract we study the manhattan sequence consensus problem msc problem in which we are given k integer sequences each of length l and we are to find an integer sequence x of length l called a consensus sequence such that the maximum manhattan distance of x from each of the input sequences is minimized a related problem with hamming distance instead of manhattan distance is called hamming string consensus hsc also known under the names of string center problem or closest string problem for binary sequences manhattan distance coincides with hamming distance hence in this case hsc is a special case of msc we design a practically efficient o l time algorithm solving msc for k 5 sequences it improves upon the quadratic algorithm by amir et al 2012 1 for hsc for k 5 binary strings similarly as in the algorithm of amir et al we use a column based framework we replace the implied general integer linear programming by its easy special cases due to combinatorial properties of msc for k 5 practicality of our algorithms has been verified experimentally we also show that for a general parameter k any instance can be reduced in linear time to a kernel of size k so the problem is fixed parameter tractable nevertheless for k 4 this is still too large for any naive solution to be feasible in practice this is a full version of an article published at spire 2014 15

gelfand shilov and gevrey smoothing effect of the cauchy problem for fokker planck equation abstract in this work we study the cauchy problem for fokker planck equation with the external potential we show that the solution of the cauchy problem enjoys gelfand shilov s 1 1 r 3 regularizing property with respect to the velocity variable and gevrey g 3 2 r 3 regularizing property with respect to the position variable

global existence and full regularity of the boltzmann equation without angular cutoff we prove the global existence and uniqueness of classical solutions around an equilibrium to the boltzmann equation without angular cutoff in some sobolev spaces in addition the solutions thus obtained are shown to be non negative and c in all variables for any positive time in this paper we study the maxwellian molecule type collision operator with mild singularity one of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator this norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated h theorem

a direct method for the regularity of the gain term in the boltzmann equation this paper presents an essentially simple and direct method to prove the regularizing properties of the collision gain term in the first equation of the boltzmann hierarchy some corollaries of the main results of this paper are given to improve the previous results on the regularity of the gain term in the boltzmann equation an extension of a new fundamental result concerning separated variable kernels is also given to some general kernels

sharp regularity and cauchy problem of the spatially homogeneous boltzmann equation with debye yukawa potential abstract in this paper we study the cauchy problem for the linear spatially homogeneous boltzmann equation with debye yukawa potential using the spectral decomposition of the linear operator we prove that for an initial datum in the sense of distribution which contains the dual of the sobolev spaces there exists a unique solution which belongs to a more regular sobolev space for any positive time we also study the sharp regularity of the solution

on the boltzmann equation for long range interactions we study the boltzmann equation without grad s angular cutoff assumption we introduce a suitable renormalized formulation that allows the cross section to be singular in both the angular and the relative velocity variables angular singularities occur as soon as one is interested in long range interactions while singularities in the relative velocity variable occur in the study of soft potentials in particular coulomb interaction together with several new estimates this new formulation enables us to prove existence of weak solutions and to give a proof of a conjecture by lions appearance of strong compactness under general fully realistic assumptions 2001 john wiley sons inc

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

the boltzmann equation without angular cutoff in the whole space i global existence for soft potential it is known that the singularity in the non cutoff cross section of the boltzmann equation leads to the gain of regularity and gain of weight in the velocity variable by defining and analyzing a non isotropy norm which precisely captures the dissipation in the linearized collision operator we first give a new and precise coercivity estimate for the non cutoff boltzmann equation for general physical cross sections then the cauchy problem for the boltzmann equation is considered in the framework of small perturbation of an equilibrium state in this part for the soft potential case in the sense that there is no positive power gain of weight in the coercivity estimate on the linearized operator we derive some new functional estimates on the nonlinear collision operator together with the coercivity estimates we prove the global existence of classical solutions for the boltzmann equation in weighted sobolev spaces

gelfand shilov and gevrey smoothing effect for the spatially inhomogeneous non cutoff kac equation abstract we consider the spatially inhomogeneous non cutoff kac s model of the boltzmann equation we prove that the cauchy problem for the fluctuation around the maxwellian distribution enjoys gelfand shilov regularizing properties with respect to the velocity variable and gevrey regularizing properties with respect to the position variable

estimates of clinically useful measures in competing risks survival analysis competing risks occur frequently in follow up clinical studies to assess treatment or covariate effects measures of clinical impact based on crude cumulative incidence should be considered such as relative risks or the absolute risk reduction in this work transformation models through suitable link functions provide a straightforward approach to obtain point and interval estimates of such measures an extension of the klein and andersen proposal based on pseudo values is considered non additive effects were tested by interactions between baseline spline function on time and covariates the methods are applied to the evaluation of the impact of axillary lymph node nanometastases on metastatic relapse of breast cancer patients further a literature data set on prostate cancer was used for illustration

a new regularization mechanism for the boltzmann equation without cut off we apply recent results on regularity for general integro differential equations to derive a priori estimates in holder spaces for the space homogeneous boltzmann equation in the non cut off case we also show an a priori estimate in l infty which applies in the space inhomogeneous case as well provided that the macroscopic quantities remain bounded

decompositions of gelfand shilov kernels into kernels of similar class we prove that any linear operator with kernel in a gelfand shilov space is a composition of two operators with kernels in the same gelfand shilov space we also give links on numerical approximatio

l2 solution of linear non cutoff boltzmann equation with boundary conditions abstract in this paper we are concerned about the existence of solution to linear non cutoff boltzmann equation with boundary conditions in 9 and 18 the existence of the solutions to the kinetic equation and linear boltzmann equation were obtained by characteristic line and iteration methods however their methods are not applicable in the context of non cutoff linear operators to overcome this difficulty we cut off the non cutoff linear operator l to l r the latter is compatible with the method in 9 via this process we are able to use the sequence of solutions associated to l r to approximate the solution associated to l which is corresponding to the original equation in turn obtain the weak solutions of linear non cutoff boltzmann equation with specular and diffusion reflection boundary conditions

local existence lower mass bounds and a new continuation criterion for the landau equation abstract we consider the spatially inhomogeneous landau equation with soft potentials first we establish the short time existence of solutions assuming the initial data has sufficient decay in the velocity variable and regularity no decay assumptions are made in the spatial variable next we show that the evolution instantaneously spreads mass throughout the domain the resulting lower bounds are sub gaussian which we show is optimal the proof of mass spreading is based on a stochastic process and makes essential use of nonlocality by combining this theorem with prior results we derive two important applications c smoothing even for initial data with vacuum regions and a continuation criterion the solution can be extended as long as the mass and energy densities stay bounded from above this is the weakest condition known to prevent blow up in particular it does not require a lower bound on the mass density or an upper bound on the entropy density

analysis of transformation models with censored data summary in this paper we consider a class of semi parametric transformation models under which an unknown transformation of the survival time is linearly related to the covariates with various completely specified error distributions this class of regression models includes the proportional hazards and proportional odds models inference procedures derived from a class of generalised estimating equations are proposed to examine the covariate effects with censored observations numerical studies are conducted to investigate the properties of our proposals for practical sample sizes these transformation models coupled with the new simple inference procedures provide many useful alternatives to the cox regression model in survival analysis

well posedness of spatially homogeneous boltzmann equation with full range interaction in the present work we give the coercivity estimates for the boltzmann collision operator q without angular cut off to clarify in which case the functional langle q g f f rangle will become the truly sub elliptic based on this observation and commutator estimates in alexandre et al arch rat mech anal 198 39 123 2010 the upper bound estimates for the collision operator in chen and he arch rat mech anal 201 2 501 548 2011 and the stability results in desvillettes and mouhot arch rat mech anal 193 2 227 253 2009 in the function space l 1 q cap h n we establish global well posedness or local well posedness for the spatially homogeneous boltzmann equation with full range interaction covering most of physical collision kernels

smoothing effects for classical solutions of the full landau equation in this work we consider the smoothness of the solutions to the full landau equation in particular we prove that any classical solutions such as the ones obtained by guo in a close to equilibrium setting become immediately smooth with respect to all variables this shows that the landau equation is a nonlinear and nonlocal analog of an hypoelliptic equation

sharp anisotropic estimates for the boltzmann collision operator and its entropy production abstract this article provides sharp constructive upper and lower bound estimates for the boltzmann collision operator with the full range of physical non cut off collision kernels n and s 0 1 in the trilinear l 2 r n energy q g f f these new estimates prove that for a very general class of g v the global diffusive behavior on f in the energy space is that of the geometric fractional derivative semi norm identified in the linearized context in our earlier works gressman and strain 2010 15 2011 16 we further prove new global entropy production estimates with the same anisotropic semi norm this resolves the longstanding widespread heuristic conjecture about the sharp diffusive nature of the non cut off boltzmann collision operator in the energy space l 2 r n