a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

a class of p q laplacian type equation with concave convex nonlinearities in bounded domain abstract in this paper our main purpose is to establish the existence of multiple solutions of a class of p q laplacian equation involving concave convex nonlinearities p u q u v x u r 2 u u p 2 u f x u x u 0 x where is a bounded domain in r n 0 1 r q p n and p n p n p is the critical sobolev exponent s u div u s 2 u is the s laplacian of u we prove that for any 0 0 is a constant there is a 0 such that for every 0 the above problem possesses infinitely many weak solutions we also obtain some results for the case 1 q p r p the existence results of solutions are obtained by variational methods

linear rank tests for interval censored data with application to pcb levels in adipose tissue of transformer repair workers linear rank statistics are described for testing for differences between groups when the data are interval censored the statistics are closely related to those described by prentice for right censored data problems in calculating the statistics are discussed and several approaches to computation including estimation of the efficient rank scores are described results from a small simulation study are presented the methods are applied to data from a study relating tissue levels of pcbs to occupational exposure

a multiple imputation approach to cox regression with interval censored data we propose a general semiparametric method based on multiple imputation for cox regression with interval censored data the method consists of iterating the following two steps first from finite interval censored but not right censored data exact failure times are imputed using tanner and wei s poor man s or asymptotic normal data augmentation scheme based on the current estimates of the regression coefficient and the baseline survival curve second a standard statistical procedure for right censored data such as the cox partial likelihood method is applied to imputed data to update the estimates through simulation we demonstrate that the resulting estimate of the regression coefficient and its associated standard error provide a promising alternative to the nonparametric maximum likelihood estimate our proposal is easily implemented by taking advantage of existing computer programs for right censored data

multiple solutions for a class of p x laplacian equations in involving the critical exponent in this paper we first establish a principle of concentration compactness in then based on this concentration compactness principle we study the existence of solutions for a class of p x lapl

existence and multiplicity of solutions for a discontinuous problems with critical sobolev exponents abstract in this paper we consider the equation p u u p 2 u f x u in r n with discontinuous nonlinearity where 1 p n 0 is a real parameter and p n p n p is the critical sobolev exponent under proper conditions on f applying the nonsmooth critical point theory for locally lipschitz functionals we obtain at least one nontrivial nonnegative solution provided that 0 and for any k n it has k pairs of nontrivial solutions if k where 0 and k are positive numbers in particular we obtain the existence results for f is discontinuous in just one point

p laplacian problems with critical sobolev exponents abstract we study the existence and multiplicity of solutions of p laplacian problems with critical sobolev exponents using variational methods

two solutions for an elliptic equation with fast increasing weight and concave convex nonlinearities abstract we prove the existence of two nonnegative nontrivial solutions for the equation div k x u a x k x u q 2 u b x k x u p 2 u x r n where n 3 k x exp x 4 2 and the potentials a and b have indefinite sign and satisfy some mild integrability conditions the results hold when a has small norm in a suitable weighted lebesgue space

a markov chain monte carlo em algorithm for analyzing interval censored data under the cox proportional hazards model summary this paper proposes a monte carlo em mcem algorithm for fitting the proportional hazards model for interval censored failure time data the algorithm generates orderings of the failures from their probability distribution under the model we maximize the average of the log likelihoods from these completed data sets to obtain updated parameter estimates as with the standard cox model this algorithm does not require the estimation of the baseline hazard function the performance of the algorithm is evaluated using simulations and the method is applied to data from aids and cancer studies our results indicate that our method produced more precise and unbiased estimates than methods of right and midpoint imputation

multiple positive solutions to a class of kirchhoff equation on r3 with indefinite nonlinearity abstract we study the existence and multiplicity of positive solutions to a class of kirchhoff equation 1 b r 3 u x 2 d x u x u x v x u x p 2 u x k x u x u x u h 1 r 3 when v x is sign changing in r 3 we prove that there is 0 such that the kirchhoff equation possesses at least one positive solution for 0 1 and at least two positive solutions for 1 1 here 1 is the first eigenvalue of u u k x u u h 1 r 3 a positive eigenfunction corresponding to 1 is denoted by e 1 an interesting phenomena is that the term b r 3 u 2 d x u can be used to compete with the indefinite nonlinearity and we do not assume the condition r 3 v x e 1 p d x 0 which has been shown to be a necessary condition to the existence of positive solutions for semilinear elliptic equations with indefinite nonlinearity alama and tarantello 1993

nontrivial solution for a semilinear elliptic equation in unbounded domain with critical sobolev exponent where is an unbounded domains with smooth boundary in r 2 2n n 2 a x c1 satisfies the following conditions a1 a ln 2 a2 x a x 0 such that b 4 when is a bounded domain with smooth boundary in r n 5 similar problem has been studied by many mathematicians for example in 3 brezis and nirenberg studied problem p in 4 capozzi et al prove that when

existence of solutions of a non linear eigenvalue problem with a variable weight abstract we study the non linear minimization problem on h 0 1 l q with q 2 n n 2 0 and n 4 inf u h 0 1 u l q 1 a x u u 2 u 2 where a x s presents a global minimum at x 0 0 with x 0 in order to describe the concentration of u x around x 0 one needs to calibrate the behavior of a x s with respect to s the model case is inf u h 0 1 u l q 1 x u k u 2 u 2 in a previous paper dedicated to the same problem with 0 we showed that minimizers exist only in the range k n q which corresponds to a dominant non linear term on the contrary the linear influence for k n q prevented their existence the goal of this present paper is to show that for 0 1 0 k q 2 and k n q 2 minimizers do exist

elliptic problems with lack of compactness via a new fixed point theorem abstract this paper provides a new fixed point theorem for increasing self mappings g b b of a closed ball b x where x is a banach semilattice which is reflexive or has a weakly fully regular order cone x by means of this fixed point theorem we are able to establish existence results of elliptic problems with lack of compactness

multiple positive solutions to a class of modified nonlinear schrodinger equations abstract this paper is concerned with the existence and multiplicity of positive solutions of the following equation u u 2 u 2 u a x u p 2 u k x u where u h 1 r we will prove that the modified term 2 u 2 u is helpful to find multiple positive solutions in the case of the nonlinearity with sign changing coefficient a x surprisingly we do not need a sign condition r n a x e 1 p d x 0 which has been proven to be a necessary condition to the existence of positive solutions for semilinear elliptic equations with sign changing nonlinearity alama and tarantello 1993 1

solutions of the quasilinear elliptic problem with a critical sobolev hardy exponent and a hardy type term abstract in the present paper the quasilinear elliptic problem with a critical sobolev hardy exponent and a hardy type term is considered by means of a variational method the existence of nontrivial solutions to the problem is obtained

regression analysis of failure time data with informative interval censoring interval censoring arises when a subject misses prescheduled visits at which the failure is to be assessed most existing approaches for analysing interval censored failure time data assume that the censoring mechanism is independent of the true failure time however there are situations where this assumption may not hold in this paper we consider such a situation in which the dependence structure between the censoring variables and the failure time can be modelled through some latent variables and a method for regression analysis of failure time data is proposed the method makes use of the proportional hazards frailty model and an em algorithm is presented for estimation finite sample properties of the proposed estimators of regression parameters are examined through simulation studies and we illustrate the method with data from an aids study

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

higher order singular problems of caffarelli kohn nirenberg lin type abstract we prove the existence of nontrivial critical points of the functional j u r n 1 p x a k u p h x x a k u p 1 q q x x b u q d x related to the caffarelli kohn nirenberg inequality and its higher order variant by lin as a consequence we obtain nontrivial solutions of the degenerate elliptic equation x a p u p 2 u h x x a k p u p 2 u q x x b q u q 2 u we also show that when p 2 j has infinitely many critical points

growth of balls of holomorphic sections and energy at equilibrium let l be a big line bundle on a compact complex manifold x given a non pluripolar compact subset k of x and a continuous hermitian metric e on l we define the energy at equilibrium of k as the monge ampere energy of the extremal psh weight associated to k we prove the differentiability of the energy at equilibrium with respect to and we show that this energy describes the asymptotic behaviour as k of the volume of the sup norm unit ball induced by k k on the space of global holomorphic sections h 0 x kl as a consequence of these results we recover and extend rumely s robin type formula for the transfinite diameter we also obtain an asymptotic description of the analytic torsion and extend yuan s equidistribution theorem for algebraic points of small height to the case of a big line bundle

existence of multiple positive solutions for a p q laplacian system with critical nonlinearities abstract in this paper our main purpose is to establish the existence of multiple positive solutions of a p q laplacian system with convex and sobolev critical nonlinearities by some standard variational methods whose key is to construct homotopies between and levels of the functional j and some analytical techniques

the principle of concentration compactness in lp x spaces and its application abstract in this paper we establish a principle of concentration compactness in l p x spaces and apply it to obtain the existence of solutions for p x laplacian equations with critical growth

a flexible computationally efficient method for fitting the proportional hazards model to interval censored data the proportional hazards model ph is currently the most popular regression model for analyzing time to event data despite its popularity the analysis of interval censored data under the ph model can be challenging using many available techniques this article presents a new method for analyzing interval censored data under the ph model the proposed approach uses a monotone spline representation to approximate the unknown nondecreasing cumulative baseline hazard function formulating the ph model in this fashion results in a finite number of parameters to estimate while maintaining substantial modeling flexibility a novel expectation maximization em algorithm is developed for finding the maximum likelihood estimates of the parameters the derivation of the em algorithm relies on a two stage data augmentation involving latent poisson random variables the resulting algorithm is easy to implement robust to initialization enjoys quick convergence and provides closed form variance estimates the performance of the proposed regression methodology is evaluated through a simulation study and is further illustrated using data from a large population based randomized trial designed and sponsored by the united states national cancer institute

on nonlocal choquard equations with hardy littlewood sobolev critical exponents abstract we consider the following nonlinear choquard equation with dirichlet boundary condition u u 2 x y d y u 2 2 u f u in where is a smooth bounded domain of r n 0 n 3 0 n and 2 is the critical exponent in the sense of the hardy littlewood sobolev inequality under suitable assumptions on different types of nonlinearities f u we are able to prove some existence and multiplicity results for the equation by variational methods

solutions for a class of quasilinear choquard equations with hardy littlewood sobolev critical nonlinearity abstract in this article we consider the quasilinear choquard equation with critical nonlinearity in r n e 2 u v x u e 2 u u 2 r n u 2 2 x y d y u 2 2 2 u h x u u where 0 n n 3 2 2 n n 2 is the critical exponent in the sense of hardy littlewood sobolev inequality e is a real parameter by using a change of variables the quasilinear equations are reduced to a semilinear one whose associated functionals are well defined in the usual sobolev space and satisfy the geometric conditions of the mountain pass theorem under suitable assumptions on v and h we investigate the existence and multiplicity of solutions for the above problem by using the mountain pass theorem and index theory in order to overcome the lack of compactness we apply the concentration compactness principle

a local likelihood proportional hazards model for interval censored data we discuss the use of local likelihood methods to fit proportional hazards regression models to right and interval censored data the assumed model allows for an arbitrary smoothed baseline hazard on which a vector of covariates operates in a proportional manner and thus produces an interpretable baseline hazard function along with estimates of global covariate effects for estimation we extend the modified em algorithm suggested by betensky lindsey ryan and wand we illustrate the method with data on times to deterioration of breast cosmeses and hiv 1 infection rates among haemophiliacs

rank based inference in the proportional hazards model for interval censored data summary a marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed this approach maximises a likelihood that is the sum over all rankings of the data that are consistent with the observed censoring intervals as in the usual proportional hazards model the method does not require specification of the baseline hazard function the score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model with respect to a certain distribution of rankings a gibbs sampling scheme is given to generate rankings from this distribution and stochastic approximation is used to solve the score equations simulation results under various censoring schemes give point estimates that are close to estimates obtained using actual failure times

domain level covariance analysis for multilevel survey data with structured nonresponse health care quality surveys in the united states are administered to individual respondents i e hospital patients health plan members to evaluate the performance of health care organizations i e hospitals health plans which thus constitute estimation domains for better understanding and more parsimonious reporting of dimensions of quality we analyze relationships among quality measures at the domain level rather than specifying a full parametric model for the observed responses and the nonresponse patterns at the lower patient level we first fit generalized variance covariance functions that take into account nonresponse patterns in the survey responses then specify a likelihood function for the domain mean responses using these generalized variance covariance functions this allows us to model directly the relationships among domain means for different items because the response scales are bounded we assume that these means follow a truncated multivariate normal distribution we calcu

dynamics of regular polynomial endomorphisms of c k a regular polynomial self mapping of complex euclidean space has a continuous extension to the hyperplane at infinity the induced mapping at infinity is used to describe the dynamics of the self mapping in a neighborhood of infinity a theory of external rays is developed to provide the connection between the behavior at infinity and the behavior on the finite plane

multiplicity result for a singular elliptic equation with indefinite nonlinearity via constraint minimization argument and delicate energy estimates we show the existence of two positive solutions for a singular elliptic equation with indefinite nonlinearity

nonlinear perturbations of a periodic elliptic problem with critical growth abstract using the well known mountain pass theorem due to ambrosetti and rabinowitz we establish conditions for the existence of a positive solution for a class of nonlinear elliptic problems in r n with critical growth

multiplicity of positive solutions for some quasilinear elliptic equation in rnwith critical sobolev exponent consider the equation pu g x u p 2u f x u p 2u 1 in rn where 1 0 be the principal eigenvalue of pu g x u p 2uinrn rng x u p 0 2 withu 1 0 the associated eigenfunction we prove i equation 1 has at least one positive solution if 0 1 ii suppose rn f x u 1 p 1such that 1 has at least one positive solution for 1 0 moreover ifp 2 there exists 0 1such that 1 has at least two positive solutions for 1 0

solutions for semilinear elliptic problems with critical sobolev hardy exponents in rn abstract let n 3 0 s 2 0 n 2 2 2 and 2 s 2 n s n 2 be the critical sobolev hardy exponents via variational methods and the analytic technique we prove the existence of a nontrivial solution to the singular semilinear problem u u x 2 u u 2 s 2 x s u f u u h r 1 r n for n 4 0 1 and suitable functions f u

multiple positive solutions for a critical quasilinear elliptic system abstract the existence of cat positive solutions for the p laplacian system with convex and sobolev critical nonlinearities is obtained by some standard variational methods whose key is to construct homotopies between and levels of the functional j and some analytical techniques

ground states of degenerate quasilinear schrodinger equation with vanishing potentials abstract in this paper we study the existence of nontrivial ground state solutions for the following class of p laplacian type equation div a x u v x x p u p 2 u k x x p f u in r n where 1 p n n 3 n p p e 1 d 1 e p p e n p n d p critical hardy sobolev exponent f has a quasicritical growth v and k are nonnegative potentials the function a satisfies a x u c 0 x p h 0 x u p 1 c 0 1 x p h 1 x u p 1 for any r n a e x r n for any two positive functions h 1 l l o c r n h 0 l p p 1 r n with p p

existence of solutions for an elliptic equation with indefinite weight abstract we consider the elliptic equation with indefinite weight u v x u f x u u h 1 r n where v x is a function possibly changing sign in r n under certain assumptions on f x u we obtain the existence of m n pairs of nontrivial solutions where m n and the m and n are all integers

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

solutions for quasilinear elliptic problems with critical sobolev hardy exponents abstract let n 3 2 p n 0 s p and p s p n s n p via the variational methods and analytic technique we prove the existence of nontrivial solution to the singular quasilinear problem p u u p 2 u u p s 2 x s u f u u w r 1 p r n for n p 2 and suitable functions f u

positive solutions for a critical p laplacian problem with a kirchhoff term abstract in this article the following p laplacian problem with kirchhoff term and critical exponent is studied a b r n u p d x p u u p 1 h x x r n u d 1 p r n where a 0 b 0 1 p n p n p n p p u d i v u p 2 u and h l p p 1 r n is nonzero and nonnegative when 0 with the help of the recent result of b sciunzi adv math 291 2016 12 23 infinitely many positive solutions are obtained by some analysis techniques while 0 by the variational method some results about positive solutions are obtained

existence and nondegeneracy of ground states in critical free boundary problems abstract existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature the corresponding study of higher critical points was recently initiated in jerison and perera 2018 0000 in particular the existence and nondegeneracy of a mountain pass point in a superlinear and subcritical free boundary problem related to plasma confinement was proved in jerison and perera 2018 in this paper we study ground states of a critical free boundary problem related to the brezis nirenberg problem 1983 we extend the results of jerison and perera 2018 to this problem by combining the method introduced there with the concentration compactness principle to overcome the difficulties arising from lack of compactness

bifurcation measures and quadratic rational maps we study critical orbits and bifurcations in the curves per1 within the moduli space m2 of quadratic rational maps f p 1 p 1 for each 2 c the curve per1 is dened by the condition that the map has a xed point of multiplier we prove that the curve per1 contains innitely many postcritically n ite maps if and only if 0 addressing a special case of bd2 conjecture 1 4 we also show that the two critical points of f dene distinct bifurcation measures along per 1

dynamics of rational maps lyapunov exponents bifurcations and capacity let l f log df d f denote the lyapunov exponent of a rational map f p 1 p 1 in this paper we show that for any holomorphic family of rational maps f x of degree d 1 t f dd c l f defines a natural positive 1 1 current on x supported exactly on the bifurcation locus of the family the proof is based on the following potential theoretic formula for the lyapunov exponent here f c 2 c 2 is a homogeneous polynomial lift of f g f is the escape rate function of f and capk f is the homogeneous capacity of the filled julia set of f we show in particular that the capacity of k f is given explicitly by the formula where res f is the resultant of the polynomial coordinate functions of f we introduce the homogeneous capacity of compact circled and pseudoconvex sets k c 2 and show that the levi measure determined by the geometry of k is the unique equilibrium measure such k c 2 correspond to metrics of non negative curvature on p 1 and we obtain a variational characterization of curvature

on some fourth order semilinear elliptic problems in r n the existence of two solutions for a fourth order semilinear elliptic problem involving critical growth from the viewpoint of sobolev embedding was established the basic tools used in the analysis were the mountain pass theorem constrained minimization and concentration compactness principle the existence of positive principle eigenvalues for the corresponding linear elliptic problem was also investigated

effects of mid point imputation on the analysis of doubly censored data doubly censored data arise in some cohort studies of the aids incubation period because the time of infection may be known only up to an interval defined by two successive screening tests for hiv antibody a simple analytic approach is to impute the infection time by the mid point of the interval and then apply standard survival techniques for right censored data the objective of this paper is to investigate the statistical properties of such a mid point imputation approach we investigated the asymptotic bias of the kaplan meier estimate coverage probabilities of associated confidence intervals bias in hazard ratio and the size of the logrank test we show that the statistical properties of mid point imputation depend strongly on the underlying distributions of infection times and the incubation periods and the width of the interval between screening tests in the absence of treatment the median incubation period of hiv infection is approximately 10 years and we conclude that for this situation mid point imputation is a reasonable procedure for interval widths of 2 years or less

maximization of the marginal likelihood of grouped survival data summary grouped failure time data occur in studies where subjects are monitored periodically to determine whether failure has occurred in the intervening interval here the model under consideration is cox s 1972 1975 proportional hazards model but the commonly used method of partial likelihood needs modification with grouped data due to a potentially large number of ties this paper demonstrates how the monte carlo em algorithm wei tanner 1990 can be used on grouped data to find the maximum likelihood estimate from the marginal likelihood based on the incomplete ranks of the event times the methodology is exemplified with a data set with precise failure times after artificially introducing grouping

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

on an electromagnetic schrodinger equation with critical growth abstract in this paper we consider the electromagnetic schrodinger problem i a 2 u v x u k x u 2 2 u in h a v 1 r n see the definition in section 1 according as whether the indefinite linear is resonant or nonresonant we structure different direct sums of h a v 1 r n then by applying the linking theorem twice to the corresponding functional we establish the existence results

a score test for association of a longitudinal marker and an event with missing data often clinical studies periodically record information on disease progression as well as results from laboratory studies that are believed to reflect the progressing stages of the disease a primary aim of such a study is to determine the relationship between the lab measurements and a disease progression if there were no missing or censored data these analyses would be straightforward however often patients miss visits and return after their disease has progressed in this case not only is their progression time interval censored but their lab test series is also incomplete in this article we propose a simple test for the association between a longitudinal marker and an event time from incomplete data we derive the test using a very intuitive technique of calculating the expected complete data score conditional on the observed incomplete data conditional expected score test cest the problem was motivated by data from an observational study of patients with diabetes

nodal solutions for p laplace equations with critical growth abstract this paper is concerned with the existence and nodal character of the nontrivial solutions for the following quasilinear elliptic equations involving critical sobolev exponents 1 i 1 n x i u p 2 u x i u p 2 u u p 2 u f u u w r 1 p r n where p 2 and p np n p is the critical sobolev exponent for the embedding w r 1 p r n l p r n the function f satisfies some conditions given by f1 f2 f3 in the paper the main results obtained in this paper are that there exists at least a pair of nontrivial solutions for eq 1 provided that n p2 and there exists at least a pair of nontrivial solutions uk uk of eq 1 for each k n 0 such that both uk and uk possess exactly k nodes provided that f t 0 for t 0 and n p2 p 1 p

two positive solutions of a class of schrodinger poisson system with indefinite nonlinearity abstract we study the existence and multiplicity of positive solutions of a class of schrodinger poisson system u u l x u k x u p 2 u h x u in r 3 l x u 2 in r 3 where 4 p 6 k c r 3 k changes sign in r 3 and lim x k x k 0 we mainly prove the existence of at least two positive solutions in the case that 1 and near 1 where 1 is the first eigenvalue of i d in h 1 r 3 with weight function h whose corresponding eigenfunction is denoted by e 1 an interesting phenomenon is that we do not need the condition r 3 k x e 1 p d x 0 which has been shown to be a necessary condition to the existence of positive solutions for semilinear elliptic equations with indefinite nonlinearity see e g s alama g tarantello on semilinear elliptic equations with indefinite nonlinearities calc var partial differential equations 1 1993 439 475

multiplicity of positive solutions for a p q laplacian system with concave and critical nonlinearities abstract in this paper we consider a p q laplacian system with concave and sobolev critical nonlinearities by using the n ehari manifold fibering maps and the lusternik schnirelman category we prove that the problem has at least cat 1 distinct positive solutions where cat denotes the lusternik schnirelman category of in itself

multiple imputation for interval censored data with auxiliary variables we propose a non parametric multiple imputation scheme npmle imputation for the analysis of interval censored survival data features of the method are that it converts interval censored data problems to complete data or right censored data problems to which many standard approaches can be used and that measures of uncertainty are easily obtained in addition to the event time of primary interest there are frequently other auxiliary variables that are associated with the event time for the goal of estimating the marginal survival distribution these auxiliary variables may provide some additional information about the event time for the interval censored observations we extend the imputation methods to incorporate information from auxiliary variables with potentially complex structures to conduct the imputation we use a working failure time proportional hazards model to define an imputing risk set for each censored observation the imputation schemes consist of using the data in the imputing risk sets to create an exact event time for each interval censored observation in simulation studies we show that the use of multiple imputation methods can improve the efficiency of estimators and reduce the effect of missing visits when compared to simpler approaches we apply the approach to cytomegalovirus shedding data from an aids clinical trial in which cd4 count is the auxiliary variable

isotriviality is equivalent to potential good reduction for endomorphisms of pn over function fields abstract let k k c be the function field of a complete non singular curve c over an arbitrary field k the main result of this paper states that a morphism p k n p k n is isotrivial if and only if it has potential good reduction at all places v of k this generalizes results of benedetto for polynomial maps on p k 1 and baker for arbitrary rational maps on p k 1 we offer two proofs the first uses algebraic geometry and geometric invariant theory and it is new even in the case n 1 the second proof uses non archimedean analysis and dynamics and it more directly generalizes the proofs of benedetto and baker we will also give two applications the first states that an endomorphism of p k n of degree at least two is isotrivial if and only if it has an isotrivial iterate the second gives a dynamical criterion for whether after base change a locally free coherent sheaf e of rank n 1 on c decomposes as a direct sum l l of n 1 copies of the same invertible sheaf l

the nehari manifold for a semilinear elliptic problem with the nonlinear boundary condition abstract using the nehari manifold and fibering maps we prove the existence theorem of the nonlinear boundary problem u u u p 2 u for x u n u q 2 u for x on a bounded domain r n we discuss how the nehari manifold changes as changes and show how the existence of solutions depends on the properties of the nehari manifold

multiplicity of positive solutions to a p q laplacian equation involving critical nonlinearity abstract in this paper our main purpose is to establish the existence of multiple solutions of a p q laplacian equation with convex and sobolev critical nonlinearity by some standard variational methods whose key is to construct homotopies between and levels of the functional i and some analytical techniques

on ground state solutions for quasilinear elliptic equations with a general nonlinearity in the critical growth abstract in this paper we consider the following problem p u v u p 2 u f u u w 1 p r n where 1 p n and f has critical growth the purpose of this paper is to study the existence of the ground state solution for a class of quasilinear elliptic equations some recent results are extended

multiple solutions for nonhomogeneous elliptic equations involving critical sobolev exponent we consider the following problem where is continuous on r n and h x 0 by using ekeland s variational principle and the mountain pass theorem without ps conditions through a careful inspection of the energy balance for the approximated solutions we show that the probelm has at least two solutions for some 0 and 0 in particular if p 2 in a different way we prove that problem with 1 and h x 0 has at least two positive solutions as

semiparametric regression analysis of interval censored data summary we propose a semiparametric approach to the proportional hazards regression analysis of interval censored data an em algorithm based on an approximate likelihood leads to an m step that involves maximizing a standard cox partial likelihood to estimate regression coefficients and then using the breslow estimator for the unknown baseline hazards the e step takes a particularly simple form because all incomplete data appear as linear terms in the complete data log likelihood the algorithm of turnbull 1976 journal of the royal statistical society series b38 290 295 is used to determine times at which the hazard can take positive mass we found multiple imputation to yield an easily computed variance estimate that appears to be more reliable than asymptotic methods with small to moderately sized data sets in the right censored survival setting the approach reduces to the standard cox proportional hazards analysis while the algorithm reduces to the one suggested by clayton and cuzick 1985 applied statistics34 148 156 the method is illustrated on data from the breast cancer cosmetics trial previously analyzed by finkelstein 1986 biometrics42 845 854 and several subsequent authors