efficient estimation for the proportional hazards model with interval censoring the maximum likelihood estimator mle for the proportional hazards model with case 1 interval censored data is studied it is shown that the mle for the regression parameter is asymptotically normal with n convergence rate and achieves the information bound even though the mle for the baseline cumulative hazard function only converges at n 1 3 rate estimation of the asymptotic variance matrix for the mle of the regression parameter is also considered to prove our main results we also establish a general theorem showing that the mle of the finite dimensional parameter in a class of semiparametric models is asymptotically efficient even though the mle of the infinite dimensional parameter converges at a rate slower than n the results are iliustrated by applying them to a data set from a tumorigenicity study

rotation numbers eigenvalues and the poincare birkhoff theorem using the relation between rotation numbers and eigenvalues we prove the existence of nontrivial t periodic solutions having precise oscillatory properties for a class of asymptotically linear second order differential equations

semiparametric nonlinear mixed effects models and their applications nonlinear mixed effects models nlmms and self modeling nonlinear regression semor models are often used to fit repeated measures data they use a common function shared by all subjects to model variation within each subject and some fixed and or random parameters to model variation between subjects the parametric nlmm may be too restrictive and the semiparametric semor model ignores correlations within each subject in this article we propose a class of semiparametric nonlinear mixed effects models snmms that extend nlmms semor models and many other existing models in a natural way a snmm assumes that the mean function depends on some parameters and nonparametric functions the parameters provide an interpretable data summary the nonparametric functions provide flexibility to allow the data to decide some unknown or uncertain components such as the shape of the mean response over time a second stage model with fixed and random effects is used to model the parameters smoothing splines are us

a two dimensional version of the goldschmidt sims conjecture abstract the goldschmidt sims conjecture asserts that there is a finite number of conjugacy classes of edge transitive lattices in the automorphism group of a regular tree with prime valence we prove a similar theorem for irreducible lattices transitive on the 2 cells of the product of two regular trees of prime valences

on a class of functionals invariant under a zn action abstract this document considers a system of ordinary differential equations of the form q v sub q t q f t where f and v are periodic in t v is periodic in the components of q q sub 1 q sub m and the mean value of f vanishes by showing that a corresponding functional is invariant under a natural z sub n action a simple variational argument yields at least n 1 distinct periodic solutions of more general versions of are also treated as is a class of neumann problems for semilinear elliptic partial differential equations

poincare birkhoff theorems in random dynamics we propose a generalization of the poincare birkhoff theorem on area preserving twist maps to area preserving twist maps f that are random with respect to an ergodic probability measure in this direction we will prove several theorems concerning existence density and type of the fixed points to this end first we introduce a randomized version of generalized generating functions and verify the correspondence between its critical points and the fixed points of f a fact which we successively exploit in order to prove the theorems the study we carry out needs to combine probabilistic techniques with methods from nonlinear pde and from differential geometry notably moser s method and conley zehnder theory our stochastic model in the periodic case coincides with the classical setting of the poincare birkhoff theorem

periodic solutions of second order equations via rotation numbers abstract we consider the problem of the existence and multiplicity of periodic solutions associated to a class of scalar equations of the form x f t x 0 the class considered is such that the behaviour of its solutions near zero and infinity can be compared two suitable piecewise linear systems we show how a rotation number approach together with the poincare birkhoff theorem and the phase plane analysis of the spiral properties allows to obtain multiplicity results in terms of the gap between the rotation numbers of the referred piecewise linear systems at zero and at infinity these systems may also be resonant in particular our approach can be used to deal with the problems without both global existence of the cauchy problems associated to the equation and the sign assumption on f the typical example is a partially superlinear second order equation our main result generalizes some classical results of jacobowitz and hartman among others

on the order of borel subgroups of group amalgams and an application to locally transitive graphs abstract a permutation group is called semiprimitive if each of its normal subgroups is either transitive or semiregular given nontrivial finite transitive permutation groups l 1 and l 2 with l 1 not semiprimitive we construct an infinite family of rank two amalgams of permutation type l 1 l 2 and borel subgroups of strictly increasing order as an application we show that there is no bound on the order of edge stabilisers in locally l 1 l 2 graphs we also consider the corresponding question for amalgams of rank k 3 we completely resolve this by showing that the order of the borel subgroup is bounded by the permutation type l 1 l k only in the trivial case where each of l 1 l k is regular

universal presheaves on group geometries and modular representations abstract we extend the ideas of sheaf homology on buildings m a ronan and s d smith j algebra 96 1985 319 346 to more general geometries with transitive automorphism groups the main technical result is the construction of a universal extension of certain partial sheaves this guarantees a rich supply of sheaves on such geometries computation of zero homology then affords representations of the group we consider various applications of the technique for example to modular irreducibles for sporadic simple groups

coexistence of bouncing and classical periodic solutions of generalized lazer solimini equation abstract the paper deals with the singular differential equation x g x p t where g has a weak singularity at x 0 sufficient conditions for a coexistence of two types of periodic solutions are presented the first type is a classical periodic solution which is strictly positive on r and does not reach the singularity the second type is a bouncing periodic solution which reaches the singularity at isolated points in particular we state a constant k 0 such that there exist at least two 2 periodic bouncing solutions having their maximum less than k and at least one 2 periodic classical solution having its minimum greater than k the proofs are based on the ideas of the poincare birkhoff twist map theorem and approximation principles

bouncing solutions of an equation with attractive singularity for any n m 2 in it is proved the existence of 2m periodic solutions with n bouncings in each period for a second order forced equa tion with attractive singularity by using the approach of successor map and poincare birkho twist theorem

generic results for the existence of nondegenerate periodic solutions of some differential systems with periodic nonlinearities the infinite dimensional version of sard s theorem due to smale 9 is very useful in the study of boundary value problems of the form here a is a cl fredholm map from a banach space e to a banach space f in some applications the existence of a solution is proved only when

a topological version of the poincare birkhoff theorem with two fixed points the main result of this paper gives a topological property satisfied by any homeomorphism of the annulus mathbb a mathbb s 1 times 1 1 isotopic to the identity and with at most one fixed point this generalizes the classical poincare birkhoff theorem because this property certainly does not hold for an area preserving homeomorphism h of mathbb a with the usual boundary twist condition we also have two corollaries of this result the first one shows in particular that the boundary twist assumption may be weakened by demanding that the homeomorphism h has a lift h to the strip tilde mathbb a mathbb r times 1 1 possessing both a forward orbit unbounded on the right and a forward orbit unbounded on the left as a second corollary we get a new proof of a version of the conley zehnder theorem in mathbb a if a homeomorphism of mathbb a isotopic to the identity preserves the area and has mean rotation zero then it possesses two fixed points

inference for a linear regression model with an interval censored covariate interval censored observations of a response variable are a common occurrence in medical studies and usually result when the response is the elapsed time until some event whose occurrence is periodically monitored in this paper we consider a multivariate regression setting in which the explanatory variable is interval censored use of an ad hoc method of analysis for such data such as taking the midpoint of the interval censored covariate and applying ordinary least squares is not in general valid we develop a likelihood approach together with a two step conditional algorithm to jointly estimate the regression coefficients as well as the marginal distribution of the covariate the resulting estimators are asymptotically normal the performance of the method is assessed via simulations and illustrated using data from a recent hiv aids clinical trial to assess the association between waiting time between indinavir failure and subsequent viral load at enrolment extensions of the procedure to other parametric distributions are discussed

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

infinity of subharmonics for asymmetric duffing equations with the lazer leach dancer condition abstract in this paper based on a generalized version of the poincare birkhoff twist theorem by franks we establish the existence of infinitely many subharmonics for the asymmetric duffing equation with the classical lazer leach dancer condition as a consequence of our result we obtain a sufficient and necessary condition for existence of arbitrarily large amplitude periodic solutions for a class of asymmetric duffing equations at resonance

rotation vectors and fixed points of area preserving surface diffeomorphisms we consider the homological rotation vectors for area preserving diffeomorphisms of compact surfaces which are homotopic to the identity there are two main results the first is that if 0 is in the interior of the convex hull of the rotation vectors for such a diffeomorphism then f has a fixed point of positive index the second result asserts that if f has a vanishing mean rotation vector then f has a fixed point of positive index there are several applications including a new proof of the arnold conjecture for area preserving diffeomorphisms of compact surfaces in this paper we investigate area preserving diffeomorphisms of compact surfaces we are concerned with rotation vectors defined in terms of homology which can be associated to the points of the surface there are two main results the first is that if f is an area preserving diffeomorphism of a compact surface which is homotopic to the identity and 0 is in the interior of the convex hull of the rotation vectors of f then f has a fixed point of positive index the second result concerns the mean rotation vector of f it asserts that if this vector vanishes then f has a fixed point of positive index a special case of this second result when the surface in question is a surface of genus zero was proved in f5 in 6 we give several applications including a new proof of the arnold conjecture for area preserving diffeomorphisms of compact surfaces

ghost circles for twist maps abstract completely ordered invariant circles are found for the gradient of the energy flow in the state space containing the critical sets corresponding to the birkhoff orbits of all rotation number in particular these ghost circles contain the aubry mather sets and map invariant circles as completely critical sets when these exist we give a criterion for a sequence of rational ghost circles to converge to a completely critical one

periodic approximations of irrational pseudo rotations using pseudoholomorphic curves we prove that every c 1 smooth area preserving dieomorphism of the closed 2 disk having not more than one periodic point is the uniform limit of periodic c 1 smooth dieomorphisms in particular every smooth irrational pseudo rotation can be c 0 approximated by integrable systems this partially answers a long standing question of a katok regarding zero entropy hamiltonian systems in low dimensions our approach uses pseudoholomorphic curve techniques from symplectic geometry

rotation numbers and instability sets translation and rotation numbers have played an interesting and important role in the qualitative description of various dynamical systems in this exposition we are especially interested in applications which lead to proofs of periodic motions in various kinds of dynamics on the annulus the applications include billiards and geodesic flows going beyond this simple qualitative invariant in the study of the dynamics of area preserving annulus maps g d birkhoff was led to the concept of regions of instability for twist maps we discuss the closely related notion of instability sets for a generic area preserving surface diffeomorphism and develop their properties

a constructive proof of the poincare birkhoff theorem in this paper with the use of the homotopy method a constructive proof of the poincare birkhoff theorem is given this approach provides a global method for finding fixed points of area preserving maps and periodic solutions of duffing equations

periodic orbits of hamiltonian homeomorphisms of surfaces john franks and michael handel fh2 have recently proved that any nontrivial hamiltonian diffeomorphism of a closed surface of genus at least one has periodic orbits of arbitrarily large period they proved a similar result for a nontrivial area preserving diffeomorphism of a sphere with at least three fixed points we extend these results to the case of the homeomorphisms when the genus is at least one we prove moreover that the periodic orbits may be chosen contractible if the set of contractible fixed points is contained in a disk when the surface is a sphere we extend the result to the case of a nontrivial homeomorphism with no wandering points the proofs make use of an equivariant foliated version of brouwer s plane translation theorem see b proposition 2 1 and some properties of the linking number of fixed points

classical locally finite tits chamber systems of rank 3 a chamber system v 9 j zi is over some index set z is a set of chambers together with partitions in z of v if ze z and c e v then bj is the join of all partitions fijzi e z and d c is the element of fij containing c d c is again a chamber system over j with fij restricted to z we say q is connected if d c furthermore 111 is the rank of v the most important examples of chamber systems are those obtained from groups if g is a group b a subgroup of g and xi ie z are subgroups of g containing b then 5 g b xi icl has as chambers the cosets bg g e g two such cosets bg bh being i adjacent if and only if xi g xih then g acts chamber transitively on with kernel b n bg and is connected if and only if g x 1 i e z furthermore each chamber system with transitive automorphism group g can be obtained in this way by setting b g and xi gd cr a rank 2 chamber system u hi fi is called a classical generalized ma gon mq 3 if is isomorphic to g b pi p where g is an essentially simple rank 2 group of lie type in the sense of cl b is a bore1 subgroup and p pj are the two maximal parabolic subgroups of g containing b here md is given by the relation vu wj wiw g 1 defined by the weyl group of g a rank 2 chamber system is a generalized digon if is isomorphic to v g pin p pi p where pi p are different proper subgroups of g satisfying g pipj pjpi a connected chamber system over z is called a classical tits chamber system if for each ce and i j c z di j c is either a generalized digon or a classical generalized m gon for some mi e n is focally finite if all d c are finite for motivation to consider such classical locally finite tits chamber systems see 15 and 16 if is a classical tits chamber system then the diagram d z is defined in 9 0021 8693 89 3 00

fusion systems of f_2 type we prove results on 2 fusion systems related to the 2 fusion systems of groups of lie type over the field of order 2 and certain sporadic groups the results are used in a later paper to determine the n systems the 2 fusion systems of n groups

periodic solutions of duffing s equations with superquadratic potential abstract this paper is devoted to the study of harmonic and subharmonic solutions for the second order scalar nonlinear duffing s equation x g x p t x x where g and p are continuous functions with p bounded and periodic in the first variable and g satisfying the assumption g x sign x as x among other results we prove the existence of infinitely many harmonic and subharmonic solutions of any order p p t and if the potential g x of g x satisfies certain conditions of superquadratic growth at the new existence results can be applied to situations in which the more classical superlinear growth condition g x x as x is not satisfied in this manner various preceding theorems are improved and sharpened see the introduction for more details proofs are based on a generalized version of the poincare birkhoff twist theorem due to w ding

a note on the thin finite simple groups in a previous paper 11 the author described a new approach to nonabelian simple groups of characteristic 2 type in which every 2 local subgroup of odd index is solvable and has cyclic sylow subgroups for all odd primes in fact we imposed these conditions only on certain special 2 local subgroups of odd index the approach was made possible by certain new general results concerning groups of characteristic 2 type which divide into the following three categories

saturated fusion systems with parabolic families abstract let g be a group a finite p subgroup s of g is a sylow p subgroup if every finite p subgroup of g is conjugate to a subgroup of s in this paper we examine the relations between the fusion system over s which is given by conjugation in g and a certain chamber system c on which g acts chamber transitively with chamber stabilizer n g s next we introduce the notion of a fusion system with a parabolic family and we show that a chamber system can be associated to such a fusion system we determine some conditions the chamber system has to fulfill in order to assure the saturation of the underlying fusion system we give an application to fusion systems with parabolic families of classical type

some results of hamiltonian homeomorphisms on closed aspherical surfaces abstract on closed symplectically aspherical manifolds by using floer homology schwarz proved a classical result i e that the action function of a nontrivial hamiltonian diffeomorphism is not constant in this article we generalize schwarz s theorem to the c 0 case on closed aspherical surfaces our methods are purely topological and involve the theory of transverse foliations for dynamical systems of surfaces and the recent progress inspired by le calvez as an application we prove that the contractible fixed points set and consequently the fixed points set of a nontrivial hamiltonian homeomorphism is not connected we also get a similar result for an orientation preserving nonwandering point homeomorphism of the two sphere in the end we give further applications based on the c 0 schwarz theorem

linearization of conservative toral homeomorphisms we give an equivalent condition for the existence of a semi conjugacy to an irrational rotation for conservative homeomorphisms of the two torus this leads to an analogue of poincare s classification of circle homeomorphisms for conservative toral homeomorphisms with unique rotation vector and a certain bounded mean motion property for minimal toral homeomorphisms the result extends to arbitrary dimensions further we provide a basic classification for the dynamics of toral homeomorphisms with all points non wandering

a 3 local identification of two almost simple extensions of pω8 2 abstract we provide 3 local characterizations of the almost simple groups p 8 2 3 and p 8 2 sym 3 both groups are examples of groups of parabolic characteristic three and we identify them from the structure of the centralizer of an element of order three

erratum to generalizations of the poincare birkhoff theorem other results of 1 which rely on theorem 2 1 are correct as stated and follow from the result above a disk u in the covering space a is called positively returning for f if f u u and fn u t k u for some n k 0 where t is the generator of the infinite cyclic group of covering translations negatively returning disks are defined similarly the difference in the statement of the theorem above and the statement of theorem 2 1 of 1 is the additional requirement in item 3 that the positively and negatively returning disks in the covering space are lifts of disks in the annulus equivalently the positively and negatively returning disks in the covering space must be disjoint from their image under t k k 0 standard arguments show it suffices that t u u this additional hypothesis is satisfied in other results from 1 which use theorem 2 1 i do not know whether theorem 2 1 of 1 as originally stated is true or not

amalgams of prime index this serves as a motivation for our main theorem from the theory of the classification of finite simple groups indeed our result classifies all such configurations and in particular it says that in all the interesting cases we must have ip n p i d 2 and ip p n p i 3 or 5 the basic definitions we use are the same as in gs which we quickly repeat for the convenience of the reader an umalgatn consists of two monomorphisms 4 and dz of groups such that

sieve estimation for the proportional odds failure time regression model with interval censoring abstract estimation of the proportional odds failure time regression model with interval censoring is considered conditions that allow for positive information for the regression parameter are discussed the efficient score is characterized by a fredholm equation of the second kind the sieve maximum likelihood estimator for the finite dimensional regression parameter is shown to be asymptotically normal with n convergence rate and to achieve the information bound data analysis and simulations assist in clarifying our thoughts regarding the choice of sieve for finite sample problems

geodesics on s2 and periodic points of annulus homeomorphisms we show that an area preserving homeomorphism of the open or closed annulus which has at least one periodic point must in fact have infinitely many interior periodic points a consequence is the theorem that every smooth riemannian metric ons2 with positive gaussian curvature has infinitely many distinct closed geodesics

generalizations of the poincare birkhoff theorem in this article we prove some generalizations of the classical poincar birkhoff theorem on area preserving homeomorphisms of the annulus which satisfy a boundary twist condition the work of g d birkhoff on this theorem and its applications can be found in b1 b2 and chapter v of b3 a more modern treatment can be found in b n we prove a theorem for the open annulus a s1 x 0 1 since as we will see the theorem for the closed annulus can easily be obtained from this result for the open annulus however it is not immediately obvious what should be the analogue of the twist condition it turns out that the most general hypothesis and the most natural from the point of view of our proof involves the notion of positively and negatively returning disks for some lift of f to the covering space a r x 0 1 more precisely if f a a is a lift of f a a we will say that the e is a positively returning disk for f if there is an open disk u c a such that f u n u 0 and fp u n u k 0 forsome n k 0 here u k denotes the set x k t i x t e u thus u is disjoint from its image but under iteration by f returns to a positive translate of itself a negatively returning disk is defined similarly but with k 0 such that fl u n u 0 in section 2 we prove the following

nonparametric inference in hidden markov models using p splines summary hidden markov models hmms are flexible time series models in which the distribution of the observations depends on unobserved serially correlated states the state dependent distributions in hmms are usually taken from some class of parametrically specified distributions the choice of this class can be difficult and an unfortunate choice can have serious consequences for example on state estimates and more generally on the resulting model complexity and interpretation we demonstrate these practical issues in a real data application concerned with vertical speeds of a diving beaked whale where we demonstrate that parametric approaches can easily lead to overly complex state processes impeding meaningful biological inference in contrast for the dive data hmms with nonparametrically estimated state dependent distributions are much more parsimonious in terms of the number of states and easier to interpret while fitting the data equally well our nonparametric estimation approach is based on the idea of representing the densities of the state dependent distributions as linear combinations of a large number of standardized b spline basis functions imposing a penalty term on non smoothness in order to maintain a good balance between goodness of fit and smoothness

a geometric presentation for the adjoint module of sl3 k abstract let k be a field the points and lines of the projective plane p k 3 determine corresponding subspaces in the space of 3 3 traceless matrices the adjoint module for the group sl 3 k we show that these subspaces conversely determine the module as their direct limit modulo derivations of the field k

a multiplicity result for periodic solutions of second order differential equations with a singularity abstract by the use of the poincare birkhoff fixed point theorem we prove a multiplicity result for periodic solutions of a second order differential equation where the nonlinearity exhibits a singularity of repulsive type at the origin and has linear growth at infinity our main theorem is related to previous results by rebelo 1996 1997 4 5 and rebelo and zanolin 1996 6 7 in connection with a problem raised by del pino et al 1992 1

fusion systems and amalgams we study reduced fusion systems from the point of view of their essential subgroups using the classification by goldschmidt and fan of amalgams of prime index to analyze certain pairs of such subgroups our results are applied here to study reduced fusion systems over 2 groups of order at most 64 and also reduced fusion systems over 2 groups having abelian subgroups of index two more applications are given in later papers

parabolic systems the gf 3 case parabolic systems defined over gf q have been classified by timmesfeld for q 4 and by stroth for q 2 see references we deal with the case q 3

on the dynamics of homology preserving homeomorphisms of the annulus we consider the homeomorphisms of the compact annulus a s 1 x 1 1 isotopic to the symmetry s a which interchanges the two boundary components we prove that if such a homeomorphism is in some sense conservative and twisted then it possesses a periodic orbit of period exactly two this can be regarded as a counterpart of the poincare birkhoff theorem in the isotopy class of sa

periodic bouncing solutions for attractive singular second order equations abstract in this paper by using an approximation approach and phase plane analysis for the successor map of the impact oscillator we obtain an existence result for periodic bouncing solutions for a second order forced equation x g x p t where g has an attractive singularity which improves on the previous result in the conditions for both g and p

rotation sets for homeomorphisms and homology in this article we propose a definition of rotation sets for homeomorphisms of arbitrary compact manifolds this approach is based on taking the suspended flow and using ideas of schwartzmann on homology and winding cycles for flows our main application is to give a generalisation of a theorem of libre and mackay for tori to the context of surfaces of higher genus

regression analysis of case k interval censored failure time data in the presence of informative censoring summary interval censored failure time data occur in many fields such as demography economics medical research and reliability and many inference procedures on them have been developed sun 2006 chen sun and peace 2012 however most of the existing approaches assume that the mechanism that yields interval censoring is independent of the failure time of interest and it is clear that this may not be true in practice zhang et al 2007 ma hu and sun 2015 in this article we consider regression analysis of case k interval censored failure time data when the censoring mechanism may be related to the failure time of interest for the problem an estimated sieve maximum likelihood approach is proposed for the data arising from the proportional hazards frailty model and for estimation a two step procedure is presented in the addition the asymptotic properties of the proposed estimators of regression parameters are established and an extensive simulation study suggests that the method works well finally we apply the method to a set of real interval censored data that motivated this study

homeomorphisms of the annulus with a transitive lift let f be a homeomorphism of the closed annulus a that preserves the orientation the boundary components and that has a lift tilde f to the infinite strip a which is transitive we show that if the rotation numbers of both boundary components of a are strictly positive then there exists a closed nonempty unbounded set b subset tilde a such that b is bounded to the right the projection of b to a is dense b 1 0 subset b and tilde f b subset b moreover if p 1 is the projection on the first coordinate of a then there exists d 0 such that for any tilde z in b limsup n to infty frac p 1 tilde f n tilde z p 1 tilde z n d in particular using a result of franks we show that the rotation set of any homeomorphism of the annulus that preserves orientation boundary components which has a transitive lift without fixed points in the boundary is an interval with 0 in its interior

multiple solutions of the periodic boundary value problem for some forced pendulum type equations if f x c 0 and e is a constant t then integrating 0 1 over 0 272 after multiplication of both members of the equation by x shows that the only possible solutions are constant and hence satisfy a sin x c consequently if we exclude the trivial translation by a multiple of 275 0 1 will have no solution if dj a one solution if lp a and two solutions if lc l a in 0th er t erms the intersection of the range of the operator d2 dt2 c d dt f u sin acting on zn periodic functions of class g with the subspace of constant functions in the space c o 2711 of real continuous functions on 0 27r is the closed interval a a whose interior points are images of two distinct solutions and boundary points of one we try to obtain similar results for the case where e is no more constant and

a pushing up result and some consequences for the embedding of 2 constrained subgroups let m m1 be maximal 2 locai subgroups of some finite group g with o g 1 satisfying qi o mi f mi for i 0 1 is it possible in this situation that q1 qo the bulk of the proof of l consists of showing that there exists no k group g of characteristic 2 type satisfying these and certain non generational conditions for mi which by results of g seitz strongly restrict the structure of mr if one tries to consider this problem more generally one realizes that it splits naturally into two cases

empirical bayes confidence intervals based on bootstrap samples abstract consider the model with data generated by the following two stage process first a parameter is sampled from a prior distribution g and then an observation is sampled from the conditional distribution f y if the prior distribution is known then the bayes estimate under squared error loss is the posterior expectation of conditional on the data y for example if g is gaussian with mean and variance 2 and f y is gaussian with mean and variance 2 then the posterior distribution is gaussian with mean b 1 b y and variance 2 1 b where b 2 2 2 inferences about are based on this distribution we study the application of the bootstrap to situations where the prior must be estimated from the data empirical bayes methods for this model we observe data y t y 1 y k t each independent y k following the compound model described previously as first shown by james and stein 1961 setting each k equal to its estimated posterior mean where and pr

sieve maximum likelihood regression analysis of dependent current status data current status data occur in contexts including demographic studies and tumorigenicity experiments in such cases each subject is observed only once and the failure time of interest is either left or right censored kalbfleisch prentice 2002 many methods have been developed for the analysis of such data huang 1996 sun 2006 most of which assume that the failure time and the observation time are independent completely or given covariates in this paper we present a sieve maximum likelihood approach for current status data when independence does not hold a copula model and monotone i splines are used and the asymptotic properties of the resulting estimators are established in particular the estimated regression parameters are shown to be semiparametrically efficient an illustrative example is provided

lagrange stability for impulsive pendulum type equations in the present paper we prove the boundedness of all solutions for some impulsive pendulum type equations by moser s twist theorem we also prove the existence of quasi periodic solutions for the impulsive pendulum type equations

semiparametric regression analysis of interval censored data with informative dropout interval censored data arise when the event time of interest can only be ascertained through periodic examinations in medical studies subjects may not complete the examination schedule for reasons related to the event of interest in this article we develop a semiparametric approach to adjust for such informative dropout in regression analysis of interval censored data specifically we propose a broad class of joint models under which the event time of interest follows a transformation model with a random effect and the dropout time follows a different transformation model but with the same random effect we consider nonparametric maximum likelihood estimation and develop an em algorithm that involves simple and stable calculations we prove that the resulting estimators of the regression parameters are consistent asymptotically normal and asymptotically efficient with a covariance matrix that can be consistently estimated through profile likelihood in addition we show how to consistently estimate the survival function when dropout represents voluntary withdrawal and the cumulative incidence function when dropout is an unavoidable terminal event furthermore we assess the performance of the proposed numerical and inferential procedures through extensive simulation studies finally we provide an application to data on the incidence of diabetes from a major epidemiological cohort study

on mixing diffeomorphisms of the disc we prove that a c k k ge 2 pseudo rotation f of the disc with non brjuno rotation number is c k 1 rigid the proof is based on two ingredients 1 we derive from franks lemma on free discs that a pseudo rotation with small rotation number compared to its c 1 norm must be close to the identity map 2 using pesin theory we obtain an effective finite information version of the katok closing lemma for an area preserving surface diffeomorphism f that provides a controlled gap in the possible growth of the derivatives of f between exponential and sub exponential our result on rigidity together with a kam theorem by russmann allow to conclude that analytic pseudo rotations of the disc or the sphere are never topologically mixing due to a structure theorem by franks and handel of zero entropy surface diffeomorphisms it follows that an analytic conservative diffeomorphism of the disc or the sphere that is topologically mixing must have positive topological entropy

irreducible modules and parabolic subgroups summary it seems desirable from the point of view of finite group theorists to develop further the representation theory of finite chevalley groups in the characteristic of their definition say p by focusing attention on the full array of p local subgroups that is the parabolics rather than the usual single borel or cartan subgroup the following observation may be regarded as a generalization to arbitrary parabolic subgroups of the standard result 3 theorem 39 d for a borel subgroup namely that in an irreducible module the subspace fixed by a maximal unipotent subgroup is 1 dimensional and so affords an irreducible module for a levi complement which is an abelian cartan subgroup it seems natural to state the result first for algebraic groups

forcing theory for transverse trajectories of surface homeomorphisms this paper studies homeomorphisms of surfaces isotopic to the identity by means of purely topological methods and brouwer theory the main development is a novel theory of orbit forcing using maximal isotopies and transverse foliations this allows us to derive new proofs for some known results as well as some new applications among which we note the following we extend franks and handel s classification of zero entropy maps of mathbb s 2 for non wandering homeomorphisms we show that if f is a hamiltonian homeomorphism of the annulus then the rotation set of f is either a singleton or it contains zero in the interior proving a conjecture posed by boyland we show that there exist compact convex sets of the plane that are not the rotation set of some torus homeomorphisms proving a first case of the franks misiurewicz conjecture we extend a bounded deviation result relative to the rotation set to the general case of torus homeomorphisms

periodic solutions for the 1 dimensional p laplacian equation abstract existence of infinitely many periodic solutions for the 1 dimensional p laplacian equation d d t d x d t p 2 d x d t g x f t x is proved by means of the poincare birkhoff fixed point theorem where g c r r and is p sublinear at the origin in the sense lim x 0 g x x p 2 x and f c r r r is 1 periodic in the time t and small with respect to g

sheaf homology and complete reducibility abstract in the study of finite simple groups by means of the geometries provided by their local subgroups problems of structure often reduce to questions about modular representations in finite characteristic of particular interest are modules spanned by fixed points of sylow groups including high weight modules for chevalley groups for which the homology methods of ronan and smith 6 can be very useful this note presents an elementary sufficient condition for splitting of some reducible modules of this type among the applications we generalize a number of results appearing in recent work of timmesfeld 11 which provided the original inspiration for this analysis some of the ideas had appeared in a special case in 10

maslov index poincare birkhoff theorem and periodic solutions of asymptotically linear planar hamiltonian systems abstract we study the relationship between the twist condition in the poincare birkhoff fixed point theorem and the assumptions on the maslov index for asymptotically linear planar hamiltonian systems for this aim we develop a variant of the poincare birkhoff theorem which together with its classical version allows to obtain a lower bound for the number of nontrivial periodic solutions in terms of the gap between the maslov indexes associated to the linearizations of the planar system at zero and at infinity