scalar curvature of a metric with unit volume the problem of finding riemannian metrics on a closed manifold with prescribed scalar curvature function is now fairly well understood from the works of kazdan and warner in 1970 s 10 and references cited in it in this paper we shall consider the same problem under a constraint on the volume for this purpose it is useful to introduce an invariant p m of a smooth closed manifold m which will be called the yamabe number of m defined as the supremum of m c of all conformal classes c of riemannian metrics on m

on the multiplicity of solutions of a nonlinear elliptic problem on riemannian manifolds we show that the number of solutions of a nonlinear elliptic problem on a riemannian manifold depends on the topological properties of the manifold in particular we consider the lusternik schnirelmann category and the poincare polynomial of the manifold

the influence of random effects on the unconditional hazard rate and survival functions summary the consequences of introducing random effects have been a major issue in models for survival analysis a general result is derived to establish the underestimation of the unconditional hazard rate when a random effect is present also the survival time is shown to be underestimated no distributional assumption regarding the random effect is required the random effects survival model has been a major focus in the recent literature heckman singer 1984 littlewood 1984 clayton cuzick 1985 heckman robb walker 1990 honore 1990 when a hazard rate function is estimated it is conventional practice to assume that observations are taken from a homogeneous group if they are based on several heterogeneous subgroups we should estimate their hazard rate functions separately however if we could assume that the hazard rate function from one group is parallel to those of other groups we can deal with all observations at the same time by taking account of covariate variables by setting an t ao t exp fl x where ao t is a specified hazard rate x is a vector of fixed covariates and the subscript n is attached to emphasize that this is a nominal hazard rate i e without heterogeneity this helps to describe the differences among subgroups but if we want to describe all differences exactly we have to use too many covariates this is not realistic since the number of observations available is limited thus we choose several important covariates and regard the remaining covariates as random in order to introduce heterogeneity into the population via a random effect we let the hazard rate for an individual be van t or v2o t exp fl x where v is a random variable such that pr v 0 1 e v 1 and pr v 1 o and an t 0 using fu t and fc t iv by taking an expected value of fc t i

aubin s lemma for the yamabe constants of infinite coverings and a positive mass theorem aubin s lemma says that if the yamabe constant of a closed conformal manifold m c is positive then it is strictly less than the yamabe constant of any of its non trivial finite conformal coverings we generalize this lemma to the one for the yamabe constant of any m c of its infinite conformal coverings provided that 1 m has a descending chain of finite index subgroups tending to 1 m moreover if the covering m is normal the limit of the yamabe constants of the finite conformal coverings associated to the descending chain is equal to that of m c for the proof of this we also establish a version of positive mass theorem for a specific class of asymptotically flat manifolds with singularities

a positive mass theorem in three dimensional cauchy riemann geometry in this note we summarize the results from 6 on the positive mass problem in 3 dimensional cr cauchy riemann geometry

renormalizing curvature integrals on poincare einstein manifolds abstract after analyzing renormalization schemes on a poincare einstein manifold we study the renormalized integrals of scalar riemannian invariants the behavior of the renormalized volume is well known and we show any scalar riemannian invariant renormalizes similarly we consider characteristic forms and their behavior under a variation of the poincare einstein structure and obtain from the renormalized integral of the pfaffian an extension of the gauss bonnet theorem

the prescribed scalar curvature problem for metrics with unit total volume we solve the modified kazdan warner problem of finding metrics with prescribed scalar curvature and unit total volume

identifiability and rates of estimation for scale parameters in location mixture models in this paper we consider the problem of identifiability and estimation for the scale parameter 0 in the location mixture model 0 x y where x has a known distribution independent of the y whose distribution is unknown identification of 0 is ensured by constraining y based on the tail behavior of the distribution for x rates for estimation are described for those x which can be written as a square summable series of exponential variables as a special case our analysis shows that the structural parameters in the weibull semiparametric mixture heckman and singer are not estimable at the usual parametric op 1 xn rate the exact relationship between identifying constraints and achievable rates is explained 1 introduction heckman and singer 1984 studied economic theories concerning continuous durations of occupancy of states in order to properly estimate structural parameters in the presence of population heterogeneity they proposed the use of a semiparametric mixture model as a method for modeling duration data the model they proposed was the weibull semiparametric mixture

computations of the orbifold yamabe invariant we consider the yamabe invariant of a compact orbifold with finitely many singular points we prove a fundamental inequality for the estimate of the invariant from above which also includes a criterion for the non positivity of it moreover we give a sufficient condition for the equality in the inequality in order to prove it we also solve the orbifold yamabe problem under a certain condition we use these results to give some exact computations of the yamabe invariant of compact orbifolds

the yamabe invariant for non simply connected manifolds the yamabe invariant is an invariant of a closed smooth manifold defined using conformal geometry and the scalar curvature recently petean showed that the yamabe invariant is nonnegative for all closed simply connected manifolds of dimension 5 we extend this to show that yamabe invariant is nonnegative for all closed manifolds of dimension 5 with fundamental group of odd order having all sylow subgroups abelian the main new geometric input is a way of studying the yamabe invariant on toda brackets a similar method of proof shows that all closed oriented manifolds of dimension 5 with non spin universal cover with finite fundamental group having all sylow subgroups elementary abelian admit metrics of positive scalar curvature once one restricts to the complement of manifolds whose homology classes are toral the exceptional toral homology classes only exist in dimensions not exceeding the rank of the fundamental group so this proves important cases of the gromov lawson rosenberg conjecture once the dimension is sufficiently large

sieve m inference on irregular parameters abstract this paper presents sieve inferences on possibly irregular i e slower than root n estimable functionals of semi nonparametric models with i i d data we provide a simple consistent variance estimator of the plug in sieve m estimator of a possibly irregular functional and the asymptotic standard normality of the sieve t statistic we show that for hypothesis testing of irregular functionals the sieve likelihood ratio statistic is asymptotically chi square distributed these results are useful in inference on structural parameters that may have singular semiparametric efficiency bounds a simulation study and an empirical application of heckman and singer 1984 duration model are presented

testing for unobserved heterogeneity in exponential and weibull duration models abstract we examine the use of the likelihood ratio lr statistic to test for unobserved heterogeneity in duration models based on mixtures of exponential or weibull distributions we consider both the uncensored and censored duration cases the asymptotic null distribution of the lr test statistic is not the standard chi square as the standard regularity conditions do not hold instead there is a nuisance parameter identified only under the alternative and a null parameter value on the boundary of the parameter space as in cho and white 2007a we accommodate these and provide methods delivering consistent asymptotic critical values we conduct a number of monte carlo simulations comparing the level and power of the lr test statistic to an information matrix im test due to chesher 1984 and lagrange multiplier lm tests of kiefer 1985 and sharma 1987 our simulations show that the lr test statistic generally outperforms the im and lm tests we also revisit the work of van den berg and ridder 1998 on unemployment durations and of ghysels et al 2004 on interarrival times between stock trades and as it turns out affirm their original informal inferences

on delay dependent stability under model transformations of some neutral linear systems this paper focuses on the stability analysis of a class of neutral linear systems some sufficient delay dependent stability conditions are derived in terms of an appropriate model transformation of the original system transformation similar to the one used in the retarded case the analysis makes use of an appropriate construction of a degenerate lyapunov krasovskii functional several computational schemes and frequency domain interpretations as well as an example are also presented

semiparametric estimation of a proportional hazard model with unobserved heterogeneity the proportional hazard model with unobserved heterogeneity gives the hazard function of a random variable conditional on covariates and a second random variable representing unobserved heterogeneity this paper shows how to estimate the baseline hazard function and the distribution of the unobserved heterogeneity nonparametrically the baseline hazard function and heterogeneity distribution are assumed to satisfy smoothness conditions but are not assumed to belong to known finite dimensional parametric families existing estimators assume that the baseline hazard function or heterogeneity distribution belongs to a known parametric family thus the estimators presented here are more general than existing ones

mixtures of exponential distributions arbitrary nonparametric mixtures of exponential and weibull fixed shape distributions are considered as possible models for a lifetime distribution a characterization of such distributions is given by the well known characterization of laplace transforms the maximum likelihood estimate of the mixing distribution is investigated and found to be supported on a finite number of points it is shown to be unique and weakly convergent to the true mixing measure with probability one a practical algorithm for computing the maximum likelihood estimate is described its performance is briefly discussed and some illustrative examples given

manifolds of positive scalar curvature and conformal cobordism theory for a supergoup we study closed manifolds with positive conformal classes we use the relative yamabe invariant from 2 to define the conformal cobordism relation on the category of such manifolds we prove that the corresponding conformal cobordism groups are isomorphic to the cobordism groups defined by stolz in 19 as a corollary we show that the conformal concordance relation on positive conformal classes coincides with the standard concordance relation on positive scalar curvature metrics our main technical tools come from analysis and conformal geometry

classification of prime 3 manifolds with σ invariant greater than rp 3 in this paper we compute the invariants sometimes also called the smooth yamabe invariants of rp 3 and rp 2 s 1 which are equal and show that the only prime 3 manifolds with larger invariants are s 3 s 2 s 1 and s 2 s 1 the nonorientable s 2 bundle over s 1 more generally we show that any 3 manifold with invariant greater than rp 3 is either s 3 a connect sum with an s 2 bundle over s 1 or has more than one nonorientable prime compo

degenerate solutions of a nonlinear elliptic equation on the sphere abstract we consider the equation u u u q on the round sphere s m m 3 with 0 and 1 q m 2 m 2 by studying the local structure of solutions bifurcating from the constant solution we show that for any isoparametric hypersurface m in the sphere there is a value of and a solution of the equation at which the linearized equation has nontrivial solutions at the same time we obtain new solutions of the equation

blow up phenomena for the yamabe equation it is well known that the pde 1 has at least one positive solution for any choice of m g if n 6 and m g is not locally conformally flat this follows from results of t aubin 3 the remaining cases were solved by r schoen using the positive mass theorem 16 solutions to 1 are not usually unique as an example consider the product metric on 51 l x 5n 1 l if l is sufficiently small then the yamabe pde has a unique solution on the other hand there are many non minimizing solutions if l is large d pollack 14 has used gluing techniques to construct high energy solutions on more general background manifolds given any conformai class with positive yamabe constant and any positive integer iv there exists a new conformai class which is close to the original one in the c norm and contains at least n metrics of constant scalar curvature see 14 theorem 0 1 it is an interesting question whether the set of all solutions to the yamabe pde is compact in the c2 topology say a well known conjecture states that this should be true unless m p is conformally equivalent to the round sphere see 17 18 19 this conjecture has been verified in low dimensions and in the locally conformally flat case if m g is locally conformally flat compactness follows from work of r schoen 17 18 moreover schoen proposed a strategy for proving the conjecture in the non locally conformally flat case based on the pohozaev identity

on asymptotic stability of delay difference systems in this paper we obtain some criteria for determining the asymptotic stability of the zero solution for some classes of delay difference systems by using a discrete version of the second lyapunov method our results can be well suited for computational purposes

boundary regularity uniqueness and non uniqueness for ah einstein metrics on 4 manifolds abstract this paper studies several aspects of asymptotically hyperbolic ah einstein metrics mostly on 4 manifolds we prove boundary regularity at infinity for such metrics and establish uniqueness under natural conditions on the boundary data by examination of explicit black hole metrics it is shown that neither uniqueness nor finiteness holds in general for ah einstein metrics with a prescribed conformal infinity we then describe natural conditions which are sufficient to ensure finiteness

new stability analysis for uncertain neutral system with time varying delay in this paper a class of uncertain neutral system with time varying delay is studied based on lyapunov functional approach and linear matrix inequality technology the stability criteria are given numerical examples show the effectiveness of our theoretical results and the influence of uncertainties to the stability of the neutral system

conformal entropy rigidity through yamabe flows we introduce two versions of the yamabe flow which preserve negative scalar curvature bounds first we show existence and smooth convergence of solutions to these flows we then show that a metric with negative scalar curvature is controlled by the yamabe metrics in the same conformal class with constant extremal scalar curvatures this implies that the volume entropy of our original metric is controlled by the entropies of these yamabe metrics we eventually use these yamabe flows to prove an entropy rigidity result when the yamabe metric has negative sectional curvature the entropy of a metric in the same conformal class is extremal if and only if the metric has constant extremal scalar curvature

on novel stability criterion of neutral system with time varying delay this article studies the neutral system with time varying delay and uncertainties novel stability criteria of the neutral system are derived by using lyapunov method and linear matrix inequality technology which can be easily solved by efficient convex optimization algorithms some numerical examples are given to illustrate our theoretical results

simple estimation of a duration model with unobserved heterogeneity this paper presents a simple estimator of the shape parameter in a weibull duration model with unobserved heterogeneity the estimator is consistent and asymptotically normal under mild conditions and a consistent estimator of the asymptotic variance is available a monte carlo study indicates that the asymptotic distribution of the estimator provides a good approximation to the finite sample distribution the estimation strategy can be extended to a model with regressors and to a log logistic model with unobserved heterogeneity the advantages of the estimator are that it is easy to calculate and that its asymptotic distribution can be derived copyright 1990 by the econometric society

multiplicity results for the yamabe equation by lusternik schnirelmann theory abstract let m g be any closed riemannianan manifold and n h be a riemannian manifold of constant positive scalar curvature we prove that the yamabe equation on the riemannian product m n g h has at least cat m 1 solutions for small enough where cat m denotes the lusternik schnirelmann category of m the solutions obtained are functions of m and c a t m of them have energy arbitrarily close to the minimum

some sufficient conditions for exponential stability of linear neutral functional differential equations abstract in this paper we give some sufficient conditions for exponential stability of linear neutral functional differential equations the obtained results are extensions of the recent results in d q cao p he stability criteria of linear neutral systems with a single delay appl math comput 148 2004 135 143 d q cao p he sufficient conditions for stability of linear neutral systems with a single delay appl math lett 17 2004 139 144 g d hu g d hu x f zou stability of linear neutral systems with multiple delays boundary criteria appl math comput 148 2004 707 715 j h park s won a note on stability of neutral delay differential systems j franklin inst 336 1999 1 9 to linear neutral functional differential equations

an obstruction to the positivity of relative yamabe invariants for a supergroup gamma we describe an obstruction to the existence of positive scalar curvature metrics with minimal boundary condition on a compact n dimensional gamma manifold w with nonempty boundary m 3 leq n leq 8 in terms of the bordism class m in the stolz obstruction group r n 1 gamma associated to gamma st2 in par ticular when w is a 5 dimensional spin manifold and the alpha invariant of a connected component of m is nonzero we prove that w does not admit a positive scalar curvature metric with minimal boundary condition

the singularity of the information matrix of the mixed proportional hazard model this paper presents new identification conditions for the mixed proportional hazard model in particular the baseline hazard is assumed to be bounded away from 0 and near t 0 these conditions ensure that the information matrix is nonsingular the paper also presents an estimator for the mixed proportional hazard model that converges at rate n 1 2

the spinorial tau invariant and 0 dimensional surgery let m be a compact manifold with a metric g and with a fixed spin structure chi let lambda 1 g be the first non negative eigenvalue of the dirac operator on m g chi we set tau m chi sup inf lambda 1 g where the infimum runs over all metrics g of volume 1 in a conformal class g 0 on m and where the supremum runs over all conformal classes g 0 on m let m chi be obtained from m chi by 0 dimensional surgery we prove that tau m chi geq tau m chi as a corollary we can calculate tau m chi for any riemann surface m

algebraic criteria for stability of linear neutral systems with a single delay abstract the stability of linear neutral delay differential systems with a single delay via routh hurwitz and schur cohn criteria is investigated some algebraic criteria for delay independent stability are presented these criteria may complement those reported in the literature finally two examples illustrate the criteria

a new delay dependent criterion for neural systems with multiple delays in this paper the problem of the stability analysis for neutral systems with multiple delays is investigated using lyapunov method we present a new delay dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities lmis which can be easily solved by various convex optimization algorithms a numerical example is given to illustrate the effectiveness of the proposed method

collapsing riemannian manifolds to ones of lower dimensions on considere l effondrement d une suite de varietes de riemann mi vers un espace de dimension inferieure x on etudie le cas ou l espace limite x est une variete de riemann et les courbures sectionnelles de mi sont bornees

maskit combinations of poincare einstein metrics we establish a boundary connected sum theorem for asymptotically hyperbolic einstein metrics and also show that if the two metrics have scalar positive conformal infinities then the same is true for this boundary join this construction is also extended to spaces with a finite number of interior conic singularities and as a result we show that any 3 manifold which is a finite connected sum of quotients of s3 and s2 s1 bounds such a space with conic singularities putatively any 3 manifold admitting a metric of positive scalar curvature is of this form

heterogeneity and selection in dynamic panel data abstract the data generating process dgp for generic dynamic panel data consists of a law of state dynamics g a selection or attrition rule h and an initial condition f i study nonparametric identifiability of this complete dgp g h f using short unbalanced panel data allowing for nonseparability between observed states and unobserved heterogeneity in each of g h and f for t 3 the dgp is identified by using a proxy variable for t 6 the three additional periods construct a proxy and thus the dgp is identified without an auxiliary variable

some simple criteria for stability of neutral delay differential systems this paper deals with the stability of linear neutral delay differential systems some simple criteria for delay independent stability of this class of problems which are described by evaluating the measure and norm of corresponding matrices are presented the main results proposed in this study are sharper than those reported in the literature

gluing eguchi hanson metrics and a question of page in 1978 gibbons pope and page proposed a physical picture for the ricci flat kahler metrics on the k3 surface based on a gluing construction in this construction one starts from a flat torus with 16 orbifold points and resolves the orbifold singularities by gluing in 16 small eguchi hanson manifolds that all have the same orientation this construction was carried out rigorously by topiwala lebrun singer and donaldson in 1981 page asked whether the above construction can be modified by reversing the orientations of some of the eguchi hanson manifolds this is a subtle question if successful this construction would produce einstein metrics that are neither kahler nor self dual in this paper we focus on a configuration of maximal symmetry involving eight small eguchi hanson manifolds of each orientation that are arranged according to a chessboard pattern by analyzing the interactions between eguchi hanson manifolds with opposite orientation we identify a nonvanishing obstruction to the gluing problem thereby destroying any hope of producing a metric of zero ricci curvature in this way using this obstruction we are able to understand the dynamics of such metrics under ricci flow as long as the eguchi hanson manifolds remain small in particular for the configuration described above we obtain an ancient solution to the ricci flow with the property that the maximum of the riemann curvature tensor blows up at a rate of t 1 2 while the maximum of the ricci curvature converges to 0 2016 wiley periodicals inc

collapsing riemannian manifolds while keeping their curvature bounded i soit y n une variete de riemann connexe complete et p y n le rayon d injectivite i p de l application exponentielle en p est defini comme etant le plus petit r tel que exp p b r p n est pas un diffeomorphisme sur son image on etudie la situation dans laquelle la taille du rayon d injectivite est petite relativement a la courbure

stability criteria of linear neutral systems with a single delay this article studies the asymptotic stability of linear neutral delay differential systems using the characteristic equation of the system new simple delay independent stability criteria are derived in terms of the spectral radius of modulus matrices numerical examples are given to demonstrate the validity of our main criteria

kernel estimation of hazard functions when observations have dependent and common covariates abstract we propose a hazard model where dependence between events is achieved by assuming dependence between covariates this model allows for correlated variables specific to observations as well as macro variables which all observations share this setup better fits many economic and financial applications where events are not independent nonparametric estimation of the hazard function is then studied kernel estimators proposed in nielsen and linton 1995 and linton et al 2003 are shown to have similar asymptotic properties compared with the i i d case mixing conditions ensure the asymptotic results follow these results depend on adjustments to bandwidth conditions simulations are conducted which verify the impact of dependence on estimators bandwidth selection accounting for dependence is shown to improve performance in an empirical application trade intensity in high frequency financial data is estimated

stability in linear delay equations abstract for linear autonomous differential difference equations of retarded or neutral type necessary and sufficient conditions are given for the zero solution to be stable hyperbolic for all values of the delays

einstein metrics and complex singularities this paper is concerned with the construction of special metrics on non compact 4 manifolds which arise as resolutions of complex orbifold singularities our study is close in spirit to the construction of the hyperkahler gravitational instantons but we focus on a different class of singularities we show that any resolution x of an isolated cyclic quotient singularity admits a complete scalar flat kahler metric which is hyperkahler if and only if k x is trivial and that if k x is strictly nef then x also admits a complete non kahler self dual einstein metric of negative scalar curvature in particular complete self dual einstein metrics are constructed on simply connected non compact 4 manifolds with arbitrary second betti number

wormholes in ach einstein manifolds we give a new construction of einstein manifolds which are asymptotically complex hyperbolic inspired by the work of mazzeo pacard in the real hyperbolic case the idea is to develop a gluing theorem for 1 handle surgery at infinity which generalizes the klein construction for the complex hyperbolic metric

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

maximum likelihood estimation in semiparametric regression models with censored data summary semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies the presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models we present several classes of semiparametric regression models which extend the existing models in important directions we construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters the maximum likelihood estimators are consistent and asymptotically normal with efficient variances we develop simple and stable numerical techniques to implement the corresponding inference procedures extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings applications to three medical studies yield important new insights we conclude that there is no reason theoretical or numerical not to use maximum likelihood estimation for semiparametric regression models we discuss several areas that need further research

identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity we extend the identification results for nonparametric simultaneous equations models in matzkin 2008 to situations where the observations on the vector of dependent variables might be limited and where the number of exogenous unobservable variables is larger than the number of dependent variables