a quadratic bolza type problem in a riemannian manifold abstract a classical nonlinear equation d s x x v x s 0 on a complete riemannian manifold m is considered the existence of solutions connecting any two points x 0 x 1 m is studied i e for t 0 the critical points of the functional j t x 1 2 0 t x x ds 0 t v x s ds with x 0 x0 x t x1 when the potential v has a subquadratic growth with respect to x jt admits a minimum critical point for any t 0 infinitely many critical points if the topology of m is not trivial when v has an at most quadratic growth i e v x s d 2 x x k this property does not hold but an optimal arrival time t 0 exists such that if 0 m can be joined by a critical point of the corresponding functional for the existence and multiplicity results variational methods and ljusternik schnirelman theory are used the optimal value t 2 is fulfilled by the harmonic oscillator these ideas work for other related problems

a problem with the likelihood ratio test for a change point hazard rate model summary a likelihood ratio test for constant hazard against a step change alternative has received considerable attention in recent years additional information in the maximum likelihood estimate of the change point can seriously affect interpretation of test results some simple modifications are considered for which exact percentage points can be derived monte carlo power and mean squared error comparisons are encouraging

estimation in change point hazard rate models summary this paper discusses the estimation of parameters in hazard rate models with a changepoint due to the irregularity of the models the classical maximum likelihood method and the method of moments cannot be used a consistent estimator of the change point is obtained by examining the properties of the density represented as a mixture the performance of the estimator is checked via simulation

a sequential testing approach to detecting multiple change points in the proportional hazards model the semi parametric proportional hazards model has been widely adopted in clinical trials with time to event outcomes a key assumption in the model is that the hazard ratio function is a constant over time which is frequently violated as there is often a lag period before an experimental treatment reaches its full effect one existing approach uses maximal score tests and monte carlo sampling to identify multiple change points in the hazard ratio function which requires the number of change points that exist in the model to be known we propose a sequential testing approach to detecting multiple change points in the hazard ratio function using likelihood ratio tests and the distributions of the likelihood ratio statistics under the null hypothesis are evaluated via resampling an important feature of the proposed approach is that the number of change points in the model is inferred from the data and does not need to be specified numerical results based on simulated clinical trials and a real time to event study show that the proposed approach can accurately detect the change points in the hazard ratio function

towards a unified field theory for classical electrodynamics in this paper we introduce a model which describes the relation of matter and the electromagnetic field from a unitarian standpoint in the spirit of ideas of born and infeld in this model based on a semilinear perturbation of maxwell equations the particles are finite energy solitary waves due to the presence of the nonlinearity in this respect the matter and the electromagnetic field have the same nature finite energy means that particles have finite mass and this makes electrodynamics consistent with the special relativity we analyze the invariants of the motion of the semilinear maxwell equations sme and their static solutions in the magnetostatic case i e when the electric field e 0 and the magnetic field h does not depend on time sme are reduced to the semilinear equation open image in new window where denotes the curloperator f is the gradient of a strictly convex smooth function f r3 r and a r3 r3 is the gauge potential related to the magnetic field h h a due to the presence of the curl operator 1 is a strongly degenerate elliptic equation moreover physical considerations impel f to be flat at zero f 0 0 and this fact leads us to study the problem in a functional setting related to the orlicz space lp lq the existence of a nontrivial finite energy solution of 1 is proved under suitable growth conditions on f the proof is carried out by using a suitable variational framework related to the hodge splitting of the vector field a

geodesic connectedness of multiwarped spacetimes abstract a new technique for the study of geodesic connectedness in a class of lorentzian manifolds is introduced it is based on arguments of brouwer s topological degree for the solution of functional equations it is shown to be very useful for multiwarped spacetimes which include different types of relativistic spacetimes connectedness by causal geodesics is also proved

orthogonal trajectories on riemannian manifolds and applications to plane wave type spacetimes abstract we present a result on trajectories of a lagrangian system joining two given submanifolds of a riemannian manifold under the action of an unbounded potential as an application we consider geodesics in a class of semi riemannian manifolds the plane wave type spacetimes

a monte carlo approach for change point detection in the cox proportional hazards model detecting a time lag of treatment effect or identifying change points in a hazard function is of great interest and importance in survival analysis the testing procedures hereto are primarily based on analytical approximations for the asymptotic null distribution of either the likelihood ratio test or the score test in the presence of random censoring and or covariates however the justification for the limiting distribution often requires some technical assumptions and conditions that are difficult to verify in practice moreover a satisfactory asymptotic theory for testing the existence of multiple change points in hazard function has not emerged in this paper we consider maximal score tests for detecting change point s in the cox proportional hazards model with censored data we propose to use a simple monte carlo approach for assessing the statistical significance of tests the proposed approach is applicable for testing a single change point in the cox model with covariates and sample stratifications over various types of candidate regions including discrete time point sets or disjoint intervals we also show that the proposed test statistics and the monte carlo procedure are well applicable under situations with multiple change points simulation studies and an analysis of a real data from a randomized cancer trial are conducted to demonstrate the finite sample performance of the proposed approach

trajectories in godel type space times under the action of a vector field abstract in this paper we consider a godel type lorentz manifold m and look for curves 0 1 m joining two fixed points in m or having prescribed period y t satisfying the system d s s 1 2 curl a s s we find timelike trajectories of these problems

structure of lorentzian tori with a killing vector field all lorentzian tori with a non discrete group of isometries are characterized and explicitly obtained they can lie into three cases a flat b conformally flat but non flat and c geodesically incomplete a detailed study of many of their properties including results on the logical dependence of the three kinds of causal completeness on geodesic connectedness and on prescribed curvature is carried out the incomplete case is specially analyzed and several known examples and results in the literature are generalized from a unified point of view

lightlike rays in stationary spacetimes with critical growth abstract the aim of this paper is to extend some previous results on the existence of lightlike geodesics joining a point to a line to the case of stationary lorentzian manifolds whose metric coefficients have an optimal growth

testing for change point in the covariate effects based on the cox regression model models with change point in covariates have wide applications in cancer research with the response being the time to a certain event a cox model with change point in covariate is considered at which the pattern of the change point effects can be flexibly specified to test for the existence of the change point effects three statistical tests namely the maximal score maximal normalized score and maximal wald tests are proposed the asymptotic properties of the test statistics are established monte carlo approaches to simulate the critical values are suggested a large scale simulation study is carried out to study the finite sample performance of the proposed test statistics under the null hypothesis of no change points and various alternative hypothesis settings each of the proposed methods provides a natural estimate for the location of the change point but it is found that the performance of the maximal score test can be sensitive to the true location of the change point in some cases while the performance of the maximal wald test is very satisfactory in general even in cases with moderate sample size for illustration the proposed methods are applied to two medical datasets concerning patients with primary biliary cirrhosis and breast cancer respectively

closed timelike geodesics in compact spacetimes let m be a compact spacetime which admits a regular globally hyperbolic covering and c a nontrivial free timelike homotopy class of closed timelike curves in m we prove that c contains a longest curve which must be a closed timelike geodesic if and only if the timelike injectivity radius of c is finite i e c has a bounded length as a consequence among others we deduce that for a compact static spacetime there exists a closed timelike geodesic within every nontrivial free timelike homotopy class having a finite timelike injectivity radius

closed geodesies on compact lorentzian manifolds of splitting type in this paper we consider the problem of the existence of a spacelike closed geodesic on compact lorentzian manifolds tipler and galloway proved that under suitable topological properties of the manifold there exists a closed timelike geodesic in their proofs they use the hypothesis that the time coordinate of one timelike geodesic has derivative always different from zero this clearly fails for spacelike geodesies using variational methods and applying the relative category theory we prove the existence of a closed spacelike geodesic on a compact manifold of splitting type observe that thanks to the previous results the existence of at least two geometrically distinct closed geodesies on follows

on a class of geodesically connected lorentzian manifolds in this paper we study the geodesical connectedness of lorentzian manifolds we consider a connected manifold m m0 r where m0is a complete riemannian manifold endowed with a lorentzian metricgof splitting type we prove that under suitable hypotheses on the coefficients of the metricg mis geodesically connected

multiple critical points for indefinite functionals and applications abstract in this paper we prove a multiplicity result for critical points of an indefinite functional on a manifold by using a generalization of the ljusternik schnirelman category the abstract result is applied to prove the existence of multiple timelike trajectories for lorentzian manifolds of splitting type

on the geodesical connectedness for a class of semi riemannian manifolds we prove a variational principle for geodesics on a semi riemannian manifold m of arbitrary index k and possessing k linearly independent killing vector fields that generate a timelike distribution on m using such a principle and a suitable completeness condition for m we prove some existence and multiplicity results for geodesics joining two fixed points of m

weighted log rank type statistics for comparing survival curves when there is a time lag in the effectiveness of treatment summary in certain long term treatment trials one expects some lag period before the treatment is fully effective this paper presents two weighted log rank type statistics designed to have good efficiency over a wide range of lags a maximin efficiency robust statistic and a simplified version of this statistic both statistics can be computed as easily as the log rank statistic asymptotic efficiency calculations supported by small sample simulations show that the two proposed statistics are substantially more efficient than the conventional log rank statistic in certain lag situations with comparatively little efficiency loss relative to the log rank statistic when no lag exists we recommend the maximin statistic for situations where a lag is expected but cannot be specified precisely in advance

global hyperbolicity and palais smale condition for action functionals in stationary spacetimes abstract in order to apply variational methods to the action functional for geodesics of a stationary spacetime some hypotheses useful to obtain classical palais smale condition are commonly used pseudo coercivity bounds on certain coefficients of the metric etc we prove that these technical assumptions admit a natural interpretation for the conformal structure causality of the manifold as a consequence any stationary spacetime with a complete timelike killing vector field and a complete cauchy hypersurface thus globally hyperbolic is proved to be geodesically connected

category of loop spaces of open subsets in euclidean space has been studied in several recent papers e g l 2 5 6 91 in situations where the potential function v is singular in the sense that it is defined and c only on an open subset u of euclidean k space rk and not on the whole of rk if e wgt2 r rk is the sobolev space of t periodic functions from r to rk and e u is the subset of e of functions which map into u then the topology of e u plays a crucial role in these studies in particular the knowledge that the lusternik schnirelmann category of e u is infinite when used in conjunction with min max methods implies the existence of infinitely many critical points another subset e u which consists of those functions in e u which take the origin to a base point in u plays a dual role first of all in problems concerning the existence of geodesics in u from one subset a of u to another b of u see e g 3 the category of e u plays a role secondly the general inequality cat e u 2 cat e u see 6 when u is connected and simply connected can be applied to show that cat e u cat e u thus providing a tool for computing cat e u the topological analogue of e u is the space of free loops au c s u of continuous maps from the circle s to u and the analogue of e u is the space of based loops ru which consists of maps in au which take a base point in s to a base point in u au has the same homotopy type as e u and s2u has the same homotopy type as e u thus homotopy type invariants e g category of e u and e u may be studied through au and szu respectively the following classical theorem of serre l l is useful in this regard and is stated in terms of a general space x

extending positive definiteness the main result of this paper gives criteria for extendibility of mappings defined on symmetric subsets of semigroups to positive definite ones by specifying the mappings in question we obtain new solutions of relevant issues in harmonic analysis concerning truncations of some important multivariate moment problems like complex two sided complex and multidimensional trigonometric moment problems in addition unbounded subnormality and existence of unitary power dilation of several contractions is treated as an application of our general scheme

normal geodesics in static spacetimes with critical asymptotic behavior abstract this paper deals with the existence of normal geodesics joining two given submanifolds in a static spacetime when the coefficient of its metric has a quadratic growth a suitable variational approach allows one to use the classical ljusternik schnirelman theory