existence of maximal surfaces in asymptotically flat spacetimes we prove the existence of maximal surfaces in asymptotically flat spacetime satisfying an interior condition this uses a priori estimates which can also be applied to prescribed mean curvature surfaces in cosmological spacetimes and the dirichlet problem

inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function abstract the purpose of the present paper is to introduce several new classes of meromorphic functions defined by using a meromorphic analogue of the choi saigo srivastava operator for the generalized hypergeometric function and investigate various inclusion properties of these classes some interesting applications involving these and other classes of integral operators are also considered

classes of analytic functions associated with the choi saigo srivastava operator we investigate several properties of the linear choi saigo srivastava operator and associated classes of analytic functions which were introduced and studied by j h choi m saigo and h m srivastava j h choi m saigo h m srivastava some inclusion properties of a certain family of integral operators j math anal appl 276 2002 432 445 several theorems are an extension of earlier results of the above paper

some applications of miller mocanu lemma on certain classes of meromorphic functions in this paper making use of a linear operator we introduce and study certain new classes of meromorphic functions we derive some inclusion results these classes contain many known classes as a special case

the noor integral and strongly starlike functions abstract let a denote the class of analytic functions f z defined in the unit disc satisfying the condition f 0 f 0 1 0 we introduce some new subclasses of strongly starlike functions defined by the noor integral and study their properties

lines in space times we construct a complete timelike maximal geodesic line in a timelike geodesically complete spacetimem containing a compact acausal spacelike hypersurfaces which lies in the past of somes ray ans ray is a future complete geodesic starting ons which maximizes lorentzian distance froms to any of its points if the timelike convergence condition strong energy condition holds a line exists only ifm is static i e it splits geometrically as space time so timelike completeness must fail for a nonstatic spacetime with strong energy condition which contains a closed universe s with the above properties

on some applications of certain integral operators in this paper we investigate several interesting applications and inclusion results of a certain integral operator and its associated classes of analytic functions in the unit disc

the lorentzian splitting theorem without the completeness assumption on demontre le theoreme de decomposition lorentzien pour des espace temps globalement hyperboliques obeissant a la condition d energie forte sans hypothese de completude geodesique du genre temps

remarks on cosmological spacetimes and constant mean curvature surfaces we give a general condition which ensures the existence of constant mean curvature cmc cauchy surfaces in cosmological spacetimes however there is an example of a spacetime which does not satisfy this condition and does not admit any cmc cauchy surfaces we discuss conditions under which cmc surfaces may exist

inclusion properties of certain subclasses of analytic functions defined by a multiplier transformation let a denote the class of analytic functions with the normalization 0 0 1 0 in the open unit disk u set f l s z z k 2 k l1 l sz k s l 1 z u and define l m s in terms of the hadamard productf l s z f l m s z z 1 z m m 0 z u in this paper the authors introduce several new subclasses of analytic functions defined by means of the operator i l m s a a given byi l m sf z f l m s z f z f a s l 1 m 0 inclusion properties of these classes and the classes involving the generalized libera integral operator are also considered

some inclusion properties of a certain family of integral operators abstract the authors introduce several new subclasses of analytic functions which are defined by means of a general integral operator i and investigate various inclusion properties of these subclasses many interesting applications involving these and other families of integral operators are also considered

some inclusion relationships and integral preserving properties of certain subclasses of meromorphic functions associated with a family of integral operators the object of the present paper is to investigate a family of integral operators defined on the space of normalized meromorphic functions by making use of these novel integral operators we introduce and investigate several new subclasses of starlike convex close to convex and quasi convex meromorphic functions in particular we establish some inclusion relationships associated with the aforementioned integral operators several interesting integral preserving properties are also considered

geometric analysis of lorentzian distance function on spacelike hypersurfaces some analysis on the lorentzian distance in a spacetime with controlled sectional or ricci curvatures is done in particular we focus on the study of the restriction of such distance to a spacelike hypersurface satisfying the omori yau maximum principle as a consequence and under appropriate hypotheses on the sectional or ricci curvatures of the ambient spacetime we obtain sharp estimates for the mean curvature of those hypersurfaces moreover we also give a sufficient condition for its hyperbolicity

the isometry groups of asymptotically flat asymptotically empty space times with timelike adm four momentum we give a complete classification of all connected isometry groups together with their actions in the asymptotic region in asymptotically flat asymptotically vacuum space times with timelike adm four momentum

a new dirichlet process for mining dynamic patterns in functional data this paper proposes a novel model for mining patterns including dynamic function clustering segmentation and forecasting values of dependent variables simultaneously the proposed dependent dirichlet process piecewise regression mixture ddpprm model is capable of handling dynamic nature of data by detecting evolving clusters at each time step this evolution manifests dynamically in three states of clusters newly created existing and transient states of clusters the model is also able to generate clusters over time infinitely it is capable of learning the optimal number of clusters rather than using the fixed predefined clusters however other clustering methods such as fuzzy c regression model and piecewise regression mixture technique support none of those capabilities the proposed model is also capable of showing regime changes and segmenting functions in regression time series problems a two step gibbs sampling method is utilized for assigning data to clusters expectation maximization method is used for finding the optimal values of parameters of functions and probability distributions the model is validated by using some numerical experiments and calculating three validity indexes as well as mean square error of the model the results indicate that the proposed method outperforms other clustering segmentation and forecasting models in literature

some inclusion relationships associated with dziok srivastava operator in this paper we introduce and study some new subclasses of p valent starlike convex close to convex and quasi convex functions defined by dziok srivastava operator inclusion relationships are established and integral operator of functions in these subclasses is discussed

parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes spacelike hypersurfaces of prescribed mean curvature in cosmological spacetimes are constructed as asymptotic limits of a geometric evolution equation in particular an alternative constructive proof is given for the existence of maximal and constant mean curvature slices

inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators abstract by making use of a general linear operator i p a c the authors introduce several new subclasses of multivalent functions and investigate various inclusion relationships and argument properties associated with these subclasses some interesting applications involving such and other families of linear operators are also considered the results presented here include a number of known results as their special cases

some results about the level sets of lorentzian busemann function and bartnik s conjecture some results about the level sets of busemann functions are obtained for spacetimes and in a special case cosmological spacetime these results will be used to prove the conjecture stated by r bartnik in b under some special conditions in this paper we employ some results of galloway horta and eschenburg

splitting theorems for spatially closed space times a lorentzian splitting theorem is obtained for spatially closed spacetimes the proof employs and extends some recent results of bartnik and gerhardt concerning the existence and rigid uniqueness of compact maximal hypersurfaces in spatially closed space times a splitting theorem for spatially closedtime periodic space times which generalizes a result first considered by avez is derived as a corollary

inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations making use of a multiplier transformation which is defined here by means of the hadamard product or convolution the authors introduce some new subclasses of meromorphic functions and investigate their inclusion relationships and argument properties some integral preserving properties in a given sector are also considered

regularity of lorentzian busemann functions a general theory of regularity for lorentzian busemann functions in future timelike geodesically complete spacetimes is presented this treatment simplifies and extends the local regularity developed by eschenburg galloway and newman to prove the lorentzian splitting theorem criteria for global regularity are obtained and used to improve results in the literature pertaining to a conjecture of bartnik

some preserving subordination and superordination of analytic functions involving the liu owa integral operator in this paper we obtain some subordination and superordination preserving results of analytic functions involving the liu owa integral operator sandwich type result is also obtained

classes of multivalent functions associated with a convolution operator we investigate several properties of the linear aouf silverman srivastava operator and associated classes of multivalent analytic functions which were introduced and studied by aouf et al m k aouf h silverman h m srivastava some families of linear operators associated with certain subclasses of multivalent functions comp math appl 55 2008 535 549 several theorems are extensions of earlier results of the above paper

on integral operators abstract let fn z z 1 z n 1 n no and f 1 n be defined such that f n f 1 n z 1 z where denotes convolution hadamard product let f be analytic in the unit disc e we define a new operator inf f 1 n f which is analogous to one defined by ruscheweyh using this operator the classes m n are defined a function f analytic in e is in m n if and only if inf is close to convex the properties of f m n are discussed in some detail it is shown that m n m n 1 for n no and for n 0 1 m n consists entirely of univalent functions closure properties of some integral operators defined on m n are also given

a unified class of analytic functions involving a generalization of the srivastava attiya operator in this paper we present a unified class of analytic functions defined by a new convolution operator j p q b s a introduced recently by srivastava and gaboury 2014 which generalizes the well known srivastava attiya operator investigated by srivastava and attiya 2007 we derive coefficient inequalities growth and distortion theorems extreme points and fekete szego problem for this new function class

differential subordinations and inequalities in the complex plane abstract let p be analytic in the unit disc u and let q be univalent in u in addition let be a set in c and let c3 u c the authors determine conditions on so that p z zp z z 2 p z z z u p u q u applications of this result to differential inequalities differential subordinations and integral inequalities are presented

decomposition theorems for lorentzian manifolds with nonpositive curvature soit m g un espace temps globalement hyperbolique de dimension 2 avec partout des courbures sectionnelles du genre temps non positives k 0 qui contient une ligne du genre temps complete m g alors m g est isometrique a un produit r h dt 2 h ou h h est une variete de riemann complete le facteur r dt 2 est represente par et h h est represente par un ensemble de niveau d une fonction de busemann associee a

on certain subclasses of multivalent functions associated with an extended fractional differintegral operator abstract in the present paper an extended fractional differintegral operator z p p 1 p n suitable for the study of multivalent functions is introduced various mapping properties and inclusion relationships between certain subclasses of multivalent functions are investigated by applying the techniques of differential subordination relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out