lagrangian hamiltonian unified formalism for field theory the rusk skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems it incorporates all the characteristics of lagrangian and hamiltonian descriptions of these systems including dynamical equations and solutions constraints legendre map evolution operators equivalence etc in this work we extend this unified framework to first order classical field theories and show how this description comprises the main features of the lagrangian and hamiltonian formalisms both for the regular and singular cases this formulation is a first step toward further applications in optimal control theory for partial differential equations

multivector fields and connections setting lagrangian equations in field theories the integrability of multivector fields in a differentiable manifold is studied then given a jet bundle j1e e m it is shown that integrable multivector fields in e are equivalent to integrable connections in the bundle e m that is integrable jet fields in j1e this result is applied to the particular case of multivector fields in the manifold j1e and connections in the bundle j1e m that is jet fields in the repeated jet bundle j1j1e in order to characterize integrable multivector fields and connections whose integral manifolds are canonical lifting of sections these results allow us to set the lagrangian evolution equations for first order classical field theories in three equivalent geometrical ways in a form similar to that in which the lagrangian dynamical equations of nonautonomous mechanical systems are usually given then using multivector fields we discuss several aspects of these evolution equations both for the regular and singular cases namely the existence and nonuniqueness o

u statistic processes a martingale approach for i i d data x 1 x n and a kernel h the associated u statistic process is defined as formule mathematique variants of these processes occur for example in the representation of the product limit estimator ofa lifetime distribution for censored truncated data or in trimmed u statistics we derive an almost sure representation of u n under weak moment assumptions on h proofs rely on a proper decomposition of the remainder term into strong two parameter martingales

stein compacts in levi flat hypersurfaces we explore connections between geometric properties of the levi foliation of a levi flat hypersurface m and holomorphic convexity of compact sets in m or bounded in part by m applications include extendability of cauchy riemann functions solvability of the b equation approximation of cauchy riemann and holomorphic functions and global regularity of the neumann operator

the bar partial cauchy problem and nonexistence of lipschitz levi flat hypersurfaces in mathbb c p n with n ge 3 in this paper we study the cauchy riemann equation in complex projective spaces specifically we use the modified weight function method to study the bar partial neumann problem on pseudoconvex domains in these spaces the solutions are used to study function theory on pseudoconvex domains via the bar partial cauchy problem we apply our results to prove nonexistence of lipschitz levi flat hypersurfaces in complex projective spaces of dimension at least three which removes the smoothness requirement used in an earlier paper of siu

analytic subvarieties with many rational points we give a generalization of the classical bombieri schneider lang criterion in transcendence theory we give a local notion of lg germ which is similar to the notion of e function and gevrey condition and which generalize and replace the condition on derivatives in the theorem quoted above let k subset mathbb c be a number field and x a quasi projective variety defined over k let m x be an holomorphic map of finite order from a parabolic riemann surface to x such that the zariski closure of the image of it is strictly bigger then one suppose that for every p in x k cap gamma m the formal germ of m near p is an lg germ then we prove that x k cap gamma m is a finite set then we define the notion of conformally parabolic kahler varieties this generalize the notion of parabolic riemann surface we show that on these varieties we can define a value distribution theory the complementary of a divisor on a compact kahler manifold is conformally parabolic in particular every quasi projective variety is suppose that a is conformally parabolic variety of dimension m over mathbb c with kahler form and a x is an holomorphic map of finite order such that the zariski closure of the image is strictly bigger then m suppose that for every p in x k cap gamma a the image of a is an lg germ then we prove that there exists a current t on a of bidegree 1 1 such that int at wedge omega m 1 explicitly bounded and with lelong number bigger or equal then one on each point in 1 x k in particular if a is affine 1 x k is not zariski dense

hamilton jacobi theory in multisymplectic classical field theories the geometric framework for the hamilton jacobi theory developed in the studies of carinena et al int j geom methods mod phys 3 7 1417 1458 2006 carinena et al int j geom methods mod phys 13 2 1650017 2015 and de leon et al variations geometry and physics nova science publishers new york 2009 is extended for multisymplectic first order classical field theories the hamilton jacobi problem is stated for the lagrangian and the hamiltonian formalisms of these theories as a particular case of a more general problem and the classical hamilton jacobi equation for field theories is recovered from this geometrical setting particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms and the equivalence between them is proved the use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation some examples are analyzed and in particular the h

weighted boundary limits of the generalized kobayashi royden metrics on weakly pseudoconvex domains the purpose of this paper is to study the existence of weighted boundary limits of the generalized kobayashi royden metrics on weakly pseudoconvex domains in cn and to explore the connections between the limits and the levi invariants the main result extends graham s result on strongly pseudoconvex domains to a large class of weakly pseudoconvex domains

multivector field formulation of hamiltonian field theories equations and symmetries we state the intrinsic form of the hamiltonian equations of first order classical field theories in three equivalent geometrical ways using multivector fields jet fields and connections thus these equations are given in a form similar to that in which the hamiltonian equations of mechanics are usually given then using multivector fields we study several aspects of these equations such as the existence and non uniqueness of solutions and the integrability problem in particular these problems are analysed for the case of hamiltonian systems defined in a submanifold of the multimomentum bundle furthermore the existence of first integrals of these hamiltonian equations is considered and the relation between cartan noether symmetries and general symmetries of the system is discussed noether s theorem is also stated in this context both the classical version and its generalization to include higher order cartan noether symmetries finally the equivalence between the lagrangian and hamiltonian formalisms is also discussed

l 2 serre duality on domains in complex manifolds and applications an l 2 version of the serre duality on domains in complex manifolds involving duality of hilbert space realizations of the operator is established this duality is used to study the solution of the equation with prescribed support applications are given to closed extension of forms as well to bochner hartogs type extension of cr functions comp e with the quotient topology where we endow spaces of compactly supported forms with the natural inductive limit topology in fact condition that the two maps in 1 have closed range is also necessary for the duality theorem to hold see 9 also see 26 27 28 for further results of this type serre s original proof 33 is based on sheaf theory and the theory of topological vector spaces a different approach to this result in the case when is a compact complex manifold was given by kodaira using hodge theory see 23 or 7 in this note we extend kodaira s method to non compact hermitian manifolds to obtain an l 2 analog of the serre duality special cases of serre duality using l 2 methods have appeared before in many contexts see 25 or 11 theorem 5 1 7 and 19 20 for example our treatment aims to streamline and systematize these results with emphasis on non compact manifolds and point out its close relation with the choice of l 2 realizations of the cauchy riemann operator or alternatively choice of boundary conditions for the l 2 realizations of the formal complex laplacian e e e e the l 2 duality can be interpreted in many ways at one level it is a duality between the standard laplacian with neumann boundary conditions and thec laplacian with dual dirichlet boundary conditions using another approach results regarding solution of the equation in l 2 can be converted to statements regarding the solution of the c equation this leads to a solution of the cauchy problem i e solution of the equation with prescribed support at the heart of the matter lies the existence of

goldilocks domains a weak notion of visibility and applications in this paper we introduce a new class of domains in complex euclidean space called goldilocks domains and study their complex geometry these domains are defined in terms of a lower bound on how fast the kobayashi metric grows and an upper bound on how fast the kobayashi distance grows as one approaches the boundary strongly pseudoconvex domains and weakly pseudoconvex domains of finite type always satisfy this goldilocks condition but we also present families of goldilocks domains that have low boundary regularity or have boundary points of infinite type we will show that the kobayashi metric on these domains behaves in some sense like a negatively curved riemannian metric in particular it satisfies a visibility condition in the sense of eberlein and o neill this behavior allows us to prove a variety of results concerning boundary extension of maps and to establish wolff denjoy theorems for a wide collection of domains c 2017 elsevier inc all rights reserved

locally adaptive hazard smoothing we consider nonparametric estimation of hazard functions and their derivatives under random censorship based on kernel smoothing of the nelson 1972 estimator one critically important ingredient for smoothing methods is the choice of an appropriate bandwidth since local variance of these estimates depends on the point where the hazard function is estimated and the bandwidth determines the trade off between local variance and local bias data based local bandwidth choice is proposed a general principle for obtaining asymptotically efficient data based local bandwiths is obtained by means of weak convergence of a local bandwidth process to a gaussian limit process several specific asymptotically efficient bandwidth estimators are discussed we propose in particular an asymptotically efficient method derived from direct pilot estimators of the hazard function and of the local mean squared error this bandwidth choice method has practical advantages and is also of interest in the uncensored case as well as for density estimation

on the normal bundle of levi flat real hypersurfaces let x be a connected complex manifold of dimension ge 3 and m a smooth compact levi flat real hypersurface in x we show that the normal bundle to the levi foliation does not admit a hermitian metric with positive curvature along the leaves this generalizes a result obtained by brunella

some asymptotic properties of kernel estimators of a density function in case of censored data on considere l adaptation de l estimateur du noyau a des donnees censurees en utilisant l estimateur de kaplan meier

the pluricomplex poisson kernel for strongly convex domains let d be a bounded strongly convex domain in the complex space of dimension n for a fixed point p epsilon partial derivative d we consider the solution of a homogeneous complex monge ampere equation with a simple pole at p we prove that such a solution enjoys many properties of the classical poisson kernel in the unit disc and thus deserves to be called the pluricomplex poisson kernel of d with pole at p in particular we discuss extremality properties such as a generalization of the classical phragmen lindelof theorem relations with the pluricomplex green function of d uniqueness in terms of the associated foliation and boundary behaviors finally using such a kernel we obtain explicit reproducing formulas for plurisubharmonic functions

integrable three particle systems hidden symmetries and deformations of the calogero moser system the properties of some three particle systems are studied using as an approach the theory of generalized or hidden symmetries it is proven that the existence of a family that possesses in addition to the energy function two nonlinear constants of motion in involution this family of integrable systems is obtained by considering deformations of the lagrangian of the calogero moser system finally the generalization of the results to the general case of n particles is discussed

geometry of multisymplectic hamiltonian first order field theories in the jet bundle description of field theories multisymplectic models in particular there are several choices for the multimomentum bundle where the covariant hamiltonian formalism takes place as a consequence several proposals for this formalism can be stated and on each one of them the differentiable structures needed for setting the formalism are obtained in different ways in this work we make an accurate study of some of these hamiltonian formalisms showing their equivalence in particular the geometrical structures canonical or not needed for the hamiltonian formalism are introduced and compared and the derivation of hamiltonian field equations from the corresponding variational principle is shown in detail furthermore the hamiltonian formalism of systems described by lagrangians is performed both for the hyper regular and almost regular cases finally the role of connections in the construction of hamiltonian field theories is clarified

quasicontinuity and maximality of quaternionic plurisubharmonic functions abstract in this paper we establish the quaternionic versions of several results in the complex pluripotential theory by using the quaternionic closed positive currents which were introduced in 24 we show that quasicontinuity one of the most important properties of complex plurisubharmonic functions holds also for quaternionic plurisubharmonic functions in h n moreover we prove an equivalent characterization of the maximality which is central to the pluripotential theory a locally bounded plurisubharmonic function u is maximal if and only if it satisfies the homogeneous quaternionic monge ampere equation u n 0

the bergman metric on complete kahler manifolds we use the existence of a bounded uniformly holder continuous plurisubharmonic exhaustion function to characterize the bergman completeness of a complete kahler manifold as an application we proved that any simply connected complete kahler manifold with sectional curvature bounded above by a negative constant is bergman complete

bootstrap selection of the smoothing parameter in nonparametric hazard rate estimation abstract an asymptotic representation of the mean weighted integrated squared error for the kernel based estimator of the hazard rate in the presence of right censored samples is obtained for different bootstrap resampling methods as a consequence a new bandwidth selector based on the bootstrap is introduced very satisfactory simulations results are obtained in comparison to the cross validation selector for different models using warped i e binned versions of the estimators

sur l existence et la regularite de solutions radiales pour des equations de type monge ampere complexe on etablit des resultats d existence et de regularite pour l equation de type monge ampere complexe suivante dans la boule de c n det u ij f z u z xu z z b u b 0 ou f est une fonction positive et radiale en la premiere variable dans b r 2 et x est le champ radial regulier x i 1 2n x i xi

a correction to and improvement of strong approximations of some biometric estimates under random censorship in the proof of the main result of the original paper there is an error instead of repairing that proof to get just the original result at the critical spot we improve the proof and obtain a much better result in particular we approximate the product limit and empirical cumulative hazard processes by suitable copies of the corresponding limiting gaussian processes with rates of approximation that on appropriate fixed half lines reduce to the rates of komlos major and tusnady for the uncensored empirical process

constrained variational calculus for higher order classical field theories we develop an intrinsic geometrical setting for higher order constrained field theories as a main tool we use an appropriate generalization of the classical skinner rusk formalism some examples of applications are studied in particular to the geometrical description of optimal control theory for partial differential equations

a histogram estimator of the hazard rate with censored data a histogram type estimator of the hazard rate of lifetimes which are randomly right censored is studied this estimator is based on random spacings of the order statistics of uncensored observations and extends the idea of the histogram density estimation suggested by van ryzin 1973 to censored data in this paper we establish pointwise large sample properties of the estimator including strong consistency strong uniform consistency on a bounded interval and two asymptotic distribution results of particular interest is the distribution result obtained by imposing extra symmetry conditions on the interval covering the given point in fact it yields the best attainable rate of convergence among all nonnegative estimators comparisons of our results with the kernel type estimators proposed in the literature are also given

k cosymplectic manifolds and lagrangian field theories a geometrical description of classical field theories of first order is given the underlying k cosymplectic structure permits to derive the corresponding field equations

reduction of polysymplectic manifolds the aim of this paper is to generalize the classical marsden weinstein reduction procedure for symplectic manifolds to polysymplectic manifolds in order to obtain quotient manifolds which inherit the polysymplectic structure this generalization allows us to reduce polysymplectic hamiltonian systems with symmetries such as those appearing in certain kinds of classical field theories as an application of this technique an analogue to the kirillov kostant souriau theorem for polysymplectic manifolds is obtained and some other mathematical examples are also analyzed our procedure corrects some mistakes and inaccuracies in previous papers gunther 1987 j differ geom 25 23 53 munteanu et al 2004 j math phys 45 1730 51 on this subject

a note on the variable kernel estimator of the hazard function from randomly censored data in a recent paper tanner and wong 1983b a family of data based nonparametric hazard estimators was introduced several of these estimators were studied in an extensive simulation experiment the estimator which allows for variable bandwidth was found to have a superior performance in this note sufficient conditions for the variable kernel estimator to be strongly consistent are presented

an integrable three particle system a study of the existence of some integrable systems with nonlinear constants of motion is presented using the approach of the theory of generalized dynamical or hidden symmetries two lagrangians are considered both obtained by modifying the toda lagrangian first a two particle system is studied and then the results are generalized to a three particle system it is shown that in both cases the lagrangians possess nonlinear constants of motion in involution and thus they are integrable

monge ampere equations and moduli spaces of manifolds of circular type abstract a bounded manifold of circular type is a complex manifold m of dimension n admitting a bounded exhaustive real function u defined on m minus a point x o so that a it is a smooth solution on m x o to the monge ampere equation d d c u n 0 b x o is a singular point for u of logarithmic type and e u extends smoothly on the blow up of m at x o c d d c e u 0 at any point of m x o this class of manifolds naturally includes all smoothly bounded strictly linearly convex domains and all smoothly bounded strongly pseudoconvex circular domains of c n a set of modular parameters for bounded manifolds of circular type is considered in particular for each biholomorphic equivalence class of them it is proved the existence of an essentially unique manifold in normal form it is also shown that the class of normalizing maps for an n dimensional manifold m is a new holomorphic invariant with the following property it is parameterized by the points of a finite dimensional real manifold of dimension n 2 when m is a non convex circular domain while it is of dimension n 2 2 n when m is a strictly linearly convex domain new characterizations of the circular domains and of the unit ball are also obtained

a sobolev mapping property of the bergman kernel we prove that if d is a pseudoconvex domain with lipschitz boundary having an exhaustion function rho such that rho eta is plurisubharmonic then the bergman projection maps the sobolev space w s boundedly to itself for any s eta 2

on a kind of noether symmetries and conservation laws in k cosymplectic field theory this paper is devoted to studying symmetries of certain kinds of k cosymplectic hamiltonian systems in first order classical field theories thus we introduce a particular class of symmetries and study the problem of associating conservation laws to them by means of a suitable generalization of noether s theorem

quasianalyticity and pluripolarity be the graph of in c2 the set tf is always pluripolar when is a real analytic function in df diederich and fornaess give an example of a c function with nonpluripolar graph in c2 the paper lmp contains an example of a holomorphic function on the unit disk u continuous up to the boundary such that the graph of over s is not pluripolar as a subset of c2 thus a priori the pluripolarity of graphs of functions on s is indeterminate in this paper we prove that graphs of quasianalytic functions are still pluripolar all necessary definitions can be found in the next section more precisely

a quantitative analysis of oka s lemma in this paper we will examine a strong form of oka s lemma which provides sufficient conditions for compact and subelliptic estimates for the overline partial neumann operator on lipschitz domains on smooth domains the condition for subellipticity is equivalent to d angelo finite type and the condition for compactness is equivalent to catlin s condition p as an application we will prove regularity for the overline partial neumann operator in the sobolev space ws 0 leq s frac 1 2 on c2 domains

nonparametric inference for copulas and measures of dependence under length biased sampling and informative censoring length biased data are often encountered in cross sectional surveys and prevalent cohort studies on disease durations under length biased sampling subjects with longer disease durations have great

the polysymplectic hamiltonian formalism in field theory and calculus of variations i the local case on presente un formalisme hamiltonien geometrique invariant pour des problemes variationnels a integrale multiple et des theories de champ le formalisme est base sur la notion de forme polysymplectique qui est une generalisation a valeur vectorielle des formes symplectiques on etudie des equations hamiltoniennes des transformations canoniques des systemes de lagrange des symetries des applications en pulsion de theorie du champ et une classification des systemes de theorie du champ g homogenes sur une generalisation des orbites coadjointes

density and hazard rate estimation for censored data via strong representation of the kaplan meier estimator we study the estimation of a density and a hazard rate function based on censored data by the kernel smoothing method our technique is facilitated by a recent result of lo and singh 1986 which establishes a strong uniform approximation of the kaplan meier estimator by an average of independent random variables note that the approximation is carried out on the original probability space which should be distinguished from the hungarian embedding approach pointwise strong consistency and a law of iterated logarithm are derived as well as the mean squared error expression and asymptotic normality which is obtain using a more traditional method as compared with the hajek projection employed by tanner and wong 1983

the gunther s formalism in classical field theory momentum map and reduction the polysymplectic formalism in local field theory developed by gunther j diff geom 25 23 1987 is revised a new approach and new results on momentum maps and reduction are given

k symplectic structures the basic properties of k symplectic structures are introduced and developed in analogy with the well known symplectic differential geometry examples of such structures related to k symplectic lie algebras are given

the diederich fornaess index i for domains of non trivial index abstract we study bounded pseudoconvex domains in complex euclidean space we define an index associated to the boundary and show this new index is equivalent to the diederich fornaess index defined in 1977 this connects the diederich fornaess index to boundary conditions and refines the levi pseudoconvexity we also prove the worm domain is of index 2 it is the first time that a precise non trivial diederich fornaess index in euclidean spaces is obtained this finding also indicates that the diederich fornaess index is a continuum in 0 1 not a discrete set the ideas of proof involve a new complex geometric analytic technique on the boundary and detailed estimates on differential equations

q complete domains with corners in mathbb p n and extension of line bundles we show that if a compact set x in mathbb p n is laminated by holomorphic submanifolds of dimension q then mathbb p n setminus x is q 1 complete with corners consider a manifold u q complete with corners let mathcal n be a holomorphic line bundle in the complement of a compact in u we study when mathcal n extends as a holomorphic line bundle in u we give applications to the non existence of some levi flat foliations in open sets in mathbb p n the results apply in particular when u is a stein manifold of dimension n 3 then every holomorphic line bundle in the complement of a compact extends holomorphically to u

the product limit estimator and the bootstrap some asymptotic representations the product limit estimator and its quantile process are represented as i i d mean processes with a remainder of ordern 3 4 logn 3 4 a s corresponding bootstrap versions of these representations are given which can help one visualize how the bootstrap procedure operates in this set up

plurisubharmonic approximation and boundary values of plurisubharmonic functions we study the problem of approximating plurisubharmonic functions on a bounded domain omega by continuous plurisubharmonic functions defined on neighborhoods of omega over bar it turns out that t

an extremal problem for generalized lelong numbers we look for pointwise bounds on a plurisubharmonic function near its singularity point given the value of its generalized lelong number with respect to a plurisubharmonic weight to this end an extremal problem is considered in certain cases the problem is solved explicitly

hazard function estimators a simulation study kernel based methods for the smooth non parametric estimation of the hazard function have received considerable attention in the statistical literature although the mathematical properties of the kernel based hazard estimators have been carefully studied their statistical properties have not we reviewed various kernel based methods for hazard function estimation from right censored data and compared the statistical properties of these estimators through computer simulations our simulations covered seven distributions three levels of random censoring four types of bandwidth functions two sample sizes and three types of boundary correction we conducted a total of 504 simulation experiments with 500 independent samples each our results confirmed the advantages of two recent innovations in kernel estimation boundary correction and locally optimal bandwidths the median relative improvement decrease in mean square error over fixed bandwidth estimators without boundary correction was 3 per cent for fixed bandwidth estimators with left boundary correction 52 per cent locally optimal bandwidths without boundary correction and 66 per cent for locally optimal bandwidths with left boundary correction the locally optimal bandwidth estimators with left boundary correction also outperformed three previously published and publicly available algorithms with median relative improvements in mean square error of 31 per cent 77 per cent and 80 per cent

nonparametric analysis of changes in hazard rates for censored survival data an alternative to change point models summary as a nonparametric estimator for the point of the most rapid change of a hazard rate we propose the location of an extremum of a nonparametric estimate of the derivative or equivalently of a zero of a nonparametric estimate of the second derivative using the kernel method for the nonparametric estimation of derivatives of the hazard rate the asymptotic local limiting distribution and uniform consistency are applied to prove consistency and to find the limiting distribution of these estimators under random censoring and to construct confidence intervals both for the derivatives of the hazard rate and for the point of most rapid change an application to leukaemia data illustrates this concept and we discuss its relations to change point modelling the monte carlo method is used to assess the reliability of finite sample analyses and in particular of the given example

superintegrable n 2 systems quadratic constants of motion and potentials of drach the properties of superintegrable systems in two degrees of freedom possessing three independent globally defined constants of motion are studied using as an approach the existence of hidden symmetries and the generalized noether s theorem the potentials are obtained as solution of a system of two partial differential equations first the case of standard lagrangians is studied and then the method is applied to the case of lagrangians with a pseudo euclidean kinetic term finally the results are related with other approaches and with a family of potentials admitting a second integral of motion cubic in the velocities obtained by drach

extended hamiltonian systems in multisymplectic field theories we consider hamiltonian systems in first order multisymplectic field theories we review the properties of hamiltonian systems in the so called restricted multimomentum bundle including the variational principle which leads to the hamiltonian field equations in an analogous way to how these systems are defined in the so called extended symplectic formulation of nonautonomous mechanics we introduce hamiltonian systems in the extended multimomentum bundle the geometric properties of these systems are studied the hamiltonian equations are analyzed using integrable multivector fields the corresponding variational principle is also stated and the relation between the extended and the restricted hamiltonian systems is established all these properties are also adapted to certain kinds of submanifolds of the multimomentum bundles in order to cover the case of almost regular field theories

compact and subelliptic estimates for the overline partial neumann operator on c2 pseudoconvex domains in this paper we will show that catlin s property p implies regularity for the overline partial neumann operator in w 1 on c 2 domains we will also look at the subelliptic case and derive the natural generalization to c k domains when k 2

two sample inference for median survival times based on one sample procedures for censored survival data abstract confidence intervals for median survival times are derived for censored survival data the intervals are obtained by using the quantiles of the kaplan meier product limit estimator and have the same pitman efficiency as the intervals found by inverting the sign test two sample tests and confidence intervals for the difference in median survival times are then developed based on the comparison of the one sample confidence intervals several methods for choosing the confidence coefficients of the corresponding one sample confidence intervals are developed the pitman efficiencies of these two sample tests are the same as that of the median test proposed by brookmeyer and crowley 1982a the procedures can also be used for the accelerated failure time model proportional hazard model and the behrens fisher problem nonparametric two sample inference procedures are useful in comparing the responses of treatment and control groups in medical follow up studies the data are usually subjected to cens

estimates for the neumann problem and nonexistence of c 2 levi flat hypersurfaces in cp n letbe a pseudoconvex domain with c 2 boundary in cp n n 2 we prove that the neumann operator n exists for square integrable forms on furthermore there exists a number 0 0 such that the operators n n n and the bergman projection are regular in the sobolev space w for 0 and n 2 as a consequence we prove the nonexistence of c 2 levi flat hypersurfaces in cp n

higher order noether symmetries and constants of the motion the authors identify a class of symmetries for lagrangian systems called higher order noether symmetries which yield a corresponding first integral without further integrations first a version of noether s theorem is recalled in which noether symmetries are considered to be symmetries of the two form d theta theta being the cartan form nth order noether symmetries are then defined by the requirement lynd theta 0 the picture is further generalised by exploring various ways in which the computation of repeated lie derivatives of d theta can lead to the identification of first integrals a number of illustrative examples are discussed

approximation of plurisubharmonic functions by multipole green functions for a strongly hyperconvex domain d c c n we prove that multipole pluricomplex green functions are dense in the cone in l 1 d of negative plurisubharmonic functions with zero boundary values

the estimation of the hazard function from randomly censored data by the kernel method by convolution smoothing of the empirical hazards a kernel estimate of the hazard function from censored data is obtained small and large sample expressions for the mean and the variance of the estimator are given conditions for asymptotic normality are investigated using the hajek projection method

laws of the iterated logarithm for nonparametric density estimators we establish a law of the iterated logarithm for a triangular array of independent random variables and apply it to obtain laws for a large class of nonparametric density estimators we consider the case of rosenblatt parzen kernel estimators trigonometric series estimators and orthogonal polynomial estimators in detail and point out that our technique has wider application

the bergman metric and the pluricomplex green function we improve a lower bound for the bergman distance in smooth pseudoconvex domains due to diederich and ohsawa as the main tool we use the pluricomplex green function and an l 2 estimate for the operator of donnelly and fefferman

hamiltonian systems on k cosymplectic manifolds the hamiltonian framework on symplectic and cosymplectic manifolds is extended in order to consider classical field theories to do this the notion of k cosymplectic manifold is introduced and a suitable hamiltonian formalism is developed so that the field equations for scalar and vector hamiltonian functions are derived