computing moments of discrete order statistics from non identical distributions abstract in life testing and reliability studies it is commonly assumed that the lifetimes come from a continuous distribution while this often makes derivations more tractable under certain circumstances it may be more realistic to assume a discrete distribution recent literature has heavily focused on the former and with this results have been aimed at deriving properties in the case of independent and identically distributed random variables and associated order statistics in this paper we consider the case of discrete order statistics from non identical distributions we derive expression for single and product moments and with this covariances we demonstrate the results for the geometric and binomial distributions

a semi implicit scheme for stationary statistical properties of the infinite prandtl number model we propose a semidiscrete in time semi implicit numerical scheme for the infinite prandtl model for convection besides the usual finite time convergence this scheme enjoys the additional highly desirable feature that the stationary statistical properties of the scheme converge to those of the infinite prandtl number model at vanishing time step one of the key characteristics of the scheme is that it preserves the dissipativity of the infinite prandtl number model uniformly in terms of the time step so far as we know this is the first rigorous result on convergence of stationary statistical properties of numerical schemes for infinite dimensional dissipative complex systems

boundary layers associated with incompressible navier stokes equations the noncharacteristic boundary case abstract the goal of this article is to study the boundary layer of wall bounded flows in a channel at small viscosity when the boundaries are uniformly noncharacteristic i e there is injection and or suction everywhere at the boundary following earlier work on the boundary layer for linearized navier stokes equations in the case where the boundaries are characteristic no slip at the boundary and non permeable we consider here the case where the boundary is permeable and thus noncharacteristic the form of the boundary layer and convergence results are derived in two cases linearized equation and full nonlinear equations we prove that there exists a boundary layer at the outlet downwind of the form e uz e where u is the speed of injection suction at the boundary z is the distance to the outlet of the channel and e is the kinematic viscosity we improve an earlier result of s n alekseenko 1994 siberian math j 35 no 2 209 230 where the convergence in l 2 of the solutions of the navier stokes equations to that of the euler equations at vanishing viscosity was established in the two dimensional case we are able to derive the physically relevant uniform in space l norm estimates of the boundary layer the uniform in space estimate is derived by properly developing our previous idea of better control on the tangential derivative and the use of an anisotropic sobolev imbedding to the best of our knowledge this is the first rigorously proved result concerning boundary layers for the full nonlinear navier stokes equations for incompressible fluids

hardy spaces and the szegő projection of the non smooth worm domain dβ we define hardy spaces hp d p 1 on the non smooth worm domain d z1 z2 c2 imz1 log z2 2 2 log z2 2 2 and we prove a series of related results such as the existence of boundary values on the distinguished boundary d of the domain and a fatou type theorem i e pointwise convergence to the boundary values thus we study the szeg projection operator s and the associated szeg kernel kd more precisely if hp d denotes the space of functions which are boundary values for functions in hp d we prove that the operator s extends to a bounded linear operator s lp d hp d for every p 1 and s wk p d wk p d for every k 0 here wk p denotes the sobolev space of order k and underlying lp norm p 1 as a consequence of the lp boundedness of s we prove that hp d c d is a dense subspace of hp d

toeplitz operators and weighted bergman kernels abstract for a smoothly bounded strictly pseudoconvex domain we describe the boundary singularity of weighted bergman kernels with respect to weights behaving like a power possibly fractional of a defining function and more generally of the reproducing kernels of sobolev spaces of holomorphic functions of any real order this generalizes the classical result of fefferman for the unweighted bergman kernel finally we also exhibit a holomorphic continuation of the kernels with respect to the sobolev parameter to the entire complex plane our main tool are the generalized toeplitz operators of boutet de monvel and guillemin

blowup of solutions of the unsteady prandtl s equation we prove that for certain class of compactly supported c initial data smooth solutions of the unsteady prandtl s equation blow up in nite time

the bergman kernel function and proper holomorphic mappings it is proved that a proper holomorphic mapping f between bounded complete reinhardt domains extends holomorphically past the boundary and that if in addition f 1 0 01 then f is a polynomial mapping the proof is accomplished via a transformation rule for the bergman kernel function under proper holomorphic mappings

initial boundary layer associated with the nonlinear darcy brinkman oberbeck boussinesq system abstract in this paper we study the vanishing darcy number limit of the nonlinear darcy brinkman oberbeck boussinesq system dbob this singular perturbation problem involves singular structures both in time and in space giving rise to initial layers boundary layers and initial boundary layers we construct an approximate solution to the dbob system by the method of multiple scale expansions the convergence with optimal convergence rates in certain sobolev norms is established rigorously via the energy method

computing the moments of order statistics from nonidentically distributed weibull variables this paper presents a table for computing all single moments of any order of all order statistics o s arising from n independent nonidentically distributed weibull random variables r v s the table is very useful as it will enable one to evaluate all moments in a simple algorithm it is interesting to mention that the coefficients table is similar to pascal s rule

initial boundary layer associated with the nonlinear darcy brinkman system abstract we study the interaction of initial layer and boundary layer in the nonlinear darcy brinkman system in the vanishing darcy number limit in particular we show the existence of a function of corner layer type so called initial boundary layer in the solution of the nonlinear darcy brinkman system an approximate solution is constructed by the method of multiple scale expansion in space and in time we establish the optimal convergence rates in various sobolev norms via energy method

the lp boundedness of the bergman projection for a class of bounded hartogs domains abstract we generalize the hartogs triangle to a class of bounded hartogs domains and we prove that the corresponding bergman projection is bounded on l p if and only if p is in the range 2 n n 1 2 n n 1

boundary layer analysis of the navier stokes equations with generalized navier boundary conditions we study the weak boundary layer phenomenon of the navier stokes equations with generalized navier friction boundary conditions u n 0 s u n tan au 0 in a bounded domain in r3 when the viscosity e 0 is small here s u is the symmetric gradient of the velocity u and a is a type 1 1 tensor on the boundary when a i we obtain navier boundary conditions and when a is the shape operator we obtain the conditions u n curlu n 0 by constructing an explicit corrector we prove the convergence as e tends to zero of the navier stokes solutions to the euler solution both in the natural energy norm and uniformly in time and space

defining equations for real analytic real hypersurfaces in ⁿ a defining function for a real analytic real hypersurface can be utliquely written as 2 re h e where h is holomorphic and e contains no pure terms we study how h and e change when we perform a local biholomorphic change of coordinates or multiply by a unit one of the main results is necesary and sufficient conditions on the first nonvanishing homogeneous part of e expanded in terms of h beyond eoo that serve as obstructions to writing a defining equation as 2 re h e where e is independent of h we also find necessary pluriharmonic obstructions to doing this which arise from the easier case of attempting to straighten the hypersurface

on the vanishing viscosity limit in a disk we say that a solution of the navier stokes equations converges in the vanishing viscosity limit to a solution of the euler equations if their velocities converge in the energy l2 norm uniformly in time as the viscosity vanishes we show that a necessary and sufficient condition for the vanishing viscosity limit to hold in a disk is that the space time energy density of the solution to the navier stokes equations in a boundary layer of width proportional to vanish with and that one need only consider spatial variations whose frequencies in the radial or tangential direction lie in a band centered around 1

equation de lewy resolubilite globale de l equation partial_b u f sur la frontiere de domaines faiblement pseudo convexes de mathbf c 2 mathrm ou mathbf c n

the euler limit of the navier stokes equations and rotating fluids with boundary in this paper we study the convergence of weak solutions of the navier stokes equations in some particular domains with different horizontal and vertical viscosities when they go to zero with different speeds the difficulty here comes from the dirichlet boundary conditions precisely we show that if the ratio of the vertical viscosity to the horizontal viscosity also goes to zero then the solutions converge to the solution of the euler system we study the same limit for rotating fluids with rossby number also going to zero

boundary layer associated with the darcy brinkman boussinesq model for convection in porous media abstract we study the asymptotic behavior of the infinite darcy prandtl number darcy brinkman boussinesq system for convection in porous media at a small brinkman darcy number the existence of a boundary layer with thickness proportional to the square root of the brinkman darcy number for the velocity field is established in both the l h 1 norm in 2 and 3 d and the l l norm in 2d this improves in several respects an earlier result of payne and straughan 1998 60 where the vanishing brinkman darcy number limit is studied without resolving the boundary layer

product domains multi cauchy transforms and the equation abstract solution operators for the equation u f are constructed on general product domains in c n when the factors are one dimensional the operator is a simple integral operator specific derivatives of f are integrated against iterated cauchy kernels for higher dimensional factors the solution is constructed by solving sub equations with modified data on the factors estimates in several norms are proved

discrete kato type theorem on inviscid limit of navier stokes flows the inviscid limit of wall bounded viscous flows is one of the unanswered central questions in theoretical fluid dynamics here we present a somewhat surprising result related to numerical approximation of the problem more precisely we show that numerical solutions of the incompressible navier stokes equations converge to the exact solution of the euler equations at vanishing viscosity and vanishing mesh size provided that small scales of the order of u in the directions tangential to the boundary are not resolved in the scheme here is the kinematic viscosity of the fluid and u is the typical velocity taken to be the maximum of the shear velocity at the boundary for the inviscid flow such a result is somewhat counterintuitive since the convergence is ensured even in the case that small scales predicted by the conventional theory of turbulence and boundary layer are not resolved since under resolution which is allowed in our theorem in advection dominated problem usually leads to oscillation whic

the bergman projection on hartogs domains in estimates in l 2 sobolev norms are proved for the bergman projection in certain smooth bounded hartogs domains in c 2 in particular 1 if the domain is pseudoconvex and nonwormlike the normal vector does not wind on a critical set in the boundary then the bergman projection is regular and 2 barrett s counter example domains with irregular bergman projection nevertheless admit a priori estimates

moments of order statistics from dnid discrete random variables with application in reliability abstract in this paper we present methods of obtaining single moments of order statistics arising from possibly dependent and non identically distributed discrete random variables we derive exact and approximate formulas convenient for numerical evaluation of such moments to demonstrate their use we tabulate means and second moments of order statistics from random vectors having some typical discrete distributions with selected parameter values next we apply our results in reliability theory we establish moments of discrete lifetimes of coherent systems consisting of heterogeneous and not necessarily independently working components in particular we obtain expression for expectations and variances of lifetimes of such systems we give some illustrative examples

sobolev estimates for the bar partial neumann operator on domains inc n admitting a defining function that is plurisubharmonic on the boundary neumann operator on domains inc n admitting a defining function that is plurisubharmonic on the boundary

on the automorphism group of a certain infinite type domain in c2 abstract in this study we consider an infinite type domain p in c 2 the aim of this study is to investigate the holomorphic vector fields tangent to an infinite type model in c 2 vanishing at an infinite type point and to give an explicit description of the automorphism group of p

a multivariate extension of hoeffding s lemma abstract hoeffding s lemma gives an integral representation of the covariance of two random variables in terms of difference between their joint and marginal probability functions this identity has been found to be useful tool in studying the dependence structure of various random vectors a generalization of this result for more than 2 random variables is given this involves an integral representation of the multivariate joint cumulant applications of this result include characterizations of independence relationships with various types of dependence are also given author

characterizing strong pseudoconvexity obstructions to biholomorphisms and lyapunov exponents in this paper we consider the following question for bounded domains with smooth boundary can strong pseudoconvexity be characterized in terms of the intrinsic complex geometry of the domain our approach to answering this question is based on understanding the dynamical behavior of real geodesics in the kobayashi metric and allows us to prove a number of results for domains with low regularity for instance we show that for convex domains with c 2 epsilon boundary strong pseudoconvexity can be characterized in terms of the behavior of the squeezing function near the boundary the behavior of the holomorphic sectional curvature of the bergman metric near the boundary or any other reasonable measure of the complex geometry near the boundary the first characterization gives a partial answer to a question of fornaess and wold as an application of these characterizations we show that a convex domain with c 2 epsilon boundary which is biholomorphic to a strongly pseudoconvex domain is also strongly pseudoconvex

on the global existence of solutions to the prandtl s system abstract in this paper we establish a global existence of weak solutions to the two dimensional prandtl s system for unsteady boundary layers in the class considered by oleinik j appl math mech 30 1966 951 provided that the pressure is favourable this generalizes the local well posedness results due to oleinik 1966 mathematical models in boundary layer theory chapman hall london 1999 for the proof we introduce a viscous splitting method so that the asymptotic behaviour of the solution near the boundary can be estimated more accurately by methods applicable to the degenerate parabolic equations

boundary regularity of proper holomorphic mappings it s main result is formulated in theorem 2 below although the answer to the conjecture in the general case is still unknown it has been shown to hold in many special cases a fairly detailed history of this subject will be contained in 14 one class of positive answers deals with cases in which one knows that f21 and 2 posses fairly large classes of holomorphic automorphisms that extend holomorphically across the boundaries like for instance reinhardt domains see e g h cartan 8 w kaup 16 and st bell 6 in these situations one even often does not need a smoothness assumption on the boundaries of 1 and 22 on the other hand the first result without a priori knowledge on automorphisms which gave c extendability was proved by ch fefferman in 1974 in 15 and says

on three dimensional cauchy riemann manifolds of the almost complex tensor of c2 multiplication by i the collection of these subspaces hp m forms a bundle hm c tm called the horizontal or contact bundle indeed strict pseudoconvexity of m implies that the plane field hpm is nondegenerate i e defines a contact structure the almost complex tensor of c2 then restricts to a bundle endomorphism j hm hm such that j2 id the bundle hm c tm together with this endomorphism j defines the cr structure of m slightly more generally let d d u m be a four dimensional compact manifold with boundary m interior d endowed with a smooth almost complex tensor which is integrable on d if d is strictly pseudoconvex i e in a neighborhood of any p e m there is a smooth strictly plurisubharmonic function u negative on d 0 on m but du 0 on m then m inherits a strictly pseudoconvex cr structure from d in this case we shall say that m bounds a strictly pseudoconvex surface this leads us to the abstract definition a strictly pseudoconvex threedimensional cr manifold is a compact manifold m without boundary dim m 3 endowed with a contact structure hm hpm p e m c tm and an endomorphism j of hm such that j2 id throughout this paper unless otherwise stated we shall be working with infinitely differentiable objects thus m hm j are assumed to be smooth in this sense furthermore a differentiable function f m c is a cr function if for any p e m the restriction df ihm hpm tf p c

behavior of the bergman projection on the diederich fornaess worm w 1 introduction in this paper we show that the bergman projection operator for certain smooth bounded pseudoconvex domains does not preserve smoothness as measured by sobolev norms let q be a smooth bounded pseudoconvex domain in c and let p t denote the orthogonal projection from l2 f onto the bergman subspace b ff l2 f3 r with respect to the weighted norm i fll j olf z l 2 e t lzll2dv l 2 let wk t denote the sobolev space consisting of functions whose derivatives of order to k g2 on the other hand there is a large collection of results implying that for certain types of domains the unweighted bergman projection p pr preserves w k for all k 0 see fk for the strictly pseudoconvex case for results on weakly pseudoconvex domains the reader may consult ko2 ca si and the recent bstl ch as well as the references cited therein most of these results are focused on the a neumann operator rather than p see bst2 for the connection also except for kol positive results in this area are typically valid for any choice of smooth positive weight function on 0 the question of whether or not p is similarly well behaved for all weakly pseudoconvex domains has remained open for many years in this paper we show that this is not the case in fact when q is the so called worm domain of diederich and forna ss then p does not map w to w k when k zr total amount of winding this latter quantity is explained in section 4 below where the construction of the worm is reviewed and the main result is proved the proof depends on computations for a piecewise levi flat model domain depending in turn on certain one dimensional computations these are treated in sections 3 and 2 respectively section 5 contains additional remarks and questions

condition r and proper holomorphic maps between equidimensional product domains we consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex euclidean space where both source and target can be represented as cartesian products of smoothly bounded domains it is shown that such mappings extend smoothly up to the closures of the domains provided each factor of the source satisfies condition r it also shown that the number of smoothly bounded factors in the source and target must be the same and the proper holomorphic map splits as a product of proper mappings between the factor domains c 2013 elsevier inc all rights reserved

duality and approximation of bergman spaces abstract expected duality and approximation properties are shown to fail on bergman spaces of domains in c n via examples when the domain admits an operator satisfying certain mapping properties positive duality and approximation results are proved such operators are constructed on generalized hartogs triangles on a general bounded reinhardt domain norm convergence of laurent series of bergman functions is shown this extends a classical result on hardy spaces of the unit disc