a new approach to analyticity of dirichlet neumann operators this paper outlines the theoretical background of a new approach towards an accurate and well conditioned perturbative calculation of dirichlet neumann operators dnos on domains that are perturbations of simple geometries previous work on the analyticity of dnos has produced formulae that as we have found are very ill conditioned we show how a simple change of variables can lead to recursions that satisfy analyticity estimates without relying on subtle cancellation properties at the heart of previous formulae

sharp estimates for pseudo differential operators with symbols of limited smoothness and commutators we consider here pseudo differential operators whose symbol x is not infinitely smooth with respect to x decomposing such symbols into four sometimes five components and using tools of paradifferential calculus we derive sharp estimates on the action of such pseudo differential operators on sobolev spaces and give explicit expressions for their operator norm in terms of the symbol x we also study commutator estimates involving such operators and generalize or improve the so called kato ponce and calderon coifman meyer estimates in various ways

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

estimation of parent offspring correlation summary when families have different numbers of offspring srivastava 1984 provided an easily computable estimator as an alternative to the maximum likelihood estimator of parentoffspring correlation some properties of this estimator are discussed vis a vis with those of ensemble and pairwise estimators further we derive the small sample distribution of srivastava s estimator under the assumption of null parent offspring correlation in the process we demonstrate that a certain function of the classical sib mean estimator has student s t distribution despite differing sib ship sizes

well posedness for the motion of an incompressible liquid with free surface boundary we study the motion of an incompressible perfect liquid body in vacuum this can be thought of as a model for the motion of the ocean or a star the free surface moves with the velocity of the liquid and the pressure vanishes on the free surface this leads to a free boundary problem for euler s equations where the regularity of the boundary enters to highest order we prove local existence in sobolev spaces assuming a physical condition related to the fact that the pressure of a fluid has to be positive

estimation of interclass correlation under circular covariance summary the maximum likelihood estimates of the parent sib interclass correlation and other parameters are obtained when the between sibs correlation matrix has a circular structure the problem of testing hypotheses about interclass correlation is also considered

a note on statistical methods adjusting for intraclass correlation on utilise un resultat sur les distributions de robbins et pitman 1949 pour obtenir une procedure de calcul exacte des vraies p valeurs des tests de signification

large time existence for 1d green naghdi equations we consider here the 1d green naghdi equations that are commonly used in coastal oceanography to describe the propagation of large amplitude surface waves we show that the solution of the green naghdi equations can be constructed by a standard picard iterative scheme so that there is no loss of regularity of the solution with respect to the initial condition

well posedness and blow up phenomena for a higher order shallow water equation this paper deals with the cauchy problem for a higher order shallow water equation yt auxy buyx 0 where y 2ku i x2 ku and k 2 the local well posedness of solutions for the cauchy problem in sobolev space hs r with s 7 2 is obtained under some assumptions the existence and uniqueness of the global solutions to the equation are shown and conditions that lead to the development of singularities in finite time for the solutions are also acquired finally the weak solution for the equation is considered

surface mesh smoothing regularization and feature detection we describe a hybrid algorithm that is designed to reconstruct a piecewise smooth surface mesh from noisy input while denoising our method simultaneously regularizes triangle meshes on flat regions for further mesh processing and preserves crease sharpness for faithful reconstruction a clustering technique which combines k means and geometric a priori information is first developed and refined it is then used to implement vertex classification so that we can not only apply different smoothing operators on different vertex groups for different purposes but also succeed in crease detection where the tangent plane of the surface is discontinuous without any significant cost increase consequently we are capable of efficiently obtaining different mesh segmentations depending on user input and thus suitable for various applications

stability and instability of the kdv solitary wave under the kp i flow we consider the kp i and gkp i equations in mathbb r times mathbb r 2 pi mathbb z we prove that the kdv soliton with subcritical speed 0 c in the spirit of the work by duyckaerts and merle gafa 18 1787 1840 2009 we sharpen our previous instability result and construct a global solution which is different from the solitary wave and its translates and which converges to the solitary wave as time goes to infinity this last result also holds for the gkp i equation

the local well posedness existence and uniqueness of weak solutions for a model equation for shallow water waves of moderate amplitude abstract this paper deals with the cauchy problem for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime which was proposed by constantin and lannes 2009 20 applying the pseudoparabolic regularization technique the local well posedness of strong solutions in sobolev space h s r with s 3 2 is established via a limiting procedure moreover a sufficient condition for the existence of weak solutions of the equation in lower order sobolev space h s r with 1 s 3 2 is obtained

well posedness for the linearized motion of a compressible liquid with free surface boundary we study the motion of a compressible perfect liquid body in vacuum this can be through of as a model for the motion of the ocean or a star the free surface moves with the velocity of the liquid and the pressure vanishes on the free surface this leads to a free boundary problem for euler s equations where the regularity of the boundary enters to highest order we prove linearized stability in sobolev space assuming a physical condition related to the fact that the pressure of a fluid has to be positive

a hybrid variational front tracking level set mesh generator for problems exhibiting large deformations and topological changes we present a method for generating 2 d unstructured triangular meshes that undergo large deformations and topological changes in an automatic way we employ a method for detecting when topological changes are imminent via distance functions and shape skeletons when a change occurs we use a level set method to guide the change of topology of the domain mesh this is followed by an optimization procedure using a variational formulation of active contours that seeks to improve boundary mesh conformity to the zero level contour of the level set function our method is advantageous for arbitrary lagrangian eulerian ale type methods and directly allows for using a variational formulation of the physics being modeled and simulated including the ability to account for important geometric information in the model such as for surface tension driven flow furthermore the meshing procedure is not required at every time step and the level set update is only needed during a topological change hence our method does not significantly affect computational cost

long wave approximations for water waves in this paper we obtain new nonlinear systems describing the interaction of long water waves in both two and three dimensions these systems are symmetric and conservative rigorous convergence results are provided showing that solutions of the complete free surface euler equations tend to associated solutions of these systems as the amplitude becomes small and the wavelength large using this result as a tool a rigorous justification of all the two dimensional approximate systems recently put forward and analysed by bona chen and saut is obtained in the two dimensional context our methods also allows a significant improvement of the convergence estimate obtained by schneider and wayne in their justification of the decoupled korteweg de vries approximation of the two dimensional euler equations it also follows from our theory that coupled models provide a better description than the decoupled ones over short time scales results are obtained both on an unbounded domain for solutions that evanesce at infinity as well as for solutions that are spatially periodic

the zero surface tension limit of two dimensional water waves we consider two dimensional water waves of infinite depth periodic in the horizontal direction it has been proven by wu in the slightly different nonperiodic setting that solutions to this initial value problem exist in the absence of surface tension recently ambrose has proven that solutions exist when surface tension is taken into account in this paper we provide a shorter more elementary proof of existence of solutions to the water wave initial value problem both with and without surface tension our proof requires estimating the growth of geometric quantities using a renormalized arc length parametrization of the free surface and using physical quantities related to the tangential velocity of the free surface using this formulation we find that as surface tension goes to 0 the water wave without surface tension is the limit of the water wave with surface tension far from being a simple adaptation of previous works our method requires a very original choice of variables these variables turn out to be physical and well adapted to both cases c

accurate correction of surface noises of polygonal meshes summary in this paper we propose a new algorithm for accurate correction of surface noises of polygonal meshes it consists of three basic components a feature preserving pre smoothing b partitioning of feature and non feature regions c second order predictor for non feature regions and median filter for feature regions the unique contributions of our approach include a an idea of partitioning an input surface into feature and non feature regions so that different smoothing algorithms which are best suited for either feature or non feature regions can be respectively applied b a secondorder predictor that provides higher smoothing accuracy and better convergence on smoothly curved surfaces in comparison with several existing algorithms our algorithm is evaluated quantitatively in terms of surface normal and vertex distance error metrics numerical experiments indicate the effectiveness of our approach in the aspects of convergence and accuracy copyright 2005 john wiley sons ltd

validity of the korteweg de vries approximation for the two dimensional water wave problem in the arc length formulation we consider the two dimensional water wave problem in an infinitely long canal of finite depth both with and without surface tension it has been proven by several authors that long wavelength solutions to this problem can be approximated over a physically relevant timespan by solutions of the korteweg de vries equation or for certain values of the surface tension by solutions of the kawahara equation these proofs are formulated either in lagrangian or in eulerian coordinates in this paper we provide a new proof which is simpler more elementary and shorter moreover the rigorous justification of the kdv approximation can be given for the cases with and without surface tension together by one proof in our proof we parametrize the free surface by arc length and use some geometrically and physically motivated variables with good regularity properties this formulation of the water wave problem has already been of great usefulness for ambrose and masmoudi to simplify the proof of the local well posedness of the water wave problem in sobolev spaces 2011 wiley periodicals inc

nonstrictly hyperbolic nonlinear systems on etudie le caractere bien pose du probleme aux valeurs initiales localement en temps pour une classe de systemes hyperboliques non lineaires

a shallow water approximation to the full water wave problem we demonstrate that the system of the green naghdi equations as a two directional nonlinearly dispersive wave model is a close approximation to the two dimensional full water wave problem based on the energy estimates and the proof of the well posedness for the green naghdi equations and the water wave problem we compare solutions of the two systems showing that without restrictions on the wave amplitude any two solutions of the two systems remain close at least in some finite time within the shallow water regime provided that their initial data are close in the banach space hs hs 1 for some s as a consequence we show that if the depth of the water compared with the wavelength is sufficiently small the two solutions exist for the same finite time using the uniformly bounded energies defined in the paper 2006 wiley periodicals inc

almost global wellposedness of the 2 d full water wave problem we consider the problem of global in time existence and uniqueness of solutions of the 2 d infinite depth full water wave equation it is known that this equation has a solution for a time period 0 t e for initial data of the form e where t depends only on in this paper we show that for such data there exists a unique solution for a time period 0 e t e this is achieved by better understandings of the nature of the nonlinearity of the full water wave equation

large time existence for 3d water waves and asymptotics we rigorously justify in 3d the main asymptotic models used in coastal oceanography including shallow water equations boussinesq systems kadomtsev petviashvili kp approximation green naghdi equations serre approximation and full dispersion model we first introduce a variable nondimensionalized version of the water waves equations which vary from shallow to deep water and which involves four dimensionless parameters using a nonlocal energy adapted to the equations we can prove a well posedness theorem uniformly with respect to all the parameters its validity ranges therefore from shallow to deep water from small to large surface and bottom variations and from fully to weakly transverse waves

processing textured surfaces via anisotropic geometric diffusion a multiscale method in surface processing is presented which carries over image processing methodology based on nonlinear diffusion equations to the fairing of noisy textured parametric surfaces the aim is to smooth noisy triangulated surfaces and accompanying noisy textures as they are delivered by new scanning technology while enhancing geometric and texture features for an initial textured surface a fairing method is described which simultaneously processes the texture and the surface considering an appropriate coupling of the two smoothing processes one can take advantage of the frequently present strong correlation between edge features in the texture and on the surface edges the method is based on an anisotropic curvature evolution of the surface itself and an anisotropic diffusion on the processed surface applied to the texture here the involved diffusion tensors depends on a regularized shape operator of the evolving surface and on regularized texture gradients a spatial finite element discretization on arbitrary unstructured triangular grids and a semi implicit finite difference discretization in time are the building blocks of the corresponding numerical algorithm a normal projection is applied to the discrete propagation velocity to avoid tangential drifting in the surface evolution different applications underline the efficiency and flexibility of the presented surface processing tool

well posedness in sobolev spaces of the full water wave problem in 2 d we consider the motion of the interface of 2 d irrotational incompressible inviscid water wave with air above water and surface tension zero we show that the interface is always not accelerating into the water region normal to itself as rapidly as the normal acceleration of gravity as long as the interface is nonself intersect we therefore obtain the existence and uniqueness of solutions of the full water wave problem locally in time for any initial interface which is nonself intersect including the case that the interface is of multiple heights

well posedness of the water waves equations 1 1 presentation of the problem the water waves problem for an ideal liquid consists of describing the motion of the free surface and the evolution of the velocity field of a layer of perfect incompressible irrotational fluid under the influence of gravity in this paper we restrict our attention to the case when the surface is a graph parameterized by a function x where t denotes the time variable and x xi xd rd the horizontal spatial variables the method developed here works equally well for any integer d 1 but the only physically relevant cases are of course d 1 and d 2 the layer of fluid is also delimited from below by a not necessarily flat bottom parameterized by a time independent function b x we denote by q t the fluid domain at time t the incompressibility of the fluids is expressed by 1 1 div v 0 in qu t 0

well posedness of the free surface incompressible euler equations with or without surface tension we provide a new method for treating free boundary problems in perfect fluids and prove local in time well posedness in sobolev spaces for the free surface incompressible 3d euler equations with or without surface tension for arbitrary initial data and without any irrotationality assumption on the fluid this is a free boundary problem for the motion of an incompressible perfect liquid in vacuum wherein the motion of the fluid interacts with the motion of the free surface at highest order

well posedness in sobolev spaces of the full water wave problem in 3 d we consider the motion of the interface separating an inviscid incompressible irrotational fluid from a region of zero density in three dimensional space we assume that the fluid region is below the vacuum the fluid is under the influence of gravity and the surface tension is zero assume that the density of mass of the fluid is one the gravitational field is 0 0 1 the free interface is t at time t 0 and the fluid occupies the region t the motion of the fluid is described by vt v v 0 0 1 p on t t 0 euler s equation 1 1 div v 0 on t t 0 incompressible 1 2 curl v 0 on t t 0 irrotational 1 3 where v v1 v2 v3 is the fluid velocity p is the fluid pressure since we neglect the surface tension the pressure is zero on the interface so on the interface p 0 on t 1 4 1 v is tangent to the free surface t t 1 5 we want to find solutions of system 1 1 1 5 taking prescribed initial data such that for every fixed t 0 t approaches the xy plane at infinity and v x y z t 0 vt x y z t 0 as x y z since the fluid is assumed irrotational incompressible we can reduce the study of the entire motion to the motion of the free surface the above model is a 3 d water wave model it is generally known that when surface tension is neglected the motion of the interface between an inviscid fluid and vacuum under the influence of gravity can be subject to taylor instability 8 22 in a previous work 24 we studied the 2 dimensional water wave model we showed that for a 2 d water wave the sign condition relating to taylor instability always holds for nonself intersecting interface that is the motion of the interface is not subject to taylor instability we showed further that the 2 d full nonlinear water wave problem is uniquely solvable in sobolev spaces locally in time for any initially nonself intersecting interface earlier works on the well posedness in sobolev spaces of the 2 d water wave problem include nalimov 18 yosihara 25 and walter craig 6 where the main results concern the well posedness of the

the long wave limit for the water wave problem i the case of zero surface tension the korteweg de vries equation boussinesq equation and many other equations can be formally derived as approximate equations for the two dimensional water wave problem in the limit of long waves here we consider the classical problem concerning the validity of these equations for the water wave problem in an infinitely long canal without surface tension we prove that the solutions of the water wave problem in the long wave limit split up into two wave packets one moving to the right and one to the left where each of these wave packets evolves independently as a solution of a korteweg de vries equation our result allows us to describe the nonlinear interaction of solitary waves 2000 john wiley sons inc

geometry and a priori estimates for free boundary problems of the euler s equation in this paper we derive estimates to the free boundary problem for the euler equation with surface tension and without surface tension provided the rayleigh taylor sign condition holds we prove that as the surface tension tends to 0 when the rayleigh taylor condition is satisfied solutions converge to the euler flow with zero surface tension 2007 wiley periodicals inc