impacts of noise on a class of partial differential equations abstract this paper is concerned with effects of noise on the solutions of partial differential equations we first provide a sufficient condition to ensure the existence of a unique positive solution for a class of stochastic partial differential equations then we prove that noise could induce singularities finite time blow up of solutions finally we show that a stochastic allen cahn equation does not have finite time singularities and the unique solution exists globally

gossip coverage control for robotic networks dynamical systems on the space of partitions future applications in environmental monitoring delivery of services and transportation of goods motivate the study of deployment and partitioning tasks for groups of autonomous mobile agents these tasks may be achieved by recent coverage algorithms based upon the classic methods by lloyd these algorithms however rely upon critical requirements on the communication network information is exchanged synchronously among all agents and long range communication is sometimes required this work proposes novel coverage algorithms that require only gossip communication i e asynchronous pairwise and possibly unreliable communication which robot pair communicates at any given time may be selected deterministically or randomly a key innovative idea is describing coverage algorithms for robot deployment and environment partitioning as dynamical systems on a space of partitions in other words we study the evolution of the regions assigned to each agent rather than the evolution of the agents positions the proposed gossip algorithms are shown to converge to centroidal voronoi partitions under mild technical conditions our treatment features a broad variety of results in topology analysis and geometry first we establish the compactness of a suitable space of partitions with respect to the symmetric difference metric second with respect to this metric we establish the continuity of various geometric maps including the voronoi diagram as a function of its generators the location of a centroid as a function of a set and the widely known multicenter function studied in facility location problems third we prove two convergence theorems for dynamical systems on metric spaces described by deterministic and stochastic switches

an optimal algorithm for constructing the weighted voronoi diagram in the plane let s denote a set of n points in the plane such that each point p has assigned a positive weight w p which expresses its capability to influence its neighbourhood in this sense the weighted distance of an arbitrary point x from p is given by de x p w p where de denotes the euclidean distance function the weighted voronoi diagram for s is a subdivision of the plane such that each point p in s is associated with a region consisting of all points x in the plane for which p is a weighted nearest point of s an algorithm which constructs the weighted voronoi diagram for s in o n2 time is outlined in this paper the method is optimal as the diagram can consist of n2 faces edges and vertices

continuous dependence on the coefficients and global existence for stochastic reaction diffusion equations abstract we prove convergence of the solutions x n of semilinear stochastic evolution equations on a banach space b driven by a cylindrical brownian motion in a hilbert space h d x n t a n x t f n t x n t d t g n t x n t d w h t x n 0 n assuming that the operators a n converge to a and the locally lipschitz functions f n and g n converge to the locally lipschitz functions f and g in an appropriate sense moreover we obtain estimates for the lifetime of the solution x of the limiting problem in terms of the lifetimes of the approximating solutions x n we apply the results to prove global existence for reaction diffusion equations with multiplicative noise and a polynomially bounded reaction term satisfying suitable dissipativity conditions the operator governing the linear part of the equation can be an arbitrary uniformly elliptic second order elliptic operator

ornstein uhlenbeck processes with singular drifts integral estimates and girsanov densities we consider a perturbation of a hilbert space valued ornstein uhlenbeck process by a class of singular nonlinear non autonomous maximal monotone time dependent drifts the only further assumption on the drift is that it is bounded on balls in the hilbert space uniformly in time first we introduce a new notion of generalized solutions for such equations which we call pseudo weak solutions and prove that they always exist and obtain pathwise estimates in terms of the data of the equation then we prove that their laws are absolutely continuous with respect to the law of the original ornstein uhlenbeck process in particular we show that pseudo weak solutions always have continuous sample paths in addition we obtain integrability estimates of the associated girsanov densities some of our results concern non random equations as well while probabilistic results are new even in finite dimensional autonomous settings

a convergent finite volume scheme for diffusion on evolving surfaces a finite volume scheme for transport and diffusion problems on evolving hypersurfaces is discussed the underlying motion is assumed to be described by a fixed not necessarily normal velocity field the ingredients of the numerical method are an approximation of the family of surfaces by a family of interpolating simplicial meshes where grid vertices move on motion trajectories a consistent finite volume discretization of the induced transport on the simplices and a proper incorporation of a diffusive flux balance at simplicial faces the semi implicit scheme is derived via a discretization of the underlying conservation law and discrete counterparts of continuous a priori estimates in this geometric setup are proved the continuous solution on the continuous family of evolving surfaces is compared to the finite volume solution on the discrete sequence of simplicial surfaces and convergence of the family of discrete solutions on successively refined meshes is proved under suitable assumptions on the geometry and the discrete meshes furthermore numerical results show remarkable aspects of transport and diffusion phenomena on evolving surfaces and experimentally reflect the established convergence results finally we discuss how to combine the presented scheme with a corresponding finite volume scheme for advective transport on the surface via an operator splitting and present some applications

finite element approximation of the cahn hilliard equation on surfaces abstract in this paper we consider the phase separation on general surfaces by solving the nonlinear cahn hilliard equation using a finite element method a fully discrete approximation scheme is introduced and we establish a priori estimates for the discrete solution that does not rely on any knowledge of the exact solution beyond the initial time this in turn leads to convergence and optimal error estimates of the discretization scheme numerical examples are also provided to substantiate the theoretical results

generalized measures of fault tolerance for bubble sort networks abstract the k and k are two generalized measurements for fault tolerance of large scale processing system for the bubble sort networks bn this paper determines k b n k b n 2 k n k 1 for k n 2 the results show that to disconnect bn with each vertex in resulting graph has at least k fault free neighbors at least 2 k n k 1 faulty vertices or faulty edges have to occur in particular the results also settle affirmatively a conjecture proposed by shi and wu acta math appl sin e 33 4 2017 933 944

conditional connectivity of recursive interconnection networks respect to embedding restriction abstract large scale multiprocessor systems always take some recursive interconnection networks as underlying topologies let g n be an n dimensional recursive interconnection network the m embedding restricted connectivity m g n resp the m embedding restricted edge connectivity m g n of g n is the cardinality of a minimum subset of nodes resp edges if any whose deletion disconnects g n and each node of the remaining components lies in an undamaged m dimensional sub network g m in this paper we present some relationships between the proposed indices and other conditional connectivity indices in general recursive interconnection networks we give some bounds on these two indices in k ary n cubes and bubble sort networks in addition we determine these two indices in k ary n cubes and bubble sort networks in some cases

constrained centroidal voronoi tessellations for surfaces centroidal voronoi tessellations are useful for subdividing a region in euclidean space into voronoi regions whose generators are also the centers of mass with respect to a prescribed density function of the regions their extensions to general spaces and sets are also available for example tessellations of surfaces in a euclidean space may be considered in this paper a precise definition of such constrained centroidal voronoi tessellations ccvts is given and a number of their properties are derived including their characterization as minimizers of an energy deterministic and probabilistic algorithms for the construction of ccvts are presented and some analytical results for one of the algorithms are given computational examples are provided which serve to illustrate the high quality of ccvt point sets finally ccvt point sets are applied to polynomial interpolation and numerical integration on the sphere

on curvature element size control in metric surface mesh generation summary a new procedure is suggested for controlling the element size distribution of surface meshes during automatic adaptive surface mesh generation in order to ensure that the geometry of the surface can be accurately captured the curvature properties of the surface are first analyzed based on the principal curvatures and principal directions of the surface the curvature element size requirement is defined in form of a metric tensor field this element size controlling metric tensor field which can either be isotopic or anisotopic depends on the user requirement is then employed to control the element size distribution during mesh generation the suggested procedure is local adaptive and can be easily used with many parametric surface mesh generators as the proposed scheme defines the curvature element size requirement in an implicit manner it can be combined with any other user defined element size specification using the standard metric intersection procedure this eventually leads to a simple implementation procedure and a high computational efficiency numerical examples indicate that the new procedure can effectively control the element size of surface meshes in the cost of very little additional computational effort

anisotropic centroidal voronoi tessellations and their applications in this paper we introduce a novel definition of the anisotropic centroidal voronoi tessellation acvt corresponding to a given riemann metric tensor a directional distance function is used in the definition to simplify the computation we provide algorithms to approximate the acvt using the lloyd iteration and the construction of anisotropic delaunay triangulation under the given riemannian metric the acvt is applied to the optimization of two dimensional anisotropic delaunay triangulation to the generation of surface cvt and high quality triangular mesh on general surfaces various numerical examples demonstrating the effectiveness of the proposed method are presented

embedded connectivity of recursive networks let gn be an n dimensional recursive network the h embedded connectivity h gn resp edge connectivityh gn of gn is the minimum number of vertices resp edges whose removal results in disconnected and each vertex is contained in an h dimensional subnetwork gh this paper determinesh andh for the hypercube qn and the star graph sn and 3 for the bubble sort network bn

optimal control of semilinear stochastic evolution equations the aim of this paper is to initiate a semigroup theory based approach to characterization of optimal markov controls for controlled semilinear stochastic evolution equations it may be recalled that markov controls are those that depend only on the current state at each time for finite dimensional controlled stochastic differential equations with a nondegenerate diffusion matrix this task is traditionally achieved through the hamilton jacobi bellman equation of dynamic programming associated with the problem and an accompanying verification theorem the latter states that an optimal markov control can be explicitly obtained by the pointwise minimization of a hamiltonian derivable from the solution of the hjb equation moreover any optimal markov control is obtainable in this manner

variational surface reconstruction based on delaunay triangulation and graph cut a novel method for surface reconstruction from an unorganized point set is presented an energy functional based on a weighted minimal surface model is proposed for surface reconstruction which is efficiently minimized by graph cut methods by solving the minimization problem on the graph dual to a delaunay based tetrahedral mesh the advantages of explicit and implicit methods for surface reconstruction are well integrated a triangular surface mesh homeomorphic to the original surface can be extracted directly from the tetrahedral mesh provided a sufficient sampling density exists difficult cases involving undersampling non uniformity noises and topological complexities can be handled effectively as well furthermore for the first time multi phase surface reconstruction is realized based on the graph cut methods various examples are included for demonstrating the efficiency and effectiveness of the proposed method copyright 2010 john wiley sons ltd

fast delaunay triangulation in three dimensions abstract an efficient algorithm for delaunay triangulation of a given set of points in three dimensions based on the point insertion technique is presented various steps of the triangulation algorithm are reviewed and many acceleration procedures are devised to speed up the triangulation process new features include the search of a neighbouring point by the layering scheme locating the containing tetrahedron by random walk formulas of important geometrical quantities of a new tetrahedron based on those of an existing one a novel approach in establishing the adjacency relationship the use of adjacency table and the management of memory the resulting scheme is one of the fastest triangulation algorithms known to the authors which is able to generate tetrahedra generation rate of 15 000 tetrahedra per second for randomly generated points on a hp 735 machine

a finite volume method on general surfaces and its error estimates abstract in this paper we study a finite volume method and its error estimates for the numerical solution of some model second order elliptic partial differential equations defined on a smooth surface the discretization is defined via a surface mesh consisting of piecewise planar triangles and piecewise polygons the optimal error estimates of the approximate solution are proved in both the h 1 and l 2 norms which are of first order and second order respectively under mesh regularity assumptions some numerical tests are also carried out to experimentally verify our theoretical analysis

on the minimum average distortion of quantizers with index dependent distortion measures in many applications one is interested in optimally deploying a network of unidentical agents to a certain area of interest examples include heterogeneous sensor networks and cellular networks such deployment problems can equivalently be formulated as quantizer design problems where different distortion measures should be associated with different quantization indices in this paper we consider the case where the distortion measure is the r th power r geq 1 of the distance between the reproduction point and the source sample weighted by a factor that varies from one index to another for a uniform distribution of source samples we determine the corresponding optimal scalar quantizers and their average distortions for nonuniform distributions and vector quantization we provide a high resolution analysis of the minimum possible average distortion applications to sensor and cellular networks are also discussed together with numerical design examples

a physics motivated centroidal voronoi particle domain decomposition method in this paper we propose a novel domain decomposition method for large scale simulations in continuum mechanics by merging the concepts of centroidal voronoi tessellation cvt and voronoi particle dynamics vp the cvt is introduced to achieve a high level compactness of the partitioning subdomains by the lloyd algorithm which monotonically decreases the cvt energy the number of computational elements between neighboring partitioning subdomains which scales the communication effort for parallel simulations is optimized implicitly as the generated partitioning subdomains are convex and simply connected with small aspect ratios moreover voronoi particle dynamics employing physical analogy with a tailored equation of state is developed which relaxes the particle system towards the target partition with good load balance since the equilibrium is computed by an iterative approach the partitioning subdomains exhibit locality and the incremental property numerical experiments reveal that the proposed centroidal voronoi particle cvp based algorithm produces high quality partitioning with high efficiency independently of computational element types thus it can be used for a wide range of applications in computational science and engineering

centroidal voronoi tessellation based finite element superconvergence in this article a finding on finite element superconvergence is reported the laplacian operator with dirichlet boundary condition is considered the linear finite element solutions have an o h2 0 5 superconvergence in l2 norm at nodes on an almost equilateral triangular mesh generated based on centroidal voronoi tessellation for an arbitrary 2d bounded domain extensive numerical examples are presented to demonstrate the superconvergence property copyright 2008 john wiley sons ltd

3d delaunay mesh generation coupled with an advancing front approach abstract this paper describes a fully automatic mesh generation method suitable for domains of any shape in r 3 initially a so called boundary mesh is generated wherein internal points are created using advancing front point placement and inserted using a delaunay method the algorithm combines the advantages of efficiency and nice mathematical properties of a delaunay approach with advancing front high quality point placement strategy several three dimensional examples are presented to demonstrate the overall efficiency and the relevance of the combined procedure the present method can be extended to isotropic or anisotropic adaptive mesh generation

optimal delaunay point insertion summary an efficient algorithm for delaunay triangulation of a given set of points in d dimensions is presented various steps of the point insertion algorithm are reviewed and many acceleration procedures are implemented to speed up the triangulation process new features include the search for a neighbouring point by a layering scheme locating the containing simplex by a random walk formulas of important geometrical quantities of a new simplex based on those of an old one a novel approach in establishing the adjacency relationship using connection matrices the resulting scheme seems to be one of the fastest triangulation algorithms known which enables us to generate tetrahedra in r3 with a linear generation rate of 15 ooo tetrahedra per second for randomly generated points on an hp 735 workstation

lower estimates of transition densities and bounds on exponential ergodicity for stochastic pde s a formula for the transition density of a markov process defined by an infinite dimensional stochastic equation is given in terms of the ornstein uhlenbeck bridge and a useful lower estimate on the density is provided as a consequence uniform exponential ergodicity and v ergodicity are proved for a large class of equations we also provide computable bounds on the convergence rates and the spectral gap for the markov semigroups defined by the equations the bounds turn out to be uniform with respect to a large family of nonlinear drift coefficients examples of finite dimensional stochastic equations and semilinear parabolic equations are given

adaptive finite element methods for elliptic pdes based on conforming centroidal voronoi delaunay triangulations a new triangular mesh adaptivity algorithm for elliptic pdes that combines a posteriori error estimation with centroidal voronoi delaunay tessellations of domains in two dimensions is proposed and tested the ability of the first ingredient to detect local regions of large error and the ability of the second ingredient to generate superior unstructured grids result in a mesh adaptivity algorithm that has several very desirable features including the following errors are very well equidistributed over the triangles at all levels of refinement the triangles remain very well shaped even if the grid size at any particular refinement level when viewed globally varies by several orders of magnitude and the convergence rates achieved are the best obtainable using piecewise linear finite elements this methodology can be easily extended to higher order finite element approximations or mixed finite element formulations although only the linear approximation is considered in this paper

fault tolerance measures for m ary n dimensional hypercubes based on forbidden faulty sets in this paper we study fault tolerance measures for m ary n dimensional hypercubes based on the concept of forbidden faulty sets in a forbidden faulty set certain nodes cannot be faulty at the same time and this model can better reflect fault patterns in a real system than the existing ones specifically we study the bounds of the minimum vertex cut set for m ary n dimensional hypercubes by requiring each node to have at least k healthy neighbors our result enhances and generalizes a result by latifi et al for binary hypercubes our study also shows that the corresponding result based on the traditional fault model where k is zero tends to underestimate network resilience of large networks such as m ary n dimensional hypercubes

on the abstract cauchy problem of parabolic type in spaces of continuous functions on etudie l existence l unicite et les proprietes de regularite des solutions du probleme de cauchy u t au r f t o t t u o u 0 ou a d a ce e est un operateur lineaire clos dans l espace de banach e

exponential mixing properties of stochastic pdes through asymptotic coupling we consider parabolic stochastic partial differential equations driven by white noise in time we prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions these conditions amount essentially to the fact that the equation transmits the noise to all its determining modes several examples are investigated including some where the noise does not act on every determining mode directly

grid generation and optimization based on centroidal voronoi tessellations centroidal voronoi tessellations cvts are voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding voronoi regions such tessellations are of use in very diverse applications including data compression clustering analysis cell biology territorial behavior of animals and optimal allocation of resources in this paper we explore the use of cvts in grid generation in connection with finite element approximations of partial differential equations we being by describing these tessellations and methods for their determination we then discuss their application to mesh generation and finish with some examples of their use for the solution of partial differential equations

finite volume methods on spheres and spherical centroidal voronoi meshes we study in this paper a finite volume approximation of linear convection diffusion equations defined on a sphere using the spherical voronoi meshes in particular the spherical centroidal voronoi meshes the high quality of spherical centroidal voronoi meshes is illustrated through both theoretical analysis and computational experiments in particular we show that the l2 error of the approximate solution is of quadratic order when the underlying mesh is given by a spherical centroidal voronoi mesh we also demonstrate numerically the high accuracy and the superconvergence of the approximate solutions

parametric surface meshing using a combined advancing front generalized delaunay approach an indirect method for meshing parametric surfaces conforming to a user specifiable size map is presented first from this size specification a riemannian metric is defined so that the desired mesh is one with unit length edges with respect to the related riemannian space the so called unit mesh then based on the intrinsic properties of the surface the riemannian structure is induced into the parametric space finally a unit mesh is generated completely inside the parametric space such that it conforms to the metric of the induced riemannian structure this mesh is constructed using a combined advancing front delaunay approach applied within a riemannian context the proposed method can be applied to mesh composite parametric surfaces several examples illustrate the efficiency of our approach copyright 2000 john wiley sons ltd

convergence of the lloyd algorithm for computing centroidal voronoi tessellations centroidal voronoi tessellations cvts are voronoi tessellations of a bounded geometric domain such that the generating points of the tessellations are also the centroids mass centers of the corresponding voronoi regions with respect to a given density function centroidal voronoi tessellations may also be defined in more abstract and more general settings due to the natural optimization properties enjoyed by cvts they have many applications in diverse fields the lloyd algorithm is one of the most popular iterative schemes for computing the cvts but its theoretical analysis is far from complete in this paper some new analytical results on the local and global convergence of the lloyd algorithm are presented these results are derived through careful utilization of the optimization properties shared by cvts numerical experiments are also provided to substantiate the theoretical analysis

random perturbations of reaction diffusion equations the quasi deterministic approximation on considere des champs aleatoires u e t x u 1 e t x u n e t x definis comme les solutions d un systeme d equations aux derivees partielles u k e t l k u k e f k x u 1 e u n e e k t x les l k sont des operateurs elliptiques lineaires d ordre 2 k sont des champs gaussiens bruit blanc

regridding surface triangulations an advancing front surface gridding technique that operates on discretely defined surfaces i e triangulations is presented different aspects that are required to make the procedure reliable for complex geometries are discussed notable among these are a the recovery of surface features and discrete surface patches from the discrete data b filtering based on point and side normals to remove undesirable data close to cusps and corners c the proper choice of host faces for ridges and d fast interpolation procedures suitable for complex geometries post generation surface recovery or repositioning techniques are discussed several examples ranging from academic to industrial demonstrate the utility of the proposed procedure forab initiosurface meshing from discrete data such as those encountered when the surface description is already given as discrete the improvement of existing surface triangulations as well as remeshing applications during runs exhibiting significant change of domain

tetrahedral mesh generation and optimization based on centroidal voronoi tessellations the centroidal voronoi tessellation based delaunay triangulation cvdt provides an optimal distribution of generating points with respect to a given density function and accordingly generates a high quality mesh in this paper we discuss algorithms for the construction of the constrained cvdt from an initial delaunay tetrahedral mesh of a three dimensional domain by establishing an appropriate relationship between the density function and the specified sizing field and applying the lloyd s iteration the constrained cvdt mesh is obtained as a natural global optimization of the initial mesh simple local operations such as edges faces flippings are also used to further improve the cvdt mesh several complex meshing examples and their element quality statistics are presented to demonstrate the effectiveness and efficiency of the proposed mesh generation and optimization method copyright 2003 john wiley sons ltd

conditional connectivity of star graph networks under embedding restriction the n dimensional star graph s n is one of the most attractive interconnection networks of large scale multiprocessor systems the k embedding restricted edge connectivity h k s n z k s n of s n is defined to be the cardinality of a minimum subset of edges nodes if any whose deletion disconnects s n and each node of the remaining components lies in an undamaged k dimensional substar s k in this paper we investigate the k embedding restricted edge connectivity of s n and determine the values of h k s n and z k s n for some k s

nondegeneracy and weak global convergence of the lloyd algorithm in mathbb r d the lloyd algorithm originated in the context of optimal quantization and represents a fixed point iteration for computing an optimal quantizer reducing average distortion at every step it constructs a voronoi partition of the domain and replaces each generator with the centroid of the corresponding voronoi cell optimal quantization is obtained in the case of a centroidal voronoi tessellation cvt which is a special voronoi tessellation of a domain omega in mathbb r d having the property that the generators of the voronoi diagram are also the centers of mass with respect to a given density function rho geq 0 of the corresponding voronoi cells the lloyd iteration is currently the most popular and elegant algorithm for computing cvts and optimal quantizers but many questions remain about its convergence especially in d dimensional spaces d 1 in this paper we prove that any limit point of the lloyd iteration in any dimensional spaces is nondegenerate provided that omega is a convex and bounded set and rho belongs to l 1 omega and is positive almost everywhere this ensures that the fixed point map remains closed and hence the standard theory of descent methods guarantees weak global convergence of the lloyd iteration to the set of nondegenerate fixed point quantizers while previously only conjectured the convergence properties of the lloyd iteration are rigorously justified under such minimal regularity assumptions on the density functional the results presented in this paper go beyond existing convergence theories for cvts and optimal quantization related algorithms and should be of interest to both the mathematical and engineering communities

adaptive anisotropic meshing for steady convection dominated problems obtaining accurate solutions for convection diffusion equations is challenging due to the presence of layers when convection dominates the diffusion to solve this problem we design an adaptive meshing algorithm which optimizes the alignment of anisotropic meshes with the numerical solution three main ingredients are used first the streamline upwind petrov galerkin method is used to produce a stabilized solution second an adapted metric tensor is computed from the approximate solution third optimized anisotropic meshes are generated from the computed metric tensor by an anisotropic centroidal voronoi tessellation algorithm our algorithm is tested on a variety of two dimensional examples and the results shows that the algorithm is robust in detecting layers and efficient in avoiding non physical oscillations in the numerical approximation

adaptive triangular quadrilateral mesh generation in this paper we begin by recalling an adaptive mesh generation method governed by isotropic and anisotropic discrete metric maps by means of the generation of a unit mesh with respect to a riemannian structure we propose then an automatic triangular to quadrilateral mesh conversion scheme which generalizes the standard case to the anisotropic context in addition we introduce an optimal vertex smoothing procedure application test examples in particular a cfd test are given to demonstrate the eciency of the proposed method 1998 john wiley sons ltd int j numer meth engng 41 915 934 1998

well centered triangulation meshes composed of well centered simplices have nice orthogonal dual meshes the dual voronoi diagram this is useful for certain numerical algorithms that prefer such primal dual mesh pairs we prove that well centered meshes also have optimality properties and relationships to delaunay and minmax angle triangulations we present an iterative algorithm that seeks to transform a given triangulation in two or three dimensions into a well centered one by minimizing a cost function and moving the interior vertices while keeping the mesh connectivity and boundary vertices fixed the cost function is a direct result of a new characterization of well centeredness in arbitrary dimensions that we present ours is the first optimization based heuristic for well centeredness and the first one that applies in both two and three dimensions we show the results of applying our algorithm to small and large two dimensional meshes some with a complex boundary and obtain a well centered tetrahedralization of the cube we also show numerical evidence that our algorithm preserves gradation and that it improves the maximum and minimum angles of acute triangulations created by the best known previous method

non explosion boundedness and ergodicity for stochastic semilinear equations abstract sufficient conditions for non explosion boundedness and ergodicity of solutions of a class of semilinear stochastic equations are given applications of the results are based on a new regularity theorem for solutions of the linear problem

anisotropic delaunay mesh generation anisotropic meshes are triangulations of a given domain in the plane or in higher dimensions with elements elongated along prescribed directions anisotropic triangulations are known to be well suited for interpolation of functions or solving pdes assuming that the anisotropic shape requirements for mesh elements are given through a metric field varying over the domain we propose a new approach to anisotropic mesh generation relying on the notion of anisotropic delaunay meshes an anisotropic delaunay mesh is defined as a mesh in which the star of each vertex v consists of simplices that are delaunay for the metric associated to vertex v this definition works in any dimension and allows us to define a simple refinement algorithm the algorithm takes as input a domain and a metric field and provides after completion an anisotropic mesh whose elements are sized and shaped according to the metric field

convergence to equilibrium for classical and quantum spin systems the paper is devoted to stochastic equations describing the evolution of classical and quantum unbounded spin systems on discrete lattices and on euclidean spaces existence and asymptotic properties of the corresponding transition semigroups are studied in a unified way using the theory of dissipative operators on weighted hilbert and banach spaces this paper is an enlarged and rewritten version of the paper 7

blow up of solutions for semilinear stochastic delayed reaction diffusion equations with levy noise abstract this paper is concerned with a class of semilinear stochastic delayed reaction diffusion equations driven by levy noise in a separable hilbert space we establish sufficient conditions to ensure the existence of a unique positive solution moreover we study blow up of solutions in finite time in mean l p norm sense several examples are given to illustrate applications of the theory

meshfree probabilistic determination of point sets and support regions for meshless computing new algorithms are presented for the determination of point sets and associated support regions that can then be used in meshless computing methods the algorithms are probabilistic in nature so that they are totally meshfree i e they do not require at any stage the use of any coarse or fine boundary conforming or superimposed meshes computational examples are provided that show for both uniform and non uniform point distributions that the algorithms result in high quality point sets and high quality support regions furthermore the algorithms lend themselves well to parallelization

revisiting optimal delaunay triangulation for 3d graded mesh generation nsfc 61100107 61100105 61272019 61332015 natural science foundation of fujian province of china 2012j01291 2011j05007 national basic research program of china 2011cb302400 research grant council of hong kong 718209 718010 718311 717012 nsf 61222206 chinese academy of sciences

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments