morphological shape decomposition a technique for decomposing a binary shape into a union of simple binary shapes is presented the decomposition is shown to be unique and invariant to translation rotation and scaling the techniques used in the decomposition are based on mathematical morphology the shape description produced can be used in object recognition and in binary image coding

classification of rotational special weingarten surfaces of minimal type in mathbb s 2 times mathbb r and mathbb h 2 times mathbb r in this paper we classify the complete rotational special weingarten surfaces in mathbb s 2 times mathbb r and mathbb h 2 times mathbb r i e rotational surfaces in mathbb s 2 times mathbb r and mathbb h 2 times mathbb r whose mean curvature h and extrinsic curvature ke satisfy h f h2 ke for some function f in mathcal c 1 0 infty such that f 0 0 and 4x f x 2 1 for any x 0 furthermore we show the existence of non complete examples of such surfaces

improved bounds for the overall properties of a nonlinear composite dielectric the construction of generalized hashin shtrikman bounds for nonlinear composite problems relies on the introduction of a comparison material in recent work a nonlinear comparison medium has been used however this requires detailed knowledge of the properties of the trial fields that are employed the fields used have the property of bounded mean oscillation and this enables the size of the penalty exacted by using a nonlinear comparison material to be controlled some recent results concerning riesz transforms and the beurling operator are used here to reduce the effect of the penalty and hence to generate improved bounds in addition an exact solution is established for a particular class of composites

the codazzi equation for surfaces abstract in this paper we study the classical codazzi equation in space forms from an abstract point of view and use it as an analytic tool to derive global results for surfaces in different ambient spaces in particular we study the existence of holomorphic quadratic differentials the uniqueness of immersed spheres in geometric problems height estimates and the geometry and uniqueness of complete or properly embedded weingarten surfaces

sets of conductivity and elasticity tensors stable under lamination a complete characterization is obtained of any set of constitutive conductivity or elasticity tensors that is stable under lamination between any two of the elements of the set the conditions are local and are expressed in terms of the curvature and tangent plane at points on the boundary of the set they are checked to hold for several well known examples of sets stable under a more general process of homogenization a companion paper investigates the link between these conditions and quasiconvexity 1994 john wiley sons inc

morphological texture based maximum likelihood pixel classification based on local granulometric moments abstract morphological granulometries are one parameter filter sequences that monotonically decrease image area a size distribution is generated by measuring the residual area after each iteration of the filter sequence normalization yields a probability distribution function whose moments can be employed as image signatures by measuring residual area locally over a window about each point of an image instead of over the entire image local texture features are generated at each pixel and these features can be employed for pixel classification by using several granulometric structuring element generating sequences numerous moment sets result each carrying different textural information a detailed analysis of this pixel classification methodology using a gaussian maximum likelihood classifier is provided included is a statistical study of classification accuracy feature optimization and robustness with respect to various relevant noise models

optimal bounds on the effective bulk modulus of polycrystals the classical problem of bounding the effective bulk modulus of isotropic polycrystalline aggregates built from a single anisotropic phase is studied for three dimensional composites we find that the voigt and reuss bounds are each attained by multi layered laminate geometries and hence are optimal for two dimensional composites the reuss lower bound is proved to be optimal while a new optimal upper bound is derived

embedded constant mean curvature surfaces in euclidean three space in this paper we refine the construction and related estimates for complete constant mean curvature surfaces in euclidean three space developed in kapouleas ann math 131 239 330 1990 by adopting the more precise and powerful version of the methodology which was developed in kapouleas invent math 119 3 443 518 1995 as a consequence we remove the severe restrictions in establishing embeddedness for complete constant mean curvature surfaces in kapouleas ann math 131 239 330 1990 and we produce a very large class of new embedded examples of finite topology

existence of translating solutions to the flow by powers of mean curvature on unbounded domains in this paper we prove the existence of classical solutions to the dirichlet problem of a class of quasi linear elliptic equations on an unbounded cone and a u type domain in rn n 2 this problem comes from the study of mean curvature flow or its generalization the flow by powers of mean curvature our approach is a modified version of the classical perron method where the solutions to the minimal surface equation are used as sub solutions and a family auxiliary functions are constructed as super solutions

new entire positive solution for the nonlinear schrodinger equation coexistence of fronts and bumps in this paper we construct new kinds of positive solutions of delta u u u p 0 quad rm on bbb r 2 when p 2 these solutions have the following asymptotic behavior u x z sim omega x f z sum i 1 infty omega 0 x z xi i vec e 1 as l rightarrow infty where omega is a unique positive homoclinic solution of omega omega omega p 0 in bbb r omega 0 is the two dimensional positive solution and vec e 1 1 0 and xi j are points such that xi j jl cal o 1 for all j geq 1 this represents a first result on the it coexistence of fronts and bumps geometrically our new solutions correspond to it triunduloid in the theory of cmc surface

a generalized discrete morphological skeleton transform with multiple structuring elements for the extraction of structural shape components a common problem shared by several leading morphological shape representation algorithms is that there is much overlapping among the representative disks of the same size a shape component represented by a group of connected disk centers sometimes uses many heavily overlapping representative disks to represent a relatively simple shape part a shape component may also contain a large number of representative disks that form a complicated structure we introduce a generalized discrete morphological skeleton transform that uses eight structuring elements to generate skeleton subsets so that no two skeletal points from the same skeleton subset are adjacent to each other each skeletal point represents a shape part that is in general an octagon with four pairs of parallel opposing sides the number of representative points needed to represent a given shape is significantly lower than that in the standard skeleton transform a collection of shape components needed to build a structural representation is easily derived from the generalized skeleton transform each shape component covers a significant area of the given shape and severe overlapping is avoided the given shape can also be accurately approximated using a small number of shape components

on decay and blow up of the solution for a viscoelastic wave equation with boundary damping and source terms abstract in this paper we consider the decay and blow up properties of a viscoelastic wave equation with boundary damping and source terms we first extend the decay result for the case of linear damping obtained by lu et al on a viscoelastic equation with nonlinear boundary damping and source terms global existence and decay of the solution nonlinear analysis real world applications 12 1 2011 295 303 to the nonlinear damping case under weaker assumption on the relaxation function g t then we give an exponential decay result without the relation between g t and g t for the linear damping case provided that g l 1 0 is small enough finally we establish two blow up results one is for certain solutions with nonpositive initial energy as well as positive initial energy for both the linear and nonlinear damping cases the other is for certain solutions with arbitrarily positive initial energy for the linear damping case

dirichlet problem for anisotropic prescribed mean curvature equation on unbounded domains abstract in this paper we consider the dirichlet problem for hypersurfaces m graph u of anisotropic prescribed mean curvature h h x u n on unbounded domain where n is the unit normal to m at x u as a corollary of the result we obtain the existence of translating solutions to the mean curvature flow with a forcing term on unbounded domains the approach used here is a modified version of classical perron s method where the solutions to minimal surface equation are used as supersolutions and a family of auxiliary functions is constructed as local subsolutions

multiple solutions of h systems and rellich s conjecture soit x y r 2 x 2 y 2 1 on considere une fonction u r 3 satisfaisant le systeme h u 2hu x u y sur avec l une des conditions suivantes soit dirichlet u sur soit plateau u x 2 u y 2 u x u y 0 sur u et u non decroissante sur

on the wave equation with semilinear porous acoustic boundary conditions the goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary interior sources and a nonlinear boundary interior damping first applying the nonlinear semigroup theory we show the existence and uniqueness of local in time solutions the main difficulty in proving the local existence result is that the neumann boundary conditions experience loss of regularity due to boundary sources using an approximation method involving truncated sources and adapting the ideas in lasiecka and tataru 1993 28 we show that the existence of solutions can still be obtained second we prove that under some restrictions on the source terms then the local solution can be extended to be global in time in addition it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ode and depends on the behavior of the damping terms in several situations the obtained ode can be easily solved and the decay rates can be given explicitly third we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping then the solution ceases to exists and blows up in finite time moreover in either the absence of the interior source or the boundary source then we prove that the solution is unbounded and grows as an exponential function

cylindrically bounded constant mean curvature surfaces in mathbb h 2 times mathbb r in this paper we prove that a properly embedded constant mean curvature surface in h 2 r which has finite topology and stays at a finite distance from a vertical geodesic line is invariant by rotation around a vertical geodesic line

a new shape decomposition scheme for graph based representation nowadays the part based representation of a given shape plays a significant role in shape related applications such as those involving content based retrieval object recognition and so on in this paper to represent both 2 d and 3 d shapes as a relational structure i e a graph a new shape decomposition scheme which recursively performs constrained morphological decomposition cmd is proposed the cmd method adopts the use of the opening operation with the ball shaped structuring element and weighted convexity to select the optimal decomposition for the sake of providing a compact representation the merging criterion is applied using the weighted convexity difference therefore the proposed scheme uses the split and merge approach finally we present experimental results for various modified 2 d shapes as well as 3 d shapes represented by triangular meshes based on the experimental results it is believed that the decomposition of a given shape coincides with that based on human insight for both 2 d and 3 d shapes and also provides robustness to scaling rotation noise shape deformation and occlusion

pattern spectrum and multiscale shape representation the results of a study on multiscale shape description smoothing and representation are reported multiscale nonlinear smoothing filters are first developed using morphological opening and closings g matheron 1975 used openings and closings to obtain probabilistic size distributions of euclidean space sets continuous binary images these distributions are used to develop a concept of pattern spectrum a shape size descriptor a pattern spectrum is introduced for continuous graytone images and arbitrary multilevel signals as well as for discrete images by developing a discrete size family of patterns large jumps in the pattern spectrum at a certain scale indicate the existence of major protruding or intruding substructures of the signal at the scale an entropy like shape size complexity measure is also developed based on the pattern spectrum for shape representation a reduced morphological skeleton transform is introduced for discrete binary and graytone images this transform is a sequence of skeleton components sparse images which represent the original shape at various scales it is shown that the partially reconstructed images from the inverse transform on subsequences of skeleton components are the openings of the image at a scale determined by the number of eliminated components in addition two way correspondences are established among the degree of shape smoothing via multiscale openings or closings the pattern spectrum zero values and the elimination or nonexistence of skeleton components at certain scales

efficient morphological shape representation with overlapping disk components this paper proposes a new morphological shape representation algorithm in which a two dimensional 2 d binary shape is represented as a union of certain disks contained in the given shape the representative disks of different sizes may overlap but excessive overlapping between them is avoided the algorithm combines the advantages of the morphological skeleton transform mst and the morphological shape decomposition msd the representative disks have simple and well defined mathematical characterizations the algorithm is simple and efficient to implement the experimental results show that the number of representative disks used by our algorithm is significant lower than that used by the msd the overlapping level between the representative disks is much lower than that of the mst a simple procedure can be used to combine the representative disks into more meaningful shape components these shape components seem to correspond better to the natural shape parts than those generated by the msd it is also possible to build a good approximation for a given shape using only a small number of major components

the classification of cmc foliations of bbb r 3 and bbb s 3 with countably many singularities in this paper we generalize our previous local removable singularity theorem for minimal laminations to the case of weak h laminations with h in bbb r constant in a punctured ball of a riemannian three manifold we also obtain a curvature estimate for any weak cmc foliation with possibly varying constant mean curvature from leaf to leaf of a compact riemannian three manifold n with boundary solely in terms of a bound of the absolute sectional curvature of n and of the distance to the boundary of n we then apply these results to classify weak cmc foliations of bbb r 3 and bbb s 3 with a closed countable set of singularities

negatively curved sets on surfaces of constant mean curvature in ℝ3 are large it is proved that the negatively curved set m on a nonparametric surface m of constant mean curvature in 3 must extend to the boundary m if m is nonempty for m parametric if m is compactly included in the interior of m then m is at least as large as an extremal domain the results imply certain convexity results on elliptic partial differential equations second order calculus of variation is employed

shape decomposition and representation using a recursive morphological operation abstract this paper presents a recursive morphological operation developed in order to perform efficient shape representation this operation uses a structuring element as a geometrical primitive to evaluate the shape of an object it results in a set of loci of the translated structuring elements that are included in the object but which do not overlap the analysis of its computational complexity shows that it is usually less time consuming than morphological erosion by using this operation an object decomposition algorithm is then developed for shape representation it decomposes an object into a union of simple and non overlapping object components the object is represented by the sizes and loci of its object components this representation is information preserving shift and scale invariant and non rebundant it has been compared with skeletons morphological decomposition chain codes and quatrees in terms of compression ability and image processing facility experimental results shows that it is very compact especially if information loss is allowed because of the non overlap between object components many image processing tasks can be easily performed by directly using this shape representation

the periodic isoperimetric problem given a discrete group g of isornetries of r 3 we study the g isoperimetric problem which consists of minimizing area modulo g among surfaces in r 3 which enclose a g invariant region with a prescribed volume fraction if g is a line group we prove that solutions are either families of round spheres or right cylinders in the doubly periodic case we prove that for most rank two lattices solutions must be spheres cylinders or planes for the remaining rank two lattices we show among other results an isoperimetric inequality in terms of the topology of the isoperimetric surfaces finally we study the case where g pm3m the group of symmetries of the integer rank three lattice z 3 and other crystallographic groups of cubic type we prove that isoperimetric solutions must be spheres if the prescribed volume fraction is less than 1 6 and we give an isoperimetric inequality for g invariant regions that for instance implies that the area modulo z 3 of a surface dividing the three space in two g invariant regions with equal volume fractions is at least 2 19 the conjectured solution is the classical p schwarz triply periodic minimal surface whose area is 2 34 another consequence of this isoperimetric inequality is that pm3m symmetric surfaces other than families of spheres cannot be isoperimetric for the lattice group z 3

complete embedded minimal surfaces of finite total curvature we will survey what is known about minimal surfaces s r 3 which are complete embedded and have finite total curvature int s k da infty the only classically known examples of such surfaces were the plane and the catenoid the discovery by costa 14 15 early in the last decade of a new example that proved to be embedded sparked a great deal of research in this area many new examples have been found even families of them as will be described below the central question has been transformed from whether or not there are any examples except surfaces of rotation to one of understanding the structure of the space of examples

the global structure of constant mean curvature surfaces in a recent ground breaking paper kapouleas constructed this century s first examples of complete finite topology properly embedded surfaces with non zero constant mean curvature ka l geometrically these surfaces are quite easy to visualize as we explain below the purpose of the present paper is to characterize the extent to which kapouleas examples are typical of all embedded constant mean curvature surfaces first and throughout this paper we scale space so that the constant mean curvature the trace of the second fundamental form of our surface l is identically one and we call such a surface an mc1 surface the only complete embedded mc1 surfaces of finite topology known before kapouleas work arise from the 1parameter family of axially symmetric and periodic examples found by delaunay in 1841 using the maximum axial radius r of such a surface as a parameter this family begins with the cylinder r 1 and evolves through embedded periodic surfaces until the family degenerates to a linear chain of touching spheres r 2 the delaunay family continues for all r 2 as periodic immersions kapouleas construction of embedded surfaces begins with a piecewise linear graph in r 3 having the property that edges are either finite segments with length a multiple of 4 or half infinite rays and with the further property that at each vertex some linear combination of their direction vectors with positive coefficients adds to zero see fig 1 he constructs an approximate solution to the problem by centering radius r 2 spheres at all vertices and connecting these smoothly by delaunay segments having r 2 but near 2 with axes along the graph edges since the periods of the delaunay surfaces are slightly longer than 4 he must assume also a flexibility condition on the graph to guarantee that such a gluing

optimal g closure bounds via stability under lamination optimal bounds for a two dimensional g closure problem are proved they are obtained by combining together bounds derived using fine properties of quasiconformal mappings and a stability property of the g closure which is known as stability under lamination

level curves of constant mean curvature graphs over convex domains abstract we consider a compact graph of constant mean curvature h 0 and with planar convex boundary we prove that a level curve is convex provided its height with respect to the boundary plane is bigger than 1 2 h

existence and nonexistence of a global solution for coupled nonlinear wave equations with damping and source abstract we consider the system of nonlinear wave equations u t t u t m 1 u t div u 2 u f 1 u v x t 0 t v t t v t r 1 v t div v 2 v f 2 u v x t 0 t with initial and dirichlet boundary conditions under some suitable assumptions on the functions f 1 and f 2 the initial data and the parameters in the equations the theorems of global existence and nonexistence are proved

constant mean curvature spheres in rm sol _3 based on work of daniel and mira we prove that for each h0 there exists a unique up to ambient isometry immersed constant mean curvature h sphere s h in rm sol 3 where rm sol 3 is the non abelian solvable 3 dimensional lie group equipped with its usual left invariant metric that makes it into a model space for one of the eight thurston geometries see bonahon or scott for a discussion of the thurston geometries that can occur for compact 3 manifolds since this proof also demonstrates that s h has index one the results in daniel mira imply s h is embedded and the left invariant gauss map of s h is a diffeomorphism one key new result that we prove in order to obtain these results for constant mean curvature spheres is the existence of height estimates for certain constant mean curvature h graphs in rm sol 3 which depend only on any fixed positive lower bound for h by the work in daniel mira the existence of the spheres s h for all h0 implies the existence for all h geq 0 of a complex holomorphic only when h 0 quadratic differential q h defined on all constant mean curvature h surfaces m in rm sol 3 and which for h0 vanishes on an open set of m if and only if m is contained in some left translation of s h furthermore when q h is not identically zero on m it has isolated zeros on m and negative index at these zeros

uniform decay of solutions for a quasilinear system of viscoelastic equations abstract in this paper we consider a system of two coupled quasilinear viscoelastic equations in canonical form with dirichlet boundary condition we use the perturbed energy method to show that the dissipations given by the viscoelastic terms are strong enough to ensure uniform decay with exponential and polynomial rates of the solutions energy which extends some existing results for a single equation to the case of a coupled system

existence and decay of solutions of a viscoelastic equation with a nonlinear source abstract in a bounded domain we consider u tt u 0 t g t u d u u where 0 and g is a nonnegative and decaying function we prove a local existence theorem and show for certain initial data and suitable conditions on g and that this solution is global with energy which decays exponentially or polynomially depending on the rate of the decay of the relaxation function g

nonlinear damped wave equation in this paper we consider the following nonlinear wave equation with variable exponents uttu aut ut m 2 bu u p 2 where a b are positive constants by using the faedogalerkin method the existence of a unique weak solution is established under suitable assumptions on the variable exponents m and p we also prove the finite time blow up of solutions and give a two dimension numerical example to illustrate the blow up result

geometry and topology of some overdetermined elliptic problems we study necessary conditions on the geometry and the topology of domains in r2 that support a positive solution to a classical overdetermined elliptic problem u f u 0in u 0on u constanton the ideas and tools we use come from constant mean curvature surface theory in particular we obtain a partial answer to a question posed by h berestycki l caffarelli and l nirenberg in 1997 we investigate also some boundedness properties of the solution u some of our results generalize to higher dimensions

a link between sets of tensors stable under lamination and quasiconvexity a link is found between quasiconvexity and the conditions for a set l of conductivity or elasticity tensors to be stable under lamination these conditions derived in the companion paper are shown here to be equivalent to the condition that for every point b on the boundary of the set l an operator tb dependent on the tangent plane and curvature of the set at b is a quasiconvex translation operator a separate class of quasiconvex translation operators is obtained which are candidates for proving that l is stable under homogenization the region stable under homogenization associated with any one of these operators shares a common boundary point and tangent plane with the set l and has curvature at that point not greater than the curvature of l the conditions under which there exists a representative subclass of these operators such that the associated regions stable under homogenization wrap around l remains unresolved it is proved that l can be characterized by minimizations of sums and dual energies in much the same way that convex sets can be characterized by their legendre transforms 1994 john wiley sons inc

constant mean curvature surfaces with three ends abstract we announce the classification of complete almost embedded surfaces of constant mean curvature with three ends and genus zero they are classified by triples of points on the sphere whose distances are the asymptotic necksizes of the three ends

block decomposition and segmentation for fast hough transform evaluation the decomposition of binary images using rectangular blocks of foreground pixels as primitives is considered based on this type of decomposition a fast method for evaluating the hough transform is introduced a complexity analysis of the proposed block hough transform algorithm sets constraints on the complexity of algorithms used for block decomposition so that the total decomposition and hough transform application time is much less than the time consumed by the usual point hough transform using this analysis we propose two algorithms for the decomposition and segmentation of binary images into rectangular blocks a combination of these methods leads to significant acceleration in the identification of linear features which is demonstrated in various image processing experiments 1999 pattern recognition society published by elsevier science ltd all rights reserved

classification des surfaces de type delaunay we define and study complete and noncomplete rotational special weingarten surfaces in euclidean space we prove general existence and uniqueness theorems for such complete surfaces

blow up of positive initial energy solutions of a nonlinear viscoelastic hyperbolic equation abstract in this paper we consider the nonlinear viscoelastic equation u t t u 0 t g t u d u t u t m 2 u u p 2 with initial conditions and dirichlet boundary conditions for nonincreasing positive functions g and for p m we prove that there are solutions with positive initial energy that blow up in finite time

a height estimate for h surfaces and existence of h graphs let be a bounded planar domain which is convex although not necessarily strictly convex with area a we prove that for each real number h satisfying ah 2 2 with 5 1 2 there exists a graph on with constant mean curvature h and boundary this existence theorem is deduced as a consequence of an l estimate for compact constant mean curvature surfaces with planar boundary in terms of the l 1 norm of a component of its gauss map which will be obtained in this paper

efficient morphological shape representation by varying overlapping levels among representative disks abstract the morphological skeleton transform the morphological shape decomposition and the overlapped morphological shape decomposition are three basic morphological shape representation schemes in this paper we propose a new way of generalizing these basic representation algorithms to improve representational efficiency in all three basic algorithms a fixed overlapping policy is used to control the overlapping relationships among representative disks of different sizes in our new algorithm different overlapping policies are used to generate shape components that have different overlapping relationships among themselves the overlapping policy is selected dynamically according to local shape features experiments show that compared to the three basic algorithms our algorithm produces more efficient representations with lower numbers of representative points

a weierstrass representation for linear weingarten spacelike surfaces of maximal type in the lorentz minkowski space in this work we extend the weierstrass representation for maximal spacelike surfaces in the 3 dimensional lorentz minkowski space to spacelike surfaces whose mean curvature is proportional to its gaussian curvature linear weingarten surfaces of maximal type we use this representation in order to study the gaussian curvature and the gauss map of such surfaces when the immersion is complete proving that the surface is a plane or the supremum of its gaussian curvature is a negative constant and its gauss map is a diffeomorphism onto the hyperbolic plane finally we classify the rotation linear weingarten surfaces of maximal type

global nonexistence of positive initial energy solutions for a viscoelastic wave equation abstract in this paper we consider the nonlinear viscoelastic equation u t u t t u 0 t g t u d u t m 2 u t u p 2 u in 0 t with initial conditions and dirichlet boundary conditions for nonincreasing positive functions g we prove the nonexistence of global solutions with positive initial energy

constant mean curvature graphs on unbounded convex domains abstract in this paper we consider the dirichlet problem for the constant mean curvature equation on an unbounded convex planar domain let h 0 we prove that there exists a graph with constant mean curvature h and with boundary if and only if is included in an infinite strip of width 1 h we also establish an existence result for convex bounded domains contained in a strip

global existence and blow up phenomena for a nonlinear wave equation abstract in this paper we study the solution to the initial boundary value problem for a class of nonlinear wave equations with damping and source term by using the energy compensation method we prove that under some conditions on the initial value the growth orders of the nonlinear strain term the damping term and the source term the solution to the problem exists globally and blows up respectively and the estimate for the blow up time is given

traveling wave solutions for reaction diffusion systems abstract this paper is concerned with traveling waves of reaction diffusion systems the definition of coupled quasi upper and quasi lower solutions is introduced for systems with mixed quasimonotone functions and the definition of ordered quasi upper and quasi lower solutions is also given for systems with quasimonotone nondecreasing functions by the monotone iteration method it is shown that if the system has a pair of coupled quasi upper and quasi lower solutions then there exists at least a traveling wave solution moreover if the system has a pair of ordered quasi upper and quasi lower solutions then there exists at least a traveling wavefront as an application we consider the delayed system of a mutualistic model

morphological decomposition of 2 d binary shapes into convex polygons a heuristic algorithm in many morphological shape decomposition algorithms either a shape can only be decomposed into shape components of extremely simple forms or a time consuming search process is employed to determine a decomposition in this paper we present a morphological shape decomposition algorithm that decomposes a two dimensional 2 d binary shape into a collection of convex polygonal components a single convex polygonal approximation for a given image is first identified this first component is determined incrementally by selecting a sequence of basic shape primitives these shape primitives are chosen based on shape information extracted from the given shape at different scale levels additional shape components are identified recursively from the difference image between the given image and the first component simple operations are used to repair certain concavities caused by the set difference operation the resulting hierarchical structure provides descriptions for the given shape at different detail levels the experiments show that the decomposition results produced by the algorithm seem to be in good agreement with the natural structures of the given shapes the computational cost of the algorithm is significantly lower than that of an earlier search based convex decomposition algorithm compared to nonconvex decomposition algorithms our algorithm allows accurate approximations for the given shapes at low coding costs

the coherent potential approximation is a realizable effective medium scheme the effective electrical conductivity of an aggregate composed of grains of various conductivities is frequently estimated by the coherent potential approximation which embodies a local effective medium concept it is proved rigorously that this approximation is exact for a wide class of hierarchical model composites made of spherical grains the starting material 0 in the hierarchy is chosen arbitrarily otherwise materialj 1 2 consists of equisized spheres sayj spheres of arbitrary conductivities embedded in materialj 1 the spatial distribution of thej spheres must satisfy a mild homogeneity condition and their radiusr j must asymptotically increase faster than exponentially withj furthermore the minimum spacing 2s j between thej spheres is such that the ratios j r j diverges on the basis of these and some further ancillary conditions it is established that the coherent potential approximation becomes asymptotically exact for the effective conductivity of materialj the results extend to other effective parameters of the composites including the thermal conductivity dielectric constant and magnetic permeability in addition the model composites and the proof of realizability may be generalized to allow non spherical grains

global nonexistence of positive initial energy solutions of a system of nonlinear viscoelastic wave equations with damping and source terms this work is concerned with a system of viscoelastic wave equations with nonlinear damping and source terms acting in both equations we prove a global nonexistence theorem for certain solutions with positive initial energy

blow up in a nonlinear viscoelastic wave equation with strong damping abstract in this paper we consider the nonlinear viscoelastic equation u t t u 0 t g t u d u t u p 2 u in 0 t with initial conditions and dirichlet boundary conditions for nonincreasing positive functions g we show the finite time blow up of some solutions whose initial data have arbitrarily high initial energy

extremal domains on hadamard manifolds abstract we investigate the geometry and topology of extremal domains in a hadamard manifold i e domains that support a positive solution to an overdetermined elliptic problem oep first we study narrow properties of such domains and characterize the boundary at infinity we give an upper bound for the hausdorff dimension of its boundary at infinity and how the domain behaves at infinity this shows interesting relations with the singular yamabe problem later we focus on extremal domains in the hyperbolic space symmetry and boundedness properties will be shown in a certain sense we extend levitt rosenberg s theorem to oeps which suggests a strong relation with constant mean curvature hypersurfaces in particular we are able to prove the berestycki caffarelli nirenberg conjecture under certain assumptions either on the boundary at infinity of the extremal domain or on the oep itself also a height estimate for solutions on extremal domains in a hyperbolic space will be given

the geometry of finite topology bryant surfaces we prove that in the three dimensional hyperbolic space h 3 the properly embedded constant mean curvature one surfaces with finite topology are of finite total curvature and each ends are regular this imply in particular that the hrosphere is the only properly embedded simply connected constant mean curvature one surface in h 3

the topology and geometry of embedded surfaces of constant mean curvature si m est une surface proprement plongee dans r 3 avec une courbure moyenne constante non nulle alors m n est pas homeomorphe a une surface fermee avec un seul point elimine soit m une surface proprement plongee dans r 3 a courbure moyenne constante non nulle si m est homeomorphe a une surface fermee avec 2 points elimines alors m est une distance bornee a partir d une ligne droite soit m une surface proprement plongee de courbure moyenne non nulle qui est homeomorphe a une surface fermee avec 3 points elimines alors m reste une distance bornee a partir d un plan

some a priori bounds for solutions of the constant gauss curvature equation abstract in this work we give a priori height and gradient estimates for solutions of the prescribed constant gauss curvature equation in euclidean space we shall consider convex radial graphs with positive constant mean curvature the estimates are established by considering in such a graph the riemannian metric given by the second fundamental form of the immersion

morphological representation of 2 d binary shapes using rectangular components abstract the morphological skeleton transform is a shape representation scheme that decomposes a shape into a union of all maximal homothetics of a structuring element contained in the shape in this paper we develop an algorithm that generalizes the skeleton transform by allowing many different rectangles of different sizes and aspect ratios to be used as shape components the shape components in our representations still have simple and well defined mathematical characterizations the representation is uniquely defined and the algorithm still is simple and efficient to implement experiments show that our representations use significantly less shape components than those produced by the skeleton transform we also describe different ways to derive a new set of rectangular shape components with less overlapping from the original set of rectangles from our representation algorithm

constant mean curvature surfaces with boundary on a sphere in this article we study the shape of a compact surface of constant mean curvature of euclidean space whose boundary is contained in a round sphere we consider the case that the boundary is prescribed or that the surface meets the sphere with a constant angle we study under what geometric conditions the surface must be spherical our results apply in many scenarios in physics where in absence of gravity a liquid drop is deposited on a round solid ball and the air liquid interface is a critical point for area under all variations that preserve the enclosed volume

stationary isothermic surfaces in euclidean 3 space let omega be a domain in mathbb r 3 with partial omega partial mathbb r 3 setminus overline omega where partial omega is unbounded and connected and let u be the solution of the cauchy problem for the heat equation partial t u delta u over mathbb r 3 where the initial data is the characteristic function of the set omega c mathbb r 3 setminus omega we show that if there exists a stationary isothermic surface gamma of u with gamma cap partial omega varnothing then both partial omega and gamma must be either parallel planes or co axial circular cylinders this theorem completes the classification of stationary isothermic surfaces in the case that gamma cap partial omega varnothing and partial omega is unbounded to prove this result we establish a similar theorem for uniformly dense domains in mathbb r 3 a notion that was introduced by magnanini et al trans am math soc 358 4821 4841 2006 in the proof we use methods from the theory of surfaces with constant mean curvature combined with a careful analysis of certain asymptotic expansions and a surprising connection with the theory of transnormal functions

general decay and blow up of solution for a quasilinear viscoelastic problem with nonlinear source abstract in this paper we consider a quasilinear viscoelastic wave equation in canonical form with the homogeneous dirichlet boundary condition we prove that for certain class of relaxation functions and certain initial data in the stable set the decay rate of the solution energy is similar to that of the relaxation function this result improves earlier ones obtained by messaoudi and tatar s a messaoudi n e tatar global existence and uniform stability of solutions for a quasilinear viscoelastic problem math methods appl sci 30 2007 665 680 in which only the exponential and polynomial decay rates are considered conversely for certain initial data in the unstable set there are solutions that blow up in finite time the last result is new since it allows a larger class of initial energy which may take positive values