automatic mesh generation and adaptation by using contours a general and efficient remeshing algorithm is presented for the discretization of arbitrary planar domains into triangular elements in consistency with the given node spacing funstion the contour lines of the node spacing function at suitable calculated levels provide the natural lines of division of the problem domain into subregions where finite elements meshes of different element sizes zre generated using the available general purpose mesh generators

cellular networks as models for planck scale physics starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the planck scale one of the many problems one has to face in this enterprise is to find the discrete protoforms of the building blocks of our ordinary continuum physics and mathematics we base our own approach on what we call cellular networks consisting of cells nodes interacting with each other via bonds figuring as elementary interactions according to a certain local law geometrically our dynamical networks are living on graphs hence a substantial amount of the investigation is devoted to the development of various versions of discrete functional analysis and geometry on such almost random webs another important topic we address is a suitable concept of intrinsic fractal dimension on erratic structures of this kind in the course of the investigation we make comments concerning both different and related approaches to quantum gravity as say the spin network framework it may perhaps be said that certain parts of our programme seem to be a realization of ideas sketched by smolin some time ago

transient behavior analysis of vibrationally controlled nonlinear parabolic systems with neumann boundary conditions the transient behavior of vibrationally controlled distributed parameter systems governed by parabolic partial differential equations pdes with neumann boundary conditions is analyzed the analysis uses a certain mapping and a time invariant pde whose trajectories under this mapping yield the approximate moving averages along the trajectories of the vibrationally controlled system this approach considerably enhances the understanding of the behavior of vibrationally controlled distributed parameter systems and facilitates a selection of the parameters of stabilizing vibrations that ensure transient behavior with more desirable properties

automatic mesh generation over intersecting surfaces a fully automatic general scheme is proposed to determine and analyse the intersections between two groups of surfaces composed of triangular facets by carefully maintaining the spatial position of the lines of intersection in regenerating mesh locally around surface intersections pieces of surfaces can be arbitrarily combined and merged a great variety of objects can be easily created by selectively putting together different surface parts derived from surface intersections the new algorithm is best applied in conjunction with an existing surface mesh generator to enhance its general capability in dealing with objects built from intersecting surfaces in fact it is a powerful surface mesh manipulator and through the repeated use of the process complex structures can be rapidly and accurately constructed

the natural element method in solid mechanics the application of the natural element method nem 1 2 to boundary value problems in two dimensional small displacement elastostatics is presented the discrete model of the domain consists of a set of distinct nodes n and a polygonal description of the boundary in the natural element method the trial and test functions are constructed using natural neighbour interpolants these interpolants are based on the voronoi tessellation of the set of nodes n the interpolants are smooth c 1 everywhere except at the nodes where they are c 0 in one dimension nem is identical to linear nite elements the nem interpolant is strictly linear between adjacent nodes on the boundary of the convex hull which facilitates imposition of essential boundary conditions a methodology to model material discontinuities and non convex bodies cracks using nem is also described a standard displacement based galerkin procedure is used to obtain the discrete system of linear equations application of nem to various problems in solid mechanics which include the patch test gradient problems bimaterial interface and a static crack problem are presented excellent agreement with exact analytical solutions is obtained which exemplies the accuracy and robustness of nem and suggests its potential application in the context of other classes of problems crack growth plates and large deformations to name a few 1998 john wiley sons ltd

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

dynamical evolution in non commutative discrete phase space and the derivation of classical kinetic equations by considering a lattice model of extended phase space and using techniques of non commutative differential geometry we are led to a the concept of vector fields as generators of motion and transition probability distributions on the lattice b the emergence of the time direction on the basis of the encoding of probabilities in the lattice structure c the general prescription for the evolution of the observables in analogy with classical dynamics we show that in the limit of a continuous description these results lead to the time evolution of observables in terms of the adjoint of generalized fokker planck equations having 1 a diffusion coefficient given by the limit of the correlation matrix of the lattice coordinates with respect to the probability distribution associated with the generator of motion 2 a drift term given by the microscopic average of the dynamical equations in the present context these results are applied to one and two dimensional problems specifically we derive i the equations of diffusion smoluchowski and fokker planck in velocity space thus indicating the way random walk models are incorporated in the present context ii kramers equation by further assuming that motion is deterministic in coordinate space

necessary conditions controllability and the value function for differential difference inclusions on deduit des conditions necessaires pour la commande optimale d un systeme contraint par des inclusions differentielles aux differences

kubik an automatic three dimensional finite element mesh generator this paper describes an automatic mesh generator for finite element problems in three dimensions called kubik kubik is based on a modular concept first a set of modules is generated each with its own mesh inside then the modules are placed in contact and a matrix describing the connectivity of the entire mesh is determined finally the geometry of the mesh is specified and all nodal co ordinates are determined by the computer the user s labour required to specify a mesh which represents a certain physical configuration resumbles the labour involved when the configuration has to be specified to the machine shop workers who are supposed to build it the modules are independent except for the compatibility requirements between modules which are to be placed in contact structures of any degree of complexity can in principle be obtained using kubik only two types of modules are required except when helicoidal structures are to be generated in which case it is convenient to use a third type the finite elements used are distorted cubes but they can be divided into tetrahedra prisms of pyramids nodes are placed at the corners of the cubes and additional nodes can be introduced if desired in order to obtain other types of finite elements in use infinite elements of quadrilateral cross section are also a standard feature of kubik and can be divided in order to obtain infinite prisms of triangular cross section kubik can also generate two dimensional meshes including meshing of a three dimensional surface for use with boundary elements

asymptotic behavior of a nonlinear kirchhoff type equation with spring boundary conditions in this paper we consider the initial boundary value problem for a nonlinear kirchhoff type equation with the damping term and spring boundary conditions we establish the global existence and uniqueness of solutions to this problem in time and give an example and simulation to illustrate our results for the proof we use the faedo galerkin approximate method finally we study the asymptotic behavior of solutions and some of its simulation results results of this paper are able to apply industrial parts such as a typical model widely used to represent threads wires magnetic tapes belts band saws and so on

a knowledge based a priori approach to mesh generation in thermal problems a new approach to the finite element mesh generation for two dimensional steady state thermal problems of conduction and convection is presented unlike other approaches the proposed technique incorporates the information about the object geometry as well as the boundary and loading conditions to generate an a priori finite element mesh which is more refined around the critical regions of the problem domain a blackboard architecture expert system is developed to intelligently identify critical regions and to choose the proper mesh size for them by performing an approximate heat flux calculation from the results of the blackboard system nodes are generated in the problem domain using the new concept of wave propagation the wave propagation technique is fully automatic and does not require any user provided information except the data which define the object geometry and boundary conditions after nodes are generated well shaped triangular elements are formed ensuring the delaunay property during the triangulation process and to reduce the computation time for checking the overlapping problem a new and efficient algorithm is proposed which defines a certain range only in which a potential triangular element might overlap the previously generated elements and boundary segments several examples are presented and discussed when incorporated into and compared with the traditional approach to the adaptive finite element analysis it is expected that the proposed approach which starts the process with near optimal initial meshes will result in lower levels of error and faster convergence of the solution to the desired accuracy in less time and at less cost

polyhedral representations of discrete differential manifolds any discrete differential manifold m a finite set endowed with an algebraic differential calculus can be represented by appropriate polyhedron p m the representation is proved to be exact for a special class of manifolds called basic the links with the finitary substitutes of continuous spaces introduced by r sorkin are established

generation of tetrahedral mesh of variable element size by sphere packing over an unbounded 3d domain this paper describes an algorithm for the generation of tetrahedral mesh of specified element size over an unbounded three dimensional domain starting from an arbitrary point in space defined as the origin and guided by the concept of advancing front spheres of size compatible with the specified element size are packed tightly together one by one to form a cluster of spheres of different sizes the compactness of the cluster of spheres is achieved by packing spheres at a site closest to the origin in a densest manner with tangent but no overlapping with as many other spheres as possible in view of these criteria a rotational mechanism between spheres is innovated which allows the newly inserted sphere to follow the path by rotation between existing spheres until the lowest point is reached the centres of the packing spheres provide ideal locations for delaunay point insertion to form a triangulation of tetrahedral elements of size compatible with the specified value spheres of random size distribution or of size specified by a node spacing function are packed by the proposed algorithm in all test examples high quality tetrahedral elements of size consistent with the specified node spacing are generated the process is fast and robust and the time complexity for mesh generation is expected to be almost linear however in the present implementation a quasi linear time relationship is observed as a search for the nearest node on the front is proposed in the sphere packing process the memory requirement has been kept to a minimum as no additional data structure other than the adjacency relationship of the tetrahedral elements as required by the delaunay triangulation is stored the structure of the advancing frontal surface needs not be explicitly constructed nor updated as it is simply not required in the sphere packing process

triangular meshes for regions of complicated shape a method using techniques of computational geometry for triangular mesh generation for regions with complicated polygonal boundaries in the plane is presented the input to the method includes the desired number of triangles and a mesh smoothness parameter to be specified as well as the polygonal curves of the region s boundary and possibly internal interfaces the triangulation generated conforms to the length scales of the edges of the boundary curves but the method can be extended to provide additional control of the triangulation by a mesh distribution function the region is decomposed into convex subregions in two stages such that triangles of one length scale can be generated in each subregion this decomposition uses algorithms which run in times that are linear in the number of vertices of the input polygons details of two major computational experiments are provided

sharp energy decay estimates for the wave equation with a local degenerate dissipation we derive a fast decay estimate for the wave equation with a local degenerate dissipation of the type a x u t in a bounded domain w the dissipative coefficient a x is a nonnegative function only on a neighborhood of some part of the boundary w and may vanish somewhere in w the results obtained extend and improve on earlier results of nakao as well as those of tcheugoue tebou the method of proof is based on multipliers technique and some modified interpolation and difference inequalities

discrete riemannian geometry within a framework of noncommutative geometry we develop an analog of pseudo riemannian geometry on finite and discrete sets on a finite set there is a counterpart of the continuum metric tensor with a simple geometric interpretation the latter is based on a correspondence between first order differential calculi and digraphs the vertices of the latter are given by the elements of the finite set arrows originating from a vertex span its co tangent space if the metric is to measure length and angles at some point it has to be taken as an element of the left linear tensor product of the space of 1 forms with itself and not as an element of the nonlocal tensor product over the algebra of functions as considered previously by several authors it turns out that linear connections can always be extended to this left tensor product so that metric compatibility can be defined in the same way as in continuum riemannian geometry in particular in the case of the universal differential calculus on a finite set the euclidean geometry of polyhedra is recovered from conditions of metric compatibility and vanishing torsion in our rather general framework which also comprises structures which are far away from continuum differential geometry there is in general nothing like a ricci tensor or a curvature scalar because of the nonlocality of tensor products over the algebra of functions of forms corresponding components with respect to some module basis turn out to be rather nonlocal objects but one can make use of the parallel transport associated with a connection to localize such objects and in certain cases there is a distinguished way to achieve this in particular this leads to covariant components of the curvature tensor which allow a contraction to a ricci tensor several examples are worked out to illustrate the procedure furthermore in the case of a differential calculus associated with a hypercubic lattice we propose a new discrete analogue of the vacuum einstein equations

unstructured grid generation and a simple triangulation algorithm for arbitrary 2 d geometries using object oriented programming this paper describes the logic of a dynamic algorithm for a general 2d delaunay triangulation of arbitrarily prescribed interior and boundary nodes the complexity of the geometry is completely arbitrary the scheme is free of specific restrictions on the input of the geometrical data the scheme generates triangles whose associated circumcircles contain no nodal points except their vertices there is no predefined limit for the number of points and the boundaries the direction of generation of the triangles cannot be determined a priori as opposed to the moving front techniques an automatic node placement scheme reflecting the initial boundary point spacings is used the successive refinement scheme results in such a point distribution that the triangulation algorithm need not perform any geometric intersection check for overlapped triangles and penetrated boundaries further computational saving is provided by using a special binary tree adt in which the points are ordered such that contiguous points in the list are neighbours in physical space the method consists of a set of simple rules to understand the dynamic nature of the object oriented programming oop of the algorithms provides efficient memory management on the insertion deletion and searching processes the computational effort bears a linear relation ship between the cpu time and the total number of nodes some of the existing methods in the literature regarding triangular mesh generation are discussed in context 1997 by john wiley sons ltd

local hadamard well posedness for nonlinear wave equations with supercritical sources and damping abstract we consider the wave equation with supercritical interior and boundary sources and damping terms the main result of the paper is local hadamard well posedness of finite energy weak solutions the results obtained 1 extend the existence results previously obtained in the literature by allowing more singular sources 2 show that the corresponding solutions satisfy hadamard well posedness conditions during the time of existence this result provides a positive answer to an open question in the area and it allows for the construction of a strongly continuous semigroup representing the dynamics governed by the wave equation with supercritical sources and damping

moduli of quantum riemannian geometries on 4 points we classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously s majid commun math phys 225 131 2002 the full moduli space is found for 3 points and a restricted moduli space for 4 points generalized levi civita connections and their curvatures are found for a variety of models including models of a discrete torus the topological part of the moduli space is found for 9 points based on the known atlas of regular graphs we also remark on aspects of quantum gravity in this approach

bicovariant differential calculi on glp q 2 and quantum subgroups in a previous paper all bicovariant differential calculi on the two parameter quantum group glp q 2 were determined in this work the authors elaborate some of their properties and discuss relations with work by other authors furthermore they show that there are two different ways in which bicovariant differential calculi on glq 2 where p q induce corresponding calculi on the quantum subgroup slq 2 it is shown that on slq 2 there are only two different bicovariant differential calculi from these one obtains the 4d or calculi on suq 2 the classical limit of the two differential calculi on slq 2 is investigated revealing a relation with recent work on deformed differential calculi on commutative function algebras

local soltutions for a nonlinear degenerate hyperbolic equation on etudie l existence et l unicite des solutions locales pour le probleme mixte associe a l equation hyperbolique degenere du type 2 u 2 m u x t 2 dx u 0 ou est un ouvert borne de r n a frontiere lisse et x est un vecteur de r n

on the nonlinear wave equation utt b t ux 2 uxx f x t u ux ut associated with the mixed homogeneous conditions abstract in this paper we consider the following nonlinear wave equation 1 u tt b t u x 2 u xx f x t u u x u t x 0 1 0 2 u x 0 t h 0 u 0 t 0 u x 1 t h 1 u 1 t 0 3 u x 0 u 0 x u t x 0 u 1 x where h0 h1 are given nonnegative constants and b f u 0 u 1 are given functions in eq 1 the coefficient b t ux 2 containing an integral u x 2 0 1 u x x t 2 dx in this paper we associate with problem 1 3 a linear recursive scheme for which the existence of a local and unique solution is proved by using standard compactness argument in case of b c 2 r 2 b b0 0 b 1 c 1 r 2 b1 0 f c 2 0 r 3 and f 1 c 1 0 r 3 we obtain from the following equation u tt b t u x 2 eb 1 t u x 2 u xx f x t u u x u t ef 1 x t u u x u t associated to 2 3 a weak solution ue x t having an asymptotic expansion of order 2 in e for e sufficiently small

a natural neighbour based moving least squares approach for the element free galerkin method the element free galerkin method efg and the natural element method nem are two well known and widely used meshless methods whereas the efg method can represent moving boundaries like cracks only by modifying the weighting functions the nem requires an adaptation of the nodal set up but on the other hand the nem is computationally more efficient than efg in this paper a new concept for the automatic adjustment of nodal influence domains in the efg method is presented in order to obtain an efficiency similar to the nem this concept is based on the definition of natural neighbours for each meshless node which can be determined from a voronoi diagram of the nodal set up in this approach adapted nodal influence domains are obtained by interpolating the distances to the natural neighbours depending on the direction in the paper we show that this concept leads especially for problems with grading node density to a reduced number of influencing nodes at the interpolation points and consequently a significant reduction of the numerical effort copyright 2006 john wiley sons ltd

discrete differential calculus graphs topologies and gauge theory differential calculus on discrete sets is developed in the spirit of noncommutative geometry any differential algebra on a discrete set can be regarded as a reduction of the universal differential algebra and this allows a systematic exploration of differential algebras on a given set associated with a differential algebra is a di graph where two vertices are connected by at most two antiparallel arrows the interpretation of such a graph as a hasse diagram determining a locally finite topology then establishes contact with recent work by other authors in which discretizations of topological spaces and corresponding field theories were considered which retain their global topological structure it is shown that field theories and in particular gauge theories can be formulated on a discrete set in close analogy with the continuum case the framework presented generalizes ordinary lattice theory which is recovered from an oriented hypercubic lattice graph it also includes e g the two point space used by connes and lott and others in models of elementary particle physics the formalism suggests that the latter be regarded as an approximation of a manifold and thus opens a way to relate models with an internal discrete space a la connes et al to models of dimensionally reduced gauge fields furthermore a symmetric lattice is also studied which in a certain continuum limit turns out to be related to a noncommutative differential calculus on manifolds

differential calculus and gauge theory on finite sets we develop differential calculus and gauge theory on a finite set g an elegant formulation is obtained when g is supplied with a group structure and in particular for a cyclic group connes two point model 1986 which is an essential ingredient of his reformulation of the standard model of elementary particle physics is recovered in our approach reductions of the universal differential calculus to lower dimensional differential calculi are considered the complete reduction leads to a differential calculus on a periodic lattice

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

delaunay triangulation of non convex planar domains this paper investigates the possibility of integrating the two currently most popular mesh generation techniques namely the method of advancing front and the delaunay triangulation algorithm the merits of the resulting scheme are its simplicity efficiency and versatility with the introduction of non delaunay line segments the concept of using delaunay triangulation as a means of mesh generation is clarified an efficient algorithm is proposed for the construction of delaunay triangulations over non convex planar domains interior nodes are first generated within the planar domain these interior nodes and the boundary nodes are then linked up together to produce a valid triangulation in the mesh generation process the delaunay property of each triangle is ensured by selecting a node having the smallest associated circumcircle in contrast to convex domains intersection between the proposed triangle and the domain boundary has to be checked this can be simply done by considering only the non delaunay segments on the generation front through the study of numerous examples of various characteristics it is found that high quality triangular element meshes are obtained by the proposed algorithm and the mesh generation time bears a linear relationship with the number of elements nodes of the triangulation

simple heuristic algorithm for profile reduction of arbitrary sparse matrix the simple universal algorithm for profile reduction of arbitrary sparse matrix is described it is shown that even for intelligent strategy of generation and numbering of internal nodes suggested algorithm can reduce profile by factor 2 3 this method can be modified easily for general task of matrix transformation to arbitrary desirable form to minimize the profile further the method can be embedded in depth first search of artificial intelligence

existence and asymptotic stability for the semilinear wave equation with boundary damping and source term in this paper we consider the semilinear wave equation with boundary conditions this work is devoted to prove the existence of solutions and uniform decay rates of the wave equation with boundary damping and source term

pythagoras s theorem on a two dimensional lattice from a natural dirac operator and connes s distance formula one of the key ingredients of connes s noncommutative geometry is a generalized dirac operator which induces a metric connes s distance on the pure state space we generalize such a dirac operator devised by dimakis et al whose connes distance recovers the linear distance on an one dimensional lattice to the two dimensional case this dirac operator has the local eigenvalue property and induces a euclidean distance on this two dimensional lattice which is referred to as natural this kind of dirac operator can be easily generalized into any higher dimensional lattices

robust geometrically based automatic two dimensional mesh generation a technical description of the algorithms employed in the modified quadtree mesh generator is given although the basis of the mesh generator is the same as the original version developed by yerry and shephard 1 2 the actual algorithms on which it is built have been entirely changed for the purpose of ensuring the robustness of the technique as demonstrated in the paper the algorithmic changes made do ensure the robustness of the approach but introduce additional algorithmic difficulties the solutions of which are also presented in addition to examples showing the capability of the mesh generator the linear computational growth rate of the mesh generator is demonstrated

noncommutative differential calculus and lattice gauge theory the authors study consistent deformations of the classical differential calculus on algebras of functions and more generally commutative algebras such that differentials and functions satisfy nontrivial commutation relations for a class of such calculi it is shown that the deformation parameters correspond to the spacings of a lattice these differential calculi generate a lattice on a space continuum the whole setting of a lattice theory can then be deduced from the continuum theory via deformation of the standard differential calculus in this framework one just has to express the lagrangian for the continuum theory in terms of differential forms this expression then also makes sense for the deformed differential calculus there is a natural integral associated with the latter integration of the lagrangian over a space continuum then produces the correct lattice action for a large class of theories this is explicitly shown for the scalar field action and the action for su m gauge theory

automatic mesh generation with tetrahedron elements to reduce the manual work involved in the application of the fem in practice preprocessors can be applied for the construction of network structures which are complicated in generation strategy and do not form any optimum discrete structure the time necessary for generation can be minimized even more by the application of only one element type within the whole network structure a technique for the automatic generation of 3d network structures with tetrahedron elements is presented in this paper in this proposed technique the nodal points of the network structure must be defined manually before the generation procedure since a random positioning of points is usually undesirable for fem calculation the nodal points are connected by a program to a network structure consisting of tetrahedron elements which have optimum form for the numerical computation of the element matrices after the generation the element sides forming any part of the boundary surface of the network structure can be automatically identified if necessary the network structure can be automatically refined

generation of finite element mesh with variable size over an unbounded 2d domain with the advance of the finite element general fluid dynamic and traffic flow problems with arbitrary boundary definition over an unbounded domain are tackled this paper describes an algorithm for the generation of finite element mesh of variable element size over an unbounded 2d domain by using the advancing front circle packing technique unlike the conventional frontal method the procedure does not start from the object boundary but starts from a convenient point within an open domain the sequence of construction of the packing circles is determined by the shortest distance from the fictitious centre in such a way that the generation front is more or less a circular loop with occasional minor concave parts due to element size variation as soon as a circle is added to the generation front finite elements are directly generated by properly connecting frontal segments with the centre of the new circle in contrast to other mesh generation schemes the domain boundary is not considered in the process of circle packing this reduces a lot of geometrical checks for intersection with frontal segments and a linear time complexity for mesh generation can be achieved in case the boundary of the domain is needed simply generate an unbounded mesh to cover the entire object as the element adjacency relationship of the mesh has already been established in the circle packing process insertion of boundary segments by neighbour tracing is fast and robust details of such a boundary recovery procedure are described and practical meshing problems are given to demonstrate how physical objects are meshed by the unbounded meshing scheme followed by the insertion of domain boundaries

discrete differential manifolds and dynamics on networks a discrete differential manifold is a countable set together with an algebraic differential calculus on it this structure has already been explored in previous work and provides a convenient framework for the formulation of dynamical models on networks and physical theories with discrete space and time several examples are presented and a notion of differentiability of maps between discrete differential manifolds is introduced particular attention is given to differentiable curves in such spaces every discrete differentiable manifold carries a topology and we show that differentiability of a map implies continuity

global existence for the wave equation with nonlinear boundary damping and source terms abstract the paper deals with local and global existence for the solutions of the wave equation in bounded domains with nonlinear boundary damping and source terms the typical problem studied is u tt u 0 in 0 u 0 on 0 0 u u t m 2 u t u p 2 u on 0 1 u 0 x u 0 x u t 0 x u 1 x on where r n n 1 is a regular and bounded domain 0 1 m 1 2 p r where r 2 n 1 n 2 when n 3 r when n 1 2 and the initial data are in the energy space we prove local existence of the solutions in the energy space when m r r 1 p or n 1 2 and global existence when p m or the initial data are inside the potential well associated to the stationary problem

non commutative geometry of finite groups a finite set can be supplied with a group structure which can then be used to select classes of differential calculi on it via the notions of left right and bicovariance a corresponding framework has been developed by woronowicz more generally for hopf algebras including quantum groups a differential calculus is regarded as the most basic structure needed for the introduction of further geometric notions like linear connections and moreover for the formulation of field theories and dynamics on finite sets associated with each bicovariant first order differential calculus on a finite group is a braid operator which plays an important role for the construction of distinguished geometric structures for a covariant calculus there are notions of invariance for linear connections and tensors all these concepts are explored for finite groups and illustrated with examples some results are formulated more generally for arbitrary associative hopf algebras in particular the problem of extension of a connection on a bimodule over an associative algebra to tensor products is investigated leading to the class of extensible connections it is shown that invariance properties of an extensible connection on a bimodule over a hopf algebra are carried over to the extension furthermore an invariance property of a connection is also shared by a dual connection which exists on the dual bimodule as defined in this work

an automatic adaptive refinement finite element procedure for 2d elastostatic analysis an automatic adaptive refinement procedure for finite element analysis is presented the procedure is applied to two dimensional elastostatic problems to obtain solutions of prescribed accuracy through the combined use of new mesh generator using contour developed by lo1 and the concept of strain energy concentration high quality graded finite element meshes are generated the whole process is fully automatic and no user intervention is required during the successive cycles of the mesh refinements the zienkiewicz and zhu2 error estimator is found to be effective and has been adopted for the present implementation in the numerical examples tested the error estimator gives an accurate error norm estimation and the effectivity index of the estimator converges to a value close to unity

differential geometry of group lattices in a series of publications we developed differential geometry on discrete sets based on concepts of noncommutative geometry in particular it turned out that first order differential calculi over the algebra of functions on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set a particular class of digraphs are cayley graphs also known as group lattices they are determined by a discrete group g and a finite subset s there is a distinguished subclass of bicovariant cayley graphs with the property ad s s s we explore the properties of differential calculi which arise from cayley graphs via the above correspondence the first order calculi extend to higher orders and then allow us to introduce further differential geometric structures furthermore we explore the properties of discrete vector fields which describe deterministic flows on group lattices a lie derivative with respect to a discrete vector field and an inner

α a manifolds abstract an extension of the notion of differential manifold is presented one application of this extension is a type of manifold digitalization the model is aimed at computer simulation of the differential geometric information for the digitalized curves surfaces and other types of manifolds

stabilization for the kirchhoff type equation from an axially moving heterogeneous string modeling with boundary feedback control abstract the first objective of this paper is to make the mathematical model for vibration suppression of an axially moving heterogeneous string in order to describe the geometrical nonlinearity due to finite transverse deformation the exact expression of the strain is used the mathematical modeling is derived first by using hamilton s principle and variational lemma and the derived nonlinear pde system is the kirchhoff type equation with boundary feedback control next we show the existence and uniqueness of strong solutions of the pde system via techniques of functional analysis mainly a theorem of compactness for the analysis of the approximation of the faedo galerkin method and estimate a decay rate for the energy the theoretical results are assured by numerical results of the solution s shape and asymptotic behavior for the system

automatic merging of tetrahedral meshes summary a generic algorithm is proposed to merge arbitrary solid tetrahedral meshes automatically into one single valid finite element mesh the intersection segments in the form of distinct nonoverlapping loops between the boundary surfaces of the given solid objects are determined by the robust neighbor tracing technique each intersected triangle on the boundary surface will be triangulated to incorporate the intersection segments onto the boundary surface of the objects the tetrahedra on the boundary surface associated with the intersected triangular facets are each divided into as many tetrahedra as the number of subtriangles on the triangulated facet there is a natural partition of the boundary surfaces of the solid objects by the intersection loops into a number of zones volumes of intersection can now be identified by collected bounding surfaces from the surface patches of the partition whereas mesh compatibility has already been established on the boundary of the solid objects mesh compatibility has yet to be restored on the bounding surfaces of the regions of intersection tetrahedra intersected by the cut surfaces are removed and new tetrahedra can be generated to fill the volumes bounded by the cut surfaces and the portion of cavity boundary connected to the cut surfaces to restore mesh compatibility at the cut surfaces upon restoring compatibility on the bounding surfaces of the regions of intersection the objects are ready to be merged together as all regions of intersection can be detached freely from the objects all operations besides the determination of intersections structurally in the form of loops are virtually topological and no parameter and tolerance is needed in the entire merging process examples are presented to show the steps and the details of the mesh merging procedure copyright 2012 john wiley sons ltd

on local solutions of a mildly degenerate hyperbolic equation in this work we prove the existence of a unique nonlocal solution for the vibrations of a nonhomogeneous stretched string in sobolev spaces and without any smallness conditions on the size of the initial data

differential calculi on commutative algebras a differential calculus on an associative algebra a is an algebraic analogue of the calculus of differential forms on a smooth manifold it supplies a with a structure on which dynamics and field theory can to some extent be formulated in very much the same way we are used to in the geometrical arena underlying classical physical theories and models in previous work certain differential calculi on a commutative algebra exhibited relations with lattice structures stochastics and parametrized quantum theories this motivated the present systematic investigation of differential calculi on commutative and associative algebras various results about their structure are obtained in particular it is shown that there is a correspondence between first order differential calculi on such an algebra and commutative and associative products in the space of i forms an example of such a product is provided by the ito calculus of stochastic differentials for the case where the algebra a is freely generated by coordinates xi i 1 n we study calculi for which the differentials dxi constitute a basis of the space of 1 forms as a left a module these may be regarded as deformations of the ordinary differential calculus on rn for n or 3 a classification of all orbits under the general linear group of such calculi with constant structure functions is presented we analyse whether these calculi are reducible i e a skew tensor product of lower dimensional calculi or whether they are the extension as defined in this paper of a one dimension lower calculus furthermore generalizations to arbitrary n are obtained for all these calculi

some nonlinear degenerate wave equations on etudie la resolubilite locale du probleme aux valeurs limites et initiales suivant 2 u t 2 m gradu x t 2 dx u 0 dans 0 u 0 sur w 0 u 0 0 u t 0 dans ou m r est une fonction c 1 non negative sur 0 un domaine borne de r n a frontiere lisse w

brs symmetry in connes non commutative geometry we extend the brs and anti brs symmetry to the two point space of connes non commutative model building scheme the constraint relations are derived and the quantum lagrangian constructed we find that the quantum lagrangian can be written as a functional of the curvature for symmetric gauges with the brs anti brs auxiliary field finding a geometrical interpretation as the extension of the higgs scalar

a material based finite element analysis of heterogeneous media involving dirichlet tessellations abstract in this paper a new finite element formulation has been developed for analysis of heterogeneous media in which the second phase is randomly dispersed within the matrix it introduces a tessellation based mesh generation technique to account for the arbitrariness in location shape and size of the second phase an assumed stress hybrid formulation has been implemented to utilize the resulting voronoi polygons as elements in a finite element model the effect of the second phase has been accounted for by introducing a transformation strain based constitutive formulation numerical examples have been conducted to validate the model

asymptotic behavior analysis of a coupled time varying system application to adaptive systems asymptotic behavior of a partial state of a coupled ordinary and or partial differential equation is investigated it is specifically shown that if a signal x t is a solution to a dynamic system existing for all t spl ges 0 in an abstract banach space and pth p spl ges 1 power integrable then x t spl rarr 0 as t spl rarr spl infin the system is allowed to be nonautonomous and assumes the existence of a lyapunov function since the derivative of the lyapunov function is negative semidefinite stability or uniform stability in the sense of lyapunov would be concluded however this paper further asserts that the partial state which remains in the time derivative of the lyapunov function converges to zero asymptotically

automorphisms of associative algebras and noncommutative geometry a class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra several examples are presented in particular differential calculi on the quantum plane the h deformed plane and the quantum group glp q 2 are recovered in this way geometric structures such as metrics and compatible linear connections are introduced

design of a recursive shape controlling mesh generator a recursive shape controlling triangulation method is described the method is designed to produce a labelling which implies reduced fill in the solution of finite element equations assembled from such a triangulation and allows simple implementation of a nested disection algorithm for irregular domains this approach saves a substantial amount of time usually spent on discovering a suitable relabelling of the triangulation in addition the matrix of the resulting system is then endowed with a recursive doubly bordered block diagonal form this allows us to develop a recursive parallel bisection method for the solution of the system of equations

robust boundary triangulation and delaunay triangulation of arbitrary planar domains a simple and robust boundary triangulation algorithm is proposed and based on it completely automatic delaunay mesh generation procedures are developed the algorithm is equally applicable to convex non convex and multiply connected planar domains in this approach given the nodes the number of triangles formed is precisely known and any desired control over mesh generation is possible

linear connections on graphs in recent years discrete spaces such as graphs have attracted much attention as models for physical spacetime or as models for testing the spirit of noncommutative geometry in this work we construct the differential algebras for graphs by extending the work of dimakis et al and discuss linear connections and curvatures on graphs especially we calculate connections and curvatures explicitly for the general nonzero torsion case there is a metric but no metric compatible connection in general except the complete symmetric graph with two vertices