a non hypersingular time domain biem for 3 d transient elastodynamic crack analysis a three dimensional 3 d time domain boundary integral equation method biem is presented for transient elastodynamic crack analysis a non hypersingular traction bie formulation is used with the crack opening displacements and their derivatives as unknown quantities a collocation method in conjunction with a time stepping scheme is developed to solve the non hypersingular time domain bies to simplify the analysis and to describe the proper behaviour of the unknown quantities at the crack front a constant spatial shape function is applied for elements away from the crack front while a spatial square root crack tip shape function is adopted for elements near the crack front a linear temporal shape function is used in the time stepping scheme numerical calculations have been carried out for penny shaped and square cracks results for the elastodynamic stress intensity factors are presented as functions of the temporal and the spatial variables for the test examples considered good agreement between the present results and those of other authors is obtained

a mass matrix formulation for three dimensional dynamic fracture mechanics in this paper the dual reciprocity boundary element method is developed for the analysis of three dimensional elastodynamic fracture mechanics mixed mode problems the dual boundary element method is used to calculate the unknowns of boundary displacement and traction and the domain integrals in the elastodynamic equation are transformed into boundary integrals by the use of the dual reciprocity method dynamic stress intensity factors are determined by the crack opening displacement cod in the time domain several numerical examples are presented to demonstrate the accuracy of the method

existence of nonexpansive retractions for amenable semigroups of nonexpansive mappings and nonlinear ergodic theorems in banach spaces in this paper we study nonlinear ergodic properties for an amenable semigroup of nonexpansive mappings in a banach space we prove that ifsis an amenable semigroup and s tt t s is a nonexpansive semigroup on a closed convex subsetcin a uniformly convex banach spaceesuch that the setf s of common fixed points of s is nonempty then there exists a nonexpansive retractionpfromcontof s such thatptt ttp pfor eacht sandpx co ttx t s for eachx c in this case there exists a net a of finite averages of s such that for eacht sand for each bounded subsetbofc lim a ttx a x 0 and lim tta x a x 0 uniformly forx b also if the norm ofeis frechet differentiable then for eachx c pxis the unique common fixed point in s s co ttsx t s furthermore if is an asymptotically invariant net of means then for eachx c t x converges weakly topx

generalization of selberg s frac 3 16 theorem and affine sieve an analogue of the well known frac 3 16 lower bound for the first eigenvalue of the laplacian for a congruence hyperbolic surface is proven for a congruence tower associated with any non elementary subgroup l of sl 2 z the proof in the case that the hausdorff of the limit set of l is bigger than frac 1 2 is based on a general result which allows one to transfer such bounds from a combinatorial version to this archimedian setting in the case that delta is less than frac 1 2 we formulate and prove a somewhat weaker version of this phenomenon in terms of poles of the corresponding dynamical zeta function these spectral gaps are then applied to sieving problems on orbits of such groups

on the use of quarter point boundary elements for stress intensity factor computations this communication studies a procedure for stress intensity factor computations using traction singular quarter point boundary elements opening mode stress intensity factors are computed from the tractions nodal values at the crack tip a comparison is made between the factors calculated using this procedure and those obtained by previously recommended methods which made use of the nodal values of the displacements the proposed procedure was seen to be less discretization sensitive than any other of the considered methods accurate results were obtained even in the case of coarse meshes

convergence theorems of implicit iterative sequences for a finite family of asymptotically quasi nonexpansive type mappings abstract in this paper we introduce a new implicit iteration process generated by a finite family of asymptotically quasi nonexpansive type mappings and prove the convergence theorems of the process in a banach space or uniformly convex banach spaces our results extend and improve some recent results

isoperimetric control of the steklov spectrum abstract we prove that the normalized steklov eigenvalues of a bounded domain in a complete riemannian manifold are bounded above in terms of the inverse of the isoperimetric ratio of the domain consequently the normalized steklov eigenvalues of a bounded domain in euclidean space hyperbolic space or a standard hemisphere are uniformly bounded above on a compact surface with boundary we obtain uniform bounds for the normalized steklov eigenvalues in terms of the genus we also establish a relationship between the steklov eigenvalues of a domain and the eigenvalues of the laplace beltrami operator on its boundary hypersurface

moudafi s viscosity approximations with meir keeler contractions abstract in this paper we discuss moudafi s viscosity approximations with meir keeler contractions we first present very simple proofs of xu s theorems concerning moudafi s approximations we next prove that browder s and halpern s type convergence theorems imply moudafi s viscosity approximations using them we finally state several deduced theorems

discretization of riemannian manifolds applied to the hodge laplacian for kappa geq 0 and r 0 0 let bbb m n kappa r 0 be the set of all connected compact n dimensional riemannian manifolds such that k g leq kappa and inj m g geq r 0 we study the relation between the k rm th positive eigenvalue of the hodge laplacian on differential forms and the k rm th positive eigenvalue of the combinatorial laplacian associated to an open cover acting on v c ech cochains we show that for a fixed sufficiently small varepsilon 0 there exist positive constants c 1 and c 2 depending only on n kappa and varepsilon such that for any m in bbb m n kappa r 0 and for any varepsilon discretization x of m we have c 1 lambda k p x leq lambda k p m leq c 2 lambda k p x for any k leq k k depends on x moreover we find a lower bound for the spectrum of the combinatorial laplacian and a lower bound for the spectrum of the hodge laplacian

eigenvalue bounds spectral partitioning and metrical deformations via flows we present a new method for upper bounding the second eigenvalue of the laplacian of graphs our approach uses multi commodity flows to deform the geometry of the graph we embed the resulting metric into euclidean space to recover a bound on the rayleigh quotient using this we show that every n vertex graph of genus g and maximum degree d satisfies 2 g eo g 1 3d n this recovers the o d n bound of spielman and teng for planar graphs and compares to kelner s bound of o g 1 poly d n but our proof does not make use of conformal mappings or circle packings we are thus able to extend this to resolve positively a conjecture of spielman and teng by proving that 2 g e o dh6log h n whenever g is kh minor free this shows in particular that spectral partitioning can be used to recover o sn sized separators in bounded degree graphs that exclude a fixed minor we extend this further by obtaining nearly optimal bounds on 2 for graphs that exclude small depth minors in the sense of plotkin rao and smith consequently we show that spectral algorithms find separators of sublinear size in a general class of geometric graphs moreover while the standard sweep algorithm applied to the second eigenvector may fail to find good quotient cuts in graphs of unbounded degree our approach produces a vector that works for arbitrary graphs this yields an alternate proof of the well known nonplanar separator theorem of alon seymour and thomas that states that every excluded minor family of graphs has o sn node balanced separators

strong convergence of krasnoselskii and mann s type sequences for one parameter nonexpansive semigroups without bochner integrals abstract in this paper we prove krasnoselskii and mann s type convergence theorems for nonexpansive semigroups without using bochner integral and without assuming the strict convexity of banach spaces one of our main results is the following let c be a compact convex subset of a banach space e and let t t t 0 be a one parameter strongly continuous semigroup of nonexpansive mappings on c let t n be a sequence in 0 satisfying lim inf n t n lim sup n t n and lim n t n 1 t n 0 let 0 1 define a sequence x n in c by x 1 c and x n 1 t t n x n 1 x n for n n then x n converges strongly to a common fixed point of t t t 0

an ergodic theorem for semigroups of nonexpansive mappings in a hilbert space abstract j b baillon c r acad sci paris ser a 280 1975 1511 1514 proved an ergodic theorem for a single nonexpansive mapping in a hilbert space which is a nonlinear version of von neumann s mean ergodic theorem in this paper we study the ergodic behavior of a semigroup of nonexpansive mappings we try to find a sequence of means on the semigroup generalizing the cesaro means on n such that the corresponding sequence of nonexpansive mappings converges to a projection onto the set of common fixed points our method of proof is an appropriate modification of a pazy s proof israel j math 26 1977 197 204 of baillon s theorem

strong convergence to common fixed points of families of nonexpansive mappings abstract we introduce iteration schemes for families of nonexpansive mappings in hilbert spaces and prove that the iterates converge strongly to common fixed points of the mappings

coarse non amenability and covers with small eigenvalues given a closed riemannian manifold m and a virtual epimorphism pi 1 m twoheadrightarrow mathbb f 2 of the fundamental group onto a free group of rank 2 we construct a tower of finite sheeted regular covers left m n right n 0 infty of m such that 1 mn 0 as n this is the first example of such a tower which is not obtainable up to uniform quasi isometry or even up to uniform coarse equivalence by the previously known methods where 1 m is supposed to surject onto an amenable group

an implicit iteration process for nonexpansive semigroups let c be a closed convex subset of a banach space e let t t t 0 be a strongly continuous semigroup of nonexpansive mappings on c such that t 0f t t 0 let n and tn be sequences of real numbers satisfying appropriate conditions then for arbitrary x0 c the mann type implicit iteration process xn given by xn nxn 1 1 n t tn xn n 0 weakly strongly converges to an element of t 0f t t

random construction of riemann surfaces we develop a new approach for the study of typical riemann surfaces with high genus the method that we use is the construction of random riemann surfaces from oriented cubic graphs this construction enables us to get a control over the global geometry properties of compact riemann surfaces we use the theory of random regular graphs to show that almost all such surfaces have large first eigenvalues and large cheeger constants moreover a closer analysis of the probability space of oriented cubic graphs shows that on a typical surface there is a large embedded hyperbolic ball

bounds for laplace eigenvalues of kahler metrics abstract we prove inequalities for laplace eigenvalues of kahler manifolds generalising to higher eigenvalues the classical inequality for the first laplace eigenvalue due to bourguignon li and yau in 1994 we also obtain similar eigenvalue inequalities for analytic varieties in kahler manifolds

time domain boundary element analysis of elastic wave interaction with a crack the mathematical formulation of the problem of transient wave interaction with a crack in a homogeneous isotropic linearly elastic solid has been reduced to the solution of an integral equation over the insonified crack face the integral equation relates the unknown crack opening displacement which depends on time and position to the incident wave field the integral equation has been solved numerically by a time stepping method in conjunction with a boundary element discretization of the crack surface for normal incidence of a longitudinal step stress wave on a penny shaped crack results as functions of time have been obtained for the crack opening displacement the elastodynamic mode i stress intensity factor and the scattered far field

extremal g invariant eigenvalues of the laplacian of g invariant metrics the study of extremal properties of the spectrum often involves restricting the metrics under consideration motivated by the work of abreu and freitas in the case of the sphere s 2 endowed with s 1 invariant metrics we consider the subsequence lambda k g of the spectrum of a riemannian manifold m which corresponds to metrics and functions invariant under the action of a compact lie group g if g has dimension at least 1 we show that the functional k g admits no extremal metric under volume preserving g invariant deformations if moreover m has dimension at least three then the functional lambda k g is unbounded when restricted to any conformal class of g invariant metrics of fixed volume as a special case of this we can consider the standard o n action on s n however if we also require the metric to be induced by an embedding of s n in mathbb r n 1 we get an optimal upper bound on lambda k g

isoperimetric control of the spectrum of a compact hypersurface upper bounds for the eigenvalues of the laplace beltrami operator on a hypersurface bounding a domain in some ambient riemannian manifold are given in terms of the isoperimetric ratio of the domain these results are applied to the extrinsic geometry of isometric embeddings

strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings in the present paper we prove that the modified implicit iteration sequence for a finite family of asymptotically quasi nonexpansive mappings converges strongly to a common fixed point of the family in a uniformly convex banach space requiring one member t in the family to be semi compact our results extend and improve some recent results

a new conformal invariant and its applications to the willmore conjecture and the first eigenvalue of compact surfaces let m be a compact riemannian manifold with a fixed conformal structure then we introduce the concept of conformal volume of m in the following manner for each branched conformal immersion q9 of m into the unit sphere s n we consider the set of all branched conformal immersions obtained by composi t ion of qo with the conformal automorphisms of s we let vc n qg be the max imum volume of these branched immersions the conformal volume of m is defined to be the infimum of v n q0 where qo ranges over all branched conformal immersions of m into the unit sphere s in this paper we study the case when m is a compact surface and we call the conformal volume of m to be the conformal area of m we demonst ra te that this conformal invariant is non trivial in fact we prove that if there exists a minimal immersion of m into s where coordinate functions are first eigenfunctions then the conformal area of m is given by the area of m with respect to the induced metric this enables us to compute the conformal area for several surfaces for example the conformal area of r p z is 6n and the conformal area of the square torus is 27c 2 we believe that the computa t ion of the conformal area for general surfaces will be very impor tant in studying the geometry of compact surfaces we demonstrate this claim by applying the concept of conformal area to two different branches of surface theory the first application is to study the total curvature of a compact surface in r this problem has a long history fenchel and fary 9 proved that for a closed curve o in r slk 27c where k is its curvature then milnor 12

strong convergence theorems for nonexpansive semigroup in banach spaces abstract let k be a nonempty closed convex subset of a reflexive and strictly convex banach space e with a uniformly g teaux differentiable norm and f t t t 0 a nonexpansive self mappings semigroup of k and f k k a fixed contractive mapping the strongly convergent theorems of the following implicit and explicit viscosity iterative schemes x n are proved x n n f x n 1 n t t n x n x n 1 n f x n 1 n t t n x n and the cluster point of x n is the unique solution to some co variational inequality

on the local global conjecture for integral apollonian gaskets we prove that a set of density one satisfies the local global conjecture for integral apollonian gaskets that is for a fixed integral primitive apollonian gasket almost every in the sense of density admissible passing local obstructions integer is the curvature of some circle in the gasket

strong convergence theorems for fixed points of asymptotically pseudocontractive semi groups abstract let k be a nonempty closed convex and bounded subset of a real banach space e let t t t t r be a strongly continuous uniformly asymptotically regular and uniformly l lipschitzian semi group of asymptotically pseudocontractive mappings from k into k then for a given u k there exists a sequence y n k satisfying the equation y n 1 n t t n n y n n u for each n n where n 0 1 and t n 0 satisfy appropriate conditions suppose further that e is uniformly convex and has uniformly g teaux differentiable norm under suitable conditions on the mappings t the sequence y n converges strongly to a fixed point of t furthermore an explicit sequence x n generated from x 1 k by x n 1 1 n x n n t t n n x n n n x n x 1 for all integers n 1 where n n are positive real sequences satisfying appropriate conditions converges strongly to a fixed point of t

a fast hierarchical dual boundary element method for three dimensional elastodynamic crack problems in this work a fast solver for large scale three dimensional elastodynamic crack problems is presented implemented and tested the dual boundary element method in the laplace transform domain is used for the accurate dynamic analysis of cracked bodies the fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the laplace parameter an aca adaptive cross approximation algorithm is used for the population of the low rank blocks and its performance at varying laplace parameters is investigated a preconditioned gmres is used for the solution of the resulting algebraic system of equations the preconditioners are built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format an original strategy based on the computation of some local preconditioners only is presented and tested to further speed up the overall analysis the reported numerical results demonstrate the effectiveness of the technique for both uncracked and cracked solids and show significant reductions in terms of both memory storage and computational time

convergence theorem of common fixed points for lipschitzian pseudocontraction semigroups in banach spaces the purpose of this paper is to study the convergence problems of the implicity iteration process for an asymptotically nonexpansive semigroups in general banach spaces the results presented in this paper extend and improve the corresponding results announced by many authors

on strong convergence by the hybrid method for families of mappings in hilbert spaces abstract let c be a nonempty closed convex subset of a real hilbert space and let t n be a family of mappings of c into itself such that the set of all common fixed points of t n is nonempty we consider a sequence x n generated by the hybrid method in mathematical programming we give the new conditions of t n under which x n converges strongly to a common fixed point of t n and generalize the unified result for families of nonexpansive mappings k nakajo k shimoji w takahashi strong convergence theorems by the hybrid method for families of nonexpansive mappings in hilbert spaces taiwanese j math 10 2006 339 360 and the results for asymptotically nonexpansive mappings and semigroups t h kim h k xu strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups nonlinear anal 64 2006 1140 1152 s plubtieng and k ungchittrakool strong convergence of modified ishikawa iteration for two asymptotically nonexpansive mappings and semigroups nonlinear anal 67 2007 2306 2315

strong convergence theorem for nonexpansive semigroups in hilbert space abstract the purpose of this paper is to prove the strong convergence of a method combining the descent method and the hybrid method in mathematical programming for finding a point in the common fixed point set of a semigroup of nonexpansive mappings in hilbert space

on the friedlander nadirashvili invariants of surfaces let m be a closed smooth manifold in 1999 friedlander and nadirashvili introduced a new differential invariant i 1 m using the first normalized nonzero eigenvalue of the lalpace beltrami operator delta g of a riemannian metric g they defined it taking the supremum of this quantity over all riemannian metrics in each conformal class and then taking the infimum over all conformal classes by analogy we use k th eigenvalues of delta g to define the invariants i k m indexed by positive integers k in the present paper the values of these invariants on surfaces are investigated we show that i k m i k mathbb s 2 unless m is a non orientable surface of even genus for orientable surfaces and k 1 this was earlier shown by petrides in fact friedlander and nadirashvili suggested that i 1 m i 1 mathbb s 2 for any surface m different from mathbb rp 2 we show that surprisingly enough this is not true for non orientable surfaces of even genus for such surfaces one has i k m i k mathbb s 2 we also discuss the connection between the friedlander nadirashvili invariants and the theory of cobordisms and conjecture that i k m is a cobordism invariant

heegaard splittings the virtually haken conjecture and property τ the behaviour of finite covers of 3 manifolds is a very important but poorly understood topic there are three increasingly strong conjectures in the field that have remained open for over twenty years the virtually haken conjecture the positive virtual b1 conjecture and the virtually fibred conjecture any of these would have profound ramifications for 3 manifold theory in this paper we explore the interaction of these conjectures with the following seemingly unrelated areas eigenvalues of the laplacian and heegaard splittings

a boundary element method for dynamic plate bending problems abstract in this paper the fundamental solution for kirchhoff plate in the laplace transform domain is deduced and the boundary element formulation is established to study plate bending problem by use of the moment integral equation the dual boundary element equation is developed to solve the cracked plate problem subjected to dynamic loads durbin s laplace transform inversion method is used and the dynamic stress intensity factors are determined by equivalent stress technique an infinite plate containing an isolated crack or two cracks or one set of parallel cracks under heaviside load on the crack surfaces is studied the numerical results obtained demonstrate the efficiency and accuracy of the proposed formulation

ends of locally symmetric spaces with maximal bottom spectrum let x be a symmetric space of non compact type and gnx a locally sym metric space then the bottom spectrum l1 gnx satisfies the inequality l1 gnx e l1 x we show that if equality l1 gnx l1 x holds then gnx has either one end which is necessarily of infinite volume or two ends one of infinite volume and another of finite vol ume in the latter case gnx is isometric to r 1 n endowed with a multi warped metric where n is compact

the dual boundary element method effective implementation for crack problems summary the present paper is concerned with the effective numerical implementation of the two dimensional dual boundary element method for linear elastic crack problems the dual equations of the method are the displacement and the traction boundary integral equations when the displacement equation is applied on one of the crack surfaces and the traction equation on the other general mixed mode crack problems can be solved with a single region formulation both crack surfaces are discretized with discontinuous quadratic boundary elements this strategy not only automatically satisfies the necessary conditions for the existence of the finite part integrals which occur naturally but also circumvents the problem of collocation at crack tips crack kinks and crack edge corners examples of geometries with edge and embedded crack are analysed with the present method highly accurate results are obtained when the stress intensity factor is evaluated with the j integral technique the accuracy and efficiency of the implementation described herein make this formulation ideal for the study of crack growth problems under mixed mode conditions

variational aspects of laplace eigenvalues on riemannian surfaces abstract we study the existence and properties of metrics maximising the first laplace eigenvalue among conformal metrics of unit volume on riemannian surfaces we describe a general approach to this problem and its higher eigenvalue versions via the direct method of calculus of variations the principal results include the general regularity properties of k extremal metrics and the existence of a partially regular 1 maximiser

two dimensional transient wave propagation problems by time domain bem abstract in this paper an advanced formulation of time domain boundary element method bem for linear elastodynamics is used to study a number of problems involving wave propagation through half space as well as multi layered soils the algorithm incorporates isoparametric quadratic elements which facilitate proper modelling of problem geometry and can represent the field variables in dynamic problems very accurately which are very often wavy in nature also higher order temporal variation of functions is introduced improved techniques are employed for the accurate evaluation of both the singular and non singular spatial integrals most importantly this formulation incorporates simpler and better behaved kernels compared to those that have appeared in the recent bem literature by the present and other previous researchers with all these new and efficient features the present formulation is superior to the existing ones and as such represents a very effective tool for solving 2d transient wave propagation problems especially in infinite and semi infinite domains where other numerical methods have considerable difficulty in producing accurate solutions

mosco convergence of the sets of fixed points for one parameter nonexpansive semigroups abstract we consider the mosco convergence of the sets of fixed points for one parameter strongly continuous semigroups of nonexpansive mappings one of our main results is the following let c be a closed convex subset of a hilbert space e let t t t 0 be a strongly continuous semigroup of nonexpansive mappings on c the set of all fixed points of t t is denoted by f t t for each t 0 let be a nonnegative real number and let t n be a sequence in r satisfying t n 0 and t n 0 for n n and lim n t n 0 then f t t n converges to t 0 f t t in the sense of mosco

conformal upper bounds for the eigenvalues of the laplacian and steklov problem in this paper we find upper bounds for the eigenvalues of the laplacian in the conformal class of a compact riemannian manifold m g these upper bounds depend only on the dimension and a conformal invariant that we call min conformal volume asymptotically these bounds are consistent with the weyl law and improve previous results by korevaar and yang and yau the proof relies on the construction of a suitable family of disjoint domains providing supports for a family of test functions this method is interesting for itself and powerful as a further application of the method we obtain an upper bound for the eigenvalues of the steklov problem in a domain with c1 boundary in a complete riemannian manifold in terms of the isoperimetric ratio of the domain and the conformal invariant that we introduce

nonexpansive retractions and nonlinear ergodic theorems in banach spaces on donne des theoremes ergodiques non lineaires pour des semigroupes commutatifs d applications non dilatation sans utiliser le concept de moyenne compacte

interior stress calculations in 2 d time domain transient bem analysis abstract an improved and accurate formulation of time domain bem for determining the interior stresses in a 2 d transient dynamic analysis is presented a new set of simpler and better behaved transient dynamic stress kernels is derived with these interior stress kernels it has been possible to overcome all the analytical complexities that have hindered the accurate determination of interior stresses in the past the accuracy and stability are established via a few numerical examples including those involving stress concentrations

characterizations of common fixed points of one parameter nonexpansive semigroups and convergence theorems to common fixed points we first prove characterizations of common fixed points of one parameter nonexpansive semigroups we next present convergence theorems to common fixed points

convergence theorems for strongly continuous semi groups of asymptotically nonexpansive mappings abstract let k be a nonempty closed convex subset of a real banach space e let t t t t r be a strongly continuous semi group of asymptotically nonexpansive mappings from k into k with a sequence l t 1 suppose f t 0 then for a given u 0 k and t n 0 there exists a sequence u n k such that u n 1 n t t n u n n u 0 for n n such that n 0 1 and l t n 1 n where t n r suppose in addition that e is reflexive strictly convex with a uniformly g teaux differentiable norm and that lim n t n lim n n lim n l t n 1 n 0 then the sequence u n converges strongly to a point of f t moreover it is proved that an explicit sequence x n generated from x 1 k by x n 1 n u 1 n t t n x n n 1 converges to a fixed point of t

minimal two spheres of low index in manifolds with positive complex sectional curvature suppose that s n is given a generic riemannian metric with sectional curvatures which satisfy a suitable pinching condition formulated in terms of complex sectional curvatures this pinching condition is satisfied by manifolds whose real sectional curvatures k r sigma satisfy begin aligned 1 2 k r sigma le 1 end aligned then the number of minimal two spheres of morse index lambda for n 2 le lambda le 2n 5 is at least p 3 lambda n 2 where p 3 k is the number of k cells in the schubert cell decomposition for g 3 mathbb r n 1

volume of minimal hypersurfaces in manifolds with nonnegative ricci curvature we establish a min max estimate on the volume width of a closed riemannian manifold with nonnegative ricci curvature more precisely we show that every closed riemannian manifold with nonnegative ricci curvature admits a pl morse function whose level set volume is bounded in terms of the volume of the manifold as a consequence of this sweep out estimate there exists an embedded closed possibly singular minimal hypersurface whose volume is bounded in terms of the volume of the manifold

cheeger constants of surfaces and isoperimetric inequalities we show that if the isoperimetric profile of a bounded genus non compact surface grows faster than vt then it grows at least as fast as a linear function this generalizes a result of gromov for simply connected surfaces we study the isoperimetric problem in dimension 3 we show that if the filling volume function in dimension 2 is euclidean while in dimension 3 it is sub euclidean and there is a g such that minimizers in dimension 3 have genus at most g then the filling function in dimension 3 is almost linear

cracks in three dimensions a dynamic dual boundary element analysis in this paper the dual boundary integral equation for three dimensional dynamic problems in laplace space is presented for the first time the dual boundary element method is used to calculate dynamic stress intensity factors for three dimensional cracked structures the application of laplace transforms to the time dependent equations of elasticity reduce the problem to a static one in laplace space the displacement and traction boundary integral equations for the transformed variables are established by somigliana s identity by applying the displacement integral equation on one of the crack surfaces and the traction boundary integral equation on the other a general mixed mode crack problem can be solved in a single region in the same way as a static problem the transformed mixed mode stress intensity factors are calculated from the transformed displacement discontinuities near the crack tip the dynamic stress intensity factors in the time domain are obtained by the use of durbin s inversion method the accuracy of this method is demonstrated by its application to embedded penny shaped and elliptical cracks and edge cracks

a single region time domain bem for dynamic crack problems abstract a time domain boundary element method which allows the analysis of dynamic crack problems by using a single region formulation is presented the present method generates the distinct set of boundary integral equations by applying the displacement equation to one of the crack surfaces and the traction equation to the other the boundary of the structure is divided into continuous semi discontinuous and discontinuous quadratic elements the temporal variation of boundary displacements and tractions is approximated by piecewise linear and constant functions respectively the dynamic stress intensity factors are calculated using the crack opening displacements and the path independent integral this method is used to study dynamic behaviour of stationary cracks in finite and infinite domains in two dimensional analysis the results for two examples are compared with other reported solutions showing good agreement

extremal eigenvalues of the laplacian on euclidean domains and closed surfaces we investigate properties of the sequences of extremal values that could be achieved by the eigenvalues of the laplacian on euclidean domains of unit volume under dirichlet and neumann boundary conditions respectively in a second part we study sequences of extremal eigenvalues of the laplace beltrami operator on closed surfaces of unit area