implementation and adaptivity of a space time finite element method for structural dynamics abstract in this paper we study the implementation and adaptivity of a space time finite element method for the analysis of two dimensional problems in structural dynamics the method also known as the time discontinuous galerkin method or the dg method employs finite elements discretizations in space and time simultaneously with bilinear basis functions that are continuous in space and discontinuous in time based on using the zienkiewicz zhu error estimate in space and the jumps discontinuities of displacements and velocities in the total energy norm as a local error estimate in time an h adaptive procedure which updates the spatial mesh and the time step size automatically so as to control the estimated errors within specified tolerances is proposed numerical examples are presented showing that the considered dg method is of second order accuracy in space in l 2 and third order accuracy in time and the adaptive procedure is capable of updating the spatial meshes and the time steps when necessary making the solutions reliable and the computation efficient

unstructured grid method for stress wave propagation in elastic media a new numerical method named unstructured grid method is presented to calculate two dimensional stress wave propagation problems in elastic media this method is based on the dynamic equilibrium equations of the investigated lumps that are formed among the auxiliary unstructured grids the approach to the solution is obtained by calculating the node displacements and the central point stresses of the spatial grids alternately the stability criterion of the method is given and tested numerically analysis of dispersion for numerical phase velocity is studied the rule is provided to determine the spatial step size of discretization mesh so as to ensure the numerical accuracy of the unstructured grid method numerical results are compared with the available exact solutions and with the solutions of central difference method for demonstrating the good accuracy of the new method the unstructured grid method possesses higher calculating speed than the central difference method finally the dynamic behavior of a square plate with a hole under an impact loading is researched

twists of the iwasawa tate zeta function the intent of this paper is to develop the theory of a simple variation of the adelic zeta function first described by tate 14 and iwasawa 9 in independent efforts to simplify hecke s analysis of his l functions attached to gr6bencharakters our twists of the iwasawa tate zeta function arise in the framework of a more general theory of zeta functions associated to representations of algebraic groups many of the basic problems of this general theory have already been solved by yukie and the author see 20 and 21 1 but still await appearance in final written form thus it seems worthwhile to give here a general statement of these problems before proceeding to the very special case considered in this paper let k be a global field i e algebraic number field or function field of a curve defined over a finite field let n and a denote the ring of adeles and the group of ideles of k respectively let co be a quasicharacter of the idele group trivial on the embedded group k of nonzero elements of k the group f2 f2 k of all such quasicharacters co has a natural riemann surface structure let l i denote the usual idele norm on a and for s tl2 let co be the principal quasicharacter co t ltl let re co be the real part of co f2 defined as the unique real number a such that l o i co for any reductive linear algebraic group g defined over k let g denote the adelizat ion of g over k as defined in 16 and let gk be the group of k rational points of g embedded as a discrete group in ga for simplicity we shall fix g as g1 now although the theory to be described below can also be effected for any reductive algebraic group with at least one nontrivial k rational character let p g g1 v be an irreducible k rational representation of g in the finite dimensional vector space v of dimension m let i be the identity matrix in g by schur s lemma there is an integer d such that p ti tdp i for all scalars t we shall always assume that d 0 let dg be any convenient left invariant measure on the quotient ga gk let v be the schwartz bruhat space of functions on v for the time being let vk be any gk invariant subset of vk the zeta function associated to the representation p may now be defined

elastic plastic analysis of arbitrary heterogeneous materials with the voronoi cell finite element method abstract in this paper a voronoi cell finite element method is developed to solve small deformation elastic plasticity problems for arbitrary heterogenous materials dirichlet tessellation of microstructural representative materials results in a network of arbitrary sided polygons called voronoi cells each voronoi cell encompasses one second phase heterogeneity at most these are natural elements for the microstructure representing the basic structural elements of the material in this paper formulations are developed for directly considering voronoi cells as elements in a finite element model without any further dissection furthermore a composite voronoi cell finite element method is developed to account for the presence of the second phase within each polygonal element various numerical elastic plastic examples are executed for validating the effectiveness of this formulation finally studies are conducted to understand the effect of size shape and distribution of second phase on the averaged and true local responses of representative material elements

l estimates for the bar partial problem in a half planeproblem in a half plane l approche de dualite pour trouver des solutions de f est suffisante pour plusieurs problemes apparaissant en theorie h p on donne des operateurs solution qui permettent de resoudre des problemes non resolubles par la dualite

p sv wave propagation in heterogeneous media velocity stress finite difference method i present a finite difference method for modeling p sv wave propagation in heterogeneous media this is an extension of the method i previously proposed for modeling sh wave propagation by using velocity and stress in a discrete grid the two components of the velocity cannot be defined at the same node for a complete staggered grid the stability condition and the p wave phase velocity dispersion curve do not depend on the poisson s ratio while the s wave phase velocity dispersion curve behavior is rather insensitive to the poisson s ratio therefore the same code used for elastic media can be used for liquid media where s wave velocity goes to zero and no special treatment is needed for a liquid solid interface typical physical phenomena arising with p sv modeling such as surface waves are in agreement with analytical results the weathered layer and corner edge models show in seismograms the same converted phases obtained by previous authors this method gives stable results for step discontinuities as shown for a liquid layer above an elastic half space the head wave preserves the correct amplitude finally the corner edge model illustrates a more complex geometry for the liquid solid interface as the poisson s ratio v increases from 0 25 to 0 5 the shear converted phases are removed from seismograms and from the time section of the wave field

a polynomially bounded operator on hilbert space which is not similar to a contraction let e 0 we prove that there exists an operator te e2 2 such that for any polynomial p we have iip te ii not similar to a contraction i e there does not exist an invertible operator s f2 e f2 such that jis 1tesii tributed to halmos after his well known 1970 paper ten problems in hilbert space we also give some related finite dimensional estimates department of mathematics texas a m university college station texas 77843 universite paris vi equipe d7analyse case 186 75252 paris cedex 05 france e mail address gipqccr jussieu fr this content downloaded from 157 55 39 104 on sun 19 jun 2016 06 52 47 utc all use subject to http about jstor org terms

on numerical boundary treatment of hyperbolic systems for finite difference and finite element methods it is well known that the stability of the initial boundary value problem for a scalar equation does not necessarily imply stability for a vector equation with a similar boundary treatment in fact we show that for any boundary treatment one can construct systems for which the boundary treatment on the natural variables is not stable our main theorem is that one can introduce a treatment of the boundaries for which the stability of the system follows immediately from the stability for a scalar equation this is accomplished by operating on the characteristic variables for those quantities that are not specified on the boundary in a working code this can be accomplished by adding a correction term to the existing boundary algorithm the analysis and computational results are presented for both finite differences and semi discrete galerkin methods

the adelic zeta function associated with the space of binary cubic forms with coefficients in a function field in this paper we study the adelic zeta function associated with the prehomogeneous vector space of binary cubic forms defined over a function field we establish its rationality find its poles and residues and a simple functional equation that this zeta function satisfies introduction the subject of integral equivalence of binary cubic forms although not as popular or well developed as the theory of integral equivalence of binary quadratic forms has received a fair amount of attention the first paper on this topic 9 written by eisenstein appeared in 1844 later on several other first rate mathematicians tried their hand at the subject among others the list includes arndt cayley hermite and davenport the classical method of attacking this problem is to draw upon a one to one discriminant preserving relation between binary cubic and binary quadratic forms which assigns to a cubic form its hessian and then use the reduction theory for binary quadratic forms to obtain results on class numbers of binary cubic forms the best of the classical results are due to davenport 5 who showed that e h ir n 2 36x o x15 16 nax e h ir n v2 12x o x 5116 nax where h ir n is the class number of irreducible binary cubic forms of discriminant n the credit for a new surge of interest in the study of integral equivalence of binary cubic forms must indisputably go to shintani for it was his 1972 paper 25 that put this study on modern footing in that paper shintani introduced a certain zeta function which as it turns out decomposes into a linear combination of products of dirichlet series whose coefficients are weighted class numbers of binary cubic forms and certain mellin transforms by studying analytic properties of the zeta function shintani was able to improve the error term in davenport s result to o x576 it is of interest to note that the zeta function and the dirichlet series it received by the editors september 3 1985 1980 mathematics subject classification 1985 revision primary 12a70 secondary iocio 12a90 1987 american mathematical society 0002 9947 87 1 00 25 per page

modelling of wave propagation in composite plates using the time domain spectral element method abstract this paper presents results of numerical simulation of the propagation of transverse elastic waves corresponding to the a0 mode of lamb waves in a composite plate the problem is solved by the spectral element method spectral plate finite elements with 36 nodes defined at gauss lobatto legendre points are used as a consequence of the selection of lagrange polynomials for element shape functions discrete orthogonality is obtained leading to the diagonal form of the element mass matrix this results in a crucial reduction of numerical operations required for the solution of the equation of motion by time integration numerical calculations have been carried out for various orientations and relative volume fractions of reinforcing fibres within the plate the paper shows how the velocities of transverse elastic waves in composite materials depend on the orientation and the relative volume fraction of the reinforcement

hankel operators on bounded analytic functions for u a domain in the complex plane and g a bounded measurable function on u the generalized hankel operator sg on h u is the operator of multiplication by g followed by projection into l h under certain conditions on u we show that either sg is compact or there is an embedded on which sg is bicontinuous we characterize those g s for which sg is compact in the case that u is a behrens roadrunner domain

extensions of multilinear operators and banach space properties a new characterization of the dunford pettis property in terms of the extensions of multilinear operators to the biduals is obtained for the first time multilinear characterizations of the reciprocal dunford pettis property and pelczynski s property v are also found polynomial and holomorphic versions of these properties are given as well

strict singularity of volterra type operators on hardy spaces abstract in this paper we first characterize the boundedness and compactness of volterra type operator s g f z 0 z f g d z d defined on hardy spaces h p 0 p the spectrum of s g is also obtained then we prove that s g fixes an isomorphic copy of l p and an isomorphic copy of l 2 if the operator s g is not compact on h p 1 p in particular this implies that the strict singularity of the operator s g coincides with the compactness of the operator s g on h p at last we post an open question for further study