a comparative study of three boundary element approaches to calculate the transient response of viscoelastic solids with unbounded domains abstract as an alternative to domain discretization methods the boundary element method bem provides a powerful tool for the calculation of dynamic structural response in frequency and time domain field equations of motion and boundary conditions are cast into boundary integral equations bie which are discretized only on the boundary fundamental solutions are used as weighting functions in the bie which fulfil the sommerfeld radiation condition i e the energy radiation into a surrounding medium is modelled correctly therefore infinite and semi infinite domains can be effectively treated by the method the soil represents such a semi infinite domain in soil structure interaction problems the response to vibratory loads superimposed to static pre loads can often be calculated by linear viscoelastic constitutive equations conventional viscoelastic constitutive equations can be generalized by taking fractional order time derivatives into account in the present paper two time domain bem approaches including generalized viscoelastic behaviour are compared with the laplace domain bem approach and subsequent numerical inverse transformation one of the presented time domain approaches uses an analytical integration of the elastodynamic bie in a time step viscoelastic constitutive properties are introduced after laplace transformation by means of an elastic viscoelastic correspondence principle the transient response is obtained by inverse transformation in each time step the other time domain approach is based on the so called convolution quadrature method in this formulation the convolution integral in the bie is numerically approximated by a quadrature formula whose weights are determined by the same laplace transformed fundamental solutions used in the first method and a linear multistep method a numerical study of wave propagation problems in 3 d viscoelastic continuum is performed for comparing the three bem formulations

dynamic response of lined tunnels by an isoparametric boundary element method abstract this work investigates the dynamic stress concentration in the lining of a circular cylindrical tunnel excavated in a linear elastic or viscoelastic medium of infinite extent under conditions of plane strain the dynamic load consists of planar waves of a general transient nature the numerical method employed is the boundary element method formulated in the laplace transformed domain a numerical inverse transformation is used to bring the results obtained by the boundary element method back to the time domain isoparametric boundary elements are utilized in the discretization of the surfaces of the problem the results obtained are in very good agreement with known analytic solutions while they compare favorably with other numerical solutions the method is quite general and can be used for cylindrical tunnels of arbitrary cross section

multi domain bem for two dimensional problems of elastodynamics an advanced implementation of the boundary element technique for the periodic and transient dynamic analyses of two dimensional elastic or visco elastic solids of arbitrary shape and connectivity is presented for transient dynamic analysis the problem is first solved in the laplace transform space and then the time domain solutions are obtained by numerical inversion of transformed domain solutions the present analysis is capable of treating very large multi domain problems by substructuring and satisfying the equilibrium and compatibilities at the interfaces with the help of this substructuring capability problems related to the layered media and soil structure interaction can all be analysed this paper also introduces a new type of element called enclosing element which has been developed and used to model the infinitely extending boundaries of a half space or a layered medium a number of numerical examples are presented and through comparisons with available analytical and numerical results the accuracy stability and efficiency of the present analysis are established

boundary element method for dynamic poroelastic and thermoelastic analyses abstract a boundary element method is developed for transient and time harmonic analysis of problems in dynamic poroelasticity and generalized thermoelasticity involving both two and three dimensional geometries laplace domain infinite space fundamental solutions are employed to produce a formulation that requires only surface discretization consequently the resulting algorithm provides an attractive alternative to existing volume based methods particularly for media of infinite extent details of the formulation and numerical implementation are presented several applications are included to validate the method and to emphasize certain aspects of the dynamic theory

iwasawa theory of elliptic curves at supersingular primes over ℤ p extensions of number fields in this paper we make a study of the iwasawa theory of an elliptic curve at a supersingular prime p along an arbitrary zp extension of a number field k in the case when p splits completely in k generalizing work of kobayashi 9 and perrin riou 17 we define restricted selmer groups and invariants we then derive asymptotic formulas describing the growth of the selmer group in terms of these invariants to be able to work with non cyclotomic zp extensions a new local result is proven that gives a complete description of the formal group of an elliptic curve at a supersingular prime along any ramified zp extension of qp

on the equivariant tamagawa number conjecture for tate motives let l be a finite abelian extension of and let k be any subfield of l for each integer r with r 0 we prove the equivariant tamagawa number conjecture for the pair h0 spec l r gal l k

dynamic stress concentration studies by boundary integrals and laplace transform the dynamic stress field and its concentrations around holes of arbitrary shape in infinitely extended bodies under plane stress or plane strain conditions are numerically determined the material may be linear elastic or viscoelastic while the dynamic load consists of plane compressional waves of harmonic or general transient nature the method consists of applying the laplace transform with respect to time to the governing equations of motion and formulating and solving the problem numerically in the transfomed domain by the boundary integral equation method the stress field can then be obtaind by a numerical inversion of the trasformed solution the correspondence principle is invoked for the case of viscoelastic material behavious the method is simplified for the case of harmonic waves where no numerical inversion is involved

a simple and efficient bem implementation of quasistatic linear visco elasticity abstract a simple yet efficient procedure to solve quasistatic problems of special linear visco elastic solids at small strains with equal rheological response in all tensorial components utilizing boundary element method bem is introduced this procedure is based on the implicit discretisation in time the so called rothe method combined with a simple algebraic transformation of variables leading to a numerically stable procedure proved explicitly by discrete energy estimates which can be easily implemented in a bem code to solve initial boundary value visco elastic problems by using the kelvin elastostatic fundamental solution only it is worth mentioning that no inverse laplace transform is required here the formulation is straightforward for both 2d and 3d problems involving unilateral frictionless contact although the focus is to the simplest kelvin voigt rheology a generalization to maxwell boltzmann jeffreys and burgers rheologies is proposed discussed and implemented in the bem code too a few 2d and 3d initial boundary value problems one of them with unilateral frictionless contact are solved numerically

on the birch and swinnerton dyer conjecture let f be a finite extension of the rational field q if e is an elliptic curve defined over f then the mordell weil group e f of points on e with coordinates in f is a finitely generated abelian group let l e f s be the hasseweil zeta function of e over f which at least in the case where e has complex multiplication is known to be an analytic function on the entire complex plane birch and swinnerton dyer have conjectured that l e f s has a zero at s l of order precisely equal to the rank of e f over z the strongest result known in support of this conjecture is the following theorem of coates and wiles 4

a galerkin boundary element formulation with dual reciprocity for elastodynamics in this paper a galerkin boundary integral equation method for two dimensional elastodynamic problems is presented the formulation makes use of a static fundamental solution to weight the dynamic equilibrium equations following the galerkin approach the equations are weighted again with the interpolation functions used in the discretization of the unknowns for the numerical integration a regularization process is followed to deal with the integrands containing strong singularities the implementation of the dual reciprocity method to transfer the domain integrals to the boundary is also presented in the context of the galerkin formulation finally the hubolt integration scheme was used for the time marching process several numerical examples are presented to demonstrate the accuracy of the method copyright 2000 john wiley sons ltd

arithmetic of formal groups and applications i universal norm subgroups the theory of the norm map for the formal multiplicative group is well known as local class field theory in 1972 mazur 14 in his generalization of iwasawa theory to abelian varieties over number fields made quite clear that it is absolutely crucial for such a global theory first to understand the norm map for the formal groups attached to abelian varieties he achieved this understanding in case of formal groups of multiplicative type by using the theory of proalgebraic groups later on lubin and rosen 12 gave a completely elementary approach to mazur s results in the meantime hazewinkel 8 had settled the case of one dimensional commutative formal lie groups his method consists in an explicit and very complicated study of the properties of the power series coefficients of the logarithm of a formal group law by means of higher ramification theory in the same spirit vvedenskij 18 and konovalov 10 reproved and slightly extended hazewinkel s results let k q be a finite extension with ring of integers r and residue class field and koo k be a ramified zv extension with ring of integers r and f gal koo k let i r denote a smooth connected commutative formal r group of finite dimension d i e a commutative formal lie group if k k is the intermediate layer of degree p in koo k r its ring of integers and g gal k k its galois group then we know from the description of ff as a formal lie group that

new traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized big frac g prime g big expansion method in this paper we construct new traveling wave solutions of some nonlinear evolution equations in mathematical physics via the 3 1 dimensional potential ytsf equation the 3 1 dimensional modified kdv zakharov kuznetsev equation the 3 1 dimensional kadomtsev petviashvili equation and the 1 1 dimensional kdv equation by using a generalized expansion method where g g satisfies the jacobi elliptic equation g 2 p g here we assume that p g is a polynomial of fourth order many new exact solutions in terms of the jacobi elliptic functions are obtained

meshless local boundary integral equation method for 2d elastodynamic problems a new meshless method for solving transient elastodynamic boundary value problems based on the local boundary integral equation lbie method and the moving least squares approximation mls is proposed in this paper the lbie with the mls is applied to both transient and steady state laplace transformed elastodynamics applying the mls approximation for spatially dependent terms in the first approach the lbies are transformed into a system of ordinary differential equations for nodal unknowns this system of ordinary differential equations is solved by the houbolt finite difference scheme in the second formulation the time variable is eliminated by using the laplace transformation unknown laplace transforms of displacements and traction vectors are computed from the lbies with the mls approximation the time dependent values are obtained by the durbin inversion technique copyright 2003 john wiley sons ltd

a novel time marching scheme using numerical green s functions a comparative study for the scalar wave equation abstract the present paper presents the formulation of a novel time marching method based on the explicit green s approach exga to solve scalar wave propagation problems by means of the weighted residual method in both time and space the time integral expression concerning the exga is readily established the arising exga time integral expression is spatially discretized in a finite element sense and a recursive scheme that employs time domain numerical green s function matrices is adopted to evaluate the displacement and the velocity vectors these green s matrices are computed by the time discontinuous galerkin finite element method only at the first time step the system of coupled equations originated from the time discontinuous galerkin method is then solved by an iterative predictor multicorrector algorithm once the green s matrices are computed no iterative process is required to obtain the displacement and the velocity vectors at any time level at the end of the paper numerical examples are presented in order to compare the proposed approach with other approaches

on l functions of elliptic curves and cyclotomic towers in this paper we shall strengthen a recent theorem of ralph greenberg 1 concerning l functions of elliptic curves and anticyclotomic towers let k be an imaginary quadratic field and m an abelian extension of k possibly of infinite degree we say that the extension m k is anticyclotomic if m is galois over q and if the nontrivial element of gal k q acts on gal m k by inversion now fix a finite set p of rational primes and consider the compositum in an algebraic closure of k of all anticyclotomic extensions of k which are unramified outside p we denote this compositum by l and refer to it as the maximal anticyclotomic extension of k unramified outside p the field l may also be described as the union of all ring class fields of k with conductor divisible only by primes in p class field theory shows that gal l k is isomorphic to the product of a finite group and the group

a particular integral bem time discontinuous fem methodology for solving 2 d elastodynamic problems abstract this study proposes a time discontinuous galerkin finite element method fem for solving second order ordinary differential equations in the time domain the equations are formulated using a particular integral boundary element method bem in the space domain for elastodynamic problems the particular integral bem technique depends only on elastostatic displacement and traction fundamental solutions without resorting to commonly used complex fundamental solutions for elastodynamic problems based on the time discontinuous galerkin fem the unknown displacements and velocities are approximated as piecewise linear functions in the time domain and are permitted to be discontinuous at the discrete time levels this leads to stable and third order accurate solution algorithms for ordinary differential equations numerical results using the time discontinuous galerkin fem are compared with results using a conventional finite difference method the houbolt method both methods are employed for a particular integral bem analysis in elastodynamics this comparison reveals that the time discontinuous galerkin fem is more stable and more accurate than the traditional finite difference methods

a generalization of the coleman map for hida deformations in this paper we give a coleman perrin riou type map for an ordinary type deformation and construct a two variable p adic l function for a hida family from the beilinson kato elements 1 introduction fix a prime p 3 we denote by q jlp the extension of the rational number field q obtained by adjoining all power roots of unity we fix a complex embedding q c and a p adic embedding q qp of an algebraic closure q of q throughout the paper where c is the field of complex numbers and qp is an algebraic closure of the field qp of p adic numbers let goo be the galois group of q jjlpo q and let dqo be the group of diamond operators for the tower of modular curves fi i see 2 we have the

the p adic gross zagier formula for elliptic curves at supersingular primes let p be a prime number and let e be an elliptic curve defined over of conductor n let k be an imaginary quadratic field with discriminant prime to pn such that all prime factors of n split in k b perrin riou established the p adic gross zagier formula that relates the first derivative of the p adic l function of e over k to the p adic height of the heegner point for k when e has good ordinary reduction at p in this article we prove the p adic gross zagier formula of e for the cyclotomic p extension at good supersingular prime p our result has an application for the full birch and swinnerton dyer conjecture suppose that the analytic rank of e over is 1 and assume that the iwasawa main conjecture is true for all good primes and the p adic height pairing is not identically equal to zero for all good ordinary primes then our result implies the full birch and swinnerton dyer conjecture up to bad primes in particular if e has complex multiplication and of analytic rank 1 the full birch and swinnerton dyer conjecture is true up to a power of bad primes and 2

transient analysis of three dimensional wave propagation using the boundary element method in the past the time domain solution of the wave equation has been limited to simplified problems this was due to the limitations of analytical methods and the capacity of computers to manipulate and store large blocks of spatial information with the advent of super computers the ability to solve such problems has significantly increased this paper outlines a method for transient analysis of wave propagation in arbitrary domains using a boundary element method the technique presented will allow the definition of a domain the input of impedance conditions on the domain s surface the specification of inputs on the surface and the specification of initial conditions within the domain it will produce a complete solution of the wave equation inside the domain the techniques are demonstrated using a program with a boundary element formulation of kirchhoff s equation the elements used are triangular and compatible

a comparative study on three boundary element method approaches to problems in elastodynamics in this study three boundary element method approaches are compared by solving a typical problem in linear elastodynamics the first approach formulates and solves the problem in the real time domain in conjunction with a time stepping algorithm the other two approaches formulate and solve the problem in the laplace and the fourier transformed domains which necessitates a numerical inversion of the results to the time domain the results obtained compare favourably with available analytic solutions a detailed tabulation of the computer time and memory requirements of each approach is presented

on the p adic l function of a modular form at a supersingular prime in this paper we study the two p adic l functions attached to a modular form f sum a sb nq sp n at a supersingular prime p when a sb p 0 we are able to decompose both the sum and the difference of the two unbounded distributions attached to f into a bounded measure and a distribution that accounts for all of the growth moreover this distribution depends only upon the weight of f and the fact that a sb p vanishes from this description we explain how the p adic l function is controlled by two iwasawa functions and by two power series with growth which have a fixed infinite set of zeros theorem 5 1 asymptotic formulas for the p part of the analytic size of the tate shafarevich group of an elliptic curve in the cyclotomic direction are computed using this result these formulas compare favorably with results established by m kurihara in 11 and b perrin riou in 23 on the algebraic side moreover we interpret kurihara s conjectures on the galois structure of the tate shafarevich group in terms of these two iwasawa functions

iwasawa theory for elliptic curves at supersingular primes we give a new formulation in iwasawa theory for elliptic curves at good supersingular primes this formulation is similar to mazur s at good ordinary primes namely we define a new selmer group and show that it is of cotorsion then we formulate the iwasawa main conjecture as that the characteristic ideal is generated by pollack s p adic l function we show that this main conjecture is equivalent to kato s and perrin riou s main conjectures we also prove an inequality in the main conjecture by using kato s euler system in terms of the and the invariants of our selmer group we specify the numbers and in the asymptotic formula for the order of the tate shafarevich group by kurihara and perrin riou

the coleman map for hida families of gsp4 in this paper we construct a coleman map for ordinary hida deformations associated to the symplectic group rm gsp 4 which interpolates the dual exponential maps when arithmetic specializations of this family vary the main result theorem 3 2 will play an important role in a forthcoming work by the authors discussing a conjecture on the existence of an euler system which would give rise via our map to a three variable p adic l function

a variational approach to boundary element elastodynamic analysis and extension to multidomain problems abstract time dependent discontinuities of both tractions and displacements are considered on the boundary of a homogeneous linear elastic solid conceived as embedded in the elastic space the analysis of the dynamic response of the solid to external actions is formulated in the time domain by means of suitable integral representations of boundary displacements and of boundary tractions using time dependent fundamental solutions the integral operator generated is proven to be symmetric in both space and time with respect to a time convolutive bilinear form as a consequence the history of boundary tractions and displacements along any assigned time interval 0 is shown to be characterized by a variational theorem the variational formulation developed is generalized to zonewise homogeneous systems and to elastically constrained bodies the linear algebraic equations generated by boundary element modelling in space and time turn out to exhibit symmetry of the coefficient matrix