denseness of the generalized eigenvectors of an h s discrete operator let t be a closed densely defined linear operator in a hilbert space h and assume there exists 0 p t such that r 0 t is a hilbert schmidt operator the operator t is a special type of discrete operator a so called h s discrete operator which is shown to be a fredholm operator in h with fredholm set equal to the whole complex plane let t i i 1 where the operator t i has ascent mi let pi i 1 2 be the projection of h onto the generalized eigenspace n t i mi along r t i mi and let s and m be the subspaces of h consisting of all x h such that x i 1 pix and such that pix 0 for i 1 2 respectively sufficient conditions are introduced which guarantee that s h and m 0 these conditions require that r t be bounded on certain rays in the complex plane and r t 0 as on at least one of the rays but specific decay rates for r t are not necessary

advanced methods for calculating green s function and its derivatives for three dimensional anisotropic elastic solids abstract three advanced methods are presented for constructing and evaluating green s function and its derivatives for three dimensional anisotropic elastic solids the first one is obtained from a line integral followed by cauchy s residue theorem and expressed in terms of stroh s eigenvalues the second one is obtained by using the explicit solutions of stroh s eigenvector matrix available in two dimensional anisotropic elasticity whereas the last one is derived from the solution obtained from 2d radon transform and expressed in terms of the fundamental elasticity matrix in vertical planes which makes the derivatives simpler than those obtained from the line integral operated on an oblique plane the novelty of the first two methods lies in the construction and computation of the first and second derivatives of the green s function though the green s function itself in the first two methods is rather known in contrast the third method is quite new for both the green s function itself and its first and second derivatives the advantages and disadvantages of these three solution methods are investigated and discussed through their derivations and numerical implementations for isotropic transversely isotropic and fully anisotropic elastic solids good agreement between the results calculated by these three methods is shown in all numerical examples among these three methods the last one is proved to be the most efficient one

three dimensional green s function and its derivative for materials with general anisotropic magneto electro elastic coupling explicit expressions of green s function and its derivative for three dimensional infinite solids are presented in this paper the medium is allowed to exhibit a fully magneto electro elastic mee coupling and general anisotropic behaviour in particular new explicit expressions for the first order derivative of green s function are proposed the derivation combines extended stroh formalism radon transform and cauchy s residue theory in order to cover mathematical degenerate and non degenerate materials in the stroh formalism context a multiple residue scheme is performed expressions are explicit in terms of stroh s eigenvalues this being a feature of special interest in numerical applications such as boundary element methods as a particular case simplifications for mee materials with transversely isotropic symmetry are derived details on the implementation and numerical stability of the proposed solutions for degenerate cases are studied

on an unconditional basis of generalized eigenvectors of the nonself adjoint gribov operator in bargmann space abstract in this article we prove that the system of generalized eigenvectors of the gribov operator is an unconditional basis in bargmann space we also give a generalized diagonalization in the abel sense of the semigroups respectively associated to this operator and to its square root finally some open problems are pointed out

boundary element method for thermoelastic analysis of three dimensional transversely isotropic solids abstract thermal effects are well known to manifest themselves as additional volume integral terms in the direct formulation of the boundary integral equation bie for linear elastic solids when using the boundary element method bem this domain integral has been successfully transformed in an exact manner to surface ones only in isotropy and in 2d anisotropy thereby restoring the bem as a truly boundary solution technique the difficulties with extending it to 3d general anisotropic solids lie in the mathematical complexity of the green s function and its derivatives for such materials these quantities are required items in the bem formulation in this paper the exact analytical transformation of the volume integral associated with thermal effects to surface ones is achieved for a transversely isotropic material using a similar approach which the authors have previously employed for the same task in bem for 2d general anisotropy a numerical scheme however needs to be employed to evaluate some of the new terms introduced in the surface integrals that arise from this process here the mathematical soundness of the formulation is demonstrated by a few examples the numerical results obtained are checked by alternative means including those obtained from the commercial fem code ansys

diagonalization of non selfadjoint analytic semigroups and application to the shape memory alloys operator abstract to a densely defined but not necessarily selfadjoint operator a on a hilbert space h we consider on r h the following abstract elliptic problem of dirichlet type formula then in this paper we establish that for every t 0 the solution formula can be expanded into a series of generalized eigenvectors of the operator a provided that its resolvent belongs to carleman class c p for some p 0 1 2 a similar result holds for t large enough if the inverse a 1 belongs to carleman class c p for every p 1 2 see theorem 3 1 and theorem 3 2 furthermore we apply these obtained results to the shape memory alloys non selfadjoint operator formula and d n n x n when acting on an appropriate hilbert space e of functions on the interval 0 1 by establishing that the inverse c 1 belongs to the carleman class c p for every p 1 2 so that we get in this case more regularity in the sense that the operatorial series k 1 e tc p k converges strongly in e to the analytic semigroup e tc for every t 0 the p k are the projectors into the root subspaces of c a similar result holds for formula provided that t is large enough see theorem 4 1 and theorem 4 2 in section 4 for the precise result

treatment of body force volume integrals in bem by exact transformation for 2 d anisotropic elasticity in the boundary element method bem based on the direct formulation body force effects manifest themselves as an additional volume integral term in the boundary integral equation bie the numerical solution of the integral equation with this term destroys the notion of the bem as atruly boundary solution method this paper discusses the treatment of this volume integral for two dimensional anisotropic elasticity with body forces present the analytical basis for transforming this integral exactly into boundary ones is presented for geometrically convex regions this restores the application of the bem to such problems as a truly boundary solution technique numerical examples are presented to demonstrate the veracity of the transformation and implementation 1997 by john wiley sons ltd

densite des vecteurs propres generalises d une classe d operateurs compacts non auto adjoints et applications we consider a closed densely defined linear operatort in a hilbert spacee and assume the existence of 0 t such thatk t 0i 1 is compact and the existence ofp 0 such thats n k o n 1 p wheres n k denotes the sequence of non zero eigenvalues of the compact hermitian operator sqrt k k in this work sufficient conditions announced in 1 are introduced to assure that the closed subspace ofe spanned by the generalized eigenvectors oft coincides withe these conditions are in particular verified by a family of non self adjoint operators arising in reggeon s field theory

3d bem for general anisotropic elasticity abstract a new method for computing the system matrices g and h of the three dimensional boundary element method is presented for the elastostatic problems of general anisotropy green s functions expressed by the line integrals over a semi circle have a simple structure that allows analytical integration over the boundary elements the computation for the system matrices g and h is reduced to numerical integration of regular line integrals over the unit semi circle the proposed method has been implemented and tested with numerical examples

analysis of thermoelastic stress concentration around oblate cavities in three dimensional generally anisotropic bodies by the boundary element method abstract in this article stress concentrations around cavities in 3d generally anisotropic bodies are investigated using the boundary element method bem where the associated volume integral is analytically transformed to the boundary all derivations are based upon the fourier series representations of the fundamental solutions including green s function of displacements and its derivatives this approach of analytical transformation has fully restored the bem s distinctive notion that only the boundary needs to be discretized the goal of the present work is to investigate the thermoelastic stress concentration around cavities in 3d anisotropic bodies by use of the analytically transformed boundary integral equation bie the work has fully recovered the bem s nature of boundary discretization for treating 3d generally anisotropic thermoelasticity this is the first implemented work that successfully treats thermoelastic problems for 3d generally anisotropic solids by the analytically transformed bie in the paper interesting phenomena are observed from the analyses of stress concentrations around oblate cavities and some discussions are made

sur une valeur propre d un operateur the studied eigenvalue is the smallest one of the operator h mu mu a i lambda a a a a in the orthogonal complement of the vacuum wherea anda are the creation and annihilation operators call this eigenvaluee as attention is focused on the dependence on this eigenvalue exists and is a positive number for positive values of using the fact that the inverse ofh is a positive operator it is proved thate extends to a positive increasing analytic function on the whole real line in particular e 0 0 contrary to what might have been expected from the fact thata a a a is formally self adjoint

quelques nouvelles proprietes de regularite de l operateur de gribov in this work we establish new regularity properties for gribov s operator h a a i a a a a 2 wherea anda are the creation and annihilation operators particularly we prove that for all e 0 h 1 is in the class of carleman s operatorl1 e

analyzing interaction between coplanar square cracks using an efficient boundary element free method summary this paper examines the interaction between coplanar square cracks by combining the moving least squares mls approximation and the derived boundary integral equation bie a new traction bie involving only the cauchy singular kernels is derived by applying integration by parts to the traditional boundary integral formulation the new traction bie can be directly applied to a crack surface and no displacement bie is necessary because all crack boundary conditions both upper and lower ones are incorporated a boundary element free method is then developed by combining the derived bie and mls approximation in which the crack opening displacement is first expressed as the product of weight functions and the characteristic terms and the unknown weight is approximated with the mls approximation the efficiency of the developed method is tested for isotropic and transversely isotropic media the interaction between two and three coplanar square cracks in isotropic elastic body is numerically studied and the case of any number of coplanar square cracks is deduced and discussed copyright 2012 john wiley sons ltd

unique real variable expressions of the integral kernels in the somigliana stress identity covering all transversely isotropic elastic materials for 3d bem abstract a formulation and computational implementation of the hypersingular stress boundary integral equation for the numerical solution of three dimensional linear elastic problems in transversely isotropic solids is developed the formulation is based on a new closed form real variable expression of the integral kernel s ijk giving tractions originated by an infinitesimal dislocation loop the source of singularity work conjugated to stress tensor this expression is valid for any combination of material properties and for any orientation of the radius vector between the source and field points the expression is based on compact expressions of u ik in terms of the stroh eigenvalues on the plane normal to the radius vector performing double differentiation of u ik for deducing the second derivative kernel u ik jl the stress influence function of an infinitesimal dislocation loop ijkl loop are first obtained obtaining then the integral kernel s ijk the expressions of s ijk and of the related kernels ijkl loop and u ik jl do not suffer from the difficulties of some previous expressions obtained by other authors in different ways with complex valued functions appearing for some combinations of material parameters and or with division by zero for the radius vector at the rotational symmetry axis the expressions of the above mentioned kernels have been presented in a form suitable for an efficient computational implementation the correctness of these expressions and of their implementation in a three dimensional collocational bem code has been tested numerically by solving problems with known analytic solutions for different classes of transversely isotropic materials the obtained expressions will be useful in the development of bem codes applied to composite materials geomechanics and biomechanics in particular an application to biomechanics of the bem code developed is shown additionally these expressions can be employed in the distributed dislocation technique to solve crack problems

approximation of the semigroup generated by the hamiltonian of reggeon field theory in bargmann space abstract the reggeon field theory is governed by a non self adjoint operator constructed as a polynomial in a a the standard bose annihilation and creation operators in zero transverse dimension this hamiltonian acting in bargmann space is defined by h a 2 a 2 a a i a a a a where i 2 1 and are real numbers and the operators a a satisfy the commutation relation a a i as the quantum mechanical system described by h has a velocity dependent potential containing powers of momentum up to the fourth the problem of existence of hamiltonian path integral for the evolution operator e t h of this theory is of interest on its own in particular can we express e t h as a limit of integral operators in this article one considerably reduces the difficulty by studying the trotter product formula of h to reach two objectives the first objective is to prove a very specific error estimate for the error in a trotter product formula in trace norm for h viewed as the sum of the operators a 2 a 2 and a a i a a a a the second objective of this work is to give a approximation of the semigroup generated by h when h is split in the sum of a 2 a 2 a a and i a a a a we note that this case is entirely different in fact the usual trotter product formula is not defined because the interaction operator a a a a is not the infinitesimal generator of a semigroup on bargmann space for 0 and 0 we choose an approximation operator i i a a a a e a 2 a 2 a a and we give a connection between and e h this choice allows us to give in a intissar note on the path integral formulation of reggeon field theory preprint a generalized trotter product formula for t a a i a a a a i e for limit case as 0 and answers to the above question

derivatives of the three dimensional green s functions for anisotropic materials abstract a concise formulation is presented for the derivatives of green s functions of three dimensional generally anisotropic elastic materials direct calculation for derivatives of the green s function on the cartesian coordinate system is a common practice which however usually leads to a complicated course in this paper the green s function derived by ting and lee ting t c t lee v g 1997 the three dimensional elastostatic green s function for general anisotropic linear elastic solids the quarterly journal of mechanics and applied mathematics 50 3 407 426 is extended to obtain the derivatives using a spherical coordinate system the green s function can be shown as the composition of two independent functions one depends only on the radial distance of the field point to the origin and the other is in spherical angles the method of derivation is based on the total differential scheme and then takes its partial differentiation accordingly with the application of cauchy residue theorem the contour integral can be evaluated in terms of the stroh eigenvalues of a sextic equation for the degenerate case evaluation of residues at multiple poles is also given applications of the present result are made to examine the green s functions and stress components for isotropic and transversely isotropic materials the results are in exact agreement with existing solutions

analytical transformation of the volume integral in the boundary integral equation for 3d anisotropic elastostatics involving body force abstract in the boundary element method bem it is well known that the presence of body force shall give rise to an additional volume integral that conventionally requires domain discretization for numerical computations to restore the bem s distinctive notion of boundary discretization the present work analytically transforms the volume integral to surface ones for the body force effect in the 3d anisotropic elasticity on applying green s theorem new fundamental solutions with explicit forms of fourier series are introduced to facilitate the volume to surface transformation the coefficients of the fourier series representations are determined by solving a banded matrix formulated from integrations of the constrained equation of no doubt such an approach has fully restored the boundary element method as a truly boundary solution technique for analyzing 3d anisotropic elasticity involving body force at the end numerical verifications of the volume to surface integral transformation are presented also such an approach has been implemented in an existing bem code for demonstrating the implementation numerical examples are presented with comparisons with ansys analysis to the author s knowledge this is the first work in the open literature that reports the successful transformation for 3d anisotropic elasticity

unified analytical expressions of the three dimensional fundamental solutions and their derivatives for linear elastic anisotropic materials novel unified analytical displacement and stress fundamental solutions as well as the higher order derivatives of the displacement fundamental solutions for three dimensional generally anisotropic and linear elastic materials are presented in this paper adequate integral expressions for the displacement and stress fundamental solutions as well as the higher order derivatives of the displacement fundamental solutions are evaluated analytically by using the cauchy residue theorem the resulting explicit displacement fundamental solutions and their first and second derivatives are recast into convenient analytical forms which are valid for non degenerate partially degenerate fully degenerate and nearly degenerate cases the correctness and the accuracy of the novel unified and closed form three dimensional anisotropic fundamental solutions are verified by using some available analytical expressions for both transversely isotropic non degenerate or partially degenerate and isotropic fully degenerate linear elastic materials

boundary element elastic stress analysis of 3d generally anisotropic solids using fundamental solutions based on fourier series abstract the authors have very recently proposed an efficient accurate alternative scheme to numerically evaluate etc green s function u x and its derivatives for three dimensional general anisotropic elasticity these quantities are necessary items in the formulation of the boundary element method bem the scheme is based on the double fourier series representation of the explicit exact algebraic solution derived by ting and lee 1997 ting t c t lee v g 1997 the three dimensional elastostic green s function for general anisotropic linear elastic solid q j mech appl math 50 407 426 expressed in terms of stroh s eigenvalues by taking advantage of some its characteristics the formulations in this double fourier series approach are revised and several of the analytical expressions are re arranged in the present study this results in significantly fewer terms to be summed in the series thereby improving further the efficiency for evaluating the green s function and its derivatives these revised fourier series representations of u x and its derivatives are employed in a bem formulation for three dimensional linear elastostatics some numerical examples are presented to demonstrate the veracity of the implementation and its applicability to the elastic stress analysis of generally anisotropic solids the results are compared with known solutions in the literature where possible and with those obtained using the commercial finite element code ansys excellent agreement is obtained in all cases

on modular homology in the boolean algebra iii abstract let be a set ra ring of characteristicp 0 and denote bymkther module withk element subsets of as basis theset inclusion map mk mk 1is the homomorphism which associates to ak element subset the sum 1 2 kof all its k 1 element subsets i in this paper we study the chain formula arising from we introduce the notion ofp exactness for a sequence if is infinite we show that isp exact for all prime characteristicsp 0 this result can be extended to various submodules and quotient modules and we give general constructions arising from permutation groups with a finitary section two particular applications are the following the orbit module sequence of such a permutation group on isp exact for every primep and we give a formula for thep rank of the orbit inclusion matrix if the group has finitely many orbits onk element subsets

multiple pole residue approach for 3d bem analysis of mathematical degenerate and non degenerate materials in this paper we develop an alternative boundary element method bem formulation for the analysis of anisotropic three dimensional 3d elastic solids our implementation is based on the derivation of explicit expressions for the fundamental solution displacements and tractions of general validity for any class of anisotropic materials by means of stroh formalism and cauchy s residue theory the resulting fundamental solution remains valid for mathematical degenerate cases when stroh s eigenvalues are coincident meanwhile it does not exhibit numerical instabilities for quasi degenerate cases when stroh s eigenvalues are nearly equal a multiple pole residue approach is followed leading to general explicit expressions to evaluate the traction fundamental solution for poles of m multiplicity despite the existence of general displacement solutions in the literature and for the sake of completeness the same approach as for the traction solution is considered to derive the displacement fundamental solution as well based on these solutions an explicit bem approach for the numerical solution of 3d linear elastic problems for solids with general anisotropic behavior is presented the analysis of cracked anisotropic solids is also considered details on the numerical implementation and its validation for degenerate cases are discussed copyright 2010 john wiley sons ltd