a numerical study on the solution of the cauchy problem in elasticity this work deals with the cauchy problem in two dimensional linear elasticity the equations of the problem are discretized through a standard fem approach and the resulting ill conditioned discrete problem is solved within the frame of the tikhonov approach the choice of the required regularization parameter is accomplished through the generalized cross validation criterion on this basis a numerical experimentation has been performed and the calculated solutions have been used to highlight the sensitivity to the amount of known data the noise always present in the data the regularity of boundary conditions and the choice of the regularization parameter the aim of the numerical study is to implicitly device some guidelines to be used in the solution of this kind of problems

orthogonality preservers in c algebras jb algebras and jb triples abstract we study orthogonality preserving operators between c algebras jb algebras and jb triples let t a e be an orthogonality preserving bounded linear operator from a c algebra to a jb triple satisfying that t 1 d is a von neumann regular element then t a e 2 r d every element in t a and d operator commute in the jb algebra e 2 r d and there exists a triple homomorphism s a e 2 r d such that t l d r d s where r d denotes the range tripotent of d in e an analogous result for a being a jb algebra is also obtained when t a b is an operator between two c algebras we show that denoting h t 1 then t orthogonality preserving if and only if there exists a triple homomorphism s a b satisfying h s z s z h h s z s z h and t z l h r h s z 1 2 h r h s z s z r h h this allows us to prove that a bounded linear operator between two c algebras is orthogonality preserving if and only if it preserves zero triple products

finite element solution of two dimensional inverse elastic problems using spatial smoothing a finite element method fem is presented for calculating the surface tractions on a body from internal measurements of displacement at discrete sensor locations the solution algorithm employs a sensitivity analysis which minimizes the difference between the calculated and measured displacements at each sensor location spatial regularization is one technique employed to stabilize the minimization process by imposing various degrees of smoothness on the solution it also allows the problem to be solved with fewer sensors than traction boundary nodes as an alternative to spatial regularization a method based on keynodes is introduced which assumes that each component of the boundary traction distribution can be described by a polynomial of specified order the methods are applied to several two dimensional examples including a rolling contact problem the effects of parameters such as the number of sensors the location of the sensors and the error in the sensor displacements are discussed

biseparating maps between operator algebras we prove that a biseparating map between spaces b e and some other banach algebras is automatically continuous and a multiple of an algebra isomorphism

biseparating maps and homeomorphic real compactifications abstract if x and y are realcompact and t c x c y is a ring isomorphism then two things happen 1 there is a homeomorphism h of x onto y and 2 t is a composition map for all in c x t h we strengthen that result in propositions 2 and 3 we discard the multiplicative property of t and assume only that t is biseparating in the sense that g 0 t tg 0 it remains true that x is homeomorphic to y but this time if t is also linear it is a weighted composition map for some weight function a in c y t a h

weakly compact orthogonality preservers on c algebras we establish a complete description of weakly compact orthogonality preserving operators from a c algebra a or a jb algebra to a jb triple e we prove that any such operator is the sum of a series of mutually orthogonal triple homomorphisms from a to a certain peirce 2 subspace of e multiplied by a mutually orthogonal norm null sequence in e which enjoy certain operator commutativity relations

determination of an optimal regularization factor in system identification with tikhonov regularization for linear elastic continua this paper presents a geometric mean scheme gms to determine an optimal regularization factor for tikhonov regularization technique in the system identification problems of linear elastic continua the characteristics of non linear inverse problems and the role of the regularization are investigated by the singular value decomposition of a sensitivity matrix of responses it is shown that the regularization results in a solution of a generalized average between the a priori estimates and the a posteriori solution based on this observation the optimal regularization factor is defined as the geometric mean between the maximum singular value and the minimum singular value of the sensitivity matrix of responses the validity of the gms is demonstrated through two numerical examples with measurement errors and modelling errors copyright 2001 john wiley sons ltd

numerical solution of cauchy problems in linear elasticity in axisymmetric situations abstract an iterative method for solving axisymmetric cauchy problems in linear elasticity is presented this kind of problem consists in recovering missing displacements and forces data on one part of a domain boundary from the knowledge of overspecified displacements and forces data on another part of this boundary numerical simulations using the finite element method highlight the algorithm s efficiency accuracy and robustness to noisy data as well as its ability to deblur noisy data an application of the inverse technique to the identification of a friction coefficient is also presented

weight preserving isomorphisms between spaces of continuous functions the scalar case abstract let f be a finite field or discrete and let a and b be vector spaces of f valued continuous functions defined on locally compact spaces x and y respectively we look at the representation of linear bijections h a b by continuous functions h y x as weighted composition operators in order to do it we extend the notion of hamming metric to infinite spaces our main result establishes that under some mild conditions every hamming isometry can be represented as a weighted composition operator connections to coding theory are also highlighted

a new spatial regularization scheme for the identification of the geometric shape of an inclusion in a finite body this paper presents a system identification scheme to determine the geometric shape of an inclusion in a finite body the proposed algorithm is based on the minimization of the least squared errors between the measured displacement field and calculated displacement field by the finite element model the domain parameterization technique is adopted to manipulate the shape variation of an inclusion to stabilize the optimization process a new regularization function defined by the length of the boundary curve of an inclusion is added to the error function a variable regularization factor scheme is proposed for a consistent regularization effect the modified newton method with the active set method is adopted for optimization copyright 1999 john wiley sons ltd

numerical solution to a two dimensional inverse heat conduction problem description de la methode de programmation dynamique pour la resolution de problemes inverses de conduction thermique application a un probleme impliquant la determination de 2 evolutions dans le temps inconnues de flux thermique sur les 2 faces d une plaque execution de differentes experiences numeriques pour etudier les effets du bruit et des parametres de ponderation

zero product preserving linear maps of ccr c algebras with hausdorff spectrum in this paper we try to attack a conjecture of araujo and jarosz that every bijective linear map between c algebras with both and its inverse 1 preserving zero products arises from an algebra isomorphism followed by a central multiplier we show it is true for ccr c algebras with hausdorff spectrum and in general some special c algebras associated to continuous fields of c algebras

additive maps on standard operator algebras preserving invertibilities or zero divisors let a and b be standard operator algebras on infinite dimensional complex banach spaces x and y respectively and let be an additive surjection from a onto b we prove that if is unital and preserves any one of left right invertibility left right zero divisors left right topological divisors of zero quasi affinity injectivity surjectivity range density lower boundedness and left right maximal ideals in both directions then it has one of the following forms isomorphism conjugate isomorphism anti isomorphism and conjugate anti isomorphism we also show that preserves zero products in both directions if and only if is either an isomorphism or a conjugate isomorphism

a boundary element formulation for the inverse elastostatics problem iesp of flaw detection a boundary integral formulation is presented for the detection of flaws in planar structural members from the displacement measurements given at some boundary locations and the applied loading such inverse problems usually start with an initial guess for the flaw location and size and proceed towards the final configuration in a sequence of iterative steps a finite element formulation will require a remeshing of the object corresponding to the revised flaw configuration in each iteration making the procedure computationally expensive and cumbersome no such remeshing is required for the boundary element approach the inverse problem is written as an optimization problem with the objective function being the sum of the squares of the differences between the measured displacements and the computed displacements for the assumed flaw configuration the geometric condition that the flaw lies within the domain of the object is imposed using the internal penalty function approach in which the objective function is augmented by the constraint using a penalty parameter a first order regularization procedure is also implemented to modify the objective function in order to minimize the numerical fluctuations that may be caused in the numerical procedure due to errors in the experimental measurements for displacements the flaw configuration is defined in terms of geometric parameters and the sensitivities with respect to these parameters are obtained in the boundary element framework using the implicit differentiation approach a series of numerical examples involving the detection of circular and elliptical flaws of various sizes and orientations are solved using the present approach good predictions of the flaw shape and location are obtained

identification of geometric shapes and material properties of inclusions in two dimensional finite bodies by boundary parameterization a system identification scheme based on the boundary element method bem is proposed to determine geometric shape and elastic material properties of an inclusion in a finite body the proposed algorithm is based on the minimization of least squared errors between measured displacement and calculated displacement by a boundary element model a regularization function that consists of the geometric term and material property term is added to the error function to overcome ill posedness of inverse problems to deal with the shape variation of an inclusion during the optimization process the boundary parameterization technique is applied to the bem the recursive quadratic programming rqp technique with line search is used for optimization

a unified solution for various boundary conditions for the coupled flexural torsional instability of closed thin walled beam columns abstract the problem of coupled flexural torsional instability of closed thin walled beam columns under the combined action of axial loads and equal end moments is studied numerically the characteristic equations for stability are obtained and the load interaction curves and mode shapes are plotted for various boundary conditions from a study of the numerical results and the characteristic equations equivalent load and geometry parameters are defined these yield a single solution common for all boundary conditions for the ioad interaction curve and the mode shape the effect of various boundary conditions and mode numbers is manifest only in the value of an eigen coefficient independent of the loads which is used in defining the equivalent parameters the case of lateral instability within the elastic limit is also examined and it is shown that even when tensile axial loads are present elastic lateral instability may occur

automatic continuity of orthogonality preservers on a non commutative lp τ space abstract elements a and b of a non commutative l p space associated to a von neumann algebra n equipped with a normal semifinite faithful trace are called orthogonal if l a l b r a r b 0 where l x and r x denote the left and right support projections of x a linear map t from l p n to a normed space y is said to be orthogonality to p orthogonality preserving if t a t b p a p b p whenever a and b are orthogonal in this paper we prove that an orthogonality to p orthogonality preserving linear bijection from l p n 1 p p 2 to a banach space x is automatically continuous whenever n is a separably acting von neumann algebra if n is a semifinite factor not of type i 2 we establish that every orthogonality to p orthogonality preserving linear mapping t l p n x is continuous and invertible whenever t 0 furthermore there exists a positive constant c p 1 p p 2 so that t t 1 c p 2 for every non zero orthogonality to p orthogonality preserving linear mapping t l p n x for p 1 this inequality holds with c p 1 that is t is a multiple of an isometry

an integral equations method combined minimum norm solution for 3d elastostatics cauchy problem abstract in this paper we establish new density results for the equilibrium equations based on the denseness result of the elastic potential functions the cauchy problem for the equilibrium equations is investigated for this ill posed problem we construct a regularizing solution using the single layer potential function the well posedness of the regularizing solution as well as the convergence property is rigorously analyzed the advantage of the proposed scheme is that the regularizing solution is of the explicit analytic solution and therefore is easy to be implemented the method combines minimum norm solution with morozov discrepancy principle to solve an inverse problem convergence and stability estimates are then given with some examples for numerical verification on the efficiency of the proposed method the numerical convergence accuracy and stability of the method with respect to the discretisation about the integral equations on pseudo boundary and the distance between the pseudo boundary and the real boundary of the solution domain and decreasing the amount of noise added into the input data respectively are also analysed with some examples

dynamic stability of a thin walled beam subjected to axial loads and end moments the dynamic stability problem of thin walled beams subjected to combined action of axial loads and end moments is studied each force and moment consists of a constant part and a time dependent stochastic function closed form analytical solutions are obtained for simply supported boundary conditions by using the direct liapunov method almost sure asymptotic stability and uniform stochastic stability conditions are obtained as the function of stochastic process variance damping coefficient and geometric and physical parameters of the beam the almost sure stability regions for i cross section and narrow rectangular cross section are shown in the plane of variances of stochastic parts axial force and end moment uniform stochastic stability regions are shown in intensity of stochastic loadings and constant parts of axial loads and end moments

a boundary element solution of an inverse elasticity problem and applications to determining residual stress and contact stress abstract a boundary element solution is developed for an inverse elasticity problem in this inverse problem boundary conditions are incompletely specified strains can be determined experimentally in practice at a number of internal points and used as input to completely resolve these boundary conditions in this paper these strains including random errors are numerically simulated this inverse problem finds applications in the evaluation of residual stress and contact stress in contrast to previous studies the construction of the sensitivity matrix is embedded in the boundary element formulation thereby avoiding the solution of a series of forward problems further the effects of prescribed non zero boundary conditions and body forces are included in the relation between measured strains and the primary traction unknowns unfortunately the inverse problem is still ill posed physical constraints are introduced to stabilize the solution as a result the algorithm presented here has reasonable tolerance to error in the measurement of strains numerical examples are given to validate the inverse algorithm in these examples the input strains are numerically simulated and stable and accurate solutions are obtained with up to 5 random error in the input

stochastic vibration of axially loaded monosymmetric timoshenko thin walled beam abstract an analytical method is presented to perform the flexure torsion coupled stochastic response analysis of monosymmetric axially loaded timoshenko thin walled beam subjected to various kinds of concentrated and distributed stochastic excitations with stationary and ergodic properties the effects of warping stiffness axial force shear deformation and rotary inertia are included in the present formulations first the damped general governing differential equations of motion of axially loaded timoshenko thin walled beam are developed and the free vibration analysis is performed once the natural frequencies and mode shapes are obtained mode superposition method in conjunction with receptance method is used to compute the mean square displacement response of the axially loaded thin walled beam finally the method is illustrated by its application to two test examples to investigate the effects of warping stiffness axial force shear deformation and rotary inertia on the stochastic response of the thin walled beams

fading regularization mfs algorithm for inverse boundary value problems in two dimensional linear elasticity abstract we investigate the numerical reconstruction of the missing displacements dirichlet data and tractions neumann data on an inaccessible part of the boundary in the case of two dimensional linear isotropic elastic materials from the knowledge of over prescribed noisy measurements taken on the remaining accessible boundary part this inverse problem is solved using the fading regularization method originally proposed by cimetiere et al 2000 2001 for the laplace equation in conjunction with a meshless method namely the method of fundamental solutions mfs the stabilisation of the numerical method proposed herein is achieved by stopping the iterative procedure according to morozov s discrepancy principle morozov 1966

load distribution modelling for pin jointed trusses by an inverse approach the paper considers the load distribution modelling for pin jointed trusses when an approximate value of the normal stress on a suitable number of elements is known this inverse problem is formulated in the least square sense directly relating the stress on the elements with the external loads and successively solved using an iterative scheme which uses a standard decomposition method for the stiffness matrix and the conjugate direction strategy in order to obtain a regularized solution of this problem and so cut out the errors contained in the known term of the equation system the generalized cross validation criterion is used in a form suitable for iterative methods some numerical results allow an analysis of the algorithm s performance

investigation of regularization parameters and error estimating in inverse elasticity problems the method of tarantola1 based on bayesian statistical theory for solving general inverse problems is applied to inverse elasticity problems and is compared to the spatial regularization technique presented in schnur and zabaras 2 it is shown that when normal gaussian distributions are assumed and the error in the data is uncorrelated the bayesian statistical theory takes a form similar to the deterministic regularization method presented earlier in schnur and zabaras 2 as such the statistical theory can be used to provide a statistical interpretation of regularization and to estimate error in the solution of the inverse problem examples are presented to demonstrate the effect of the regularization parameters and the error in the initial data on the solution

linear disjointness preservers of w algebras in this paper we give a complete description of the structure of zero product and orthogonality preserving linear maps between w algebras in particular two w algebras are isomorphic if and only if there is a bijective linear map between them preserving their zero product or orthogonality structure in two directions it is also the case when they have equivalent linear and left right ideal structures

on computing the forces from the noisy displacement data of an elastic body this study is concerned with the accurate computation of the unknown forces applied on the boundary of an elastic body using its measured displacement data with noise vision based minimally intrusive force sensing using elastically deformable grasping tools is the motivation for undertaking this problem since this problem involves incomplete and inconsistent displacement force of ail elastic body it leads to an ill posed problem known as cauchy s problem in elasticity vision based displacement measurement necessitates large displacements of the elastic body for reasonable accuracy therefore we use geometrically non linear modelling of the elastic body which was not considered by others who attempted to solve cauchy s elasticity problem before we present two methods to solve the problem the first method uses the pseudo inverse of an over constrained system of equations this method is shown to be not effective when the noise in the measured displacement data is high we attribute this to the appearance of spurious forces at regions where there should not be any forces the second method focuses on minimizing the spurious forces by varying the measured displacements within the known accuracy of the measurement technique both continuum and frame elements are used in the finite element modelling of the elastic bodies considered in the numerical examples the performance of the two methods is compared using seven numerical examples all of which show that the second method estimates the forces with an error that is not more than the noise in the measured displacements an experiment was also conducted to demonstrate the effectiveness of the second method in accurately estimating the applied forces

zero product preserving additive maps on symmetric operator spaces and self adjoint operator spaces in this note we characterize the additive maps on the space of symmetric operators and the space of self adjoint operators which preserve zero products in both directions and the additive maps on the space of self adjoint operators which preserve jordan zero products in both directions we also give a complete classification of additive maps on the von neumann algebra of all bounded linear operators acting on a hilbert space which preserve square zero in both directions or preserve operators annihilated by a polynomial in both directions

a boundary element strategy for elastostatic inverse problems involving uncertain boundary conditions in this paper a convenient strategy is developed to find solutions for a class of uncertain boundary value problems by the boundary element method bem such problems are ill posed but ill conditioning of the associated algebraic systems of equations can be controlled to a large extent and useful boundary data can be obtained despite ill conditioning interior data of not only sufficient quantity but also of good quality at good locations contribute to good solutions our strategy permits the condition number of the algebraic systems as a function of interior data locations to be monitored such that measured data from displacement sensors and or strain sensors at locations found to be good ones for the problem at hand can be used the present strategy is based upon the concept of a green s function library through partitioning of the bem algebraic system algebraic systems are solved using least squares via singular value decomposition svd the library idea takes advantage of modern data storage and retrieval technology and permits the process of repeated trials in order to determine good data sensor locations to be done quickly and efficiently several numerical examples are given to demonstrate the strategy some examples examine the consequences of errors in measured data copyright 1999 john wiley sons ltd

derivations modulo elementary operators abstract let r be a prime ring with extended centroid c and symmetric martindale quotient ring q s r suppose that q s r contains a nontrivial idempotent e such that e r r e r let r r r c c be the bi additive map x y g x y x h y i a i x b i y c i where g h r r are additive maps and where a i b i c i r c c are fixed suppose that is zero product preserving that is x y 0 for x y r with x y 0 then there exists a derivation r q s r c such that both g and h are equal to plus elementary operators moreover there is an additive map f r q s r c such that x y f x y for all x y r the result is a natural generalization of several related theorems in the literature actually we prove some more general theorems

numerical solution of nonlinear inverse heat conduction problem with a radiation boundary condition a finite difference solution for the transient nonlinear heat conduction equation in a finite slab with a radiation boundary condition is proposed an implicit finite difference approximation is used which enables accurate estimation of the surface temperature as well as prevention of oscillation of computed values at the surfaces a two time level implicit method is used while taylor s forward projection method is employed for taking account of the nonlinearities an iterative method is described which predicts unknown surface conditions an example is illustrated which is typical of those that arise in practical applications the results demonstrate that the method is remarkable in its stability to predict surface conditions without debilitation

relaxation procedures for an iterative mfs algorithm for the stable reconstruction of elastic fields from cauchy data in two dimensional isotropic linear elasticity we investigate two numerical procedures for the cauchy problem in linear elasticity involving the relaxation of either the given boundary displacements dirichlet data or the prescribed boundary tractions neumann data on the over specified boundary in the alternating iterative algorithm of kozlov et al 1991 the two mixed direct well posed problems associated with each iteration are solved using the method of fundamental solutions mfs in conjunction with the tikhonov regularization method while the optimal value of the regularization parameter is chosen via the generalized cross validation gcv criterion an efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase is also presented the mfs based iterative algorithms with relaxation are tested for cauchy problems for isotropic linear elastic materials in various geometries to confirm the numerical convergence stability accuracy and computational efficiency of the proposed method

orthogonality preserving linear maps on c algebras with non zero socles abstract we study orthogonality preserving surjective linear maps from a unital c algebra with non zero socle a to a c algebra in particular we prove that when a has essential socle every biorthogonality preserving surjective linear map t a b is automatically bounded and a jordan isomorphism multiplied by an invertible element

automatic continuity of biorthogonality preservers between compact c algebras and von neumann algebras abstract we prove that every biorthogonality preserving linear surjection between two dual or compact c algebras or between two von neumann algebras is automatically continuous

boundary element solution for the cauchy problem in linear elasticity using singular value decomposition abstract in this paper the singular value decomposition svd truncated at an optimal number is analysed for obtaining approximate solutions to ill conditioned linear algebraic systems of equations which arise from the boundary element method bem discretisation of an ill posed boundary value problem in linear elasticity the regularisation parameter namely the optimal truncation number is chosen according to the discrepancy principle the numerical results obtained confirm that the svd bem produces a convergent and stable numerical solution with respect to decreasing the mesh size discretisation and the amount of noise added into the input data

some general techniques on linear preserver problems abstract several general techniques on linear preserver problems are described the first one is based on a transfer principle in model theoretic algebra that allows one to extend linear preserver results on complex matrices to matrices over other algebraically closed fields of characteristic 0 the second one concerns the use of some simple geometric technique to reduce linear preserver problems to standard types so that known results can be applied the third one is about solving linear preserver problems on more general operator algebras by reducing the problems to idempotent preservers numerous examples will be given to demonstrate the proposed techniques

disjointness preservers of aw algebras abstract in this paper we study bijective linear maps a b between a w algebras preserving either zero products or range orthogonality such a map is automatically continuous and provides an algebra or a algebra isomorphism 1 1 from a onto b our results extend previous works for the case of w algebras and also cover such maps between c algebras satisfying an extra assumption on preserving abelian c subalgebras