additive mappings on von neumann algebras preserving absolute values abstract given hilbert spaces h and k and a von neumann algebra a b h let denote the class of all additive mappings a b k satisfying a a a a the paper shows that if a contains no nonzero abelian central projection then every preserves the operation the r linear combination and up to a commuting operator multiple i 0 the ring multiplication if a contains a nonzero abelian central projection p and if the dimension of k is at least 2 or 2 rank p according to whether or not p can be chosen to be minimal then there exists an additive mapping a b k such that i is a projection and a a for all a a but is neither multiplicative nor adjoint preserving in case a b h the result was proved by molnar bull aust math soc 53 1996 391 when a contained all finite rank operators and by radjabalipour et al linear algebra appl 327 2001 197 under the redundant restriction i i k i k

a state space finite element for laminated composite plates this paper presents a semi analytical finite element solution for the stress analysis of cross ply laminated composite plates the method is based on a mixed variational principle that includes the variations of both displacements and stresses finite element approximation is introduced only for the in plane variations of displacements and stresses while the through thickness distributions of them are obtained by using the method of state equation numerical tests show that the results obtained approach the analytical three dimensional solutions moreover the use of the recursive formulation of the state equation leads to the solution of an algebra equation system whose order does not depend on the number of material layers of the laminate compared with the traditional finite element method the new solution always provides continuous distributions of both displacements and transverse stresses across material interfaces

on nonlinear maps preserving the reduced minimum modulus on differences of matrices abstract we prove that if m n c m n c is a bijective map which preserves the reduced minimum modulus on differences of matrices then is automatically bicontinuous and therefore by a result of mashreghi and stepanyan of a standard form

nonlinear maps preserving the reduced minimum modulus of operators abstract let x and y be infinite dimensional complex banach spaces and let b x resp b y denote the algebra of all bounded linear operators on x resp on y we describe bijective bicontinuous maps from b x to b y satisfying s t s t for all s t b x where t is the reduced minimum modulus of an operator t an analogue result for the finite dimensional case is obtained

spectrum nonincreasing maps on matrices abstract maps which do not increase the spectrum on complex matrices in a sense that sp a b sp a b are classified

nonlinear maps preserving the minimum and surjectivity moduli abstract let x and y be infinite dimensional complex banach spaces and let b x resp b y denote the algebra of all bounded linear operators on x resp on y we describe maps from b x onto b y satisfying c s t c s t for all s t b x where c stands either for the minimum modulus or the surjectivity modulus or the maximum modulus we also obtain analog results for the finite dimensional case

asymptotic theory for laminated piezoelectric circular cylindrical shells an asymptotic theory is presented for laminated piezoelectric circular cylindrical shells under electromechanical loads the three dimensional coupled electromechanical problem reduces to a hierarchy of two dimensional equations which can be solved systematically the proposed theory is illustrated by considering two example problems numerical results show excellent agreement with an available exact solution and also provide some suggestions in establishing new two dimensional piezoelectric shell models

maps on matrices compressing the local spectrum in the spectrum abstract let m n c be the algebra of all complex n n matrices let x 0 be a nonzero vector in c n we describe maps on m n c not linear or surjective satisfying t s x 0 t s for all t s m n c we also obtain a similar description by supposing that is surjective and t s x 0 t s for all t s m n c

caustics of the harmonic double cusp near an e_6 point the harmonic double cusp is the real singularity x 4 6x 2 y 2 y 4 its unfolding is eight dimensional and contains a stratum of codimension five corresponding to the e 6 singularity x 3 y 4 a complete description of the bifurcation set in a neighbourhood of the e 6 stratum is given by means of a tableau of two dimensional sections over the three dimensional base the tableau also gives information about the bifurcation set near other strata of high codimension notably d 6 x 2 y y 5 and a 7 x 2 y 8 and it shows how these strata fit together in optics the harmonic double cusp organizes a large family of caustics produced by generic thin lenses some predictions made by the tableau have already been confirmed by observations of caustics from liquid drops points in the tableau base correspond to experimental set ups and the fibre corresponds to the viewing screen

octet formalism for kirchhoff anisotropic plates an octet formalism is established for stretching and bending deformations of an anisotropic elastic plate based on the kirchhoff theory the plate is inhomogeneous in the thickness direction and thus includes the laminated plate as a special case by defining a 4 eigenvector associated with two in plane displacements and two rotational angles of a normal of the mid plane and a 4 eigenvector associated with four stress functions the three equilibrium equations of the plate reduce to a standard eight dimensional eigenrelation the fundamental elastic plate matrix defined in this work is found to place the two eigenvectors in reverse order to form the left and right 8 eigenvectors of the matrix the same capability has been observed for the fundamental elasticity matrix in stroh s sextic formalism for generalized plane strain elasticity thus our octet formalism symbolically preserves extensive elegant properties and identities pertaining to the capability e g the orthogonality and closure relations which have been established in the stroh sextic formalism having shown that the eigenvalues cannot be real we provide the eigenvalue representations for special cases of material and geometry the non semisimple case including an isotropic material is briefly discussed

on the rational derivation of a hierarchy of dynamic equations for a homogeneous isotropic elastic plate abstract flexural equations of motion for a homogeneous isotropic elastic plate are derived by an antisymmetric expansion in the thickness coordinate of the displacement components all but the lowest order expansion functions are eliminated with the help of the three dimensional equations of motion and are plugged into the boundary conditions eliminating between these an equation is obtained for the mean plane vertical displacement which also includes arbitrary loading on the plate surface this equation can be truncated to any order in the thickness and it is in particular noted that the corresponding dispersion relation seems to correspond to a power series expansion of the exact rayleigh lamb dispersion relation to all orders various truncations of the equation are discussed and are compared numerically with each other the exact three dimensional solution and mindlin s plate equation both the dispersion relation and the corresponding displacement components as well as an excitation problem are used for the comparisons the theories are reasonably close to each other and in order to be on the safe side none of them should in fact be used for frequencies above the cutoff of the second flexural mode

linear preservers of polynomial numerical hulls of matrices abstract let m n be the algebra of all n n complex matrices 1 k n 1 be an integer and m n m n be a linear operator in this paper it is shown that preserves the polynomial numerical hull of order k if and only if there exists a unitary matrix u m n such that either a u a u for all a m n or a u a t u for all a m n

linear maps preserving the minimum and surjectivity moduli of hilbert space operators abstract let b h be the algebra of all bounded linear operators on a complex infinite dimensional hilbert space h for every t b h let m t and q t denote the minimum modulus and surjectivity modulus of t respectively let b h b h be a surjective linear map in this paper we prove that the following assertions are equivalent i m t m t for all t b h ii q t q t for all t b h iii there exist two unitary operators u v b h such that t u t v for all t b h this generalizes the result of mbekhta 7 theorem 3 1 to the non unital case

generalized plane solution for monoclinic piezoelectric laminates an efficient method has been developed for analyzing the three dimensional electromechanical deformations of a monoclinic piezoelectric laminate subjected to surface tractions and electric displacements on the top and bottom surfaces the procedure combines the transfer matrix method with the asymptotic expansion technique the electromechanical coupled formulation is reduced to a hierarchy of problems referred to as a reference plane a closed form solution is obtained for the generalized plane deformations of a piezoelectric laminate with the top and bottom surfaces subjected to uniform electric displacements and mechanical normal tractions and edges at the midplane rigidly clamped and grounded the closed form solution is ohtained because the asymptotic expansion terminates after a few terms for some loadings the in plane electric fields can be much larger than the out of plane electric fields

linear maps preserving products of positive or hermitian matrices abstract in this note we consider linear maps on the complex n n matrix algebra m n preserving products of either two positive matrices a positive matrix and a hermitian matrix or two hermitian matrices we give characterizations of all those injections

maps on matrix algebras preserving idempotents abstract let m n be the algebra of all n n complex matrices and p n the set of all idempotents in m n suppose m n m n is a surjective map satisfying a b p n if and only if a b p n a b m n c then either is of the form a tat 1 a m n or is of the form a ta t t 1 a m n where t m n is a nonsingular matrix

shells with thickness distension abstract a deductive approach to shell theory is presented within which a shell is regarded as a constrained three dimensional continuum with special body structure more precisely admissible deformations are given a restricted form presumed to be consistent with the special shape and partitionability of a shell like body in addition to the standard balance equations of forces and torques an extra balance equation is derived allowing for a description of dilatation or contraction in the thickness dimension as an illustrative application the free oscillations of linearly elastic plates in particular thickness distension waves are studied

preservers of local spectrum of matrix jordan triple products abstract let m n be the space of n n complex matrices and for a nonzero vector e c n and t m n let t e denote the local spectrum of t at e maps on m n which preserve the local spectrum of jordan triple product of matrices at e in a sense that t s t e t s t e t s m n are characterized with no surjectivity assumption on them

preservers of radial unitary similarity functions on products of operators abstract let s be a subset of the algebra l h of all bounded linear operators on an infinite dimensional complex hilbert space h and let f s 0 be a radial unitary similarity invariant function under some assumption on s and f characterizations are obtained for surjective maps on s satisfying f t s f t s t s s where the binary operation stands for the product or the jordan semi triple product on operators analogous descriptions are obtained for the finite dimensional case without the surjectivity assumption on

on grassmannians associated with jb triples then is a complex lie group that has precisely n 1 orbits e0 en in e each er is the locally closed complex submanifold of all matrices of rank r clearly er 1 is in the closure of er for every 1 r n and en is the unique open orbit for every pair of integers p q 0 let gp q be the grassmannian of all p planes in cp q then gp q is a compact symmetric hermitian manifold of dimension pq holomorphically equivalent to gq p every er is in a canonical way a equivariant holomorphic fibre bundle

spectrum preserving linear maps abstract let x and y be banach spaces we show that a spectrum preserving surjective linear map from b x to b y is either of the form t ata 1 for an isomorphism a of x onto y or the form t bt b 1 for an isomorphism b of x onto y

imperfection sensitivity of elastically supported beams and its relation to the double cusp instability model this paper deals with the two mode initial postbuckling analysis of geometrically imperfect beams on elastic foundation under compression by adjusting the beam length to the characteristic length ratio it is found that the resulting two mode stability problem may be classified as the double cusp model in catastrophe theory the appropriate postbuckling coefficients are computed with the use of koiter s theory of elastic stability the equilibrium paths and the critical sets are plotted and analysed eight independent control parameters are suggested the paper is the first in the open literature to apply the double cusp model to a two mode stability problem which displays imperfection sensitivity

lipschitz spectrum preserving mappings on algebras of matrices abstract it is proved that for any lipschitz mapping t on the algebra m n of n n matrices over the complex numbers satisfying t 0 0 and t a t b a b a b m n there exists an invertible matrix u m n such the t a uau 1 for all a m n or t a ua t u 1 for all a m n

exact three dimensional elasticity solutions for bending of moderately thick inhomogeneous and laminated strips under normal pressure abstract an exact three dimensional solution is presented for the deformation and stress distribution in a semi infinite strip clamped along its two edges and subjected to uniform normal loading of the lateral surfaces the strip is of constant moderate thickness and composed of anisotropic elastic material which is arbitrarily inhomogeneous in the through thickness direction the only material symmetry assumed is that of reflectional elastic symmetry in planes parallel to the mid plane the important special case of an anisotropic laminated plate is given by assuming piecewise constant properties through the thickness the general method of solution is to reformulate the full three dimensional elasticity equations in a way that reduces the problem to solving a system of partial differential equations in the two in plane independent variables only and then obtaining asymptotic solutions in terms of an aspect ratio of the thickness divided by a typical in plane length in general successive terms are expressed in terms of the approximate classical laminate solution in the present problem this solution is very simple and the expansion terminates after no more than three terms this gives a closed form analytical solution that is valid for any aspect ratio

preservers of pseudo spectral radius of operator products abstract let h be an infinite dimensional complex hilbert space and let l h be the algebra of all bounded linear operators on h for e 0 and t l h let r e t denote the e pseudo spectral radius of t we characterize surjective maps on l h which satisfy r e t s r e t s for all t s l h we also obtain analogous result for the finite dimensional case without the surjectivity assumption on

three dimensional electromechanical responses of a parallel piezoelectric bimorph this paper proposes a three dimensional study for parallel piezoelectric bimorphs which are used commonly as sensors and actuators firstly a general analysis is performed based on the state space formulation combined with an asymptotic expansion technique by properly truncating the expansions a analytical expressions for the three dimensional distributions of electric and mechanical fields in the bimorph is obtained in terms of the displacements on the mid plane these displacements are governed by two dimensional equations formally similar to those in the classical plate theory thus a three dimensional solution to the bimorph generates directly provided the two dimensional equations are solved as an example a piezoelectric cantilever bender with a clamped edge is considered and detailed numerical results are illustrated

linear rank and corank preserving maps on b h and an application to semigroup isomorphisms of operator ideals abstract we characterize linear rank k nonincreasing rank k preserving and corank k preserving maps on b h the algebra of all bounded linear operators on the hilbert space h this unifies and extends finite dimensional results and results on linear rank 1 non increasing and rank 1 preserving maps in the infinite dimensional case we conclude with an application to semigroup isomorphisms of operator ideals

an exact three dimensional solution for normal loading of inhomogeneous and laminated anisotropic elastic plates of moderate thickness an exact three dimensional solution is presented for the deformation and stress distribution in an elliptical plate under uniform normal loading of the lateral surfaces and clamped along its edge the plate is assumed to be of constant moderate thickness and composed of anisotropic elastic material which is inhomogeneous in the through thickness direction but symmetric about the mid plane the only material symmetry assumed is that of reflectional symmetry in planes parallel to the mid plane a transfer matrix method is used which without making any further assumptions gives the exact solution at each point in the plate in terms of the stress and displacement at the mid plane the two dimensional differential equations governing these mid plane values are found to be the same as those for an equivalent homogeneous plate whose constant elastic moduli are determined by appropriate through thickness weighted averages of the inhomogeneous moduli the solution of the two dimensional problem is known for such a plate when subject to the specified surface and edge conditions and yields a closed form analytical solution that satisfies all the governing equations and surface conditions of the full three dimensional elasticity problem with edge displacement conditions satisfied on the mid plane the important special case of an anisotropic laminated plate is given by assuming piecewise constant properties through the thickness

spectrum preserving additive maps abstract let x and y be complex banach spaces we show that a spectrum preserving surjective additive map from b x to b y is either of the form f ata 1 for a linear isomorphism a of x onto y or of the form t bt b 1 for a linear isomorphism b of x onto y

a new approach to stress analysis of anisotropic laminated elastic cylinders we propose a new numerical method for the determination of stress and deformation in laminated and inhomogeneous anisotropic elastic and thermoelastic plates and shells the method determines numerical solutions of the three dimensional elasticity equations without recourse to any thin plate or shell approximations it is based on a transfer matrix formulation of the elasticity equations and proceeds by using finite difference approximations to derivatives in the in surface coordinate directions while retaining the derivatives in the through thickness direction this leads to a system of linear first order differential equations for the through thickness values at the grid points of the relevant stress and displacement variables these equations are solved numerically by standard methods in this paper we consider the specific problem of an anisotropic laminated circular thermoelastic cylinder in plane strain but various other problems may be formulated in a similar way we present numerical solutions to four test problems for a laminated circular cylinder under i sinusoidally varying internal pressure ii mixed boundary conditions with a through thickness temperature variation iii a spatially discontinuous internal pressure and iv both angular and radial temperature variation for problems i ii and iv analytical solutions are also derived and excellent agreement between the numerical and analytical solutions is obtained

a series solution of the exact equation for thick orthotropic plates by considering three dimensional elasticity without any initial assumptions the authors obtain the state equations for an orthotropic body a series solution for a simply supported rectangular thick plate with arbitrary ratio between thickness and width under any given load is presented every fundamental equation of three dimensional elasticity can be exactly satisfied and all the nine elastic constants can also be taken into account by the present method numerical results are obtained and compared with those of reissner s and ambartsumyan s theories and some references

maps on matrices that preserve the spectrum abstract let t be a continuous map of the space of complex n n matrices into itself satisfying t 0 0 such that the spectrum of t x t y is always a subset of the spectrum of x y there exists then an invertible n n matrix u such that either t a uau 1 for all a or t a ua t u 1 for all a we arrive at the same conclusion by supposing that the spectrum of x y is always a subset of the spectrum of t x tt y without the continuity assumption on t

on positive linear maps preserving invertibility theorem a positive linear map 4 between two c algebras is a jordan homomorphism if d preserves invertibility and the range of is a c algebra a counterexample is given for the case that the range of q is not assumed to be a c algebra this answers a question raised by b russo proc amer math sot 17