geometric aspects of the daugavet property let x be a closed subspace of a banach space y and j be the inclusion map we say that the pair x y has the daugavet property if for every rank one bounded linear operator t from x to y the following equality kj tk 1 ktk 1 holds a new characterization of the daugavet property in terms of weak open sets is given it is shown that the operators not xing

on the super fixed point property in product spaces abstract we prove that if f is a finite dimensional banach space and x has the super fixed point property for nonexpansive mappings then f x has the super fixed point property with respect to a large class of norms including all l p norms 1 p this provides a solution to the super version of the problem of khamsi 1989

the dunford pettis and the kadec klee properties on tensor products of jb triples we recall that a banach spacex satisfies the dunford pettis property dpp if every weakly compact operator t from x to another banach space is completely continuous i e t maps weakly cauchy sequences into norm convergent sequences the question if the projective tensor product of two banach spaces having the dpp also has this property has focused the attention of several researcher in 1983 m talagrand found a banach space x such that x has the schur property and l1 0 1 e does not satisfy the dpp see 34 four years latter r ryan showed that x y satisfies the dpp and contains no copies of 1 whenever x and y have both properties 33 f bombal and i villanueva prove in 7 see also 6 20 that whenever k1 and k2 are two infinite compact hausdorff spaces then the projective tensor product of c k1 and c k2 has the dpp if and only if k1 and k2 are scattered that is c k1 and c k2 contains no copies of 1 the interesting ideas developed by bombal fernandez and villanueva in 7 6 are the inspiration and the starting point for the present paper in the

a kohn sham equation solver based on hexahedral finite elements we design a kohn sham equation solver based on hexahedral finite element discretizations the solver integrates three schemes proposed in this paper the first scheme arranges one a priori locally refined hexahedral mesh with appropriate multiresolution the second one is a modified mass lumping procedure which accelerates the diagonalization in the self consistent field iteration the third one is a finite element recovery method which enhances the eigenpair approximations with small extra work we carry out numerical tests on each scheme to investigate the validity and efficiency and then apply them to calculate the ground state total energies of nanosystems c 6 0 c 1 2 0 and c 2 7 5h 1 7 2 it is shown that our solver appears to be computationally attractive for finite element applications in electronic structure study

uniform smoothness implies super normal structure property we prove that a uniformly smooth banach space x has supernormal structure property more precisely we prove that if the modulus of smoothness of x satisfies lim 0 x 1 2 then x and x are superreflexives and have super normal structure property

quiet direct simulation monte carlo with random timesteps use of a high order deterministic sampling technique in direct simulation monte carlo dsmc simulations eliminates statistical noise and improves computational performance by orders of magnitude in this paper it is also shown that if a random timestep is used in place of a fixed timestep there is an additional improvement in performance this performance can be increased by using a timestep that samples a random variable with a high kurtosis probability density function as a simple example of the method the one dimensional diffusion equation with an exponentially distributed timestep is simulated and a performance gain of approximately two is obtained applications to numerical simulations of fluids and plasmas are indicated

low rank compact operators and tingley s problem abstract let e and b be arbitrary weakly compact jb triples whose unit spheres are denoted by s e and s b respectively we prove that every surjective isometry f s e s b admits an extension to a surjective real linear isometry t e b this is a complete solution to tingley s problem in the setting of weakly compact jb triples among the consequences we show that if k h k denotes the space of compact operators between arbitrary complex hilbert spaces h and k then every surjective isometry f s k h k s k h k admits an extension to a surjective real linear isometry t k h k k h k

relatively weakly open sets in closed balls of banach spaces and real jb triples of finite rank we prove that given a real jb triple x there exists a nonempty relatively weakly open subset of the closed unit ball of x with diameter less than 2 if and only if the banach space of x is isomorphic to a hilbert space moreover we give the structure of real jb triples whose banach spaces are isomorphic to hilbert spaces such real jb triples are also characterized in two different purely algebraic ways

local and parallel finite element discretizations for eigenvalue problems based on the work of xu and zhou math comp 69 2000 pp 881 909 this paper combines the local defect correction technique and the shifted inverse power method to establish new local and parallel finite element three scale schemes for a class of eigenvalue problems it is proved that with these schemes the solution of an eigenvalue problem on a fine grid pi h is reduced to the solution of an eigenvalue problem on a much coarser grid pi h the solution of a linear algebraic system on a globally mesoscopic grid pi w and the solutions of linear systems on several locally fine grids in parallel the principle to determine the diameters of three different scale grids is given especially this paper devises a new local and parallel finite element multiscale discretization scheme theoretical analysis and numerical experiments show that the computational approach proposed in this paper is simple and easy to carry out and can be used to solve singular eigenvalue problems efficiently

the daugavet property of c algebras jb triples and of their isometric preduals a banach space x is said to have the daugavet property if every rank one operator t x x satisfies id t 1 t we give geometric characterizations of this property in the settings of c algebras jb triples and their isometric preduals we also show that in these settings the daugavet property passes to ultrapowers and thus it is equivalent to an stronger property called the uniform daugavet property

convergence and optimal complexity of adaptive finite element eigenvalue computations in this paper an adaptive finite element method for elliptic eigenvalue problems is studied both uniform convergence and optimal complexity of the adaptive finite element eigenvalue approximation are proved the analysis is based on a certain relationship between the finite element eigenvalue approximation and the associated finite element boundary value approximation which is also established in the paper

separate weak continuity of the triple product in dual real jb triples we prove that if e is a real jb triple having a predual e then e is the unique predual of e and the triple product on e is separately sigma e e continuous

on super fixed point property and super weak compactness of convex subsets in banach spaces abstract for a nonempty convex set c of a banach space x a self mapping on c is said to a linear respectively affine isometry if it is the restriction of a linear respectively affine isometry defined on the whole space x by means of super weakly compact set theory established in the recent years in this paper we first show that a nonempty closed bounded convex set of a banach space has super fixed point property for affine or equivalently linear isometries if and only if it is super weakly compact and the super fixed point property and the super weak compactness coincide on every closed bounded convex subset of a banach space under equivalent renorming sense with the application of fabian montesinos zizler s renorming theorem we finally show that every strongly super weakly compact generated banach space can be renormed so that every weakly compact convex set has super fixed point property

grothendieck s inequalities for real and complex jbw triples we prove that if m 4 1 2 3 and e 0 if v and w are complex jbw triples with preduals v andw respectively and if u is a separately weak continuous bilinear form on v w then there exist norm one functionals 1 2 v and 1 2 w satisfying u x y m u x 2 2 e 2 x 2 1 1 2 y 2 2 e 2 y 2 1 1 2 for all x y v w here for a norm one functional on a complex jb triple v stands for the prehilertian seminorm on v associated to in bf1 we arrive in this grothendieck s inequality through results of c h chu b iochum and g loupias cil and a corrected version of the little grothendieck s inequality for complex jb triples due to t barton and y friedman bf1 we also obtain extensions of these results to the setting of real jb triples 2000 mathematics subject classification 17c65 46k70 46l05 46l10 and 46l70

efficient numerical solution of stochastic differential equations using exponential timestepping we present an exact timestepping method for brownian motion that does not require gaussian random variables to be generated time is incremented in steps that are exponentially distributed random variables boundaries can be explicitly accounted for at each timestep the method is illustrated by numerical solution of a system of diffusing particles

a defect correction method for unsteady conduction convection problems ii time discretization in this paper a fully discrete defect correction mixed finite element method mfem for solving the non stationary conduction convection problems in two dimension which is leaded by combining the back euler time discretization with the two step defect correction in space is presented in this method we solve the nonlinear equations with an added artificial viscosity term on a finite element grid and correct these solutions on the same grid using a linearized defect correction technique the stability and the error analysis are derived the theory analysis shows that our method is stable and has a good convergence property some numerical results are also given which show that this method is highly efficient for the unsteady conduction convection problems

an exponential timestepping algorithm for diffusion with discontinuous coefficients abstract we present a new monte carlo algorithm to simulate diffusion processes in presence of discontinuous convective and diffusive terms the algorithm is based on the knowledge of close form analytic expressions of the resolvents of the diffusion processes which are usually easier to obtain than close form analytic expressions of the density in the case of diffusion processes with piecewise constant coefficients known as skew diffusions such close form expressions for the resolvent are available then we apply our algorithm to this particular case and we show that the approximate densities of the particles given by the algorithm replicate the particularities of the true densities well discontinuities bimodality besides numerical experiments show a quick convergence

a low variance deviational simulation monte carlo for the boltzmann equation we present an efficient particle method for solving the boltzmann equation the key ingredients of this work are the variance reduction ideas presented in baker and hadjiconstantinou l l baker n g hadjiconstantinou variance reduction for monte carlo solutions of the boltzmann equation physics of fluids 17 2005 art no 051703 and a new collision integral formulation which allows the method to retain the algorithmic structure of direct simulation monte carlo dsmc and thus enjoy the numerous advantages associated with particle methods such as a physically intuitive formulation computational efficiency due to importance sampling low memory usage no discretization in velocity space and the ability to naturally and accurately capture discontinuities in the distribution function the variance reduction achieved by simulating only the deviation from equilibrium results in a significant computational efficiency advantage for low signal flows e g low flow speed compared to traditional particle methods such as dsmc in particular the resulting method can capture arbitrarily small deviations from equilibrium at a computational cost that is independent of the magnitude of this deviation the method is validated by comparing its predictions with dsmc solutions for spatially homogeneous and inhomogeneous problems

exponential timestepping with boundary test for stochastic differential equations we present new numerical methods for scalar stochastic differential equations successive time increments are independent random variables with an exponential distribution we perform numerical experiments using a double well potential exponential timestepping algorithms are efficient for escape time problems because a simple boundary test can be performed at the end of each step

a defect correction scheme for finite element eigenvalues with applications to quantum chemistry to produce highly accurate approximations for self adjoint elliptic eigenvalues we propose a finite element defect correction scheme its efficiency is proven by theoretical and numerical evidence very satisfying applications in computational quantum chemistry are also presented

on multiplicatively closed subsets of normed algebras abstract it is well known that if s is a bounded and multiplicatively closed subset of an associative normed algebra a then there exists an equivalent algebra norm on a such that s 1 for every s s although associativity is not an essential requirement in this result it is easy to find examples of nonassociative normed algebras a where such a result fails actually it can fail even if the subset s is reduced to a nonzero idempotent we prove that it remain true in the nonassociative setting whenever the subset s is assumed to be contained in the nucleus of a in the particular case that the subset s reduces to a nonzero nuclear idempotent p we show that the equivalent algebra norm above can be chosen so that p becomes a strongly exposed point of the closed unit ball of a we study those possibly nonassociative normed algebras a satisfying the norm one boundedness property in short nbp which means that as happened in the associative case for every bounded and multiplicatively closed subset s of a there exists an equivalent algebra norm on a such that s 1 for every s s we show that absolute valued algebras jb algebras and nilpotent normed algebras fulfil the nbp we also show that if an anti commutative complete normed algebraic algebra a satisfies the nbp then there exists n n such that l a n 0 for every a a where l a denotes the operator of left multiplication by a it follows from a celebrated theorem of e i zel manov on the so called engel lie algebras that a complete normed algebraic lie algebra satisfies the nbp if and only if it is nilpotent

uniformly nonsquare banach spaces have the fixed point property for nonexpansive mappings abstract it is shown that if the modulus x of nearly uniform smoothness of a reflexive banach space satisfies x 0 1 then every bounded closed convex subset of x has the fixed point property for nonexpansive mappings in particular uniformly nonsquare banach spaces have this property since they are properly included in this class of spaces this answers a long standing question in the theory

local averaging based a posteriori finite element error control for quasilinear elliptic problems with application to electrical potential computation abstract in this paper the local averaging based a posteriori finite element error control for a class of nonlinear elliptic equations is investigated it is shown by both theory and practice that the error control is reliable and the associated adaptive computation is efficient for problems with smooth data it is also shown by numerical experiments that the error control can be successfully applied to a class of poisson boltzmann equations of which the data is not so smooth

enhancing eigenvalue approximation by gradient recovery the polynomial preserving recovery ppr is used to enhance the finite element eigenvalue approximation remarkable fourth order convergence is observed for linear elements under structured meshes as well as unstructured initial meshes produced by the delaunay triangulation with the conventional bisection refinement

three scale finite element discretizations for quantum eigenvalue problems based on globally and locally coupled discretizations some three scale finite element schemes are proposed in this paper for a class of quantum eigenvalue problems it is shown that the solution of a quantum eigenvalue problem on a fine grid may be reduced to the solution of an eigenvalue problem on a relatively coarse grid and the solutions of linear algebraic systems on a globally mesoscopic grid and the locally fine grid and the resulting solution is still very satisfactory

a multilevel correction type of adaptive finite element method for eigenvalue problems an adaptive finite element method for eigenvalue problems is proposed based on the multilevel correction scheme different from the standard adaptive finite element method which requires solving ei

polynomial preserving recovery on boundary in this paper we propose two systematic strategies to recover the gradient on the boundary of a domain the recovered gradient has comparable superconvergent property on the boundary as that in the interior of the domain this superconvergence property has been validated by several numerical experiments

the adaptive finite element method based on multi scale discretizations for eigenvalue problems in this paper adaptive finite element methods for differential operator eigenvalue problems are discussed for multi scale discretization schemes based on rayleigh quotient iteration see scheme 3 in y yang h bi a two grid discretization scheme based on shifted inverse power method siam j numer anal 49 2011 1602 1624 a reliable and efficient a posteriori error indicator is given in addition a new adaptive algorithm based on the multi scale discretizations is proposed and we apply the algorithm to the schrodinger equation for hydrogen atoms the algorithm is performed under the package of chen and satisfactory numerical results are obtained

banach space properties sufficient for normal structure in this paper we establish lower bounds for the weakly convergent sequence coefficient wcs x of a banach space x in terms of some well known moduli and coefficients by mean of these bounds we identify several properties of geometrical nature which imply normal structure we show that these properties are strictly more general than other previously known sufficient conditions for normal structure

sufficient conditions for uniform normal structure of banach spaces and their duals in this paper we present some sufficient conditions for the uniform normal structure of banach spaces and their dual spaces more precisely many known conditions implying the uniform normal structure of banach spaces are shown to imply uniform normal structure of their dual spaces as well

the fixed point property in jb triples and preduals of jbw triples abstract we prove that for every member x in the class of real or complex jb triples or preduals of jbw triples the following assertions are equivalent 1 x has the fixed point property 2 x has the super fixed point property 3 x has normal structure 4 x has uniform normal structure 5 the banach space of x is reflexive as a consequence a real or complex c algebra or the predual of a real or complex w algebra having the fixed point property must be finite dimensional

on the zelmanovian classification of prime jb triples complex jb triples are complex banach spaces endowed with a triple product subjected to suitable conditions of algebraic and analytic nature see section 1 for the definition they were introduced by w kaup in order to provide an algebraic setting for the study of bounded symmetric domains in complex banach spaces the open unit ball of every complex jb triple is a bounded symmetric domain ka1 and every bounded symmetric domain in any complex banach space is bi holomorphically equivalent to the open unit ball of a suitable complex jb triple ka3 fundamental examples of complex jb triples are provided by complex c algebras with triple product defined by xyz x 1 2 xy z zy x 1