continuum modeling of the mechanical and thermal behavior of discrete large structures in the present paper we introduce a rather straightforward construction procedure in order to derive continuum equivalence of discrete truss like repetitive structures once the actual structure is specified the construction procedure can be outlined by the following three steps a all sets of parallel members are identified b unidirectional effective continuum properties are derived for each of these sets and c orthogonal transformations are finally used to determine the contribution of each set to the overall effective continuum properties of the structure here the properties includes mechanical stiffnesses thermal coefficients of thermal expansions and material densities once expanded descriptions of the steps b and c are done the construction procedure will be applied to a wide variety of discrete structures and the results will be compared with those of other existing methods

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

an alternative daugavet property abstract we introduce a strictly weaker version of the daugavet property as follows a banach space x has this alternative daugavet property adp in short if the norm identity ade max 1 id t 1 t holds for all rank one operators t x x in such a case all weakly compact operators on x also satisfy ade we give some geometric characterizations of the alternative daugavet property in terms of the space and its successive duals we prove that the adp is stable for c0 l1 and l sums and characterize when some vector valued function spaces have the property finally we show that a c algebra or the predual of a von neumann algebra has the adp if and only if its atomic projection respectively the atomic projection of the algebra are central we also establish some geometric properties of jb triples and characterize jb triples possessing the adp and the daugavet property

the daugavet equation for polynomials on c algebras abstract in this paper we study the daugavet equation and the alternative daugavet equation for polynomials on c algebras we study separately the cases in which the c algebras are commutative and non commutative in these cases we obtain necessary and sufficient conditions on such c algebras in order that certain polynomial classes satisfy the daugavet equation and the alternative daugavet equation

a new smoothness result for caputo type fractional ordinary differential equations abstract we present a new smoothness result for caputo type fractional ordinary differential equations which reveals that subtracting a non smooth function that can be obtained by the information available a non smooth solution belongs to cm for some positive integer m

the daugavet equation for operators on function spaces abstract we prove the norm identity id t 1 t which is known as the daugavet equation for weakly compact operators t on natural function spaces such as function algebras and l 1 predual spaces provided a non discreteness assumption is met we also consider c 0 factorable operators and operators on c spaces

local and nonlocal continuum modeling of inelastic periodic networks applied to stretching dominated trusses we present a nonlocal continuum model and its numerical implementation to describe the macroscale response of periodic discrete networks via second order homogenization the scale bridging technique is applied to the specific example of stretching dominated elastic and inelastic periodic truss networks experiments on small scale truss structures have highlighted the importance of nodal connections on the effective stiffness and strength therefore we describe the mechanics of trusses by accounting for the stretching of truss members and the deformation of nodes for the representative 2d examples of lattices having square and triangular architectures and for example bar and nodal constitutive laws we show that a simple continuum model based on affinely deforming a representative unit cell is sufficient to reproduce the nonlinear elastic behavior of discrete trusses by contrast localization that arises e g from inelastic deformation requires a refined model this is where the presented nonlocal continuum model is capable of accurately capturing details of localized deformation we illustrate the performance of the model by comparing the results of example finite element simulations using the continuum constitutive model to discrete lattice calculations with elastic plastic bars optimal performance is achieved when the representative unit cell of the continuum model agrees with the actual size of the discrete truss unit cell which accounts for size effects even in regimes where a separation of scales between finite element size and unit cell size does not strictly apply

the three space problem for l 1 we construct a subspace x of l1 such that x is an 1 sum of spaces isomorphic to 11 but such that l1 x does not contain a copy of l1 we also construct two banach spaces e1 e2 that do not contain a copy of li but such that e1 x e2 contains a copy of l1 moreover the projections this content downloaded from 207 46 13 150 on thu 28 jul 2016 05 31 04 utc all use subject to http about jstor org terms the three space problem for l 29 of li on each factor are one to one and the images of the unit ball of l1 are closed these examples settle questions of j lindenstrauss p pelczynski j bourgain and h p rosenthal equipe d analyse tour 46 u a au c n r s n0 754 universitt paris vi 4 place jussieu 75230 paris cedex 05 department of mathematics ohio state university 231 w 18th avenue columbus ohio 43210 this content downloaded from 207 46 13 150 on thu 28 jul 2016 05 31 04 utc all use subject to http about jstor org terms

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

lushness numerical index one and duality we construct an example of a banach space which is not lush but whose dual space is lush this example shows that lushness is not equivalent to numerical index one a characterization of lushness for some quotient spaces of l1 spaces and new results on c rich subspaces of scalar or vector valued c k spaces are also presented

asymptotically isometric copies of c0 and l1 in bochner spaces abstract let x be a banach space and be a finite measure space it is shown that if 1 p resp 1 p l p x contains asymptotically isometric copies of c 0 resp l 1 if and only if x does

dynamic continuum modeling of beamlike space structures using finite element matrices subscripts a rational and straight forward method is introduced for developing equivalent continuum models of large beam like periodic lattice structures based on energy equivalence extended timoshenko bean model is chosen to take account of the effects due to couplings between extension transverse shear and bending deformations the procedure for developing continuum models involves utilizing well defined existing finite element matrices directly in caluclating strain and kinetic energies from which equivalent continuum structural and dynamic properties are induced the numerical results of free vibration analysis show that the method developed in this paper gives very reliable dynamic characteristics compared to other methods nomenclature

smoothness and stability of the solutions for nonlinear fractional differential equations this paper first obtains the differentiability properties of the solutions for nonlinear fractional differential equations and then the sufficient conditions for the local asymptotical stability of nonlinear fractional differential equations are also derived

equivalent continuum models of large platelike lattice structures abstract a new continuum method based on the concept of energy equivalence is introduced to represent a large platelike periodic lattice structure as an equivalent continuum plate the procedure for developing an equivalent continuum plate involves the use of existing well defined finite element matrices for easy calculation of strain and kinetic energies contained in a representative lattice cell of the lattice plate the strain and kinetic energies contained in the representative lattice cell of lattice plate and the finite element of equivalent continuum plate are expressed in terms of continuum degrees of freedom introduced in this paper with corresponding reduced stiffness and mass matrices the structural properties of the equivalent continuum plate are then obtained by simply equating the reduced stiffness and mass matrices for the equivalent continuum plate to those for the lattice plate free vibration analyses for the continuum plates are conducted to evaluate the continuum method proposed in this paper numerical tests show that the present continuum method gives very reliable structural and dynamic properties compared with other well recognized continuum methods

the daugavet equation in uniformly convex banach spaces abstract it is shown that a continuous operator t x x on a uniformly convex banach space satisfies the daugavet equation i t 1 t if and only if the norm t of the operator lies in the spectrum of t specializing this result to compact operators we see that a compact operator on a uniformly convex banach space satisfies the daugavet equation if and only if its norm is an eigenvalue the latter conclusion is in sharp contrast with the standard facts on the daugavet equation for the spaces l 1 and l a discussion of the daugavet property in the latter spaces is also included in the paper

some geometric properties of disk algebras abstract in this paper we study some geometrical properties of certain classes of uniform algebras in particular the ball algebra a u b x of all uniformly continuous functions on the closed unit ball and holomorphic on the open unit ball of a complex banach space x we prove that a u b x has k numerical index 1 for every k the lushness and also the ahsp moreover the disk algebra a d and more in general any uniform algebra whose choquet boundary has no isolated points is proved to have the polynomial daugavet property most of those properties are extended to the vector valued version a x of a uniform algebra a

a characterisation of the daugavet property in spaces of lipschitz functions abstract we study the daugavet property in the space of lipschitz functions lip 0 m on a complete metric space m namely we show that lip 0 m has the daugavet property if and only if m is a length metric space this condition also characterises the daugavet property in the lipschitz free space f m moreover when m is compact we show that either f m has the daugavet property or its unit ball has a strongly exposed point if m is an infinite compact subset of a strictly convex banach space then the daugavet property of lip 0 m is equivalent to the convexity of m

homogenization and equivalent in plane properties of two dimensional periodic lattices abstract the equivalent in plane properties for hexagonal and re entrant auxetic lattices are investigated through the analysis of partial differential equations associated with their homogenized continuum models the adopted homogenization technique interprets the discrete lattice equations according to a finite differences formalism and it is applied in conjunction with the finite element description of the lattice unit cell it therefore allows handling of structures with different levels of complexity and internal geometry within a general and compact framework which can be easily implemented the estimation of the mechanical properties is carried out through a comparison between the derived differential equations and appropriate elasticity models equivalent young s moduli poisson s ratios and relative density are estimated and compared with analytical formulae available in the literature in plane wave propagation characteristics of honeycombs are also investigated to evaluate phase velocity variation in terms of frequency and direction of propagation comparisons are performed with the values obtained through the application of bloch theorem for two dimensional periodic structures to show the accuracy of the technique and highlight limitations introduced by the long wavelength approximation associated with the homogenization technique

banach spaces with the daugavet property a banach space x is said to have the daugavet property if every operator t x x of rank 1 satisfies 11 id tl 1 fltil we show that then every weakly compact operator satisfies this equation as well and that x contains a copy of t1 however x need not contain a copy of l1 we also study pairs of spaces x c y and operators t x y satisfying i i j t i i 1 4 1f t i i where j x y is the natural embedding this leads to the result that a banach space with the daugavet property does not embed into a space with an unconditional basis in another direction we investigate spaces where the set of operators with f id tll 1 il t l i is as small as possible and give characterisations in terms of a smoothness condition