axisymmetric vibration of a circular plate with double linear variable thickness abstract the rayleigh ritz method has been employed to study the axisymmetric transverse vibration of a circular plate with two different linear variations in thickness one in the central core and the other in the outer annular region the boundary has been taken either clamped or simply supported results for linearly varying thickness and uniform thickness have been obtained as special cases and are compared with those available in the literature the effects of the various parameters on the frequencies mode shapes and the nodal radii have been examined through extensive numerical results given in the form of graphs and tables

superprojective banach spaces we study superprojective banach spaces we show that they cannot contain copies of l1 which restricts the search for non reflexive examples of these spaces we also show that the class of superprojective spaces is stable under finite products certain unconditional sums certain tensor products and other operations providing new examples

the perturbation classes problem for subprojective and superprojective banach spaces abstract we show that the perturbation class for the upper semi fredholm operators between two banach spaces x and y coincides with the strictly singular operators when x is subprojective and that the perturbation class for the lower semi fredholm operators coincides with the strictly cosingular operators when y is superprojective similar results were previously obtained under stronger conditions for x and y

free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule the generalized differential quadrature rule proposed recently by these authors is applied here to the free vibration analyses of solid circular plates with radially varying thickness and elastic restraints the thickness can vary radially in any given continuous form and it varies exponentially and linearly in this work two regularity conditions corresponding to the plate center are expressed in explicit formulae since they have been inexactly or even wrongly expressed in the literature such errors are pointed out in the application of the differential quadrature techniques and in the expression of the regularity conditions at the plate center numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

quantities characterizing semi fredholm operators and perturbation radii abstract we show that none of the operational quantities that have been introduced to characterize the upper or the lower semi fredholm operators is equivalent to the corresponding perturbation radius

a new approach to the differential quadrature method for fourth order equations a generalized and more complete methodology for treating boundary conditions in the differential quadrature method dqm is presented this improved approach eliminates the deficiencies of the type grid arrangement which represents an approximation by applying the boundary conditions exactly two kinds of basis functions chebyshev and lagrange are used for concept demonstration it is found that the new approach cures most deficiencies of the current dqm 1997 by john wiley sons ltd

free vibration of plates by the high accuracy quadrature element method in this paper a highly accurate and rapidly converging hybrid approach is presented for the quadrature element method qem solution of plate free vibration problems the hybrid qem essentially consists of a collocation method in conjunction with a galerkin finite element technique to combine the high accuracy of the differential quadrature method dqm for the efficient solution of differential equations with the generality of the finite element formulation this results in superior accuracy with fewer degrees of freedom than conventional fem or fdm a series of numerical tests is conducted to assess the performance of the quadrature plate element in free vibration problems anisotropic and stepped thickness plates are investigated as well as mixed boundary conditions and point supports at the edges in all cases the results obtained are quite accurate

transverse vibrations of circular plates and membranes with intermediate supports the present paper deals with an approximate solution of the title problem in the case of a a concentric circular support and b a secant support fundamental frequency coefficients are determined by means of the rayleigh minimization procedure the modal shapes been approximated by simple polynomial co ordinate functions in the case of a circular plate with a secant support an independent solution is obtained by means of a finite element code and very good agreement is shown to exist

the spectral rigidity of complex projective spaces revisited a classical question in spectral geometry is for each pair of nonnegative integers p n such that p le 2n if the eigenvalues of the laplacian on p forms of a compact kahler manifold are the same as those of mathbb c p n equipped with the fubini study metric then whether or not this kahler manifold is holomorphically isometric to mathbb c p n for every positive even number p we affirmatively solve this problem in all dimensions n with at most two possible exceptions we also clarify in this paper some gaps in previous literature concerned with this question among which one is related to the volume estimate of fano kahler einstein manifolds

an integral inequality for constant scalar curvature metrics on kahler manifolds abstract we present in this note a lower bound for the calabi functional in a given kahler class this yields an integral inequality for constant scalar curvature metrics which can be viewed as a refinement of s t yau s chern number inequality from the einstein metric case to constant scalar curvature metric case

obstructions to the existence of sasaki einstein metrics we describe two simple obstructions to the existence of ricci flat kahler cone metrics on isolated gorenstein singularities or equivalently to the existence of sasaki einstein metrics on the links of these singularities in particular this also leads to new obstructions for kahler einstein metrics on fano orbifolds we present several families of hypersurface singularities that are obstructed including 3 fold and 4 fold singularities of ade type that have been studied previously in the physics literature we show that the ads cft dual of one obstruction is that the r charge of a gauge invariant chiral primary operator violates the unitarity bound

application of generalized differential quadrature rule in blasius and onsager equations the generalized differential quadrature rule gdqr proposed recently by the authors is applied here to third order non linear differential equations of the blasius type and to sixth order linear onsager differential equations high 3rd order differential equations in fluid mechanics are dealt with without using point techniques the half space domain is simplified in a practical way accurate results are obtained for both kinds of problems the wide applicability of the gdqr in high order differential equations is manifested further through this work copyright 2001 john wiley sons ltd

transverse vibrations of a circular annular plate with an intermediate circular support and a free inner edge the present study deals with the determination of the fundamental frequency of transverse vibration

vibrating circular plates with stepped thickness over a concentric circular region a general approximate solution natural frequencies corresponding to axi and antisymmetric modes of vibration of the structural elements described in the title are studied using the optimized rayleigh ritz approach it is assumed that the plates are elastically restrained against translation and rotation the plate amplitude is approximated in terms of polynomial coordinate functions that satisfy the boundary conditions each one containing an undetermined exponential parameter that allows for the minimization of the eigenvalues under investigation

examples of improjective operators it has been an open question for some time whether improjective operators are always inessential here we give some examples that answer in the negative this question as well as some other related ones posed in 2 3 11 12 the description of the examples uses a indecomposable space constructed by gowers and maurey 5 and a characterization of the indecomposable banach spaces in terms of improjective operators

the unconditional basic sequence problem we construct a banach space that does not contain any infinite un conditional basic sequence and investigate further properties of this space for example it has no subspace that can be written as a topological direct sum of two infinite dimensional spaces this property implies that every operator on the space is a strictly singular perturbation of a multiple of the identity in par ticular it is either strictly singular or fredholm with index zero this implies that the space is not isomorphic to any proper subspace trinity college cambridge cb2 1tq england current address department of mathematics university college london gower street lon don wc1e 6bt england e mail address wtg l o phx cam ac uk universit paris vii u f r de mathtmatiques 2 place jussieu 75251 paris cedex 05 france current address equipe d analyse et mathematiques appliquees universite de mamne la vallee 93160 noisy le grand france e mail address maurey logiquejussieu fr this content downloaded from 157 55 39 105 on fri 07 oct 2016 04 30 48 utc all use subject to http about jstor org terms

fredholm theory for pairs of closed subspaces of a banach space we study the fredholm theory for pairs of closed subspaces of a banach space developed by kato we define the strictly singular and the strictly cosingular pairs of subspaces and we show that some of the results of operator theory can be extended to this context however there are some notable differences on the one hand the perturbation classes problem has a positive answer in this context the upper and lower semi fredholm pairs are stable under strictly singular and strictly cosingular perturbations respectively and this stability characterizes the strictly singular and the strictly cosingular pairs note that it has been proved recently that the perturbation classes problem for continuous semi fredholm operators has a negative answer on the other hand unlike in the case of operators the fredholm pairs are not stable under perturbation by strictly singular or strictly cosingular pairs we also show the stability under composition of the compact the strictly singular and the strictly cosingular pairs of subspaces

on essentially incomparable banach spaces we introduce the concept of essentially incomparable banach spaces and give some examples then for two essentially incomparable banach spaces x and y we prove that a complemented subspace of the product x x y is isomorphic to the product of a complemented subspace of x and a complemented subspace of y if additionally x and y are isomorphic to their respective hyperplanes then the group of invertible operators in x x y is not connected the results can be applied to some classical banach spaces

the perturbation classes problem in fredholm theory abstract we give a negative answer to the perturbation classes problem the perturbation class of the upper semi fredholm operators contains properly the strictly singular operators and the perturbation class of the lower semi fredholm operators contains properly the strictly cosingular operators

on the lateral vibration of thin annular and circular composite plates subject to certain complicating effects abstract series comprising orthogonally generated polynomial functions are used in the rayleigh ritz method to obtain an eigenvalue equation for the flexural vibration of thin flat annular and circular plates the plates may be of isotropic or polar orthotropic material of uniform or radially varying thickness and may pass over intermediate concentric ring supports numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

perturbation classes for semi fredholm operators on lp μ spaces abstract we study the perturbation class p l p y for the upper semi fredholm operators when l p y is non empty we show that it coincides with the strictly singular operators when 1 p 2 and y satisfies certain condition and when 2 p and y is arbitrary as a consequence we derive similar results for p x l q when 1 q

differential quadrature for multi dimensional problems the technique of differential quadrature for the solution of partial differential equations introduced by bellman et al is extended and generalized to encompass partial differential equations involving multiple space variables approximation formulae for a variety of first and second order partial derivatives and typical weighting coefficients are presented application of these formulae is demonstrated on the solution of the convection diffusion equation for the two and three dimensional space dependent cases and for both the transient and steady state dispersion of inert neutrally buoyant pollutants from continuous sources into an unbounded atmosphere

perturbation classes of semi fredholm operators in banach lattices abstract we prove some results giving positive answers to the perturbation classes problem for semi fredholm operators acting on banach lattices satisfying certain conditions and we show that these results can be applied to some lorentz and orlicz function spaces

lifting non topological divisors of zero modulo the compact operators this paper provides the first examples of non semifredholm operators s on a banach space such that the left or right multiplication operators r sr or r rs define linear embeddings of the corresponding calkin algebra into itself for instance if s is a bounded linear operator on c 0 1 with closed range such that ker s l1 then there is a constant c 0 with dist sr k c 0 1 c dist r k c 0 1 for all bounded operators r l c 0 1 here k c 0 1 stands for the compact operators on c 0 1 moreover if s l1 l1 has closed range and l1 im s contains no copies of l1 then there is a constant c 0 such that dist rs w l1 c dist r w l1 for all r l l1 here w l1 denotes the weakly compact operators on l1