finding gaps in a spectrum we propose a method for finding gaps in the spectrum of a differential operator when applied to the one dimensional hamiltonian of the quartic oscillator a simple algebraic algorithm is proposed that step by step separates with a remarkable precision all the energies even for a double well configuration in a tunnelling regime our strategy may be refined and generalised to a large class of 1d problems

vibration analysis of 3 d composite beam elements including warping and shear deformation effects abstract in this paper the dynamic analysis of 3 d composite beam elements restrained at their edges by the most general boundary conditions and subjected in arbitrarily distributed dynamic loading is presented for the solution of the problem at hand a boundary element method is developed for the construction of the 14 14 stiffness matrix and the nodal load vector of a member of an arbitrarily shaped composite cross section taking into account both torsional warping and shear deformation effects which together with the corresponding mass and damping matrices lead to the formulation of the equation of motion to account for shear deformations the concept of shear deformation coefficients is used defining these factors using a strain energy approach eight boundary value problems with respect to the variable along the bar angle of twist to the primary warping function to a fictitious function to the beam transverse and longitudinal displacements and to two stress functions are formulated and solved employing a pure bem approach both free and forced vibrations are considered taking also into account effects of transverse longitudinal rotatory torsional and warping inertia and damping resistance numerical examples are presented to illustrate the method and demonstrate its efficiency and accuracy

nodal sets for groundstates of schrodinger operators with zero magnetic field in non simply connected domains we investigate nodal sets of magnetic schrodinger operators with zero magnetic field acting on a non simply connected domain in 2 for the case of circulation 1 2 of the magnetic vector potential around each hole in the region we obtain a characterisation of the nodal set and use this to obtain bounds on the multiplicity of the groundstate for the case of one hole and a fixed electric potential we show that the first eigenvalue takes its highest value for circulation 1 2

warping shear stresses in nonuniform torsion of composite bars by bem in this paper a complete approximation of the nonuniform torsion problem of composite bars of arbitrary constant cross section using the boundary element method is developed the composite bar consists of a matrix surrounding a finite number of inclusions the materials have different elasticity and shear moduli and are firmly bonded together the bar is subjected to an arbitrarily concentrated or distributed twisting moment while its edges are restrained by the most general linear torsional boundary conditions since warping is prevented beside the saint venant torsional shear stresses the warping normal and shear stresses are also computed three boundary value problems with respect to the variable along the beam angle of twist and to the primary and secondary warping functions are formulated and solved employing a pure bem approach that is only boundary discretization is used both the warping and the torsion constants together with the torsional shear stresses and the warping normal and shear stresses are computed numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy the magnitude of the warping shear stresses due to restrained warping is investigated by numerical examples with great practical interest

counting and sampling h colourings for counting problems in p which are essentially self reducible it is known that sampling and approximate counting are equivalent however many problems of interest do not have such a structure and there is already some evidence that this equivalence does not hold for the whole of p an intriguing example is the class of h colouring problems which have recently been the subject of much study and their natural generalisation to vertex and edge weighted versions particular cases of the counting to sampling reduction have been observed but it has been an open question as to how far these reductions might extend to any h and a general graph g here we give the first completely general counting to sampling reduction for every fixed h we show that the problem of approximately determining the partition function of weighted h colourings can be reduced to the problem of sampling these colourings from an approximately correct distribution in particular any rapidly mixing markov chain for sampling h colourings can be turned into an fpras for counting h colourings

upper and lower bounds for an eigenvalue associated with a positive eigenvector when an eigenvector of a semibounded operator is positive we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue this theorem is a substantial generalization of barta type inequalities and can be applied to non necessarily purely quadratic hamiltonians an application for a magnetic hamiltonian is given and the case of a discrete schrodinger operator is also discussed it is shown how this approach leads to some explicit bounds on the ground state energy of a system made of an arbitrary number of attractive coulombian particles

deep doubly curved multilayered shell theory a two dimensional theory is presented for the analysis of deep doubly curved multilayered shells the theory is based on a kinematical approach in which the continuity conditions for displacements and shear stresses at layer interfaces and on the bounding surfaces of the shell are exactly satisfied it also takes into account refinements of the shear and membrane terms by means of trigonometric functions as proposed previously for the transverse shear the accuracy of the proposed theory is assessed through investigation of significant problems for which an exact three dimensional elasticity solution is known first the bending of a three layered laminated symmetric cross ply rectangular plate simply supported along all edges submitted to a double sinusoidal transverse loading and second the bending of a circular cylindrical panel results obtained with the model are compared with those yielded by previous theories the sensitivity of the model to edge effects for a hard clamped free edge cylindrical panel is also examined

dynamic analysis of 3 d beam elements including warping and shear deformation effects abstract in this paper the dynamic analysis of 3 d beam elements restrained at their edges by the most general linear torsional transverse or longitudinal boundary conditions and subjected in arbitrarily distributed dynamic twisting bending transverse or longitudinal loading is presented for the solution of the problem at hand a boundary element method is developed for the construction of the 14 14 stiffness matrix and the corresponding nodal load vector of a member of an arbitrarily shaped simply or multiply connected cross section taking into account both warping and shear deformation effects which together with the respective mass and damping matrices lead to the formulation of the equation of motion to account for shear deformations the concept of shear deformation coefficients is used defining these factors using a strain energy approach eight boundary value problems with respect to the variable along the bar angle of twist to the primary warping function to a fictitious function to the beam transverse and longitudinal displacements and to two stress functions are formulated and solved employing a pure bem approach that is only boundary discretization is used both free and forced transverse longitudinal or torsional vibrations are considered taking also into account effects of transverse longitudinal rotatory torsional and warping inertia and damping resistance numerical examples are presented to illustrate the method and demonstrate its efficiency and accuracy the influence of the warping effect especially in members of open form cross section is analyzed through examples demonstrating the importance of the inclusion of the warping degrees of freedom in the dynamic analysis of a space frame moreover the discrepancy in the dynamic analysis of a member of a spatial structure arising from the ignorance of the shear deformation effect necessitates the inclusion of this additional effect especially in thick walled cross section members

generalized warping effect in the dynamic analysis of beams of arbitrary cross section abstract in this paper a general formulation for the nonuniform warping dynamic analysis of beams of arbitrary simply or multiply connected cross section under arbitrary external loading and general boundary conditions is presented taking into account the effects of rotary and warping inertia the nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions respectively which are obtained by solving the corresponding boundary value problems formulated exploiting the longitudinal local equilibrium equation a shear stress correction is also performed in order to improve the stress field arising from the employed kinematical considerations ten initial boundary value problems are formulated with respect to the displacement and rotation components as well as to the independent warping parameters and solved using the analog equation method a boundary element method based technique in combination with an appropriate time integration scheme the warping functions and the geometric constants including the additional ones due to warping are evaluated employing a pure bem approach

geometric lower bounds for the spectrum of elliptic pdes with dirichlet conditions in part an extension of the lower bound lemma of boggio is given for the weak forms of certain elliptic operators which are in general nonlinear and have partially dirichlet and partially neumann boundary conditions its consequences and those of an adapted hardy inequality for the location of the bottom of the spectrum are explored in corollaries wherein a variety of assumptions are placed on the shape of the dirichlet and neumann boundaries

cantor spectrum for the almost mathieu equation for a dense g of pairs in r2 we prove that the operator hu n u n 1 u n 1 cos 2 n u n has a nowhere dense spectrum along the way we prove several interesting results about the case pq of which we mention a if q is not an integral multiple of then all gaps are open and b if q is even and is chosen suitably then the middle gap is closed for all

torsion constant for matrix analysis of structures including warping effect abstract in this research an effective torsion constant j eff for a wide flanged member with different warping restraint conditions at the ends is developed in order to derive j eff the boundary conditions for different warping restraint conditions at the ends as imposed by the use of different types of connections in steel structures are employed in the general equation of torsional rotation o this effective torsion constant can be used directly instead of the st venant torsion constant j in the conventional member stiffness matrix the use of j eff will account for the effect of warping when using the commercial computer programs which employ either a 6 x 6 member stiffness matrix for grid or a 12 x 12 member stiffness matrix for space frame a table for factor f which is the ratio of j eff to j is presented for different member properties and warping restraint conditions for the easy and rapid torsional analysis of structures composed of wide flanged members by the matrix method the solutions of a sample grid problem using j eff are compared with well known solutions to demonstrate its application

a general theory for the accurate stress analysis of homogeneous and laminated composite beams abstract this paper has a twofold purpose initially it presents a general four degrees of freedom beam theory g4dofbt which takes into consideration the effects of both transverse shear and normal deformation on the basis of this new theory it then proposes a method suitable for the accurate stress analysis of either homogeneous or laminated composite beams subjected to arbitrary edge boundary conditions the new beam theory involves two general shape functions each of which is associated with one of the two unknown displacement components upon assigning simple particular forms to these shape functions most of the well known classical and variationally consistent refined beam models may be obtained as particular cases the new method for the accurate stress analysis of beam type structures is based on the specification of a new pair of shape functions these are obtained by introducing the stress distributions caused by the assumed g4dofbt displacement field into the appropriate equations of three dimensional elasticity which are subsequently solved for simply supported edges this is considered to provide an excellent choice of both shape functions as the method then yields the exact elasticity solution presented by pagano pagano n j 1969 exact solution for composite laminates in cylindrical bending j comp mat 3 398 411 for the cylindrical bending problem of simply supported infinite strips two particular examples are considered to show the potential of the present analysis these are dealing with stress analysis of homogeneous or laminated composite beams having one edge rigidly clamped and the other edge either guided or free of external tractions

complex variable boundary element method for torsion of composite shafts the problem of torsion of composite shafts consisting of a cylindrical matrix surrounding a finite number of inclusions is solved by using the complex variable boundary element method the method consists in reducing the problem to the solution of a singular integral equation in terms of an analytic function of a complex variable using the cauchy integral the resulting integral equation is then solved numerically by discretizing the boundaries into segments called complex boundary elements and replacing the analytic function on the boundaries by interpolating function numerical examples are given for a square shaft with a circular inclusion and for an elliptic shaft with two elliptic inclusions 1997 by john wiley sons ltd

finite element analysis of saint venant torsion problem with exact integration of the elastic plastic constitutive equations abstract in this paper torsion of prismatic bars considering elastic plastic material behaviour is studied based on the presented variational formulation associated isoparametric finite elements are developed the unknown warping function is approximated using an isoparametric concept the elastic plastic stresses are obtained by an exact integration of the rate equations thus the ultimate torque can be calculated in one single load step this quantity describes the plastic reserve of a bar subjected to torsion furthermore for linear isotropic hardening no local iterations are necessary to compute the stresses at the integration points the numerical results are in very good agreement with available analytical solutions for simple geometric shapes the arbitrary shaped domains may be simply or multiple connected

ground state energy bounds for potentials x ν a theory is developed from which both upper and lower analytic bounds on schrodinger eigenvalues can be obtained we propose a recursion algorithm with which ground energies for certain potentials can be rigorously bounded to arbitrary precision these analytic and numerical methods together with existing techniques are applied to the ground state problem for power potentials x 0

nonlinear theory for plates and shells including the effects of transverse shearing nonlinear strain displacement relations for three dimensional elasticity are determined in orthogonal curvilinear coordinates to develop a two dimensiona l theory the displacements are expressed by trigonometric series representation through the thickness the nonlinear strain displacement relations are expanded into a series that contains all first and second degree terms in the series for the displacements only the first few terms are retained insertion of the expansions into the three dimensional virtual work expression leads to nonlinear equations of equilibrium for laminated and thick plates and shells that include the effects of transverse shearing equations of equilibrium and buckling equations are derived for flat plates and cylindrical shells the shell equations reduce to conventional transverse shearing shell equations when the effects of the trigonometric terms are omitted and to classical shell equations when the trigonometric terms are omitted and the shell is assumed to be thin numerical results are presented for the buckling of a thick simply supported flat rectangular plate in longitudinal compression

a procedure for analysing space frames with partial warping restraint stiffness matrices for three dimensional beam elements that include the effect of warping restraint on elastic torsional response have been derived by various investigators using one of the available stiffness matrices and assuming that the warping boundary conditions can be specified on a member by member basis an elastic warping support is introduced to represent conditions of partial warping restraint at the member ends the concept of a warping indicator is then introduced to facilitate use of warping springs following this static condensation is used to eliminate the restrained warping degrees of freedom the condensed stiffness matrices for the elements can then be assembled to yield a global stiffness matrix in the global matrix continuous warping degrees of freedom that is those internal to a member represented by several elements are expressed in local co ordinates the remainder are expressed in global co ordinates in the force recovery phase it is shown that an indirect method yields most accurate results for the bimoment and warping torsion when the twist function is represented by a cubic polynomial solutions to examples of linear elastic analysis are compared with well known analytical solutions to demonstrate the application of the method

torsional vibrations of composite bars of variable cross section by bem in this paper a boundary element method is developed for the nonuniform torsional vibration problem of doubly symmetric composite bars of arbitrary variable cross section the composite bar consists of materials in contact each of which can surround a finite number of inclusions the materials have different elasticity and shear moduli and are firmly bonded together the beam is subjected to an arbitrarily distributed dynamic twisting moment while its edges are restrained by the most general linear torsional boundary conditions a distributed mass model system is employed which leads to the formulation of three boundary value problems with respect to the variable along the beam angle of twist and to the primary and secondary warping functions these problems are solved employing a pure bem approach that is only boundary discretization is used both free and forced torsional vibrations are considered and numerical examples are presented to illustrate the method and demonstrate its efficiency and wherever possible its accuracy the discrepancy in the analysis of a thin walled cross section composite beam employing the bem after calculating the torsion and warping constants adopting the thin tube theory demonstrates the importance of the proposed procedure even in thin walled beams since it approximates better the torsion and warping constants and takes also into account the warping of the walls of the cross section

random generation of combinatorial structures from a uniform distribution abstract the class of problems involving the random generation of combinatorial structures from a uniform distribution is considered uniform generation problems are in computational difficulty intermediate between classical existence and counting problems it is shown that exactly uniform generation of efficiently verifiable combinatorial structures is reducible to approximate counting and hence is within the third level of the polynomial hierarchy natural combinatorial problems are presented which exhibit complexity gaps between their existence and generation and between their generation and counting versions it is further shown that for self reducible problems almost uniform generation and randomized approximate counting are inter reducible and hence of similar complexity

counting hypergraph matchings up to uniqueness threshold abstract we study the problem of approximately counting matchings in hypergraphs of bounded maximum degree and maximum size of hyperedges with an activity parameter each matching m is assigned a weight m the counting problem is formulated as computing a partition function that gives the sum of the weights of all matchings in a hypergraph this problem unifies two extensively studied statistical physics models in approximate counting the hardcore model graph independent sets and the monomer dimer model graph matchings for this problem the critical activity c d d k d 1 d 1 is the threshold for the uniqueness of gibbs measures on the infinite d 1 uniform k 1 regular hypertree consider hypergraphs of maximum degree at most k 1 and maximum size of hyperedges at most d 1 we show that when c there is an fptas for computing the partition function and when c there is a ptas for computing the log partition function these algorithms are based on the decay of correlation strong spatial mixing property of gibbs distributions when 2 c there is no pras for the partition function or the log partition function unless np rp towards obtaining a sharp transition of computational complexity of approximate counting we study the local convergence from a sequence of finite hypergraphs to the infinite lattice with specified symmetry we show a surprising connection between the local convergence and the reversibility of a natural random walk this leads us to a barrier for the hardness result the non uniqueness of infinite gibbs measure is not realizable by any finite gadgets

multilayered piezoelectric refined plate theory a two dimensional theory for the analysis of multilayered piezoelectric plates is presented the theory is based on a hybrid approach in which the continuity conditions for both mechanical and electric unknowns at layer interfaces as well as the imposed conditions on the bounding surfaces and at the interfaces are independently satisfied then the piezoelectric boundary value problem is stated using mechanical displacements and electrostatic potential in conjunction with the coupled piezoelectric constitutive law the proposed model is simple to use incorporating only five independent generalized displacements and one or two independent generalized electrostatic potentials as unknowns the number of electric unknowns depends on the number of layers and electric prescribed conditions the accuracy of the proposed theory is assessed through investigation of significant problems for which an exact three dimensional solution is known from heyliger first in dynamics the free vibrations of five layered piezoelectric plates and second in statics for three layered plates with an imposed force density results obtained with our model compare very well with the exact three dimensional theory

a differential method for bounding the ground state energy for a wide class of hamiltonians a novel method for obtaining lower and upper bounds for the lowest energy is presented unlike perturbative or variational techniques this method does not involve the computation of any integral a normalization factor or a matrix element it just requires the determination of the absolute minimum and maximum in the whole configuration space of the local energy associated with a normalizable trial function the calculation of the norm is not needed after a general introduction the method is applied to three non integrable systems the asymmetric annular billiard the many body spinless coulombian problem the hydrogen atom in a constant and uniform magnetic field being more sensitive than the variational methods to any local perturbation of the trial function this method can be used to systematically improve the energy bounds with a local skilled analysis an algorithm relying on this method can therefore be constructed and an explicit example for a one dimensional problem is given

a refined theory of laminated shallow shells abstract a new refined hut simple shear deformation theory of elastic shells is developed for shells laminated of orthotropic layers to evaluate the new displacement field assumed which is justified in plates from the three dimensional elasticity theory classic types of shallow shells are considered the boundary value problem is formulated by making use of the principle of virtual power in conjunction with the assumed consistent displacement field the theory accounts for cosine distribution of the transverse shear strains through thickness of the shell and tangential stress free boundary conditions on the boundary surfaces of the shell the theory also accounts for in plane inertia and rotatory inertia the navier type exact solutions are presented in staties and in vibrations for cylindrical and spherical shells under simply supported edge boundary conditions the theory is of the same order of complexity as the shear deformation theory but is very much more efficient without needing shear correction factors some numerical comparisons with other works are made

bending vibration and buckling of simply supported thick multilayered orthotropic plates an evaluation of a new displacement model abstract based upon a piecewise linear displacement field which allows the contact conditions for the displacements and the transverse shearing stresses at the interfaces to be satisfied simultaneously the non linear in the von karman sense equations of motion for thick multilayered orthotropic plates are developed successively the equations are specified to the linear boundary value problem of the bending and to the linear eigenvalue problems of the undamped vibration and buckling of rectangular plates in order to assess the accuracy of the proposed theory the sample problem of the bending free undamped vibration and buckling of a three layered symmetric cross ply square plate simply supported on all edges is investigated for purposes of comparison numerical results from the exact elasticity theory the classical lamination kirchhoff theory and the shear deformation theory timoshenko and mindlin with three different values of the shear correction factor are also presented it is found that the proposed approach is very efficient in predicting the global responses deflection natural frequencies and buckling loads of thick multilayered plates and models effects such as the distortion of the deformed normals not attainable from the classical lamination theory as well as the shear deformation theory