existence of multiple nontrivial solutions for semilinear elliptic problems the aim of this paper is to prove the existence of multiple nontrivial solutions to a semilinear elliptic problem at resonance the proofs used here are based on combining the morse theory and the minimax methods

modelling of superelements in mechanism analysis the paper deals with substructuring for dynamic analysis of flexible multibody systems three different techniques based on component synthesis are discussed corresponding respectively to fully consistent mass discretization lumped mass discretization and corotational approximation of inertia forces to simplify the computer implementation only the lumped mass and corotational approximations have been considered in detail and programmed both approaches are validated on simple examples of rotating beams for which a full elastic model is available using a fully non linear beam element the computational efficiency of the corotational inertia approach is also demonstrated on the deployment of a large flexible satellite antenna

multiple periodic solutions of ordinary differential equations with double resonance abstract in this paper we study by morse theory the existence of multiple periodic solutions of a class of ordinary differential equation with double resonance at infinity between two consecutive eigenvalues and with resonance at origin

probabilistic analysis of output cost of a heuristic search algorithm abstract by proposing a new restricted type of network model we compute the probability distribution of output costs generated by the heuristic search algorithm a of bagchi and mohanti a of nilsson in terms of the heuristic distribution

boundary element method for thermoelastoplastic problems in this paper we present the boundary integral formulation for inelastic stationary thermoelasticity including thermally induced non homogeneity generally the unique bem formulation for crack problems is achieved by using the traction boundary integral equations which are now considered in a non singular form both the two and three dimensional boundary value problems are analysed simultaneously numerical examples for 2 d problems are presented in order to illustrate the suitability of this boundary element approach in the inelastic thermoelasticity

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

multiple solutions for a class of semilinear elliptic problems with robin boundary condition abstract in this paper we show the existence of at least four nontrivial solutions for a class of semilinear elliptic problems with robin boundary condition and jumping nonlinearities solvability of oscillating equations with robin boundary condition is also investigated we prove the conclusions by using sub super solution method fucik spectrum theory mountain pass theorem in order intervals and morse theory

application of the complex variable boundary element method to solving potential problems in doubly connected domains the complex variable boundary element method cvbem developed by hromadka for the solution of potential problems in simply connected domains is extended to the solution of heat conduction problems in doubly connected domains a cut is made in the doubly connected domain and it was found that the complex potentials along the cut do not cancel out but result in a complex stream function that plays the role of perturbation in the nodal equations cauchy riemann conditions are used to derive additional equations which relate the stream functions and the boundary heat fluxes and potentials when neumann and robin conditions are imposed on the boundaries the resulting nodal equations are expressed in matrix form and coding rules and methods for checking the matrix elements are developed three solution methods implicit explicit and hybrid are described and by means of examples the efficacy of these methods is discussed and compared

search algorithms under different kinds of heuristics a comparative study three heuristic search algorithms called algorithms a b and c are presented their performance with the admissibility condition relaxed is compared using the following two criteria i number of node expansions and ii cost of solution found first a general comparison is made in this process some variations and extensions of c are also considered subsequently two types of heuristic estimates called proper and path dependent are defined and the algorithms are reexamined it is shown that on the whole a nilsson s algorithm and b martelli s algorithm are inferior to c which is a slightly modified version of b 7 references

boundary element method analysis of thermoelastic deformation in nonhomogeneous media abstract this paper presents a boundary element method bem formulation and numerical implementation of thermoelasticity problems in nonhomogeneous media the formulation uses the known kernels of the displacement equations for elasticity problems in homogeneous media this formulation leads to a domain integral containing the unknown displacement field in addition to the usual boundary integrals with displacements and tractions an iterative scheme is used to determine the displacement fields numerical results are presented for some illustrative plane strain problems the iterative scheme is shown to converge rapidly for these problems with moderate temperature gradients the bem results are compared with results from the finite element method fem for these problems and also with exact solutions whenever possible

multiplicity of solutions for a class of the quasilinear elliptic equations at resonance abstract in this paper by morse theory we obtain the existence and multiplicity for a class of the quasilinear elliptic equations at resonance

a full tangent stiffness field boundary element formulation for geometric and material non linear problems of solid mechanics the field boundary element method naturally admits the solution algorithm in the incompressible regimes of fully developed plastic flow this is not the case with the generally popular finite element method without further modifications to the method such as reduced integration or a mixed method for treating the dilatational deformation the analyses by the field boundary element method for geometric and material non linear problems are generally carried out by an incremental algorithm where the velocities or displacement increments on the boundary are treated as the primary variables and an initial strain iteration method is commonly used to obtain the state of equilibrium for problems such as buckling and diffused tensile necking involving very large strains such a solution scheme may not be able to capture the bifurcation phenomena or the convergence will be unacceptably slow when the post bifurcation behaviour needs to be analysed to avoid this predicament a full tangent stiffness field boundary element formulation which takes the initial stress velocity gradient displacement gradient coupling terms accurately into account is presented in this paper here the velocity field both inside and on the boundary are treated as primary variables the large strain plasticity constitutive equation employed is based on an endochronic model of combined isotropic kinematic hardening plasticity using the concepts of material director triad and the associated plastic spin a generalized mid point radial return algorithm is presented for determining the objective increments of stress from the computed velocity gradients numerical results are presented for problems of diffuse necking involving very large strains and plastic instability in initially perfect elastic plastic plates under tension these results demonstrate the clear superiority of the full tangent stiffness algorithm over the initial strain algorithm in the context of the integral equation formulations for large strain plasticity

graph search methods for non order preserving evaluation functions applications to job sequencing problems abstract graph search with a is frequently faster than tree search but a graph search operates correctly only when the evaluation function is order preserving in the non orderpreserving case no paths can be discarded and the entire explicit graph must be stored in memory such situations arise in one machine minimum penalty job sequencing problems when setup times are sequence dependent grec the unlimited memory version of a memory constrained search algorithm of the authors called mrec has a clear advantage over a in that it is able to find optimal solutions to such problems at the same time it is as efficient as a in solving graph search problems with order preserving evaluation functions experimental results indicate that in the non order preserving case grec is faster than both best first and depth first tree search and can solve problem instances of larger size than best first tree search

multiple solutions and sign changing solutions of a class of nonlinear elliptic equations with neumann boundary condition in this paper we study and discuss nonlinear elliptic equations with neumann boundary condition for oscillation problem we obtain infinitely many positive and negative solutions of 1 1 which are all nonconstant and get at least two nonconstant solutions in every order interval under resonance case moreover we yield infinitely many sign changing solutions of 1 1 under some assumptions furthermore we give a precise description of critical groups of some kinds of critical points we draw the conclusions by using sub sup solution method mountain pass theorem in order intervals leray schauder degree theory and morse theory

multiplicity of nontrivial solutions for quasilinear elliptic equation two nontrivial solutions are obtained by the reduction method for the nonautonomous semilinear elliptic dirichlet boundary value problem some well known multiplicity results are generalized

nonresonance conditions on the potential for a semilinear elliptic problem abstract we prove the solvability of the dirichlet problem formula for every given h under the following set of assumptions formula and formula and formula here m and m 1 denote two consecutive higher eigenvalues of on h 1 0 and g is the potential of g similar results are also obtained in the case where the nonlinearity interacts with the first eigenvalue 1

axisymmetric viscoplastic deformation by the boundary element method abstract this paper presents a boundary element formulation and numerical implementation of the problem of small axisymmetric deformation of viscoplastic bodies while the extension from planar to axisymmetric problems can be carried out fairly simply for the finite element method fem this is far from true for the boundary element method bem the primary reason for this fact is that the axisymmetric kernels in the integral equations of the bem contain elliptic functions which cannot be integrated analytically even over boundary elements and internal cells of simple shape thus special methods have to be developed for the efficient and accurate numerical integration of these singular and sensitive kernels over discrete elements the accurate determination of stress rates by differentiation of the displacement rates presents another formidable challenge a successful numerical implementation of the boundary element method with elementwise called the mixed approach or pointwise called the pure bem or bem approach determination of stress rates has been carried out a computer program has been developed for the solution of general axisymmetric viscoplasticity problems comparisons of numerical results from the bem and fem for several illustrative problems are presented and discussed in the paper it is possible to get direct solutions for the simpler class of problems for cylinders of uniform cross section and these solutions are also compared with the bem and fem results for such cases

the complex variable boundary element method applications the complex variable boundary element method cvbem is used to approximate several potential problems where analytical solutions are known a modelling result produced from the cvbem is a measure of relative error in matching the known boundary condition values of the problem a cvbem error reduction algorithm is used to reduce the relative error of the approximation by adding nodal points in boundary regions where error is large from the test problems overall error is reduced significantly by utilizing the adaptive integration algorithm

computations of critical groups and applications to some differential equations at resonance abstract in this paper we first consider the computations of the critical groups of a functional with generalized ahmad lazer paul type conditions both at zero and infinity then the abstract results are applied to investigate some new cases of the existence of nontrivial solutions of the second order hamiltonian systems and elliptic boundary value problems which may be resonant both at zero and infinity

best first search methods for constrained two dimensional cutting stock problems best first search is a widely used problem solving technique in the field of artificial intelligence the method has useful applications in operations research as well here we describe an application to constrained two dimensional cutting stock problems of the following type a stock rectangle s of dimensions l w is supplied there are n types of demanded rectangles r1 r2 rn with the ith type having length li width wi value vi and demand constraint bi it is required to produce from the stock rectangle s ai copies of ri 1 i n to maximize a1v1 a2v2 anvn subject to the constraints ai bi only orthogonal guillotine cuts are permitted all parameters are integers a best first tree search algorithm based on wang s bottom up approach is described that guarantees optimal solutions and is more efficient than existing methods

nontrivial solutions for elliptic resonant problems abstract nontrivial solutions for elliptic resonant problems are obtained via morse theory to compute the critical groups at infinity of the relevant functional we propose a new approach by combining the homotopy and reduction methods and the alexander duality theorem

boundary element method analysis of stationary thermoelasticity problems in non homogeneous media this paper presents an advanced bem formulation for the solution of stationary problems of thermoelasticity taking into consideration the thermally induced non homogeneity an iterative scheme is used to determine the displacement fields because the formulation contains a domain type integral with displacements as compared with the existing bem formulation this one does not contain a domain integral of the temperature field and furthermore the integral representation of stresses is written in the regularized from consequently all the integrals can be computed numerically by using the regular gaussian quadrature

identification of time varying structural dynamic systems an artificial intelligence approach an application of the artificial intelligence derived methodologies of heuristic search and object oriented programming to the problem of identifying the form of the model and the associated parameters of a time varying structural dynamic system is presented in this paper possible model variations due to changes in boundary conditions or configurations of a structure are organized into a taxonomy of models and a variant of best first search is used to identify the model whose simulated response best matches that of the current physical structure simulated model responses are verified experimentally an output error approach is used in a discontinuous model space and an equation error approach is used in the parameter space the advantages of the ai methods used compared with conventional programming techniques for implementing knowledge structuring and inheritance are discussed convergence conditions and example problems have been discussed in the example problem both the time varying model and its new parameters have been identified when changes

multiple nontrivial solutions for asymptotically linear discrete problem via computations of the critical groups in this paper we study the multiplicity of nontrivial solutions for asymptotically linear discrete problem by using critical point theory morse theory and minimax methods we obtained that the problem has at least two nontrivial solutions under various conditions

optimal matching of deformed patterns with positional influence abstract deformations on patterns such as substitutions deletions and insertions are extended to be positionally dependent the deformation of a primitive depends not only on its type but also on its position concepts of contextual preserved deformations cpd and contextual variant deformations cvd are proposed as are algorithms for optimal pattern matching under cpd and cvd conditions

nontrivial solutions on a kind of fourth order neumann boundary value problems abstract nontrivial solutions for the fourth order neumann boundary value problem u 4 t 2 u t u t f t u t for all t 0 1 and subject to u 0 u 1 u 0 u 1 0 are obtained via morse theory to compute the critical groups at infinity of the relevant functional we propose an approach by combining the homotopy and reduction methods

nontrivial solutions for some fourth order boundary value problems with parameters abstract in this paper we prove some new existence results concerning nontrivial solutions to some fourth order boundary value problems u 4 t u t u t f t u t 0 t 1 u 0 u 1 u 0 u 1 0 where f c 1 0 1 r r r are parameters satisfying 4 2 1 the methods used here are based on combining the minimax methods and the morse theory

on asymptotically linear elliptic equations in r n abstract in this paper we obtain the existence of solution for asymptotically linear elliptic equations in r n we mainly focus on the resonant case the nonlinearity may not be sublinear

comparison of boundary element and finite element methods in the inelastic torsion of prismatic shafts the accuracy and computational efficiency of the boundary element and the finite element methods are compared in this paper for problems of time dependent inelastic torsion of prismatic shafts several cross sections and two types of twisting history are considered in the numerical examples the shaft material is assumed to obey an elastic time hardening creep constitutive model

a meshless bem for isotropic heat conduction problems with heat generation and spatially varying conductivity in this paper a new and simple boundary domain integral equation is presented for heat conduction problems with heat generation and non homogeneous thermal conductivity since a normalized temperature is introduced to formulate the integral equation temperature gradients are not involved in the domain integrals the green s function for the laplace equation is used and therefore the derived integral equation has a unified form for different heat generations and thermal conductivities the arising domain integrals are converted into equivalent boundary integrals using the radial integration method rim by expressing the normalized temperature using a series of basis functions and polynomials in global co ordinates numerical examples are given to demonstrate the robustness of the presented method copyright 2005 john wiley sons ltd

a complex variable boundary element method development a generalized boundary integral equation method for the solution of the laplace equation is developed based on the cauchy integral theorem for analytical complex variable functions although the approach is complicated by the utilization of complex variable theory the resulting model involves direct integration along straight line boundary segments elements rather than using quadrature formulae that are required in current real variable boundary element formulations previously published boundary integral equation methods based on the cauchy integral theorem are shown to be a subset of the generalized model theory developed in this paper

nontrivial solutions of semilinear equations at resonance in this paper we prove new existence results concerning nontrivial solutions to semilinear elliptic problem at resonance the methods used here are based on combining the minimax methods and the morse theory

knowledge versus search a quantitative analysis using a abstract this paper analyzes the average number of nodes expanded by a as a function of the accuracy of its heuristic estimates by treating the errors h h as random variables whose distribution may vary over the nodes in the graph the search model consists of an m ary tree with unit branch costs and a unique goal state situated at a distance n from the root the main result states that if the typical error grows like h then the mean complexity of a grows approximately like g n exp c n where c is a positive constant and g n is o n 2 thus a necessary and sufficient condition for maintaining polynomial search complexity is that a be guided by heuristics with logarithmic precision e g n log n k a is shown to make much greater use of its heuristic knowledge than a backtracking procedure would under similar conditions

computation of critical groups in resonance problems where the nonlinearity may not be sublinear under weaker assumptions that require 1 4 but not 1 7 as an applica tion we obtain new existence results for asymptotically linear elliptic boundary valueproblems at resonance we refer the reader to chang 2 for a wide exposition of morse theory the notionofcritical groups at innity was introduced in 1 2 criticalgroupcomputationsfirst we assume that g

on resonant neumann problems we consider semilinear neumann problems at resonance and prove existence and multiplicity theorems the existence theorems allow resonance with respect to any eigenvalue of the negative neumann laplacian the multiplicity theorems concern problems resonant at 0 the principal eigenvalue or at the first nonzero eigenvalue our approach uses tools from critical point theory and from morse theory

geometric non linear substructuring for dynamics of flexible mechanical systems a substructure synthesis formulation is presented that permits use of established flexible multibody dynamic analysis computer codes to account for structural geometric non linear effects large relative displacement is permitted between points within bodies that undergo small strain elastic deformation components are divided into substructures on each of which the theory of linear elasticity relative to a body reference frame is adequate to describe deformation and its coupling with system motion normal vibration and static correction deformation modes are used to account for elastic deformation within each substructure compatibility conditions are derived and imposed as constraint equations at boundary points between substructures system equations of motion that include geometric non linear effects of large rotation in terms of generalized co ordinates of a reference frame for each substructure and a set of deformation modes that are defined within the substructure are assembled the method is implemented in an industry standard flexible multibody dynamics code with minimal modification use of the formulation is illustrated on the classical problem of a spinning beam with geometric stiffening and on a space structure that experiences large deformation

multiple positive solutions for a class of p superlinear elliptic problems abstract we study nonlinear elliptic dirichlet problems driven by the p laplacian and with a nonlinearity which consists of a p superlinear term perturbed by a p linear one using critical point theory coupled with suitable truncation techniques we show that the problem has two positive smooth solutions when the conditions are symmetric in the two semiaxes we have four nontrivial smooth solutions of constant sign finally for the semilinear problem using morse theory we produce a fifth nontrivial smooth solution

multiplicity results for semilinear elliptic problems at resonance and with jumping nonlinearities abstract in the present paper we develop a method to deal with multiple existence of solutions of nonlinear elliptic problems and give some multiple existence results for elliptic boundary value problems at resonance and problems with jumping nonlinearities

on the use of the boundary element method for elastoplastic large deformation problems the boundary element method is applied to large deformation problems typical in industrial forming problems a form of betti s theorem relevant to an updated lagrangian type of solution procedure is established as the basis for the boundary element formulation equilibrium iterations are needed in each load step all non linear terms are moved to the right hand side and the boundary element method can be used cross anisotropy is assumed where hill s yield criterion is adopted together with isotropic hardening the investigation has shown that the boundary element method is applicable to this type of problem giving good results within reasonable computer time

heuristic search through islands abstract a heuristic search strategy via islands is suggested to significantly decrease the number of nodes expanded algorithm i which searches through a set of island nodes island set is presented assuming that the island set contains at least one node on an optimal cost path this algorithm is shown to be admissible and expands no more nodes than a for cases where the island set does not contain an optimal cost path or any path algorithm i a modification of algorithm i is suggested this algorithm ensures a suboptimal cost path which may be optimal and in extreme cases falls back to a

inconsistent heuristics in theory and practice in the field of heuristic search it is usually assumed that admissible heuristics are consistent implying that consistency is a desirable attribute the term inconsistent heuristic has at times been portrayed negatively as something to be avoided part of this is historical early research discovered that inconsistency can lead to poor performance for a nodes might be re expanded many times however the issue has never been fully investigated and was not re considered after the invention of ida this paper shows that many of the preconceived notions about inconsistent heuristics are outdated the worst case exponential time of inconsistent heuristics is shown to only occur on contrived graphs with edge weights that are exponential in the size of the graph furthermore the paper shows that rather than being something to be avoided inconsistent heuristics often add a diversity of heuristic values into a search which can lead to a reduction in the number of node expansions inconsistent heuristics are easy to create contrary to the common perception in the ai literature to demonstrate this a number of methods for achieving effective inconsistent heuristics are presented pathmax is a way of propagating inconsistent heuristic values in the search from parent to children this technique is generalized into bidirectional pathmax bpmx which propagates values from a parent to a child node and vice versa bpmx can be integrated into ida and a when inconsistent heuristics are used with bpmx experimental results show a large reduction in the search effort required by ida positive results are also presented for a searches

generalized best first search strategies and the optimality of a this paper reports several properties of heuristic best first search strategies whose scoring functions depend on all the information available from each candidate path not merely on the current cost g and the estimated completion cost h it is shown that several known properties of a retain their form with the minmax of f playing the role of the optimal cost which helps establish general tests of admissibility and general conditions for node expansion for these strategies on the basis of this framework the computational optimality of a in the sense of never expanding a node that can be skipped by some other algorithm having access to the same heuristic information that a uses is examined a hierarchy of four optimality types is defined and three classes of algorithms and four domains of problem instances are considered computational performances relative to these algorithms and domains are appraised for each class domain combination we then identify the strongest type of optimality that exists and the algorithm for achieving it the main results of this paper relate to the class of algorithms that like a return optimal solutions i e admissible when all cost estimates are optimistic i e h h on this class a is shown to be not optimal and it is also shown that no optimal algorithm exists but if the performance tests are confirmed to cases in which the estimates are also consistent then a is indeed optimal additionally a is also shown to be optimal over a subset of the latter class containing all best first algorithms that are guided by path dependent evaluation functions

nontrivial solutions to a class of systems of second order differential equations abstract in this paper we investigate the nontrivial solutions to a class of systems of second order ordinary differential equations by using the critical groups and establish the existence results under the resonant case

on the efficiency and accuracy of the boundary element method and the finite element method the efficiency and computational accuracy of the boundary element and finite element methods are compared in this paper this comparison is carried out by employing different degrees of mesh refinement to solve a specific illustrative problem by the two methods

locating a crack of arbitrary but known shape by the method of path independent integrals abstract the solution of a crack problem of an arbitrary but known shape inside an infinite plane isotropic elastic medium can be achieved in general by the method of complex singular integral equations and their numerical solution by using the gauss or the lobatto chebyshev methods in a few special cases like straight or circular arc shaped cracks this solution is available in closed form in this paper we will not contribute to the above methods of solution of crack problems but we will propose a method for the determination of the exact position of such a crack inside a closed contour in the elastic medium by gathering and using information along this contour only by experimental techniques and applying the method of complex path independent integrals for the location of the crack this paper constitutes a nontrivial generalization of relevant previous results by the author and it is of quite general applicability in fracture mechanics for nondestructive testing numerical results for the particular case of a straight crack are displayed for the illustration of the efficiency of the method the generalization of the present results to the determination of additional geometric and loading parameters of the crack is also suggested very briefly and related numerical results concerning the length of the crack and the pressure distribution on it in the aforementioned numerical application are also presented

and or graph heuristic search methods two new marking algorithms for and or graphs called cf and cs are presented for admissible heuristics cs is not needed and cf is shown to be preferable to the marking algorithms of martelli and montanari when the heuristic is not admissible the analysis is carried out with the help of the notion of the first and second discriminants of an and or graph it is proved that in this case cf can be followed by cs to get optimal solutions provided the sumcost criterion is used and the first discriminant equals the second estimates of time and storage requirements are given other cost measures such as maxcost are also considered and a number of interesting open problems are enumerated