periods of eisenstein series the galois case let g rese fh where h is a connected reductive group over a number field f and e f is a quadratic extension we define the regularized period of an automorphic form of g relative to h and we express the regularized period of cuspidal eisenstein series in terms of intertwining periods which are relative analogues of the standard intertwining operators this leads to an analogue of the maass selberg relations the regularized periods appear in the contribution of the continuous spectrum to the relative trace formula

periods of residual automorphic forms abstract we develop a technique for computing period integrals of noncuspidal automorphic forms applications include a formula for the integral of a square integrable automorphic form on gl n a e over gl n f gl n a f 1 for a quadratic extension e of a number field f and a characterization of residual automorphic representations on which the period integral is nonvanishing

spherical characters on p adic symmetric spaces symmetric spaces over local fields and the harmonic analysis of their class one representations arise as the local calculation of jacquet s theory of the relative trace formula there is an extensive literature at the real place but few general results for p adic fields are known the objective here is to carry over to symmetric spaces as much as possible of queens and the prerequisite results of howe and to provide counterexamples for those things which do not generalize we derive the weyl integration formula local constancy of the spherical character on the regular set howe s conjecture for groups the germ expansion for spherical characters at the origin and a spherical version of howe s kirillov theory for compact p adic groups we find that the density property of regular orbital integrals fails some of the basic ideas are nascent in hakim s thesis written under herve jacquet

solving sat and sat modulo theories from an abstract davis putnam logemann loveland procedure to dpll t we first introduce abstract dpll a rule based formulation of the davis putnam logemann loveland dpll procedure for propositional satisfiability this abstract framework allows one to cleanly express practical dpll algorithms and to formally reason about them in a simple way its properties such as soundness completeness or termination immediately carry over to the modern dpll implementations with features such as backjumping or clause learning we then extend the framework to satisfiability modulo background theories smt and use it to model several variants of the so called lazy approach for smt in particular we use it to introduce a few variants of a new efficient and modular approach for smt based on a general dpll x engine whose parameter x can be instantiated with a specialized solver solvert for a given theory t thus producing a dpll t system we describe the high level design of dpll x and its cooperation with solvert discuss the role of theory propagation and describe different dpll t strategies for some theories arising in industrial applications our extensive experimental evidence summarized in this article shows that dpll t systems can significantly outperform the other state of the art tools frequently even in orders of magnitude and have better scaling properties

nonlinear structural response of laminated composite plates subjected to blast loading we are concerned with the theoretical analysis of the laminated composite plates exposed to normal blast shock waves as well as presenting correlation between the theoretical analysis and the experimental results of the strain time histories the laminated composite plate is clamped at all edges on the theoretical side of the study dynamic equations of the plates are derived by the use of the virtual work principle within the framework of the love theory of plates the geometric nonlinearity effects are taken into account with von karman assumptions then the governing equations of the laminated plate are solved by the runge kutta verner method a new displacement function is considered for the theoretical solution of the blast loaded clamped plate furthermore finite element modeling and analysis for the blast loaded composite plates are presented on the experimental side of the study tests have been carried out on the laminated composite plates with clamped edges for two different blast loads the results of theoretical and finite element methods are compared with the experimental results theoretical and finite element analyses results are in a good agreement there is a qualitative agreement between the analyses and experimental results in the first load case the predicted peak strains and response frequency are in an agreement with the experimental results for first load case thus the theoretical solution may be used for providing material in the preliminary design stage there is a difference between the analysis and experimental results in the second load case because of the extremely large deflections in this study the effects of loading conditions geometrical properties and material properties are separately examined on the dynamic behavior as well

on affine scaling algorithms for nonconvex quadratic programming we investigate the use of interior algorithms especially the affine scaling algorithm to solve nonconvex indefinite or negative definite quadratic programming qp problems although the nonconvex qp with a polytope constraint is a hard problem we show that the problem with an ellipsoidal constraint is easy when the hard qp is solved by successively solving the easy qp the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions

functional equations of weng s zeta functions for g p q it is shown that weng s zeta functions associated with arbitrary semisimple algebraic groups defined over the rational number field and their maximal parabolic subgroups satisfy the functional equations 1 introduction recently lin weng introduced a new class of abelian zeta functions associated to a pair of reductive algebraic group g and its maximal parabolic subgroup p which are related with constant terms of eisenstein series in this paper we simply refer to these zeta functions as weng s zeta functions these are motivated by and closely related to non abelian zeta functions called high rank zeta functions associated with algebraic number fields which were also introduced by weng himself from a viewpoint of arakelov geometry based on iwasawa s interpretation and tate s fourier analysis on adeles high rank zeta functions are generalizations of the dedekind zeta functions and in fact rank one zeta functions coincide with the dedekind zeta functions up to constant multiples hence the study of weng s zeta functions is not only interesting itself but also sug gestive for the study of the dedekind zeta functions the profound background the path to the discovery and the development of weng s zeta functions are detailed in his elaborated papers 13 14 15 16 one of the most significant properties for weng s zeta functions is the behav ior of their zeros weng conjectured that for any pair g p weng s zeta functions satisfy certain functional equations and the riemann hypothesis as is expected or shown for various kinds of zeta functions as for the functional equations initially weng proved them in the cases sl n n 2 3 4 5 sp 4 s o 8 and g2 a nd successively h kim weng in the cases sl n p n 1 1 for arbitrary n 2 un published as for the riemann hypothesis its validity was shown in the cases sl n n 2 3 4 5 sp 4 and g2 with their arbitrary maximal parabolic sub groups see 6 8 10 11 12 for the details in this paper we establish the functional equations in arbitrary semisimple cases in a unified way we will see that the functional equations are governed by the involutions on the weyl groups see the last paragraph of section 3 and lemma 5 3 furthermore we give the explicit forms of weng s zeta functions and

regularized orbital integrals for representations of 2 given a finite dimensional representation of sl 2 f on a vector space v defined over a local field f of characteristic zero we produce a regularization of orbital integrals and determine when the resulting distribution is non trivial

on the inner product of truncated eisenstein series introduction 1 the problem 2 residues of cuspidal eisenstein series 83 exponents 4 a comparison between two groups 5 a property of the truncation operator 6 the constant terms of eisenstein series 7 the negative dual chamber 8 coefficients of the zero exponents 9 conclusion bibliography

on the classification of k involutions let g be a connected reductive algebraic group defined over a field k of characteristic not 2 an involution of g defined over k h a k open subgroup of the fixed point group of and gk resp hk the set of k rational points of g resp h the variety gk hk is called a symmetric k variety these varieties occur in many problems in representation theory geometry and singularity theory over the last few decades the representation theory of these varieties has been extensively studied for k r and c as most of the work in these two cases was completed the study of the representation theory over other fields like local fields and finite fields began the representations of a homogeneous space usually depend heavily on the fine structure of the homogeneous space like the restricted root systems with weyl groups etc thus it is essential to study first this structure and the related geometry in this paper we give a characterization of the isomorphy classes of these symmetric k varieties together with their fine structure of restricted root systems and also a classification of this fine structure for the real numbers p adic numbers finite fields and number fields

stable relative bessel distributions on gl n over a quadratic extension we study regularized periods of eisenstein series over unitary groups they play an important role in the study of unitary periods of cusp forms a stabilization is used to express the periods in terms of l functions thanks to recent developments of jacquet and lapid we obtain certain bessel identities that generalize identities obtained by lapid rogawski these identities are applied in compact unitary periods by lapid and offen

on a local conjecture of jacquet ladder representations and standard modules let e f be a quadratic extension of p adic fields we prove that every smooth irreducible ladder representation of the group gl n e which is contragredient to its own galois conjugate possesses the expected distinction properties relative to the subgroup gl n f this affirms a conjecture attributed to jacquet for a large class of representations along the way we prove a reformulation of the conjecture which concerns standard modules in place of irreducible representations

twisted symmetric square l functions for mathrm gl _n and invariant trilinear forms following the works of bump and ginzburg and of takeda we develop a theory of twisted symmetric square l functions for mathrm gl n we characterize their pole in terms of certain trilinear period integrals determine all irreducible summands of the discrete spectrum of mathrm gl n having nonvanishing trilinear periods and construct nonzero local invariant trilinear forms on a certain family of induced representations

orbital integrals on symmetric spaces and spherical characters abstract in the first section of this paper we obtain an asymptotic expansion near semi simple elements of orbital integrals x f of c c functions f on symmetric spaces g h here g is a reductive p adic group and h is the group of fixed points of an involution on g this extends the germ expansion of j shalika and m f vigneras in the group case the main part of the paper studies examples of groups g with involution which have the property that the spherical characters associated with their spherical admissible representations are not identically zero on the regular set of g h these include g gl n m h gl n gl m for n m 1 or 2 and n 1 m 3 more general results had been obtained by j sekiguchi in the case of real symmetric spaces generalizing harish chandra s work in the group case over archimedean and non archimedean fields our interest is in the p adic case there the techniques are entirely different from sekiguchi s in fact we use the recent work of j hakim and c rader and s rallis who showed that the spherical character is smooth on the regular set and has asymptotic expansion in terms of fourier transforms of invariant distributions on the nilpotent cone as found by harish chandra in the group case our study of the nonvanishing of some spherical characters uses a construction of an explicit basis of the space of invariant distributions on the nilpotent cone this is done on regularizing spherical orbital integrals and taking suitable linear combinations this local work is motivated by concrete applications to the theory of deligne kazhdan lifting of spherical automorphic representations in some other examples concerning g gl 3 n and h gl n gl 2 n and g o 3 2 h o 2 2 we explicitly construct invariant distributions on the nilpotent cone which are equal to their fourier transform such examples do not exist in harish chandra s group case in the last two sections following harish chandra s simple proof in the group case we show that x f is locally constant on the regular set of x uniformly in f in some cases following d kazhdan s proof of his density theorem we show that an f which annihilates all spherical characters has x f 0 on the regular elliptic set

interactive learning of monotone boolean functions this paper presents some optimal interactive algorithms for some problems related to learning of monotone boolean functions these algorithms are based on the fundamental hansel theorem the advantage of the algorithms is that they are not heuristics as is often the case of many known algorithms for general boolean functions but they are optimal in the sense of the shannon function this paper also formulates a new problem for the joint restoration of two nested monotone boolean functions f1 and f2 this formulation allows one to further decrease the dialogue with an expert and restore nonmonotone functions of the form f2 f1 the effectiveness of the proposed approaches is demonstrated by some illustrative computational experiments

solving combinatorial optimization problems using karmakar s algorithm we describe a cutting plane algorithm for solving combinatorial optimization problems the primal projective standard form variant of karmarkar s algorithm for linear programming is applied to the duals of a sequence of linear programming relaxations of the combinatorial optimization problem

on the complexity of approximating a kkt point of quadratic programming we present a potential reduction algorithm to approximate a karush kuhn tucker kkt point of general quadratic programming qp we show that the algorithm is a fully polynomial time approximation scheme and its running time dependency on accuracy 0 1 is o l log l log log l compared to the previously best known result o l 2 furthermore the limit of the kkt point satisfies the second order necessary optimality condition of being a local minimizer 1998 the mathematical programming society inc published by elsevier science b v

distinction of the steinberg representation for inner forms of gl n let f be a non archimedean local field of characteristic not 2 let d be a division algebra of dimension d 2 over its center f and e a quadratic extension of f if m is a positive integer to a character chi of e one can attach the steinberg representation st chi of g gl m d otimes f e let h be the group gl m d we prove that st chi is h distinguished if and only if chi f is the quadratic character eta e f md 1 where eta e f is the character of f with kernel the norms of e we also get multiplicity one for the space of invariant linear forms

geometric side of a local relative trace formula following a scheme suggested by b feigon we investigate a local relative trace formula in the situation of a reductive p adic group g relative to a symmetric subgroup h underline h f where underline h is split over the local field f of characteristic zero and g underline g f is the restriction of scalars of underline h i e relative to a quadratic unramified extension e of f we adapt techniques of the proof of the local trace formula by j arthur in order to get a geometric expansion of the integral over h times h of a truncated kernel associated to the regular representation of g

a continuous approach to inductive inference in this paper we describe an interior point mathematical programming approach to inductive inference we list several versions of this problem and study in detail the formulation based on hidden boolean logic we consider the problem of identifying a hidden boolean function 0 1 n 0 1 using outputs obtained by applying a limited number of random inputs to the hidden function given this input output sample we give a method to synthesize a boolean function that describes the sample we pose the boolean function synthesis problem as a particular type of satisfiability problem the satisfiability problem is translated into an integer programming feasibility problem that is solved with an interior point algorithm for integer programming a similar integer programming implementation has been used in a previous study to solve randomly generated instances of the satisfiability problem in this paper we introduce a new variant of this algorithm where the riemannian metric used for defining the search region is dynamically modified computational results on 8 16 and 32 input 1 output functions are presented our implementation successfully identified the majority of hidden functions in the experiment

finite order automorphisms and a parametrization of nilpotent orbits in p adic lie algebras let k be a field with a nontrivial discrete valuation which is complete and has perfect residue field let g be the group of k rational points of a reductive linear algebraic group bf g equipped with a finite cyclic group l of order m acting on bf g by algebraic automorphisms defined over k we assume that the lie algebra of g decomposes into a direct sum of eigenspaces under the action of l with generator theta we let frak g i denote the eigenspace corresponding to eigenvalue xi i where xi is a primitive m th root of unity that is x in frak g i if and only if theta x xi ix if bf h is a k subgroup of bf g l the group of l fixed points which contains the neutral component of bf g l then h bf h k acts on each eigenspace of frak g let r in bbb r under mild restrictions on the residual characteristic of k the set of nilpotent h orbits in the xi eigenspace frak g 1 is parametrized by equivalence classes of noticed moy prasad cosets of depth r which lie in frak g 1

nonlinear dynamic behavior of simply supported laminated composite plates subjected to blast load this paper deals with the analysis and discussion of nonlinear dynamic response of a laminated composite plate subjected to blast load dynamic equations of the plate are derived by the use of the virtual work principle the geometric nonlinearity effects are taken into account with the von karman large deflection theory of thin plates approximate solutions for a simply supported plate are assumed for the space domain the single term approximation functions are selected by considering the nonlinear static deformations of plate which is obtained using finite element method the galerkin method is used to obtain the nonlinear differential equations in the time domain the finite difference method is applied to solve the system of coupled nonlinear equations the results of approximate numerical analysis are obtained and compared with the literature and finite element results good agreement is found for the character and frequencies of vibrations

newton s method with a model trust region modification a modified newton method for unconstrained minimization is presented and analyzed the modification is based upon the model trust region approach this report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified newton iteration several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis very strong convergence results are presented concerning the minimization algorithm in particular the explicit use of second order information is justified by demonstrating that the iterates converge to a point which satisfies the second order necessary conditions for minimization with the exception of very pathological cases this occurs whenever the algorithm is applied to problems with continuous second partial derivatives

synthesis of a dnf formula from a sample of strings using ehrenfeucht fraisse games abstract in order to define a dnf version of first order sentences over strings in which atomic sentences represent substring properties of strings we use results of the ehrenfeucht fraisse game over strings then given a sample of strings and the number of disjunctive clauses we investigate the problem of finding a dnf formula that is consistent with the sample we show that this problem is np complete and we solve it by a translation into boolean satisfiability we also present an extension of this problem that is robust concerning noisy samples we solve the generalized version by a codification into the maximum satisfiability problem as first order logic over strings defines exactly the class of locally threshold testable ltt languages our results can be useful in the grammatical inference framework when the goal is to find a model of a ltt language from a sample of strings

spherical functions on spherical varieties let bf x bf h backslash bf g be a homogeneous spherical variety for a split reductive group bf g over the integers frak o of a p adic field k and k bf g frak o a hyperspecial maximal compact subgroup of g bf g k we compute eigenfunctions spherical functions on x bf x k under the action of the unramified or spherical hecke algebra of g generalizing many classical results of casselman shalika type under some additional assumptions on bf x we also prove a variant of the formula which involves a certain quotient of l values and we present several applications such as 1 a statement on good test vectors in the multiplicity free case namely that an h invariant functional on an irreducible unramified representation pi is non zero on pi k 2 the unramified plancherel formula for x including a formula for the tamagawa measure of bf x frak o and 3 a computation of the most continuous part of bf h period integrals of principal eisenstein series

synthesis of quantifier free dnf sentences from inconsistent samples of strings with ef games and sat abstract we present a method to extract knowledge in terms of quantifier free sentences in disjunctive normal form from noisy samples of classified strings we show that the problem to find such a sentence is np complete and our approach for solving it is based on a reduction to the boolean satisfiability problem moreover our method bounds the number of disjuncts and the maximum number of literals per clause since sentences with few clauses and few literals per clause are easier to interpret as the logic we are considering defines exactly the class of locally threshold testable ltt languages our results can be useful in grammatical inference when the goal is to find a model of an ltt language from a sample of strings we also use results of the ehrenfeucht fraisse game over strings in order to handle consistent and inconsistent samples of strings

local periods for discrete series representations abstract let g h be a symmetric pair over a p adic field and a discrete series representation of g in this paper for some type of symmetric pairs g h we show that local periods in hom h c can be constructed by integrating the matrix coefficients of over h

non abelian zeta functions for function fields in this paper we initiate a geometrically oriented construction of non abelian zeta functions for curves defined over finite fields more precisely we first introduce new yet genuine non abelian zeta functions for curves defined over finite fields by a weighted count on rational points over the corresponding moduli spaces of semi stable vector bundles using moduli interpretation of these points then we define non abelian l functions for curves over finite fields using integrations of eisenstein series associated to l2 automorphic forms over certain generalized moduli spaces introduction in this paper we initiate a geometrically oriented construction of non abelian zeta functions for curves defined over finite fields it consists of two chapters more precisely in chapter i we first introduce new yet genuine non abelian zeta functions for curves defined over finite fields this is achieved by a weighted count on rational points over the corresponding moduli spaces of semi stable vector bundles using moduli interpretation of these points we justify our con struction by establishing basic properties for these new zetas such as functional equation and rationality and show that if only line bundles are involved our newly defined zetas coincide with artin s zeta all this in particular the ratio nality then leads naturally to our definition of global non abelian zeta functions for curves defined over number fields which themselves are justified by a con vergence result we end this chapter with a detailed study on rank two non abelian zeta functions for genus two curves based on what we call infinitesimal structures of brill noether loci and weierstrass points in chapter ii we begin with a similar construction for the field of rationals to motivate what follows in particular we show that there is an intrinsic relation between our non abelian zeta functions and eisenstein series due to this instead of introducing general non abelian l functions for curves defined over finite fields with more general test functions as what tate did in his thesis for abelian l functions we then define non abelian l functions for curves over finite fields as integrations of eisenstein series associated to l2 automorphic forms over certain generalized moduli spaces here geometric truncations play a key role basic properties for these non abelian l functions such as meromorphic continuation

multiplicity one theorems in the local characteristic 0 non archimedean case we consider distributions on gl n 1 which are invariant under the adjoint action of gl n we prove that such distributions are invariant by transposition this implies multiplicity at most one for restrictions from gl n 1 to gl n similar theorems are obtained for orthogonal or unitary groups

a semidefinite framework for trust region subproblems with applications to large scale minimization primal dual pairs of semidefinite programs provide a general framework for the theory and algorithms for the trust region subproblem trs this latter problem consists in minimizing a general quadratic function subject to a convex quadratic constraint and therefore it is a generalization of the minimum eigenvalue problem the importance of trs is due to the fact that it provides the step in trust region minimization algorithms the semidefinite framework is studied as an interesting instance of semidefinite programming as well as a tool for viewing known algorithms and deriving new algorithms for trs in particular a dual simplex type method is studied that solves trs as a parametric eigenvalue problem this method uses the lanczos algorithm for the smallest eigenvalue as a black box therefore the essential cost of the algorithm is the matrix vector multiplication and thus sparsity can be exploited a primal simplex type method provides steps for the so called hard case extensive numerical tests for large sparse problems are discussed these tests show that the cost of the algorithm is 1 n times the cost of finding a minimum eigenvalue using the lanczos algorithm where 0 n 1 is a fraction which decreases as the dimension increases

structural response of laminated composite shells subjected to blast loading comparison of experimental and theoretical methods abstract the results from a theoretical and experimental investigation of the dynamic response of cylindrically curved laminated composite shells subjected to normal blast loading are presented the dynamic equations of motion for cylindrical laminated shells are derived using the assumptions of love s theory of thin elastic shells kinematically admissible displacement functions are chosen to represent the motion of the clamped cylindrical shell and the governing equations are obtained in the time domain using the galerkin method the time dependent equations of the cylindrically curved laminated shell are then solved by the runge kutta verner method finite element modelling and analysis for the blast loaded cylindrical shell are also presented experimental results for cylindrically curved laminated composite shells with clamped edges and subjected to blast loading are presented the blast pressure and strain measurements are performed on the shell panels the strain response frequencies of the clamped cylindrical shells subjected to blast load are obtained using the fast fourier transformation technique in addition the effects of material properties on the dynamic behaviour are examined the strain time history curves show agreement between the experimental and analysis results in the longitudinal direction of the cylindrical panels however there is a discrepancy between the experimental and analysis results in the circumferential direction of the cylindrical panels a good prediction is obtained for the response frequency of the cylindrical shell panels

duality and sensitivity in nonconvex quadratic optimization over an ellipsoid abstract in this paper a duality framework is discussed for the problem of optimizing a nonconvex quadratic function over an ellipsoid additional insight is obtained from the observation that this nonconvex problem is in a sense equivalent to a convex problem of the same type from which known necessary and sufficient conditions for optimality readily follow based on the duality results some existing solution procedures are interpreted as in fact solving the dual the duality relations are also shown to provide a natural framework for sensitivity analysis

an efficient mean field approach to the set covering problem a mean field feedback artificial neural network ann algorithm is developed and explored for the set covering problem a convenient encoding of the inequality constraints is achieved by means of a multilinear penalty function an approximate energy minimum is obtained by iterating a set of mean field equations in combination with annealing the approach is numerically tested against a set of publicly available test problems with sizes ranging up to 5 103 rows and 106 columns when comparing the performance with exact results for sizes where these are available the approach yields results within a few percent from the optimal solutions comparisons with other approximate methods also come out well in particular given the very low cpu consumption required typically a few seconds arbitrary problems can be processed using the algorithm via a public domain server 2001 elsevier science b v less

twisted relative trace formulae with a view towards unitary groups we introduce a twisted relative trace formula which simultaneously generalizes the twisted trace formula of langlands et al in the quadratic case and the relative trace formula of jacquet and lai certain matching statements relating this twisted relative trace formula to a relative trace formula are also proven including the relevant fundamental lemma in the biquadratic case using recent work of jacquet lapid and their collaborators and the rankin selberg integral representation of the asai l function obtained by flicker using the theory of jacquet piatetskii shapiro and shalika we give the following application let e f be a totally real quadratic extension with gal e f let u be a quasi split unitary group with respect to a cm extension m f and let u res e f u under suitable local hypotheses we show that a cuspidal cohomological automorphic representation of u whose asai l function has a pole at the edge of the critical strip is nearly equivalent to a cuspidal cohomological automorphic representation of u that is u distinguished in the sense that there is a form in the space of admitting a nonzero period over u this provides cohomologically nontrivial cycles of middle dimension on unitary shimura varieties analogous to those on hilbert modular surfaces studied by harder langlands and rapoport

on some properties of quadratic programs with a convex quadratic constraint in this paper we consider the problem of minimizing a possibly nonconvex quadratic function with a quadratic constraint we point out some new properties of the problem in particular in the first part of the paper we show that i given a kkt point that is not a global minimizer it is easy to find a better feasible point ii strict complementarity holds at the local nonglobal minimizer in the second part of this paper we show that the original constrained problem is equivalent to the unconstrained minimization of a piecewise quartic merit function using the unconstrained formulation we give in the nonconvex case a new second order necessary condition for global minimizers in the third part of this paper algorithmic applications of the preceding results are briefly outlined and some preliminary numerical experiments are reported

a criterion for integrability of matrix coefficients with respect to a symmetric space abstract let g be a reductive group and an involution on g both defined over a p adic field we provide a criterion for g integrability of matrix coefficients of representations of g in terms of their exponents along stable parabolic subgroups the group case reduces to casselman s square integrability criterion as a consequence we assert that certain families of symmetric spaces are strongly tempered in the sense of sakellaridis and venkatesh for some other families our result implies that matrix coefficients of all irreducible discrete series representations are g integrable

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

governing equations of a stiffened laminated inhomogeneous conical shell this study presents the dynamic equations of a stiffened composite laminated conical thin shell under the influence of initial stresses the governing equations of a truncated conical shell are based on the donnell mushtari theory of thin shells including the transverse shear deformation and rotary inertia the extension bending coupling is considered in the derivation the composite laminated conical shell is also reinforced at uniform intervals by elastic rings and or stringers the stiffening elements are relatively closely spaced and therefore the stiffeners are smeared out along the conical shell the inhomogeneity of material properties because of temperature moisture or manufacturing processes is taken into account in the constitutive equations a generalized variational theorem is derived so as to describe the complete set of the fundamental equations of the conical shell next the uniqueness is examined in solutions of the dynamic equations of the conical shell and the boundary and initial conditions are shown to be sufficient for the uniqueness in solutions the equations of the laminated composite conical shell are solved by the use of the finite difference method as an illustrative example the accuracy of results is tested by certain earlier results and a good agreement is found

methods for global concave minimization a bibliographic survey the global concave minimization problem is to find the constrained global minimum of a concave function since such a function may have many local minima finding the global minimum is a computationally difficult problem in this bibliographic survey which includes most of the recent papers on constrained global concave minimization we have attempted to briefly summarize the main ideas in each paper these recent papers include those concerned with large scale global concave minimization and bilinear programming

on the spectral side of arthur s trace formula absolute convergence we derive a renement of the spectral expansion of arthur s trace formula the expression is absolutely convergent with respect to the trace norm

regular inference as vertex coloring abstract this paper is concerned with the problem of supervised learning of deterministic finite state automata in the technical sense of identification in the limit from complete data by finding a minimal dfa consistent with a sample we solve this problem by translating it in its entirety to a vertex coloring problem essentially such a problem consists of two types of constraints that restrict the hypothesis space inequivalence and equivalence constraints the inequivalence constraints translate to the vertex coloring problem in a very natural way the equivalence constraints however greatly complicate the translation to vertex coloring in previous coloring based translations these were therefore encoded either dynamically by modifying the vertex coloring instance on the fly or by encoding them as satisfiability problems we provide the first translation that encodes both types of constraints together in a pure vertex coloring instance and prove the correctness of the construction the coloring approach offers many opportunities for applying insights from combinatorial optimization and graph theory to regular inference we immediately obtain new complexity bounds as well as a family of new learning algorithms which can be used to obtain exact hypotheses as well as fast approximations we also demonstrate that satisfying all inequivalence constraints in regular inference and vertex coloring are in some sense equally hard this immediately implies that regular inference is not approximable within s 1 s being the cardinality of the sample for any 1 2 unless p np it also indicates that solving only for inequivalence constraints is easier than the full regular inference problem

square integrability of representations on p adic symmetric spaces abstract a symmetric space analogue of casselman s criterion for square integrability of representations of a p adic group is established it is described in terms of exponents of jacquet modules along parabolic subgroups associated to the symmetric space

a fully polynomial time approximation algorithm for computing a stationary point of the general linear complementarity problem we apply a potential reduction algorithm to solve the general linear complementarity problem glcp minimize xty subject to ax by cz q and x y z 0 we show that the algorithm is a fully polynomial time approximation scheme fptas for computing an e approximate stationary point of the glcp note that there are some glcps in which every stationary point is a solution xty 0 these include the lcps with row sufficient matrices we also show that the algorithm is a polynomial time algorithm for a special class of glcps

nonlinear damped vibrations of a laminated composite plate subjected to blast load this research deals with the derivation and solution of nonlinear dynamic equations of a clamped laminated plate exposed to blast load including structural damping effects dynamic equations of the plate are derived by the use of the virtual work principle the geometric nonlinearity effects are taken into account with the von karman large deflection theory of thin plates an appropriate approximate solution is assumed for the space domain considering the finite element analysis results for the large deformation static analysis of the laminated plate the galerkin method is used to obtain the nonlinear differential equations in the time domain these nonlinear differential equations include structural damping effects the finite difference method is applied to solve the system of coupled nonlinear equations the results of the theoretical analysis are compared with the experimental results good agreement is found for the peak values and frequencies effects of aspect ratio and damping on the dynamic response of the plate are examined the damping coefficient greatly affects the nonlinear dynamic response

bessel identities in the waldspurger correspondence over a p adic field in this paper we develop the local theory for a jacquet s relative trace formula the local theory is essential to the application of the trace formula it is an identity of bessel and relative bessel distributions we show that the relative bessel distribution attached to a distinguished that is self contragradient unitary representation of gl 2 k where k is a p adic field is given by a locally integrable function namely the relative bessel function we compute the relative bessel function for principal series complementary series and special representations we also show that the bessel distributions associated to unitary irreducible admissible representations of the double covers of gl 2 k and sl 2 k are given by a locally integrable bessel functions we compute these bessel functions for principal series complementary series and special representations finally we obtain the waldspurger correspondence via bessel identities between relative bessel functions on gl 2 k and bessel functions on the double cover of sl 2 k the bessel identity also implies the identity between bessel and relative bessel distributions

fourier transform and the global gan gross prasad conjecture for unitary groups by the relative trace formula approach of jacquet rallis we prove the global gan gross prasad conjecture for unitary groups under some local restrictions for the automorphic representations

on linear periods let pi be a cuspidal automorphic representation of mathrm gl 2n mathbb a which is assumed to be the jacquet langlands transfer from a cuspidal automorphic representation pi of mathrm gl 2m d mathbb a where d is a division algebra so that mathrm gl 2m d is an inner form of mathrm gl 2n in this paper we consider the relation between linear periods on pi and pi we conjecture that the non vanishing of the linear period on pi would imply the non vanishing of that on pi we illustrate an approach using a relative trace formula towards this conjecture and prove the existence of smooth transfer over non archimedean local fields

investigation of path following algorithms for signomial geometric programming problems this paper considers signomial geometric programming gp dual problems a class of nonconvex nonlinear programming problems possessing multiple locally optimal solutions the primary purpose of this paper is to investigate the quality of solutions found by use of a path following algorithm the path following method may be applied to either the original nonconvex problem or to each of a sequence of convex posynomial gp problems approximating the original problem for each test problem the algorithms were initiated with thousands of different starting points it was determined that when the stopping criterion was relaxed for early posynomial gp problems in the sequence the ultimate solution tended to be of better quality and more frequently globally optimal

z finite distributions on p adic groups abstract for a real reductive group g the center z u g of the universal enveloping algebra of the lie algebra g of g acts on the space of distributions on g this action proved to be very useful see e g 17 18 32 8 over non archimedean local fields one can replace the action of z u g by the action of the bernstein center z of g i e the center of the category of smooth representations however this action is not well studied in this paper we provide some tools to work with this action and prove the following results the wavefront set of any z finite distribution on g over any point g g lies inside the nilpotent cone of t g g g let h 1 h 2 g be symmetric subgroups consider the space j of h 1 h 2 invariant distributions on g we prove that the z finite distributions in j form a dense subspace in fact we prove this result in wider generality where the groups h i are spherical subgroups of certain type and the invariance condition is replaced by equivariance further we apply those results to density and regularity of relative characters the first result can be viewed as a version of howe s expansion of characters the second result can be viewed as a spherical space analog of a classical theorem on density of characters of finite length representations it can also be viewed as a spectral version of bernstein s localization principle in the archimedean case the first result is well known and the second remains open

inference of regular languages using state merging algorithms with search state merging algorithms have emerged as the solution of choice for the problem of inferring regular grammars from labeled samples a known np complete problem of great importance in the grammatical inference area these methods derive a small deterministic finite automaton from a set of labeled strings the training set by merging parts of the acceptor that corresponds to this training set experimental and theoretical evidence have shown that the generalization ability exhibited by the resulting automata is highly correlated with the number of states in the final solution as originally proposed state merging algorithms do not perform search this means that they are fast but also means that they are limited by the quality of the heuristics they use to select the states to be merged sub optimal choices lead to automata that have many more states than needed and exhibit poor generalization ability in this work we survey the existing approaches that generalize state merging algorithms by using search to explore the tree that represents the space of possible sequences of state mergings by using heuristic guided search in this space many possible state merging sequences can be considered leading to smaller automata and improved generalization ability at the expense of increased computation time we present comparisons of existing algorithms that show that in widely accepted benchmarks the quality of the derived solutions is improved by applying this type of search however we also point out that existing algorithms are not powerful enough to solve the more complex instances of the problem leaving open the possibility that better and more powerful approaches need to be designed

generalized harish chandra descent gelfand pairs and an archimedean analog of jacquet rallis s theorem in the first part of the paper we generalize a descent technique due to harish chandra to the case of a reductive group acting on a smooth affine variety both defined over an arbitrary local field f of characteristic zero our main tool is the luna slice theorem in the second part of the paper we apply this technique to symmetric pairs in particular we prove that the pairs gln k f gln f glk f and gln e gln f are gelfand pairs for any local field f and its quadratic extension e in the non archimedean case the first result was proven earlier by jacquet and rallis and the second by flicker we also prove that any conjugation invariant distribution on gln f is invariant with respect to transposition for non archimedean f the latter is a classical theorem of gelfand and kazhdan

an interior point algorithm to solve computationally difficult set covering problems we present an interior point approach to the zero one integer programming feasibility problem based on the minimization of a nonconvex potential function given a polytope defined by a set of linear inequalities this procedure generates a sequence of strict interior points of this polytope such that each consecutive point reduces the value of the potential function an integer solution not necessarily feasible is generated at each iteration by a rounding scheme the direction used to determine the new iterate is computed by solving a nonconvex quadratic program on an ellipsoid we illustrate the approach by considering a class of difficult set covering problems that arise from computing the 1 width of the incidence matrix of steiner triple systems

on bessel distributions for quasi split groups we show that the bessel distribution attached by gelfand and kazhdan and by shalika to a generic representation of a quasi split reductive group over a local field is given by a function when it is restricted to the open bruhat cell as in the case of the character distribution this function is real analytic for archimedean fields and locally constant for non archimidean fields

a new approach to the feasibility pump in mixed integer programming the feasibility pump is a recent highly successful heuristic for general mixed integer linear programming problems we show that the feasibility pump heuristic can be interpreted as a discrete ver

penalty for zero one integer equivalent problem the equivalence of zero one integer programming and a concave quadratic penalty function problem has been shown by raghavachari for a sufficiently large value of the penalty a lower bound for this penalty is obtained here which in specific cases cannot be reduced

constant term of smooth h_psi spherical functions on a reductive p adic group let be a smooth character of a closed subgroup h of a reductive p adic group g if p is a parabolic subgroup of g such that ph is open in g we define the constant term of every smooth function on g which transforms by under the right action of g the example of mixed models is given it includes symmetric spaces and whittaker models in this case a notion of cuspidal function is defined and studied it leads to finiteness theorems

orbits invariants and representations associated to involutions of reductive groups by an involution of an algebraic group or lie algebra we mean an automorphism 0 such that 0 2 is the identity automorphism let 0 be an involution of a complex reductive lie algebra q and let p denote the 1 eigenspace of 0 on q get g be the adjoint group of q and let k g glog go kostant and rallis 10 have made a detailed study of the action of k on p in particular they obtain very precise information concerning the orbits of k on p and the representation of k on c p the algebra of polynomial functions on p in this paper we consider a global analogue of the problem studied by kostant and rallis let g be a reductive affine algebraic group over an algebraically closed field k of characteristic 2 let 0 be an involution of g and let k gegi0 g g if g is semisimple and the base field is c then g k is the complexification of a riemannian symmetric space we study the action of k and of groups closely related to k by left translation on the coset space g k for technical reasons it is convenient to study a slightly different but equivalent problem let r g g be defined by r g g0 g i then z g p is a closed subvariety of g furthermore z is constant on left cosets of g modulo k and induces an isomorphism o g k p we have o k g k k o g k for k e k and geg thus p is stable under conjugation by k and a is a k isomorphism of affine k varieties we consider the action of k on p by conjugation let x e g have jordan decomposition x x x then we show that x e p if and only if both x and x are in p thus we have a jordan decomposition for elements of p this will play a key role in our results a torus s of g is o anisotropic if o s s 1 for every ses it is known that any two maximal 0 anisotropic tori of g are k let a be a maximal 0 anisotropic torus of g the following result characterizes semisimple elements of p

the complexity of approximating a nonlinear program we consider the problem of finding the maximum of a multivariate polynomial inside a convex polytope we show that there is no polynomial time approximation algorithm for this problem even one with a very poor guarantee unless p np we show that even when the polynomial is quadratic i e quadratic programming there is no polynomial time approximation unless np is contained in quasi polynomial time