spatial free vibration of shear deformable circular curved beams with non symmetric thin walled sections abstract for spatial free vibration of shear deformable circular curved beams with non symmetric thin walled cross sections an improved vibration theory is proposed the elastic strain and kinetic energies are first derived by considering constant curvature effects and shear deformation effects due to shear forces and restrained warping torsion next equilibrium equations and force deformation relations are obtained using a stationary condition of total potential energy and then the closed form solution for out of plane vibration of curved beam is newly derived in addition f e procedures are developed by using isoparametric curved beam element with arbitrary thin walled sections in order to illustrate the accuracy and the practical usefulness of this study closed form and numerical solutions for spatial free vibration are compared with results by available references and abaqus s shell element particularly not only shear deformation and thickness curvature effects on vibration behaviors of curved beams but also mode transition and crossover phenomena with change in curvatures and the length of beams are parametrically investigated

local random quantum circuits are approximate polynomial designs we prove that local random quantum circuits acting on n qubits composed of o t10n2 many nearest neighbor two qubit gates form an approximate unitary t design previously it was unknown whether random quantum circuits were a t design for any t 3 the proof is based on an interplay of techniques from quantum many body theory representation theory and the theory of markov chains in particular we employ a result of nachtergaele for lower bounding the spectral gap of frustration free quantum local hamiltonians a quasi orthogonality property of permutation matrices a result of oliveira which extends to the unitary group the path coupling method for bounding the mixing time of random walks and a result of bourgain and gamburd showing that dense subgroups of the special unitary group composed of elements with algebraic entries are copy tensor product expanders we also consider pseudo randomness properties of local random quantum circuits of small depth and prove that circuits of depth o t10n constitute a quantum t copy tensor product expander the proof also rests on techniques from quantum many body theory in particular on the detectability lemma of aharonov arad landau and vazirani we give applications of the results to cryptography equilibration of closed quantum dynamics and the generation of topological order in particular we show the following pseudo randomness property of generic quantum circuits almost every circuit u of size o nk on n qubits cannot be distinguished from a haar uniform unitary by circuits of size o n k 9 11 that are given oracle access to u

small violations of bell inequalities for multipartite pure random states for any finite number of parts measurements and outcomes in a bell scenario we estimate the probability of random n qudit pure states to substantially violate any bell inequality with uniformly bounded coefficients we prove that under some conditions on the local dimension the probability to find any significant amount of violation goes to zero exponentially fast as the number of parts goes to infinity in addition we also prove that if the number of parts is at least 3 this probability also goes to zero as the local hilbert space dimension goes to infinity

coupled bending torsional dynamic stiffness matrix of an axially loaded timoshenko beam element abstract analytical expressions for the coupled bending torsional dynamic stiffness matrix terms of an axially loaded uniform timoshenko beam element are derived in an exact sense by solving the governing differential equations of motion of the element the symbolic computing package reduce has been used to generate an analytical expression for each of the dynamic stiffness terms in a concise form for check purposes numerical values of the dynamic stiffness matrix terms were obtained using the derived explicit expressions as well as by an alternative nonanalytical method based on matrix inversions and matrix multiplications stiffnesses obtained from both methods agreed with each other to machine accuracy application of the developed theory is discussed with particular reference to an established algorithm the influence of axial force shear deformation and rotatory inertia on the natural frequencies of a bending torsion coupled beam with cantilever end conditions is demonstrated by numerical results such results are not generally available in the literature therefore results obtained by partially restricting the present theory are compared with the existing literature wherever possible the results indicate that the method is accurate and efficient

existence of minimizers for polyconvex and nonpolyconvex problems we study the existence of lipschitz minimizers of integral functionals mathcal i u int omega varphi x textrm det du x dx where omega is an open subset of mathbb r n with lipschitz boundary varphi omega times 0 infty to 0 infty is a continuous function and u in w 1 n omega mathbb r n u x x on partial omega we consider both the cases of varphi convex and nonconvex with respect to the last variable the attainment results are obtained passing through the minimization of an auxiliary functional and the solution of a prescribed jacobian equation

on the minimum problem for a class of noncoercive nonconvex functionals we are concerned with the problem of existence of solutions to the variational problem min left int 0 r g t v t dt v in ac 0 r v r 0 right with only one fixed endpoint prescribed the map g colon 0 r times mathbb r to overline mathbb r is a normal integrand for which neither convexity nor superlinear growth conditions are assumed as an application we give an existence result for the radially symmetric variational problem min u in wuu b r int b r f pt mod x mod nabla u x a x u x dx where b r is the ball of mathbb r n centered at the origin and with radius r 0 the map f colon 0 r times 0 infty to overline mathbb r is a normal integrand and a in l 0 r again neither convexity nor superlinear growth conditions are made on f these kinds of problems with nonconvex lagrangians with respect to nabla u arise in different fields of mathematical physics such as optimal design and nonlinear elasticity

existence of solutions for some implicit partial differential equations and applications to variational integrals involving quasi affine functions keywords implicit partial differential equations existence minimization reference caa article 2004 002doi 10 1017 s0308210500003541 record created on 2008 11 25 modified on 2017 05 12

a relevant two qubit bell inequality inequivalent to the chsh inequality we computationally investigate the complete polytope of bell inequalities for two particles with small numbers of possible measurements and outcomes our approach is limited by pitowsky s connection of this problem to the computationally hard np problem despite this we find that there are very few relevant inequivalent inequalities for small numbers for example in the case with three possible 2 outcome measurements on each particle there is just one new inequality we describe mixed 2 qubit states which violate this inequality but not the chsh the new inequality also illustrates a sharing of bi partite non locality between three qubits something not seen using the chsh inequality it also inspires us to discover a class of bell inequalities with m possible n outcome measurements on each particle

analytical formulation of dynamic stiffness abstract the dynamic stiffness matrix method enables one to model an infinite number of natural modes by means of a small number of unknowns the method has been extended to skeletal structures with uniform or non uniform straight or curved damped or undamped beam members for two dimensional structures if one of the dimensions can be eliminated by means of the kantorovich method the method still applies however for more complicated systems analytical formulation of the dynamic stiffness is tedious a computer assisted analytical method is introduced here for any structural members the differential governing equations of which are expressible in matrix polynomial form complex arithmetics are used to cater for all possible classification of the characteristic roots numerical examples are given and are compared with existing results

an existence result in a problem of the vectorial case of the calculus of variations we prove that the problem hbox minimize int omega g phi nabla t x dx quad t in t b w 0 1 infty omega rn admits at least one solution for any lower semicontinuous extended valued function g for any quasiaffine real valued function phi and for any piecewise affine boundary datum t b such that phi nabla t b is constant

exact dynamic and static stiffness matrices of shear deformable thin walled beam columns abstract total potential energy of non symmetric thin walled beam columns in the general form is presented by introducing the displacement field based on semitangential rotations and deriving transformation equations between displacement and force parameters defined at the arbitrary axis and the centroid shear center axis respectively next governing equations and force deformation relations are derived from the total potential energy for a shear deformable uniform beam element and a system of linear eigenproblem with non symmetric matrices is constructed based on 14 displacement parameters and then explicit expressions for displacement parameters are derived and exact dynamic stiffness matrices are determined using force deformatin relationships in addition the modified numerical method to eliminate multiple zero eigenvalues and to evaluate the exact static stiffness matrix is developed for spatial stability analysis finally in order to demonstrate the validity and the accuracy of this study the spatially coupled natural frequencies and buckling loads are evaluated and compared with analytical solutions or results analyzed by thin walled beam elements and abaqus s shell elements

correlation polytopes their geometry and complexity a family of polytopes correlation polytopes which arise naturally in the theory of probability and propositional logic is defined these polytopes are tightly connected to combinatorial problems in the foundations of quantum mechanics and to the ising spin model correlation polytopes exhibit a great deal of symmetry exponential size symmetry groups which leave the polytope invariant and act transitively on its vertices are defined using the symmetries a large family of facets is determined a conjecture concerning the full facet structure of correlation polytopes is formulated the conjecture however implies that np co np various complexity results are proved it is shown that deciding membership in a correlation polytope is an np complete problem and deciding facets is probably not even in np the relations between the polytope symmetries and its complexity are indicated

well posedness and porosity in the calculus of variations without convexity assumptions the tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions in zaslavski nonlinear analysis 43 2001 339 a generic well posedness result with respect to variations of the integrand of the integral functional without the convexity condition was established for a class of optimal control problems satisfying the cesari growth condition in zaslavski communications in applied analysis to appear we extended this generic well posedness result to a class of variational problems in which the values at the end points are also subject to variations more precisely we established a generic well posedness result for a class of variational problems without convexity assumptions over functions with values in a banach space e which is identified with the corresponding complete metric space of pairs f 1 2 where f is an integrand satisfying the cesari growth condition and 1 2 e are the values at the end points denoted by a we showed that for a generic f 1 2 a the corresponding variational problem is well posed in this paper we study the set of all pairs f 1 2 a for which the corresponding variational problem is well posed we show that the complement of this set is not only of the first category but also a porous set

generic well posedness of minimization problems with mixed smooth constraints abstract in this paper we study mathematical programming problems with mixed smooth constraints in a banach space and show that most of the problems in the baire category sense are well posed our result is a generalization of a result of a d ioffe et al a variational principle for problems with functional constraints siam j optim 12 2001 461 478 obtained for finite dimensional banach spaces it is also an extension of our recent result a j zaslavski generic well posedness of minimization problems with mixed continuous constraints nonlinear anal doi 10 1016 j na 2005 10 032 which was obtained for mathematical programming problems with continuous constraints

coupled vibrations of beams an exact dynamic element stiffness matrix a uniform linearly elastic beam element with non coinciding centres of geometry shear and mass is studied under stationary harmonic end excitation the euler bernoulli saint venant theory is applied thus the effect of warping is not taken into account the frequency dependent 12 12 element stiffness matrix is established by use of an exact method the translational and rotational displacement functions are represented as sums real of complex exponential terms where the complex exponents are numerically found built up structures containing beam elements of the described type can be analysed with ease and certainty using existing library subroutines

dynamic analysis of thin walled closed section beams the present paper considers the problem of dynamic behavior of thin walled beams of arbitrary closed cross section by means of an exact solution starting from benscoter s theory the differential equations of motion are derived by postulating the principle of the virtual work due to a variation of displacements in the case of simply supported thin walled beam a closed form solution for the coupled natural frequencies of free harmonic vibrations was derived the method is illustrated by examples and results are compared with analytical results analyzed by vlasov s theory as well as with fem results

generic well posedness of nonconvex optimal control problems the tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions in our previous work a generic existence and uniqueness result with respect to variations of the integrand of the integral functional without the convexity condition was established for a class of optimal control problems satisfying the cesari growth condition in this paper we extend this generic existence and uniqueness result to a class of optimal control problems in which the right hand side of differential equations is also subject to variations

stiffness matrices for flexural torsional lateral buckling and vibration analysis of thin walled beam abstract based on the power series method the static and dynamic stiffness matrices for the flexural torsional buckling and free vibration analysis of thin walled beam with non symmetric cross section subjected to linearly variable axial force are newly presented additionally the static stiffness matrix for the lateral buckling analysis of non symmetric beam is presented for the first time for this the elastic strain energy the potential energy considering the second order terms of finite rotations and the kinetic energy for thin walled beam with non symmetric cross section are introduced then equations of motion and force deformation relations are derived from the energy principle explicit expressions for displacement parameters are derived based on power series expansions of displacement components finally the static and dynamic element stiffness matrices are determined using force deformation relationships in order to verify the accuracy of this study the numerical solutions are presented and compared with the finite element solutions using the hermitian beam elements and abaqus s shell elements

almost every convex or quadratic programming problem is well posed we provide an abstract principle aimed at proving that classes of optimization problems aretypically well posed in the sense that the collection of ill posed problems within each class is s porous as a consequence we establish typical well posedness in the above sense for unconstrained minimization of certain classes of functions e g convex and quasi convex continuous as well as of convex programming with inequality constraints we conclude the paper by showing that the collection of consistent ill posed problems of quadratic programming of any fixed size has lebesgue measure zero in the corresponding euclidean space

multigraph approach to quantum non locality non contextuality nc and bell inequalities can be expressed as bounds for positive linear combinations s of probabilities of events exclusive events in s can be represented as adjacent vertices of a graph called the exclusivity graph of s in the case that events correspond to the outcomes of quantum projective measurements quantum probabilities are intimately related to the grotschel lovasz schrijver theta body of the exclusivity graph then one can easily compute an upper bound to the maximum quantum violation of any nc or bell inequality by optimizing s over the theta body and calculating the lovasz number of the corresponding exclusivity graph in some cases this upper bound is tight and gives the exact maximum quantum violation however in general this is not the case the reason is that the exclusivity graph does not distinguish among the different ways exclusivity can occur in bell inequality and similar scenarios an interesting question is whether there is a graph theoretical concept which accounts for this problem here we show that for any given n partite bell inequality an edge coloured multigraph composed of n single colour graphs can be used to encode the relationships of exclusivity between each party s parts of the events then the maximum quantum violation of the bell inequality is exactly given by a refinement of the lovasz number that applies to these edge coloured multigraphs we show how to calculate upper bounds for this number using a hierarchy of semi definite programs and calculate upper bounds for i3 i3322 and the three bipartite bell inequalities whose exclusivity graph is a pentagon the multigraph theoretical approach introduced here may remove some obstacles in the program of explaining quantum correlations from first principles this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

convex optimization and the epi distance topology let 17 x denote the proper lower semicontinuous convex functions on a banach space x equipped with the completely metrizable topology t of uniform convergence of distance functions on bounded sets a function f in 17 x is called well posed provided it has a unique minimizer and each minimizing sequence converges to this minimizer we show that well posedness of f e r x is the minimal condition that guarantees strong convergence of approximate minima of t approximating functions to the minimum of f moreover we show that most functions in 17 x taw are well posed and that this fails if 17 x is topologized by the weaker topology of mosco convergence whenever x is infinite dimensional applications to metric projections are also given including a fundamental characterization of approximative compactness

local quasi hidden variable modelling and violations of bell type inequalities by a multipartite quantum state we introduce for a general correlation scenario a new simulation model a local quasi hidden variable lqhv model where locality and the measure theoretic construction inherent to a local hidden variable lhv model are preserved but positivity of a simulation measure is dropped we specify a necessary and sufficient condition for lqhv modelling and based on this prove that every quantum correlation scenario admits a lqhv simulation via the lqhv approach we construct analogs of bell type inequalities for an n partite quantum state and find a new analytical upper bound on the maximal violation by an n partite quantum state of s1 sn setting bell type inequalities either on correlation functions or on joint probabilities and for outcomes of an arbitrary spectral type discrete or continuous this general analytical upper bound is expressed in terms of the new state dilation characteristics introduced in the present paper and not only traces quantum states admitting an s1 sn setting lhv de

a variational principle for problems with functional constraints in this paper we show that in several important classes of optimization problems like mathematical programming with k smooth data quadratic programming in a hilbert space convex programming in a banach space semi infinite programming and optimal control of linear systems with quadratic cost most of the problems in the baire category sense are well posed this is derived from a general variational principle for problems with functional constraints

lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands the study of regularity properties for minimizers of problems of the form min u u dt u e iv q r u a a u b b 1 1 has been undertaken for a long time in calculus of variations and a number of results are by now available on this subject when f t s z is a smooth coercive function problem 1 1 was considered by tonelli see 18 19 who proved that every minimizer u t of the problem 1 1 is locally lipschitz on a relatively open set of full measure in a b under some additional assumptions on f it is also possible to prove global regularity theorems see for instance cesari 3 chap 2 sect 61 in recent years much attention has been devoted to problems of the form l l on the one hand in weakening the hypotheses of tonelli s regularity results and on the other in finding counterexamples of nonregular minimizers for coercive functionals with respect to this last subject we recall that it has been shown see ball and mizel l and clarke and vinter 6 that there exist polynomial functions f t s z such that for suitable c 0 and p

density of the set of local minimizers for a generic cost function abstract in this work we study the minimization problem f x min x x where f x r 1 is a continuous function defined on a complete separable metric space x we show that for a generic function f the set of all local minimizers is everywhere dense in x

coupled bending torsional dynamic stiffness matrix for beam elements explicit expressions for the coupled bending torsional dynamic stiffness matrix of a uniform beam element are derived in an exact sense by solving the governing differential equation of the beam implementation of the derived dynamic stiffness matrix in a space frame computer program is discussed with particular reference to an established algorithm to enable vibration analysis of coupled systems to be made the application of the theory is demonstrated by an illustrative example wherein the results for a cantilever beam with a substantial amount of coupling between bending and torsion are highlighted the correctness of the theory is confirmed to a high degree of accuracy by computed results and numerical checks

solutions of vectorial hamilton jacobi equations and minimizers of nonquasiconvex functionals abstract we provide a unified approach to prove existence results for the dirichlet problem for hamilton jacobi equations and for the minimum problem for nonquasiconvex functionals of the calculus of variations with affine boundary data the idea relies on the definition of integro extremal solutions introduced in the study of nonconvex scalar variational problem

generic well posedness of optimal control problems without convexity assumptions the tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions in a j zaslavski nonlinear anal to appear a generic existence and uniqueness result with respect to variations of the integrand of the integral functional without the convexity condition was established for a class of optimal control problems satisfying the cesari growth condition in this paper we extend the generic existence and uniqueness result in a j zaslavski nonlinear anal to appear to a class of optimal control problems in which constraint maps are also subject to variations the main result of the paper is obtained as a realization of a variational principle extending the variational principle introduced in a d ioffe and a j zaslavski siam j control optim 38 2000 pp 566 581

existence of minimizers for non quasiconvex integrals keywords quasiconvexity existence of minimizers reference caa article 1995 002doi 10 1007 bf00380915 record created on 2008 11 25 modified on 2017 05 12

one dimensional infinite horizon variational problems arising in continuum mechanics in this paper we study a variational problem for real valued functions defined on an infinite semiaxis of the line to wit given x 2 we seek a minimal solution to the problem minimize the functional given by i left w left cdot right right int limits 0 infty f left w left s right ddot w left s right right ds w in ax left upsilon in w loc 2 1 left 0 infty right left upsilon left 0 right dot upsilon left 0 right x right right p

existence results for noncoerecive variational problems the aim of this paper is to give an existence result for a class of one dimensional nonconvex noncoercive problems in the calculus of variations the main tools for the proof are an existence theorem in the convex case and the closure of the convex hull of the epigraph of functions strictly convex at infinity

generic existence of lipschitzian solutions of optimal control problems without convexity assumptions the tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions in this paper we consider a large class of optimal control problems which is identified with a complete metric space of integrands without convexity assumptions and show that for a generic integrand the corresponding optimal control problem possesses a unique solution and this solution is lipschitzian

generic well posedness of variational problems without convexity assumptions the tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions in our previous work a generic well posedness result with respect to variations of the integrand of the integral functional without the convexity condition was established for a class of optimal control problems satisfying the cesari growth condition in this paper we extend this generic well posedness result to two classes of variational problems in which the values at the end points are also subject to variations the main results of the paper are obtained as realizations of a general variational principle

existence of overtaking optimal trajectories for problems with convex integrands in this work we study the existence of optimal overtaking trajectories for autonomous control systems on an infinite time interval we extend in two directions the research initiated by brock and haurie brock w a a haurie 1976 on existence of overtaking optimal trajectories over an infinite time horizon math oper res 1 337 346 first we relax the technical assumptions needed to establish the existence of overtaking optimal trajectories the assumptions in our existence result are basically those made in brock w a a haurie 1976 on existence of overtaking optimal trajectories over an infinite time horizon math oper res 1 337 346 for the existence of weakly overtaking optimal trajectories with the additional assumption that a certain linear differential equation determined by the integrand has no nontrivial periodic solutions a discussion and an example concerning this assumption are provided in particular we show that this property is generic in the epi convergence topology

generic well posedness of minimization problems with mixed continuous constraints in this paper we study mathematical programming problems with mixed constraints in a banach space and show that most of the problems in the baire category sense are well posed our result is a generalization of a result of ioffe et al siam j optim 12 2001 461 478 obtained for finite dimensional banach spaces

generic flows generated by continuous vector fields in banach spaces soit f un champ vectoriel defini sur un sous ensemble ouvert d un espace de banach reel on considere le probleme de cauchy x f t x x 0 y 7b e un sous ensemble non vide de points initiaux on etudie les f qui engendrent un flot pour y 7b e

existence of overtaking solutions to infinite dimensional control problems on unbounded time intervals the optimal control of an infinite dimensional linear control system with unbounded time interval is considered the results obtained are an extension to a hilbert space setting of the results reported in brock and haurie math oper res 1 1976 pp 337 346 in particular it is shown that under appropriate conditions overtaking optimal trajectories asymptotically approach a unique optimal steady state this is the so called turnpike property found in the economics literature when this condition is combined with an associated optimal control problem results concerning the existence of overtaking optimal solutions are obtained both distributed and boundary controls are considered finally we demonstrate the applicability of our results by considering several examples arising in the context of economics and resources management

generic convergence of descent methods in banach spaces given a continuous convex functionf on a banach spacex we consider a complete metric space of vector fieldsv onx with the topology of uniform convergence on bounded subsets with each such vector field we associate two iterative processes we show that for a genericv the values of the functionf tend to its infimum for both processes

nonclassical correlations from randomly chosen local measurements we show that correlations inconsistent with any locally causal description can be a generic feature of measurements on entangled quantum states specifically spatially separated parties who perform local measurements on a maximally entangled state using randomly chosen measurement bases can with significant probability generate nonclassical correlations that violate a bell inequality for n parties using a greenberger horne zeilinger state this probability of violation rapidly tends to unity as the number of parties increases we also show that even with both a randomly chosen two qubit pure state and randomly chosen measurement bases a violation can be found about 10 of the time among other applications our work provides a feasible alternative for the demonstration of bell inequality violation without a shared reference frame

on nonlocality as a resource theory and nonlocality measures with the advent of device independent quantum information processing nonlocality is nowadays regarded as a resource that can be used for various tasks using the analogy of entanglement theory we approach nonlocality from this perspective in order to do so we analyze in full detail the operations that can be implemented in this scenario and under which nonlocality cannot increase this provides a theoretical basis from which to study how to order and quantify nonlocal behavior finally we review several nonlocality measures and discuss their validity from this point of view this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

unbounded violation of tripartite bell inequalities we prove that there are tripartite quantum states constructed from random unitaries that can lead to arbitrarily large violations of bell inequalities for dichotomic observables as a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model this is in sharp contrast with the bipartite case where all violations are bounded by grothendieck s constant we will discuss the possibility of determining the hilbert space dimension from the obtained violation and comment on implications for communication complexity theory moreover we show that the violation obtained from generalized greenberger horne zeilinger ghz states is always bounded so that in contrast to many other contexts ghz states do not lead to extremal quantum correlations in this case in order to derive all these physical consequences we will have to obtain new mathematical results in the theories of operator spaces and tensor norms in particular we will prove the existence of bounded but not completely bounded trilinear forms from commutative c algebras finally we will relate the existence of diagonal states leading to unbounded violations with a long standing open problem in the context of banach algebras

the existence of catching up optimal solutions for a class of infinite horizon control problems with time delay the optimal control of a system whose states are governed by a nonlinear autonomous volterra integrodifferential equation with unbounded time interval is considered specifically it is assumed that the delay occurs only in the state variable the results obtained extend those of brock and haurie math oper res 1 1976 pp 337 346 and leizarowitz math oper res 10 1985 pp 450 461 in particular it is shown that under appropriate hypotheses catching up optimal solutions asymptotically approach a unique optimal steady state and thus enjoy the so called turnpike property found in the economics literature by combining this result with an associated optimal control problem the desired existence result is obtained furthermore it is remarked that in addition to extending these earlier works to the time delay case the results presented below utilize convexity seminormality and growth hypotheses that in some cases are weaker than those encountered in the above mentioned papers

variational principles and well posedness in optimization and calculus of variations the concluding result of the paper states that variational problems are generically solvable and even well posed in a strong sense without the convexity and growth conditions always present in individual existence theorems this and some other generic well posedness theorems are obtained as realizations of a general variational principle extending the variational principle of deville godefroy zizler

classifying 50 years of bell inequalities since john s bell demonstrated the interest of studying linear combinations of probabilities in relation with the epr paradox in 1964 bell inequalities have lead to numerous developments unfortunately the description of bell inequalities is subject to several degeneracies which make any exchange of information about them unnecessarily hard here we analyze these degeneracies and propose a decomposition for bell like inequalities based on a set of reference expressions which is not affected by them these reference expressions set a common ground for comparing bell inequalities we provide algorithms based on finite group theory to compute this decomposition implementing these algorithms allows us to set up a compendium of reference bell like inequalities available online at www faacets com this website constitutes a platform where registered bell like inequalities can be explored new inequalities can be compared to previously known ones and relevant information on bell inequalities can be added in a collaborative manner this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

an indirect method in the calculus of variations this article presents a new approach to the issue of the existence of solutions to the basic problem in the calculus of variations the method is indirect and applies to certain classes of problems with slow or no growth in addition to those satisfying the traditional coercivity condition the proof hinges upon showing with the help of nonsmooth analysis that a certain value function is constant examples are given to illustrate the applicability of the results and the necessity of the hypotheses

the turnpike property for approximate solutions of variational problems without convexity abstract in this work we study the structure of approximate solutions of variational problems with continuous integrands f 0 r n r n r 1 which belong to a complete metric space of functions m we do not impose any convexity assumption and establish the existence of an everywhere dense g set f m such that each integrand in f has the turnpike property this result is an extention of the main result of zaslavski nonlinear anal 42 2000 1465 which was obtained for integrands f m which were convex as a function of the last argument derivative

exact dynamic stiffness matrix of non symmetric thin walled curved beams subjected to initial axial force abstract an improved numerical method to exactly evaluate the dynamic element stiffness matrix is proposed for the spatially coupled free vibration analysis of non symmetric thin walled curved beams subjected to uniform axial force for this purpose firstly equations of motion boundary conditions and force deformation relations are rigorously derived from the total potential energy for a curved beam element next systems of linear algebraic equations with non symmetric matrices are constructed by introducing 14 displacement parameters and transforming the fourth order simultaneous differential equations into the first order simultaneous equations and then explicit expressions for displacement parameters are numerically evaluated via eigensolutions and the exact 14 14 element stiffness matrix is determined using force deformation relations in order to demonstrate the validity and the accuracy of this study the spatially coupled natural frequencies of non symmetric thin walled curved beams subjected to uniform compressive and tensile forces are evaluated and compared with analytical and finite element solutions using hermitian curved beam elements or abaqus s shell element in addition some results by the parametric study are reported

spatial stability and free vibration of shear flexible thin walled elastic beams ii numerical approach in a companion paper 1 equations of motion and closed form solutions for spatial stability and free vibration analysis of shear flexible thin walled elastic beams were analytically derived from the linearized hellinger reissner principle in this paper elastic and geometric stiffness matrices and consistent mass matrix for finite element analysis are evaluated by using isoparametric and hermitian interpolation polynomials isoparametric interpolation functions with 2 3 and 4 nodes per element are utilized in isoparametric beam elements and in hermitian beam elements the third and fifth order hermitian polynomials including shear deformation effects are newly derived and applied for the calculation of element matrices in order to verify the validity of the finite element formulation both analytic and numerical solutions for spatial buckling and free vibration problems including shear effects are presented and compared

beam element matrices derived from vlasov s theory of open thin walled elastic beams a uniform beam element of open thin walled cross section is studied under stationary harmonic end excitation an exact dynamic transcendentally frequency dependent 14 14 element stiffness matrix is derived from vlasov s coupled differential equations special attention is paid to the computational problems arising when coefficients vanish in these equations because of symmetric cross section zero warping stiffness etc the dynamic element stiffness matrix is established via a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices a static stiffness matrix is also derived and the associated consistent mass and geometric stiffness matrices are given modal masses are evaluated a fortran program and a numerical example are included

bell inequalities for arbitrarily high dimensional systems we develop a novel approach to bell inequalities based on a constraint that the correlations exhibited by local variable theories must satisfy this is used to construct a family of bell inequalities for bipartite quantum systems of arbitrarily high dimensionality which are strongly resistant to noise in particular our work gives an analytic description of previous numerical results and generalizes them to arbitrarily high dimensionality

one dimensional variational problems whose minimizers do not satisfy the euler lagrange equation in this paper we consider the problem of minimizing i u text int a b text f x u x u x dx 1 1 in the set a of absolutely continuous function u a b satisfying the end conditions u left a right text alpha text quad u left b right text beta text 1 2 where and are given constant in 1 1 a b is a finite interval denotes frac d dx and the integrand f f x u p is assumed to be smooth nonnegative and to satisfy the regularity condition f pp text 0 text 1 3

explicit lower and upper bounds on the entangled value of multiplayer xor games the study of quantum mechanical violations of bell inequalities is motivated by the investigation and the eventual demonstration of the nonlocal properties of entanglement in recent years bell inequalities have found a fruitful re formulation using the language of multiplayer games originating from computer science this paper studies the nonlocal properties of entanglement in the context of the simplest such games called xor games when there are two players it is well known that the maximum bias the advantage over random play of players using entanglement can be at most a constant times greater than that of classical players recently perez garcia et al commun mathe phys 279 455 2008 showed that no such bound holds when there are three or more players the use of entanglement can provide an unbounded advantage and scale with the number of questions in the game their proof relies on non trivial results from operator space theory and gives a non explicit existence proof leading to a game with a very large number of questions and only a loose control over the local dimension of the players shared entanglement

typical convex program is very well posed in this paper we consider the collection of convex programming problems with inequality and equality constraints in which every problem of the collection is obtained by linear perturbations of the cost function and right hand side perturbation of the constraints while the core cost function and the left hand side constraint functions are kept fixed the main result shows that the set of the problems which are not well posed is porous in a certain strong sense our results concern both the infinite and finite dimensional case in the last case the conclusions are significantly sharper

recent developments in the theory of hamiltonian systems area preserving mappings of an annulus occur as poincare mappings of hamiltonian systems they were studied extensively by g d birkhoff recently aubry and mather investigated the subclass of so called monotone twist mappings for which they constructed independently closed invariant cantor sets their work led to important new results their theory is discussed and related to hamiltonian systems satisfying a legendre condition the connection of this theory with the stability problem kam theory and in particular the disintegration of invariant tori is discussed various constructions of mather sets are explained in which minimal solutions of variational problems play a central role this theory has a close relation to the differential geometric investigations by morse and hedlund on geodesics on two dimensional surfaces