wave propagation on helices and hyperhelices a fractal regression a hyperhelix of order n is defined to be a selfsimilar object consisting of a thin elastic rod wound into a helix which is itself wound into a larger helix until this process has been repeated n

analytical and numerical study on spatial free vibration of non symmetric thin walled curved beams for spatial free vibration of non symmetric thin walled circular curved beams an accurate displacement field is introduced by defining all displacement parameters at the centroidal axis and three total potential energy functionals are consistently derived by degenerating the potential energy for the elastic continuum to that for thin walled curved beams the closed form solutions are newly obtained for in plane and out of plane free vibration analysis of monosymmetric curved beams respectively also two thin walled curved beam elements are developed using the third and fifth order hermitian polynomials in order to illustrate the accuracy and the practical usefulness of the present method analytical and numerical solutions by this study are presented and compared with previously published results or solutions by abaqus the shell element particularly effects of the thickness curvature as well as the inextensional condition are investigated on free vibration of curved beams with monosymmetric and non symmetric cross sections

a numerical study of 1d self similar waveguides relationship between localization integrated density of state and the distribution of scatterers the vibrational behaviour of 1d mechanical structures locally loaded with additional masses according to a self similar pattern is considered an analysis of the multiple scattering problem is proposed to point out the existence of strongly localized modes the eigenfrequency distribution is investigated through the vibrational integrated density of state integrated dos the features of this distribution allow one to predict the mode shapes and give an indication of the additional masses number and weight finally the role played by the distribution of the additional masses in the vibrational behaviour of the structure is discussed

free vibration analysis of cylindrical helical springs by the pseudospectral method abstract the pseudospectral method is applied to the free vibration analysis of cylindrical helical springs the displacements and the rotations are approximated by the series expansions of chebyshev polynomials and the governing equations are collocated the number of collocation points is chosen to be less than the number of the expansion terms to handle the boundary condition numerical examples are provided for fixed fixed free free fixed free and hinged hinged boundary conditions the results show good agreement with those of the transfer matrix method and the dynamic stiffness method the formulation of the pseudospectral method is straightforward and shows an exponential rate of convergence with mesh refinement

quantum correlations and distinguishability of quantum states a survey of various concepts in quantum information is given with a main emphasis on the distinguishability of quantum states and quantum correlations covered topics include generalized and least square measurements state discrimination quantum relative entropies the bures distance on the set of quantum states the quantum fisher information the quantum chernoff bound bipartite entanglement the quantum discord and geometrical measures of quantum correlations the article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them and for mathematicians looking for an up to date introductory course on these subjects which are mainly developed in the physics literature

free vibration of a beam subjected to large static deflection abstract considered in this paper is the problem of free vibration of a beam that has undergone a large static deflection the nonlinear equations of motion for the beam are derived first the equations are then decomposed into a set of nonlinear differential equations for the static deflection and a set of linear differential equations for the vibrational motion of the beam the coefficients of the vibration equations consist of the beam s static deflection the nonlinear differential equations are solved analytically to obtain the static deflection the vibration equations are solved by expanding the displacements in a power series coefficients of the power series are constructed analytically through a recursive relationship the natural frequencies of the beam under large static bending are determined by solving a 3 3 eigenvalue problem substitution of the eigenvalues and eigenvectors into the power series expansion of the displacements yields the corresponding modes of vibration several numerical examples are given to illustrate the solution procedure

dynamic stiffness analysis for in plane vibrations of arches with variable curvature this paper provides a systematic approach to solve in plane free vibrations of arches with variable curvature the proposed approach basically introduces the concept of dynamic stiffness matrix into a series solution for in plane vibrations of arches with variable curvature an arch is decomposed into as many elements as needed for accuracy of solution in each element a series solution is formulated in terms of polynomials the coefficients of which are related to each other through recurrence formulas as a result in order to have an accurate solution one does not need a lot of terms in series solution and in taylor expansion series for the variable coefficients of the governing equations due to the consideration of variable curvature finally a dynamic stiffness matrix is formed such that it can be applied to solve more complicated systems such as multiple span arches in the whole analysis the effects of rotary inertia and shear deformation have been taken into account

no hypersignaling principle a paramount topic in quantum foundations rooted in the study of the einstein podolsky rosen epr paradox and bell inequalities is that of characterizing quantum theory in terms of the spacelike correlations it allows here we show that to focus only on spacelike correlations is not enough we explicitly construct a toy model theory that while not contradicting classical and quantum theories at the level of spacelike correlations still displays an anomalous behavior in its timelike correlations we call this anomaly quantified in terms of a specific communication game the hypersignaling phenomena we hence conclude that the principle of quantumness if it exists cannot be found in spacelike correlations alone nontrivial constraints need to be imposed also on timelike correlations in order to exclude hypersignaling theories

generalized gamma approximation with rates for urns walks and trees we study a new class of time inhomogeneous polya type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma distributions with integer parameters a class which includes the rayleigh half normal and gamma distributions our main tool is stein s method combined with characterizing the generalized gamma limiting distributions as fixed points of distributional transformations related to the equilibrium distributional transformation from renewal theory we identify special cases of these urn models in recursive constructions of random walk paths and trees yielding rates of convergence for local time and height statistics of simple random walk paths as well as for the size of random subtrees of uniformly random binary and plane trees

random positive operator valued measures we introduce several notions of random positive operator valued measures povms and we prove that some of them are equivalent we then study statistical properties of the effect operators for the canonical examples starting from the limiting eigenvalue distribution we derive the large system limit for several quantities of interest in quantum information theory such as the sharpness the noise content and the probability range finally we study different compatibility criteria and we compare them for generic povms

theoretical and experimental analysis of the stop band behavior of elastic springs with periodically discontinuous of curvature the advanced design of springs with tailored transmission characteristics is proposed the existence of frequency stop bands in the transmission characteristics is theoretically predicted and experimentally validated the underlying mechanism of generating stop band behavior is the periodic discontinuity of the curvature the theoretical analysis is performed in the framework of the floquet theory for an infinitely long spring experimental results are obtained for the springs consisting of a small number of repeated periodicity cells

classical randomness in quantum measurements similarly to quantum states also quantum measurements can be mixed corresponding to a random choice within an ensemble of measuring apparatuses such mixing is equivalent to a sort of hidden variable which produces a noise of purely classical nature it is then natural to ask which apparatuses are indecomposable i e do not correspond to any random choice of apparatuses this problem is interesting not only for foundations but also for applications since most optimization strategies give optimal apparatuses that are indecomposable mathematically the problem is posed describing each measuring apparatus by a positive operator valued measure povm which gives the statistics of the outcomes for any input state the povms form a convex set and in this language the indecomposable apparatuses are represented by extremal points the analogous of pure states in the convex set of states differently from the case of states however indecomposable povms are not necessarily rank one e g von neumann measurements in this paper we give a complete classification of indecomposable apparatuses for discrete spectrum by providing different necessary and sufficient conditions for extremality of povms along with a simple general algorithm for the decomposition of a povm into extremals as an interesting application informationally complete measurements are analysed in this respect the convex set of povms is fully characterized by determining its border in terms of simple algebraic properties of the corresponding povms

l1 bounds in normal approximation the zero bias distribution w of w defined though the characterizing equation ewf w 2 ef 0 w for all smooth functions f exists for all w with mean zero and finite variance 2 for w and w defined on the same probability space the l 1 distance between f the distribution function of w with ew 0 and var w 1 and the cumulative standard normal has the simple upper bound f 1 2e w w this inequality is used to provide explicit l 1 bounds with moderate sized constants for independent sums projections of cone measure on the sphere s p simple random sampling and combinatorial central limit theorems

extreme covariant quantum observables in the case of an abelian symmetry group and a transitive value space we represent quantum observables as normalized positive operator valued measures and consider convex sets of observables which are covariant with respect to a unitary representation of a locally compact abelian symmetry group g the value space of such observables is a transitive g space we characterize the extreme points of covariant observables and also determine the covariant extreme points of the larger set of all quantum observables the results are applied to position position difference and time observables

low frequency mode transition in the free in plane vibration of curved beams the low frequency mode transition in the free in plane vibration of beams with varying curvature and cross section is examined by using perturbation analysis a simplified zeroth order equation for beam vibration in the region of the mode transition is derived this equation shows explicitly which modes undergo a transition for a particular type of beam curvature and cross section analytic approximations for frequency and mode shape are derived by the cases of beam curvature represented by symmetric and antisymmetric polynomials and their validity is illustrated by comparison with numerical solutions many features of mode transition phenomenon are revealed analytically including the effect of beam curvature on mode shape during the transition stage the similarities and distinctions between the low mode and the high mode number transitions are discussed

stein s method and birth death processes barbour introduced a probabilistic view of stein s method for estimating the error in probability approximations however in the case of approximations by general distributions on the integers there have been no purely probabilistic proofs of stein s bounds till this paper furthermore the methods introduced here apply to a very large class of approximating distributions on the non negative integers among which there is a natural class for higher order approximations by probability distributions rather than signed measures as previously the methods also produce stein magic factors for process approximations which do not increase with the window of observation and which are simpler to apply than those in brown weinberg and xia

stein s method palm theory and poisson process approximation the framework of stein s method for poisson process approximation is presented from the point of view of palm theory which is used to construct stein identities and define local dependence a general result theorem 2 3 in poisson process approximation is proved by taking the local approach it is obtained without reference to any particular metric thereby allowing wider applicability a wasserstein pseudometric is introduced for measuring the accuracy of point process approximation the pseudometric provides a generalization of many metrics used so far including the total variation distance for random variables and the wasserstein metric for processes as in barbour and brown stochastic process appl 43 1992 9 31 also through the pseudometric approximation for certain point processes on a given carrier space is carried out by lifting it to one on a larger space extending an idea of arratia goldstein and gordon statist sci 5 1990 403 434 the error bound in the general result is similar in form to that for poisson approximation as it yields the stein factor 1 as in poisson approximation it provides good approximation particularly in cases where is large the general result is applied to a number of problems including poisson process modeling of rare words in a dna sequence

dynamic stiffness formulation free vibration and wave motion of helical springs a coil spring can only be treated as a simple massless force element at low frequencies the effects of internal resonances leading to significant dynamic stiffening for an automotive suspension spring this occurs at frequencies as low as about 40 hz this paper presents an efficient method for calculating the dynamic stiffness of a helical coil spring the partial differential equations of motion are used to derive the relation between wavenumber and frequency along with the associated wave shapes by expressing the response in terms of these waves the dynamic stiffness matrix is assembled natural frequencies are obtained from the reduced stiffness matrix allowing for different boundary conditions making use of the wittrick williams algorithm the results of the dynamic stiffness method are compared with those of the transfer matrix method and the finite element method the nature of the wave propagation is also investigated although at low frequencies four wave types propagate above a particular frequency only two propagating waves remain these are composite waves which are excited by both axial and transverse motion for lower values of helix angle an intermediate frequency range exists where six propagating waves can occur

realizing a 2 d positive operator valued measure by local operations and classical communication we study the realization of a 2 d positive operator valued measure povm by local operations and classical communication locc we derive that any povm on a 2 d hilbert space in which each party s space is finite dimensional can be realized by one way locc this implies that any optimal discrimination of quantum states spanning such a 2 d hilbert space is possible by one way locc regardless of the optimality criterion used and how entangled the states are

on the convex structure of process positive operator valued measures measurements on quantum channels are described by so called process positive operator valued measures or process povms we study implementing schemes of extremal process povms as it turns out the corresponding measurement must satisfy certain extremality property which is stronger than the usual extremality given by the convex structure this property motivates the introduction and investigation of the a convex structure of povms which generalizes both the usual convex and c convex structures we show that extremal points and faces of the set of process povms are closely related to a extremal points and a faces of povms for a certain subalgebra a we also give a characterization of a extremal and a pure povms

in plane and out of plane free vibrations of curved beams with variable sections we present an approximate method to study the analysis for both the in plane and out of plane free vibration of horizontally curved beams with arbitrary shapes and variable cross sections the characteristic equation for free vibration can be derived by applying the green function which is obtained as a discrete type solution of differential equations governing the flexural behaviour of the curved beam under the action of a concentrated load

free vibration analysis of non cylindrical helices with variable cross section by using mixed fem the objective of the study is to present a mixed finite element fe formulation for the free vibration analysis of non cylindrical helices with variable cross section non cylindrical helix geometry was well approximated through the variable arc lengths and linear variations in curvatures via shape functions the mixed fe model for non cylindrical helices was developed by using the exact cylindrical helix geometry and corresponding field equations the element and consistent mass matrices are attained under these assumptions the element matrix is derived based on the timoshenko beam theory and the effects of rotary inertia are involved into the mass matrix although the formulation is quite simple the generated element is capable to provide highly accurate solutions for the conical barrel and hyperboloidal geometries of non cylindrical helices the results of presented fe model based on an approximated geometry approach are in a good agreement with the other studies in the actual literature some original examples were generated and solved for the literature as well

exponential and uniform ergodicity of markov processes general characterizations of geometric convergence for markov chains in discrete time on a general state space have been developed recently in considerable detail here we develop a similar theory for varphi irreducible continuous time processes and consider the following types of criteria for geometric convergence 1 the existence of exponentially bounded hitting times on one and then all suitably small sets 2 the existence of foster lyapunov or drift conditions for any one and then all skeleton and resolvent chains 3 the existence of drift conditions on the extended generator tilde mathscr a of the process we use the identity tilde mathscr a r beta beta r beta i connecting the extended generator and the resolvent kernels r beta to show that under a suitable aperiodicity assumption exponential convergence is completely equivalent to any of criteria 1 3 these conditions yield criteria for exponential convergence of unbounded as well as bounded functions of the chain they enable us to identify the dependence of the convergence on the initial state of the chain and also to illustrate that in general some smoothing is required to ensure convergence of unbounded functions

free vibrations of arches with variable curvature abstract the equations governing free in plane vibrations of variable curvature arches are derived and solved numerically to obtain frequencies and mode shapes for parabolic sinusoidal and elliptic geometries included are experimental validations of the lowest four predicted frequencies and mode shapes for parabolic arches

analytical formulation and evaluation for free vibration of naturally curved and twisted beams abstract an analytical study for free vibration of naturally curved and twisted beams with uniform cross sectional shapes is carried out using spatial curved beam theory based on the washizu s static model in the governing equations of motion of the beams all displacement functions and the generalized warping coordinate are defined at the centroid axis and also the effects of rotary inertia transverse shear deformations and torsion related warping are included in the proposed model explicit analytical expressions are derived for the vibrating mode shapes of a curved bending torsional shearing coupled beam under clamped clamped boundary condition with the help of symbolic computing package mathematica and a process of searching is used to determine the natural frequencies comparisons of the present results with the fem results using beam elements in ansys code show good accuracy in computation and validity of the model further the present model is used for cylindrical helical springs with circular cross section fixed at both ends and the results indicate that the natural frequencies agree well with the theoretical and experimental results available

effective methods for constructing extreme quantum observables we study extreme points of the set of finite outcome positive operator valued measures povms on finite dimensional hilbert spaces and particularly the possible ranks of the effects of an extreme povm we give results discussing ways of deducing new rank combinations of extreme povms from rank combinations of known extreme povms and using these results show ways to characterize rank combinations of extreme povms in low dimensions we show that when a rank combination together with a given dimension of the hilbert space solve a particular packing problem there is an extreme povm on the hilbert space with the given ranks this geometric method is particularly effective for constructing extreme povms with desired rank combinations

free vibration analysis of cylindrical helical springs with noncircular cross sections abstract the free vibration analysis of cylindrical helical springs with noncircular cross sections is carried out by means of an analytical study in the governing equations of motion of a spring all displacement functions and a generalized warping coordinate are defined at the centroidal principal axis the effects of the rotational inertia axial and shear deformations including torsion related warping deformations are also considered in the formulations explicit analytical expressions that give the vibrating mode shapes are derived by rigorous application of the symbolic computing package mathematica and the muller root search method is used to determine the natural frequencies numerical examples are provided for springs with elliptic rectangular and equilateral triangular cross sections and subjected to clamped clamped and clamped free boundary conditions the natural frequencies are presented for a range of geometric parameters in the case of elliptical wires results are presented for the aspect ratio a b ranging from 3 5 to 5 3 the helix pitch angle from 5 to 12 5 the number of active turns n from 6 to 12 and the ratio of cylinder radius to minor axis r 2a ranging from 20 3 to 50 3 validation of the proposed model has been achieved through comparison with a finite element model using three dimensional solid elements and the results available in published literature which in these cases indicates a good correlation

a bound on the mutual information and properties of entropy reduction for quantum channels with inefficient measurements the holevo bound is a bound on the mutual information for a given quantum encoding in 1996 schumacher westmoreland and wootters phys rev lett 76 3452 1996 derived a bound that reduces to the holevo bound for complete measurements but that is tighter for incomplete measurements the most general quantum operations may be both incomplete and inefficient here we show that the bound derived by sww can be further extended to obtain one that is yet again tighter for inefficient measurements this allows us in addition to obtain a generalization of a bound derived by hall and to show that the average reduction in the von neumann entropy during a quantum operation is concave in the initial state for all quantum operations this is a quantum version of the concavity of the mutual information we also show that both this average entropy reduction and the mutual information for pure state ensembles are schur concave for unitarily covariant measurements that is for these measurements information

generalized coherent states and extremal positive operator valued measures we present a correspondence between positive operator valued measures povms and sets of generalized coherent states povms describe quantum observables and similar to quantum states quantum observables can also be mixed we show how the formalism of generalized coherent states leads to a useful characterization of extremal povms we prove that covariant phase space observables related to squeezed states are extremal while those related to number states are not extremal this article is part of a special issue of journal of physics a mathematical and theoretical devoted to coherent states mathematical and physical aspects

clean positive operator valued measures in quantum mechanics the statistics of the outcomes of a measuring apparatus is described by a positive operator valued measure povm a quantum channel transforms povms into povms generally irreversibly thus losing some of the information retrieved from the measurement this poses the problem of which povms are undisturbed i e they are not irreversibly connected to another povm we will call such povms clean in a sense the clean povms would be perfect since they would not have any additional extrinsical noise quite unexpectedly it turns out that such a cleanness property is largely unrelated to the convex structure of povms and there are clean povms that are not extremal and vice versa in this article we solve the cleannes classification problem for number n of outcomes n d d dimension of the hilbert space and we provide a set of either necessary or sufficient conditions for n d along with an iff condition for the case of informationally complete povms for n d2

vibrations of beams and helices with arbitrarily large uniform curvature an analytical numerical and experimental study of the vibrational modes of beams with constant curvature ranging from small values up to helices with large numbers of turns is presented it is shown that after an initial stage at low curvature in which extensional symmetrical modes hybridize so as to become inextensional all modes show a decrease in frequency with increasing beam curvature the frequency reaches a minimum at a value of the curvature which is a function of mode number and successive minima are separated by steps of in the opening angle of the beam for large values of curvature it is shown that for both symmetric and antisymmetric modes there are two types of vibrational modes with comparable frequencies modes develop into one or the other of these types in a way that is precisely defined but that has the appearance of being random physical descriptions of the processes involved are given and the modes of the two types are described

extreme commutative quantum observables are sharp it is well known that in the description of quantum observables positive operator valued measures povms generalize projection valued measures pvms and they also turn out be more optimal in many tasks we show that a commutative povm is an extreme point in the convex set of all povms if and only if it is a pvm this results implies that non commutativity is a necessary ingredient to overcome the limitations of pvms

zero biasing and a discrete central limit theorem we introduce a new family of distributions to approximate p w a for a 2 1 0 1 2 and w a sum of independent integer valued random variables 1 2 n with finite second moments where with large probability w is not concentrated on a lattice of span greater than i the well known berry esseen theorem states that for z a normal random variable with mean e w and variance var w p z e a provides a good approximation to p w a for a of the form 00 x however for more general a such as the set of all even numbers the normal approximation becomes unsatisfactory and it is desirable to have an appropriate discrete non normal distribution which approximates w in total variation and a discrete version of the berry esseen theorem to bound the error in this paper using the concept of zero biasing for discrete random variables cf goldstein and reinert j theoret probab 18 2005 237 260 we introduce a new family of discrete distributions and provide a discrete version of the berry esseen theorem showing how members of the family approximate the distribution of a sum w of integer valued variables in total variation

natural frequencies of axial torsional coupled motion in springs and composite bars the natural frequencies corresponding to axial torsional extension twist coupled motion of a helical spring or the corresponding motion induced through material coupling in a composite bar are considered using an equivalent continuum approach closed form solution of the governing differential equations leads either to an exact dynamic stiffness matrix or to a number of exact relationships between the natural frequencies corresponding to coupled and uncoupled motion the latter relationships both guarantee that the wittrick williams root finding algorithm can still be used to converge on any required natural frequency despite any lack of reciprocity arising from differential coupling and for the case of symmetric material coupling coefficients enable their value to be determined precisely from experimental results a number of examples are then given to confirm the accuracy of the proposed theory and to indicate its range of application

quantum measuring processes of continuous observables the purpose of this paper is to provide a basis of theory of measurements of continuous observables we generalize von neumann s description of measuring processes of discrete quantum observables in terms of interaction between the measured system and the apparatus to continuous observables and show how every such measuring process determines the state change caused by the measurement we establish a one to one correspondence between completely positive instruments in the sense of davies and lewis and the state changes determined by the measuring processes we also prove that there are no weakly repeatable completely positive instruments of nondiscrete observables in the standard formulation of quantum mechanics so that there are no measuring processes of nondiscrete observables whose state changes satisfy the repeatability hypothesis a proof of the wigner araki yanase theorem on the nonexistence of repeatable measurements of observables not commuting conserved quantities is given in our framework we also discuss the implication of these results for the recent results due to srinivas and due to mercer on measurements of continuous observables

convex optimization based parameter estimation and experiment design for pauli channels in this technical note we study the problem of parameter estimation for quantum channels which are completely positive maps acting on quantum states we focus on an important subclass of channels called pauli channels which are characterized by a certain set of vectors directions and a number of scalar parameters for the case where the directions are known a special parametrization turns the parameter estimation problem into a convex optimization problem for the case of unknown directions we give a simple algorithm to estimate the directions for qubit pauli channels these results assume that the identification experiment configuration is given namely a set of quantum states are given on which the channel acts and a set of positive measurement operator s are fixed from which information is gathered in the second part of the technical note we consider the problem of determining the experiment design namely determining states and measurements for optimal parameter identification of the channels we formalize this problem as a maximization problem for fisher information and assuming known channel directions prove that this problem is convex we also prove that the optimal states to be used in experiments are pure and the optimal measurements are extremal for qubit pauli channels we prove that both the optimal pure input states and projective measurements should be directed towards the channel directions we illustrate the results of the technical note with numerical examples and simulations

simulating positive operator valued measures with projective measurements standard projective measurements pms represent a subset of all possible measurements in quantum physics defined by positive operator valued measures we study what quantum measurements are projective simulable that is can be simulated by using projective measurements and classical randomness we first prove that every measurement on a given quantum system can be realized by classical randomization of projective measurements on the system plus an ancilla of the same dimension then given a general measurement in dimension two or three we show that deciding whether it is pm simulable can be solved by means of semidefinite programming we also establish conditions for the simulation of measurements using projective ones valid for any dimension as an application of our formalism we improve the range of visibilities for which two qubit werner states do not violate any bell inequality for all measurements from an implementation point of view our work provides bounds on the amount of white noise a measurement tolerates before losing any advantage over projective ones

an analytic model for the free in plane vibration of beams of variable curvature and depth in this study a flexible and powerful model is presented for the in plane vibration of a beam whose curvature and depth are arbitrary constrained only to such smoothness as can be accommodated by a quartic polynomial in the centerline arc length the model includes the effects of shear deformation rotary inertia and centerline extensibility the equations of motion are solved by an extension of the classic galerkin method wherein the effect of boundary residuals is included timoshenko models are compared to other theoretical models and to experimental results the comparisons are done for a variety of support schemes a detailed study of a cantilever beam of variable curvature and depth is done and finally the utility and flexibility of the model is demonstrated for an arch whose shape is given only by a scale drawing devoid of any other information except material properties

generalized probabilistic theories and conic extensions of polytopes generalized probabilistic theories gpt provide a general framework that includes classical and quantum theories it is described by a cone c and its dual c we show that whether some one way communication complexity problems can be solved within a gpt is equivalent to the recently introduced cone factorization of the corresponding communication matrix m we also prove an analogue of holevo s theorem when the cone c is contained in the classical capacity of the channel realized by sending gpt states and measuring them is bounded by polytopes and optimising functions over polytopes arise in many areas of discrete mathematics a conic extension of a polytope is the intersection of a cone c with an affine subspace whose projection onto the original space yields the desired polytope extensions of polytopes can sometimes be much simpler geometric objects than the polytope itself the existence of a conic extension of a polytope is equivalent to that of a cone factorization of the slack matrix of the polytope on the same cone we show that all polytopes whose vertices can be recognized by a polynomial size circuit which includes as a special case the travelling salesman polytope and many other polytopes from combinatorial optimization have small conic extension complexity when the cone is the completely positive cone using recent exponential lower bounds on the linear extension complexity of polytopes this provides an exponential gap between the communication complexity of gpt based on the completely positive cone and classical communication complexity and a conjectured exponential gap with quantum communication complexity our work thus relates the communication complexity of generalizations of quantum theory to questions of mainstream interest in the area of combinatorial optimization

asymptotic analysis of the free in plane vibrations of beams with arbitrarily varying curvature and cross section abstract an asymptotic analysis is carried out for the equations of free vibrations of a beam having varying curvature and cross section the effect of splitting the asymptotic limit for eigen values into two families is revealed and its connection with boundary conditions is discussed the analysis of the properties of the asymptotic solution explains the phenomenon of transformation of mode shape with change in curvature and provides a method for predicting the spectrum of curved beams the asymptotic solution obtained also gives a simple approximation for high mode number extensional vibrations of curved beams which are difficult to analyse by other means the asymptotic behaviour of the solution is illustrated numerically for different types of curvature including antisymmetric curvature an experimental verification of the asymptotic behaviour of mode frequencies is presented

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

linear dynamics of elastic helical springs asymptotic analysis of wave propagation helical springs serve as vibration isolators in virtually any suspension system a variety of theories to describe the dynamic behaviour of these structural elements which involves interaction of flexural torsion and longitudinal waves can be found in the literature alongside this various approximate methods are employed to determine the eigenfrequencies of vibrations of springs in this paper the validity ranges of alternative theories are assessed by comparison of the location of the dispersion curves this paper also contains a rigorous asymptotic analysis of the exact dispersion equation with two small parameters being employed it allows for the identification of significant regimes of linear wave motion in a helical spring in each of these regimes simple formulae for wavenumbers are obtained by the dominant balance method and their validity ranges are checked against direct numerical solution mode shapes associated with each wavenumber are also analysed

in plane vibrations of non circular arcs of non uniform cross section abstract the title problem is solved by using polynomial co ordinate functions and the ritz method to generate the frequency equation symmetric and unsymmetric structural systems are considered the agreement with results available in the literature or with eigenvalues determined by means of a finite element code is good from an engineering viewpoint

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

barycentric decomposition of quantum measurements in finite dimensions we analyze the convex structure of the set of positive operator valued measures povms representing quantum measurements on a given finite dimensional quantum system with outcomes in a given locally compact hausdorff space the extreme points of the convex set are operator valued measures concentrated on a finite set of k d2 points of the outcome space d being the dimension of the hilbert space we prove that for second countable outcome spaces any povm admits a choquet representation as the barycenter of the set of extreme points with respect to a suitable probability measure in the general case krein milman theorem is invoked to represent povms as barycenters of a certain set of povms concentrated on k d2 points of the outcome space

complete characterization of extreme quantum observables in infinite dimensions we give a complete characterization for extreme quantum observables i e for normalized positive operator valued measures povms which are extremals in the convex set of all povms the characterization is valid both in discrete and continuous cases and also in the case of an infinite dimensional hilbert space we show that sharp povms are pre processing clean i e they cannot be irreversibly connected to other povms via quantum channels