the bender dunne basis operators as hilbert space operators the bender dunne basis operators t m n 2 n k 0nnkqkp mqn k where q and p are the position and momentum operators respectively are formal integral operators in position representation in the entire real line r for positive integers n and m we show by explicit construction of a dense domain that the operators t m n s are densely defined operators in the hilbert space l2 r

toward a hybrid trefftz element with a hole for elasto plasticity the paper deals with the modelling of riveted assemblies for full scale complete aircraft crashworthiness many comparisons between experiments and fe computations of bird impacts onto aluminium riveted panels have shown that macroscopic plastic strains were not sufficiently developed and localised in the riveted shell fe in the impact area consequently fe models never succeed in initialising and propagating the rupture in the sheet metal plates and along rivet rows as shown by experiments without calibrating the input data especially the damage and failure properties of the riveted shell fe to model the assembly correctly it appears necessary to investigate on fe techniques such as hybrid trefftz finite element method h t fem indeed perforated fe plates developed for elastic problems based on a hybrid trefftz formulation have been found in the open literature our purpose is to find a way to extend this formulation so that the super element can be used for crashworthiness to reach this aim the main features of an elastic hybrid trefftz plate are presented and are then followed by a discussion on the possible extensions finally the interpolation functions of the element are evaluated numerically

a high precision element with a central circular hole an eight node rectangular membrane element with a central circular hole has been developed using complex potentials to define stress and strain functions this new element type can be combined with the conventional elements e g isoparametric elements with no modifications required two numerical examples were employed to illustrate the superiority and versatility of the proposed element type the results obtained using the said element type are closer to the theoretical results as compared with those obtained by similar types of elements

nonuniqueness of the mathcal c operator in mathcal p mathcal t symmetric quantum mechanics the operator in symmetric quantum mechanics satisfies a system of three simultaneous algebraic operator equations and these equations are difficult to solve exactly so perturbative methods have been used in the past to calculate the usual approach has been to express the hamiltonian as h h0 h1 and to seek a solution for in the form where q q q p is odd in the momentum p even in the coordinate q and has a perturbation expansion of the form q q1 3q3 5q5 in previous work it has always been assumed that the coefficients of even powers of in this expansion would be absent because their presence would violate the condition that q p q is odd in p in an earlier paper it was argued that the operator is not unique because the perturbation coefficient q1 is nonunique here the nonuniqueness of is demonstrated at a more fundamental level it is shown that the perturbation expansion for q actually has the more general form q q0 q1 2q2 in which all powers and not just odd powers of appear for the case in which h0 is the harmonic oscillator hamiltonian q0 is calculated exactly and in closed form and it is shown explicitly to be nonunique the results are verified by using powerful summation procedures based on analytic continuation it is also shown how to calculate the higher coefficients in the perturbation series for q

weyl ordered series form for the angle variable of the time dependent oscillator the definition of the phase variable for a classical time dependent oscillator as the natural variable canonically conjugated to the ermakov invariant is revised some implications of the result at the quantum level are discussed and an exact formal expression in terms of weyl ordered operators is given for the associated phase operator

reply to comments by r piltner on development of two dimensional elements with a central circular hole comput methods appl mech engrg 188 2000 431 440

ghost circles for twist maps abstract completely ordered invariant circles are found for the gradient of the energy flow in the state space containing the critical sets corresponding to the birkhoff orbits of all rotation number in particular these ghost circles contain the aubry mather sets and map invariant circles as completely critical sets when these exist we give a criterion for a sequence of rational ghost circles to converge to a completely critical one

spectral problems for the weyl ordered form of operators 1pnqn in this paper we consider quantization of powers of the ratio between the hamiltonian coordinates for position and momentum in one dimensional systems the domain of the operators consists of square integrable functions over a finite real interval to ensure boundedness and self adjointness the spectral problems for the operators that result from using weyl ordering are discussed by introducing fredholm integral operator forms in position representation and the symmetry of the actions of the parity and time reversal operators on the kernels is discussed finally the general structures and properties of the eigenfunctions and eigenvalues are also derived and analyzed

construction of invariant measures of lagrangian maps minimisation and relaxation if f is an exact symplectic map on the it d dimensional cylinder mathbb t d times mathbb r d with a generating function h having superlinear growth and uniform bounds on the second derivative we construct a strictly gradient semiflow phi on the space of shift invariant probability measures on the space of configurations mathbb r d mathbb z stationary points of phi are invariant measures of f and the rotation vector and all spectral invariants are invariants of phi using phi and the minimisation technique we construct minimising measures with an arbitrary rotation vector rho in mathbb r d and with an additional assumption that f is strongly monotone we show that the support of every minimising measure is a graph of a lipschitz function using phi and the relaxation technique assuming a weak condition on phi satisfied e g in hedlund s counter example and in the anti integrable limit we show existence of double recurrent orbits of f and f ergodic measures with an arbitrary rotation vector rho in mathbb r d and action arbitrarily close to the minimal action a rho

pauli s theorem and quantum canonical pairs the consistency of a bounded self adjoint time operator canonically conjugate to a hamiltonian with non empty point spectrum in single hilbert space pauli s wellknown theorem implies that the existence of a selfadjoint time operator canonically conjugate to a given hamiltonian requires the hamiltonian to possess complet

a fully consistent lie algebraic representation of quantum phase and number operators a fully consistent realization of the quantum operators corresponding to the canonically conjugate phase and number variables is proposed resorting to the 1 positive discrete series of the irreducible unitary representation of the lie algebra su 1 1 of the double covering group of so 1 2 t he realization holds in subspace f 0 the system fock space minus the vacuum state a possible way to extend it to the full space of states based on recourse to a dilated extension of hilbert space is discussed

pt symmetric cubic anharmonic oscillator as a physical model there is a factor of 2 error in equation 61 of this paper correcting this error leads to minor changes in equations 62 and 63 please see pdf for details

comments on development of two dimensional elements with a central circular hole a k soh z f long comput methods appl mech engrg 188 2000 431 440

variational principles for softening gradient dependent plasticity abstract a gradient dependent plasticity model is analysed in which the yield function not only depends on the stress tensor and an invariant plastic strain measure but also on the spatial derivatives of the latter quantity a minimum variational principle is obtained by analysing the structure discretized into sufficiently small plastic elements and thus the uniqueness of fe solutions can be ensured for softening plasticity the positive definiteness of the variational functional is determined only by the sign of the diffuse coefficient associated with the highest order derivative of the plastic multiplier in the yield function in order to adopt mix hybrid elements several general variational principles are obtained by relaxing the associated constraints on the displacement strain stress and or plastic multiplier gradient radiation fields

development of two dimensional elements with a central circular hole abstract two new two dimensional 2d elements one is a eight node rectangular and the other is a eight node circular element each with a central circular hole have been developed using complex potentials to define stress and strain functions these new elements can be combined with the conventional elements e g isoparametric elements with no modifications required two numerical examples were employed to illustrate the potential accuracy and versatility of the proposed elements the results obtained using these two elements are in good agreement with the theoretical results moreover the proposed rectangular element performs better than the proposed circular element

self adjoint time operator is the rule for discrete semi bounded hamiltonians we prove explicitly that to every discrete semibounded hamiltonian with constant degeneracy and with a finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span th

equivalence of uniform hyperbolicity for symplectic twist maps and phonon gap for frenkel kontorova models there is a well known correspondence between the dynamics of symplectic twist maps which represent an important class of hamiltonian systems and the equilibrium states of a class of variational problems in solid state physics known as frenkel kontorova models in this paper it is shown that the key concepts of uniform hyperbolicity in the first context and phonon gap in the second context are equivalent this allows one to transfer many ideas between the two and hence to deduce new results for example we prove the uniform hyperbolicity of certain invariant sets for symplectic twist maps constructed from so called non degenerate anti integrable limits by aubry and abramovici using the concept of phonon gap and deduce that they have measure zero we prove existence of many multi defect equilibrium states for a frenkel kontorova system if it has a single non degenerate defect equilibrium state via standard results in the theory of uniform hyperbolicity

a variational principle for gradient plasticity abstract we elaborate on a generalized plasticity model which belongs to the class of gradient models suggested earlier by aifantis and co workers the generalization of the conventional theory of plasticity has been accomplished by the inclusion of higher order spatial gradients of the equivalent plastic strain in the yield condition first it is shown how these gradients affect the critical condition for the onset of localization and allow for a wavelength selection analysis leading to estimates for the width and or spacing of shear bands due to the presence of higher order gradients additional boundary conditions for the equivalent plastic strain are required this question and also the associated problem of the formulation and solution of general boundary value problems were left open in the previous work we demonstrate here that upon assuming a certain type of additional boundary conditions the structural symmetries of the gradient dependent constitutive model are such that there exists a variational principle for the displacement rates and the rate of the equivalent plastic strain the variational principle can serve as a basis for the numerical solution of boundary value problems in the sense of the finite element method explicit expressions for the tangent stillness matrix and the generalized nodal point forces are given

three dimensional hybrid trefftz stress finite elements for plates and shells three dimensional hybrid trefftz stress finite elements for plates and shells are proposed two independent fields are approximated stresses within the element and displacement on their boundary the required stress field derived from the papkovitch neuber solution of the navier equation which a priori satisfies the trefftz constraint is generated using homogeneous harmonic polynomials restriction on the polynomial degree in the coordinate measured along the thickness direction is imposed to reduce the number of independent terms explicit expressions of the corresponding independent polynomials are listed up to the fifth order illustrative applications to evaluate displacements and stresses are carried out by hexahedral hybrid trefftz stress element models the hierarchical p refinement and h refinement strategy are exploited in the numerical tests

quantum first time of arrival operators this paper undertakes the problem of constructing first time of arrival operators for arbitrary everywhere analytic potentials in the space of operators spanned by the bender dunne basis bender and dunne 1989 phys rev d 40 3504 the operators are conjugate with their respective system hamiltonians and reduce to their corresponding classical time of arrival expressions for infinitesimal the supraquantized time of arrival operators galapon 2004 j math phys 45 3180 and the confined time of arrival operators galapon et al 2004 phys rev lett 93 180406 galapon 2006 j mod phys a 21 6351 are then shown to be two distinct representations of the time of arrival operators constructed in the bender dunne space