a polar theory for vibrations of thin elastic shells abstract in relation to a polar continuum this paper presents a 2 d shear deformable theory for the high frequency vibrations of a thin elastic shell to begin with the 3 d fundamental equations of the micropolar elastic continuum are expressed as the euler lagrange equations of a unified variational principle next the kinematic variables of the shell are represented by the power series expansions in its thickness coordinate and then they are used to establish the 2 d theory by means of the variational principle the 2 d theory is derived in invariant variational and differential forms and governs all the types of vibrations of the functionally graded micropolar shell lastly the uniqueness is investigated in solutions of the initial mixed boundary value problems defined by the 2 d theory and some of special cases are indicated in the theory

three dimensional vibration analysis of circular and annular plates via the chebyshev ritz method abstract a three dimensional free vibration analysis of circular and annular plates is presented via the chebyshev ritz method the solution procedure is based on the linear small strain three dimensional elasticity theory selecting chebyshev polynomials which can be expressed in terms of cosine functions as the admissible functions a convenient governing eigenvalue equation can be derived through the ritz method according to the geometric properties of circular and annular plates the vibration is divided into three distinct categories axisymmetric vibration torsional vibration and circumferential vibration each vibration category can be further subdivided into the antisymmetric and symmetric ones in the thickness direction convergence and comparison study demonstrated the high accuracy and efficiency of the present method the present approach shows a distinct advantage over some other ritz solutions in that stable numerical operation can be guaranteed even when a large number of admissible functions is employed therefore not only lower order but also higher order eigenfrequencies can be obtained by using sufficient terms of the chebyshev polynomials finally some valuable results for annular plates with one or both edges clamped are given and discussed in detail

commuting periodic operators and the periodic wigner function commuting periodic operators cpo depending on the coordinate and the momentum operators are defined the cpo are functions of the two basic commuting operators and with a being an arbitrary constant a periodic wigner function pwf w x p is defined and it is shown that it is applicable in a normal expectation value calculation to the cpo as done in the original wigner paper moreover this pwf is non negative everywhere and it can therefore be interpreted as an actual probability distribution the pwf w x p is shown to be given as an expectation value of the periodic dirac delta function in the phase plane

spatial and behavioral types in the pi calculus we present a framework that combines ideas from spatial logics and behavioral type systems type systems for the pi calculus are proposed where newly declared restricted names are annotated with spatial process properties predicating on those names that are expected to hold in the scope of the declaration types are akin to ccs terms and account for the process abstract behavior and shallow spatial structure type checking relies on spatial model checking but properties are checked against types rather than against processes type soundness theorems ensure that for a certain class of spatial properties well typed programs are also well annotated in the sense that processes in the scope of any restriction do satisfy the corresponding annotation at run time the considered class of properties is rather general differently from previous proposals it includes both safety and liveness ones and is not limited to invariants we also elaborate a distinction between locally and globally checkable properties

dispersion of waves and characteristic wave surfaces in functionally graded piezoelectric plates an inhomogeneous layer element method is presented to analyze the dispersion of waves and characteristic wave surfaces in plates of functionally graded piezoelectric material fgpm in this method the fgpm plate is divided into a number of layered elements the elemental elastic and electric properties are assumed as linear functions of the thickness to adopt the variety of the material property of fgpm the hamilton principle is applied to determine the governing equations the phase velocity surface phase slowness surface phase wave surface group velocity surface group slowness surface and group wave surface for fgpm plate are formulated using rayleigh quotient and the orthogonality condition of the eigenvectors these six surfaces are then used to illustrate the characteristics of waves in fgpm plates numerical examples are presented using the present formulations to analyze dispersions and characteristics of waves in fgpm plates

responses of cross ply laminates with viscous interfaces in cylindrical bending the responses of a simply supported cross ply laminate in cylindrical bending with viscous interfaces are studied in this paper because of the introduction of viscous interfaces the elastic fields in the laminate will depend on the time variable the problem is solved exactly in the space domain but approximately in the time domain state space method which is very powerful for analyzing laminated structures is employed the variations of state variables with time are simulated using power series expansions numerical examples are considered and comparison with existent results validates the efficiency of the present method

galois quantum systems irreducible polynomials and riemann surfaces finite quantum systems in which the position and momentum take values in the galois field gf pl are studied ideas from the subject of field extension are transferred in the context of quantum mechanics the frobenius automorphisms in galois fields lead naturally to the frobenius formalism in a quantum context the hilbert space splits into frobenius subspaces which are labeled with the irreducible polynomials associated with the ypl y the frobenius maps transform unitarily the states of a galois quantum system and leave fixed all states in some of its galois subsystems where the position and momentum take values in subfields of gf pl an analytic representation of these systems in the l sheeted complex plane shows deeper links between galois theory and riemann surfaces

galois quantum systems a finite quantum system in which the position and momentum take values in the galois field gf p is constructed from a smaller quantum system in which the position and momentum take values in using field extension the galois trace is used in the definition of the fourier transform the heisenberg weyl group of displacements and the sp 2 gf p group of symplectic transformations are studied a class of transformations inspired by the frobenius maps in galois fields is introduced the relationship of this galois quantum system with its subsystems in which the position and momentum take values in subfields of gf p is discussed

linear canonical transformations and quantum phase a unified canonical and algebraic approach the algebra of generalized linear quantum canonical transformations is examined in the perspective of schwinger s unitary canonical operator basis formulation of the quantum phase problem within the theory of quantum canonical transformations and in particular with the generalized quantum action angle phase space formalism is established and it is shown that the conceptual foundation of the quantum phase problem lies within the algebraic properties of the canonical transformations in the quantum phase space the representations of the wigner function in the generalized action angle unitary operator pair for certain hamiltonian systems with dynamical symmetry is examined this generalized canonical formalism is applied to the quantum harmonic oscillator to examine the properties of the unitary quantum phase operator as well as the action angle wigner function

the state vector methods for space axisymmetric problems in multilayered piezoelectric media abstract the state vector equations for space axisymmetric problems of transversely isotropic piezoelectric media are established from the basic equations using the hankel transform the state vector equations are reduced to a system of ordinary differential equations an analytical solution of the problems in the hankel transform space is presented in the form of the product of initial state vector and transfer matrix the transfer matrices are given for the three distinct eigenvalues applications of the solutions are discussed an analytical solution for the transversely isotropic semi infinite piezoelectric media subjected to concerted point loads on the surface z 0 is presented in the hankel transform space using transfer matrix and the continuity conditions at the layer interfaces the general solution formulation of n layered transversely isotropic piezoelectric media is given a selected set of numerical solutions is presented for a layered semi infinite piezoelectric solid

on the fundamental equations of piezoelasticity of quasicrystal media abstract the three dimensional fundamental equations of elasticity of quasicrystals with extension to quasi static electric effect are expresses in both differential and variational invariant forms for a regular region of quasicrystal material the principle of conservation of energy is stated for the regular region and the constitutive relations are obtained for the piezoelasticity of material a theorem is proved for the uniqueness in solutions of the fundamental equations by means of the energy argument the sufficient boundary and initial conditions are enumerated for the uniqueness hamilton s principle is stated for the regular region and a three field variational principle is obtained under some constraint conditions the constraint conditions which are generally undesirable in computation are removed by applying an involutory transformation then a unified variational principle is obtained for the regular region with one or more fixed internal surface of discontinuity the variational principle operating on all the field variables generates all the fundamental equations of piezoelasticity of quasicrystals under the symmetry conditions of the phonon stress tensor and the initial conditions the resulting equations which are expressible in any system of coordinates and may be used through simultaneous approximation upon all the field variables in a direct method of solutions pave the way to the study of important dislocation fracture and interface problems of both elasticity and piezoelasticity of quasicrystal materials

phase space functions and correspondence rules it is shown that positive quantum joint distributions in phase space lead to quantum mechanical operators depending on the state to be considered it is also shown that a simple requirement of canonical invariance leads to the weyl correspondence rule as the only allowed one

modal analysis of magneto electro elastic plates using the state vector approach the state vector approach is proposed to analyze the free vibration of magneto electro elastic laminate plates the extended displacements and stresses can be divided into the so called in plane and out of plane variables once the state equation for the out of plane variables is obtained a complex boundary value problem is converted into an equivalent simple initial value problem through the state equation the propagator matrix between the top and bottom interfaces of every layer can be easily derived the global propagator matrix can also be assembled using the continuity conditions it is obvious that the order of global propagator matrix is not related to the number of layers consequently this approach possesses certain virtues including simple formulation less expensive computation etc to test the formulation the developed solution is then applied to a simply supported multilayered plate constructed of piezoelectric and or piezomagnetic materials the natural frequencies and corresponding mode shapes are computed and compared with existing results furthermore the fundamental modes along with a couple of other higher modes which have never been reported in previous literature are presented therefore this completed set of frequencies and mode shapes can be used as benchmarks for future research in this field it is also believed that the approach could be useful in the analysis and design of smart structures constructed from piezoelectric piezomagnetic composites

quantum mechanics on p adic numbers a quantum system with positions in and momenta in is studied displacement operators in the phase space of this system and the corresponding heisenberg weyl group are studied it is shown that such a system can be constructed from a semi infinite chain of spins which are coupled in a particular way

multisets and structural congruence of the pi calculus with replication in the calculus with replication two processes are multiset congruent if they have the same semantics in the multiset transition system m it is proved that extended structural congruence is the same as multiset congruence and that it is decidable

three dimensional static analysis of multi layered piezoelectric hollow spheres via the state space method a general non axisymmetric exact analysis of the statics of a laminated piezoelectric hollow sphere is presented in the paper by using a state space method to select a proper set of state variables three displacement functions and two stress functions are introduced it is found that the basic equations of a spherically isotropic piezoelectric medium are eventually turned to two separated state equations with constant coefficients the solutions of which are then obtained by virtue of matrix theory the continuity conditions at each interface are then used to derive two relationships between respective boundary variables at the inner and outer spherical surfaces no matter how many layers the sphere contains the orders of the final solving equations remain unaltered

quantum systems with finite hilbert space and chebyshev polynomials abstract finite quantum systems are considered and the heisenberg weyl group of discrete displacements in the z d z d phase space is studied matrix elements of various operators are calculated and the result is given in terms of chebyshev polynomials and their derivatives the sl 2 z d group of transformations in the phase space is studied the general theory is applied in the context of spherical harmonics and provides a mathematical framework for the study of the angle angular momentum quantum phase space

coherent evolution in a multiply connected space in the presence of a fractional magnetic flux the back reaction effect electric charges on a circle in the presence of a fractional magnetic flux are considered a winding operator and a flux operator are defined and the corresponding phase space is shown to describe the global properties of the system the heisenberg weyl group of discrete displacements and the sl 2 z q group of discrete bogoliubov transformations in the s w phase space are studied they describe coherent evolution of the system going beyond the external field approximation and taking into account the back reaction of the electric charge on the magnetic flux when q is the power of a prime z q is a galois field and stronger results can be proved

the transient responses of a special non homogeneous magneto electro elastic hollow cylinder for axisymmetric plane strain problem by virtue of the introduction of new dependent variable and the separation of variables technique the transient responses of a special non homogeneous magneto electro elastic hollow cylinder are transformed to two volterra integral equations of the second kind of about two functions with respect to time these integral equations can be solved successfully by means of the interpolation method then the complete solutions of displacements stresses electric potential electric displacements magnetic potential and magnetic inductions are obtained the present method is suitable for a magneto electro elastic hollow cylinder with an arbitrary thickness subjected to arbitrary axisymmetric mechanical and electromagnetic loads numerical results are finally presented

on the fundamental equations of electromagnetoelastic media in variational form with an application to shell laminae equations abstract the fundamental equations of elasticity with extensions to electromagnetic effects are expressed in differential form for a regular region of materials and the uniqueness of solutions is examined alternatively the fundamental equations are stated as the euler lagrange equations of a unified variational principle which operates on all the field variables the variational principle is deduced from a general principle of physics by modifying it through an involutory transformation then a system of two dimensional shear deformation equations is derived in differential and fully variational forms for the high frequency waves and vibrations of a functionally graded shell also a theorem is given which states the conditions sufficient for the uniqueness in solutions of the shell equations on the basis of a discrete layer modeling the governing equations are obtained for the motions of a curved laminae made of any numbers of functionally graded distinct layers whenever the displacements and the electric and magnetic potentials of a layer are taken to vary linearly across its thickness the resulting equations in differential and fully variational invariant forms account for various types of waves and coupled vibrations of one and two dimensional structural elements as well the invariant form makes it possible to express the equations in a particular coordinate system most suitable to the geometry of shell plate or laminae the results are shown to be compatible with and to recover some of earlier equations of plane and curved elements for special material geometry and or effects

a state space formalism for anisotropic elasticity part ii cylindrical anisotropy abstract a state space formalism for thermoelastic analysis of a cylindrically anisotropic elastic body is developed by proper grouping of the stress and taking r ij instead of ij as the stress variables the three dimensional equations of elasticity in the cylindrical coordinates are concisely formulated into a state equation and an output equation using matrix notations the general solution for the generalized plane problems is derived in a simple manner effects of extension torsion bending temperature change and body force are accounted for systematically the eigen relation arising from the solution process and the degenerate cases of repeated eigenvalues are examined to demonstrate the power of the formalism exact solutions to extension torsion bending and thermo mechanical loading of a general cylindrically anisotropic circular tube or bar are obtained the surface tractions and temperature field may vary in but not in z displacement as well as traction boundary conditions are considered it appears that many problems of anisotropic elasticity are best viewed and treated in the state space framework

static fields in magnetoelectroelastic laminates the through thickness elastic electric and magnetic fields of laminates composed of elastic piezoelectric and magnetostrictive layers are considered under static conditions to determine their fundamental behavior and to investigate the limits of simplified plate theories in which the fields are assumed to possess a specific type of behavior the weak form of the equations of motion equilibrium gauss s law and gauss s law for magnetism are formulated for a rectangular laminate with arbitrary edge boundary conditions under the application of applied surface displacement traction electric potential electric flux or magnetic potential magnetic flux the layers within the laminate are allowed to possess any linear constitutive law consistent with a magnetoelectroelastic solid and the number of layers is arbitrary the ritz method is used in combination with a discrete layer theory and approximate solutions for the displacements electric potential and magnetic potential are sought to the weak form of the governing equations the use of linear combinations of through thickness approximations along with separate approximations for the in plane behavior allows an accurate representation of the break in variable slope across an interface with dissimilar material properties the model is applied to problems with either known exact solutions or a finite element approximation to the governing equations excellent agreement is obtained for all cases

finite dimensional hilbert space and frame quantization the quantum observables used in the case of quantum systems with finite dimensional hilbert space are defined either algebraically in terms of an orthonormal basis and discrete fourier transformation or by using a continuous system of coherent states we present an alternative approach to these important quantum systems based on the finite frame quantization finite systems of coherent states usually called finite tight frames can be defined in a natural way in the case of finite quantum systems novel examples of such tight frames are presented the quantum observables used in our approach are obtained by starting from certain classical observables described by functions defined on the discrete phase space corresponding to the system they are obtained by using a finite frame and a klauder berezin toeplitz type quantization semi classical aspects of tight frames are studied through lower symbols of basic classical observables

alternative state space formulations for magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates abstract by introducing two displacement functions and two stress functions the governing equations of the linear theory of magneto electro thermo elasticity with transverse isotropy are simplified on selecting certain physical quantities as the basic unknowns two new state equations are established each of them is order reduced when compared with the one reported recently in literature leading to a higher numerical efficiency the material inhomogeneity along the axis of symmetry z direction can be taken into account and an approximate laminate model is employed to facilitate deriving analytical solutions the validity of new formulations is examined by considering a laminated magneto electro elastic rectangular plate and good agreement is obtained with existent results a plate with a functionally graded property is then analyzed the effect of magnetoelectric coupling in a batio3 cofe2o4 composite predicted from the micromechanics simulation is studied quantitatively

infinite dimensional algebras and a trigonometric basis for the classical lie algebras this paper explores features of the infinite dimensional algebras that have been previously introduced in particular it is shown that the classical simple lie algebras an bn cn dn may be expressed in an egalitarian basis with trigonometric structure constants the transformation to the standard cartan weyl basis and the particularly transparent n limit that this formulation allows is provided

state vector approach to analysis of multilayered magneto electro elastic plates abstract the state vector equations for three dimensional orthotropic and linearly magneto electro elastic media are derived from the governing equations by eliminating x y xy b x b y d x and d y an efficient method is presented for analysis of multilayered magneto electro elastic plates the methodology is based on the mixed formulation in which basic unknowns are formed by collecting not only displacements electrical potential and magnetic potential but also some of stresses electrical displacements and magnetic induction as special case simply supported and multilayered rectangular plate is analyzed under the surface loading numerical results are presented graphically the procedure of numerical calculation shows that the formulation presented here is simple and direct

exact two dimensional solutions for in plane natural frequencies of laminated circular arches exact analysis on the in plane free vibration of simply supported laminated circular arches is carried out based on the two dimensional theory of elasticity the method of separation of variables is employed to expand all the variables into fourier series about the longitudinal coordinate so that the system of partial differential equations is reduced to the ordinary one about the radial coordinate the state space method is used to derive a series of simultaneous first order differential equations due to the variable coefficients posed by the radial coordinate analytical solutions are rather unpractical and hence the approximate laminate model is adopted to translate the state equation into the one with constant coefficients the relation between the state vector at the inner and outer surface of the arch is finally obtained according to the continuity conditions at interfaces and the traction free conditions at the two lateral surfaces the formulation is validated by comparing the present results to those available in literature effects of geometric parameters and stacking sequences on the natural frequencies of circular arches are investigated and discussed numerical results presented in this paper provide benchmarks for future analysis of circular arches

connection between static electromagnetoelasticity and anisotropic elasticity and its applications connection between electromagnetoelasticity and anisotropic elasticity is explored in the state space setting in the absence of electric charges and currents the basic equations of static electromagnetoelasticity are formulated into a state equation and an output equation which bear a remarkable resemblance to the corresponding equations of elasticity accordingly the solutions for various steady state problems of electromagnetoelasticity can be determined in parallel to their elastic counterparts for illustration the generalized plane problems are treated within the context exact solutions for the electromagnetoelastic fields in a half space subjected to line loads and in an infinite plate with an elliptic notch under extension are determined in a simple way

free vibration studies of simply supported non homogeneous functionally graded magneto electro elastic finite cylindrical shells in this article free vibration studies on functionally graded materials fgm magneto electro elastic cylindrical shells have been carried out a series solution is assumed in circumferential and axial direction such that the three dimensional character of the solution is preserved the finite element model is derived based on constitutive equation of magneto electro elastic material accounting for coupling between elasticity electric and magnetic effect frequency behavior with the variation of power law index is analyzed and explained on the basis of constitutive material one of the aims of the study is to evaluate the influence of magnetic and piezoelectric effect on the structural frequency in addition influence of length to radius ratio and radius to thickness ratio on the frequency behaviour of such shells have been attempted

free vibration of simply supported functionally graded and layered magneto electro elastic plates by finite element method in this article free vibration studies on functionally graded anisotropic and linear magneto electro elastic plates have been carried out by semi analytical finite element method a series solution is assumed in the plane of the plate and finite element procedure is adopted across the thickness of the plate such a way that the three dimensional 3 d character of the solution is preserved the finite element model is derived based on constitutive equation of magneto electro elastic material accounting for coupling between elasticity electric and magnetic effect the present finite element is modeled with displacement components electric potential and magnetic potential as nodal degree of freedom the functionally graded material is assumed to be exponential in the thickness direction the numerical results obtained by the present model are in good agreement with the isotropic 3 d exact benchmark solutions available in literature numerical study includes the influence of the different exponential factor magneto electro elastic properties and effect of mechanical and electrical type of loading on induced magneto electro elastic fields further study has been carried out on higher harmonic study has been extended on functionally graded and layered magneto electro elastic plate

a unified approach to acoustic fields induced in inhomogeneous spheres by external sources abstract the evaluation of acoustic fields induced in inhomogeneous spheres by external sources based on volume integral equations is simplified considerably using ivakin s integral equation and the use of the well known expansion for the green dyadic the method presented here overcomes the difficulties of calculation arising from the possible step discontinuities in the density allowing a quick and accurate evaluation of the fields so the simple hybrid analytical numerical scalar method developed previously for spheres with variable even discontinuous compressibility is easily extended to the general case of inhomogeneous density in a manner requiring the least possible analytical and computational effort

on free vibration of non homogeneous transversely isotropic magneto electro elastic plates two independent state equations are established for transversely isotropic magneto electro elastic media by introducing proper stress and displacement functions the free vibration problem of simply supported rectangular plates with general inhomogeneous functionally graded material properties along the thickness direction is then considered an approximate laminate model is employed to transform the state equations with variable coefficients to the ones with constant coefficients two different classes of vibrations are found in particular the frequency of the first class is only related to the elastic property of the plate while that of the second class is affected by the couplings among the elastic electric and magnetic fields numerical results are presented and some important issues are discussed

some comments on the higher order theories of piezoelectric piezothermoelastic and thermopiezoelectric rods and shells in this note the derivations of the higher order 1 d or 2 d theories are discussed for the dynamic analysis of electroelastic i e piezoelectric piezothermoelastic and thermopiezoelectric structural elements of uniform cross section or uniform thickness certain oversights are clarified concerning the higher order theories including their variational formulation invariant form and uniqueness of solutions that obscure the availability of earlier contributions in the open literature in this respect a higher order theory with some applications by wu et al most recently appeared in this journal int j solids struct 39 2002 5325 is mentioned as one of the examples

free vibrations of functionally graded piezoceramic hollow spheres with radial polarization by introducing displacement functions as well as stress functions two independent state equations with variable coefficients are established from the three dimensional equations of a radially inhomogeneous spherically isotropic piezoelastic medium by virtue of the laminated approximation method the state equations are then transformed into the ones with constant variables in each layer and the state variable solutions are presented based on the solutions linear algebraic equations about the state variables only at the inner and outer spherical surfaces are derived by utilizing the continuity conditions at each interface frequency equations corresponding to two independent classes of vibrations are finally obtained from the free surface conditions numerical calculations are presented and the effect of the material gradient index on natural frequencies is discussed

wigner quantisation of arrival time and oscillator phase by means of the wigner distribution function an expression is derived for the quasiprobability that a free particle in one dimension arrives at the origin during a given time interval and also for the quasiprobability that the phase of a one dimensional harmonic oscillator lies in a given segment of the circle it is shown that the best bounds on these quasiprobabilities p are 0 1559 or p or 1 0077 independent of the size of the interval it is shown that on disjoint unions of infinitely many intervals the quasiprobabilities may add up to any positive or negative real value it is briefly indicated how negative probabilities can be avoided altogether in an alternative approach to the quantisation of arrival time and oscillator phase

tomographically complete sets of orthonormal bases in finite systems quantum systems where the position and momentum are in the ring d is an odd integer are considered a tomographically complete set of bases i e a set of bases such that probabilities from tomography experiments corresponding to these bases can be used for the calculation of an arbitrary density matrix is considered such a set of bases is constructed by considering a factorization of a system with dimension d p1p2 where p1 p2 are prime numbers in terms of two subsystems with dimensions p1 and p2 appropriate combination of the mutually unbiased bases in the subsystems leads to a tomographically complete set of bases in the full system this set leads to probabilities along all the lines through the origin 0 0 in the phase space with exactly d points it is shown that the number of these lines is d the dedekind function the general theory is exemplified with examples

structural inclusion in the pi calculus with replication three notions of structural inclusion between process terms of the calculus are considered and proven to be decidable and to have axiomatizations that are sound and complete in the multiset semantics m of the calculus all three are strong simulation relations

conjugate variables in finite phase plane we construct two pairs of quasicoordinates and quasimomenta in a finite phase plane which form sets of conjugate variables in such a plane the coordinate x is quantized with a step c and the momentum p with a step where mc is the size of the phase plane in the x direction the construction depends crucially on the possibility of writing m m1m2 with m1 and m2 relatively prime the conjugate variables are applied to harper like hamiltonians it is shown how to design physical systems with energy spectra containing any desired number of discrete energy levels say m1 each of them having a prescribed degeneracy m2

energy momentum tensor in phase space a connection between schrodinger energy momentum tensor and terletsky distribution function schrodinger energy momentum tensor for a matter field interacting with an external electromagnetic field is represented in phase space by means of terletsky distribution function the explicit form of this distribution function in the case of a hydrogen type atom is found the structure of the schrodinger energy momentum tensor in phase space is compared with the structure of a real fluid and its local pressure and local energy are presented in the fundamental state of a hydrogen type atom the negative values of the terletsky distribution function are not rejected in view of their participation in the phase space energy momentum tensor the negative part of the quantum distribution function could be interpreted as phase space density for anti constituents in a hypothetical sub quantum level of the matter

free vibrations of piezoelectric cylindrical shells filled with compressible fluid abstract three displacement functions are introduced to represent each mechanical displacement according to the three dimensional theory after expanding these functions and the electric potential with orthogonal series the free vibration equation of piezoelectric cylindrical shells satisfying ss3 edge conditions can be obtained the equation was solved by utilizing bessel functions with complex arguments the effects of compressible fluid on shells are considered and some new phenomena which are exclusive for piezoelectric cylindrical shells are reported results of empty infinite piezoelectric cylindrical shells are compared to those presented in relative references some lowest frequencies that were missed by paul and venkatesan paul h s and venkatesan m 1987 vibrations of hollow circular cylinder of piezoelectric ceramics journal of the acoustic society of america82 852 856 were discovered

quantum systems with finite hilbert space galois fields in quantum mechanics a galois quantum system in which the position and momentum take values in the galois field gf pl is considered it is comprised of l component systems which are coupled in a particular way and is described by a certain class of hamiltonians displacements in the gf pl gf pl phase space and the corresponding heisenberg weyl group are studied symplectic transformations are shown to form the sp 2 gf pl group wigner and weyl functions are defined and their properties are studied frobenius symmetries which are based on frobenius automorphisms in the theory of galois fields are a unique feature of these systems for l 2 if they commute with the hamiltonian there are constants of motion which are discussed an analytic representation in the l sheeted complex plane provides an elegant formalism that embodies the properties of frobenius transformations the difference between a galois quantum system and other finite quantum systems where the position and momentum take values in the ring is discussed

generalized variational principles for micromorphic magnetoelectroelastodynamics a family of generalized variational principles is established for the initial boundary value problem of micromorphic magnetoelectroelastodynamics by he s semi inverse method this paper aims at providing a more complete theoretical basis for the finite element applications

loop gauge theory and group cohomology a generalized fiber bundle model in which the fibers are hilbert spaces is studied unitary transformations are used to define a unitary isomorphism parallelism among them the weyl group is first used to connect the projective hilbert spaces ray spaces and to introduce a one form connection that defines which coset at a point y is parallel to a given coset at another point x then the central extension of the weyl group by u 1 is studied in order to introduce the most general mapping between the elements of these cosets this leads to a two form connection and makes the model a good candidate for a fiber bundle approach to string theories

simplified gurtin type generalized variational principles for fully dynamic magneto electro elasticity with geometrical nonlinearity abstract the fundamental equations governing all the variables of the initial boundary value problem in fully dynamic magneto electro elasticity with geometrical nonlinearity are expressed in covariant differential form the generalized principle of virtual work is given in terms of convolutions for the present problem two simplified gurtin type generalized variational principles directly leading to all the fundamental equations are deduced by using he s semi inverse method instead of laplace transforms by enforcing some fundamental equations as constraint conditions one of various constrained variational principles is given as an example by simply dropping out selected field functions several reduced variational principles are obtained as special forms for piezoelectricity elastodynamics and electromagnetics respectively this paper aims at providing a more complete theoretical foundation for the finite element applications for the discussed problem

quantum canonical invariance a moyal approach the quasiclassical generalised moyal quantisation procedure is applied to the problem of quantum canonical invariance simple new formulae for the moyal bracket corresponding to various correspondence rules are given and are used to calculate the additional potential terms arising from a point canonical transformation made on a free hamiltonian the status of canonical transformations in other equivalent quantum phase space formulations is also reviewed

weak mutually unbiased bases quantum systems with variables in are considered the properties of lines in the phase space of these systems are studied weak mutually unbiased bases in these systems are defined as bases for which the overlap of any two vectors in two different bases is equal to d 1 2 or alternatively to one of the d 1 2i 0 where di is a divisor of d apart from d 1 they are designed for the geometry of the phase space in the sense that there is a duality between the weak mutually unbiased bases and the maximal lines through the origin in the special case of prime d there are no divisors of d apart from 1 d and the weak mutually unbiased bases are mutually unbiased bases

a note on the static behavior of simply supported laminated piezoelectric cylinders an exact three dimensional solution of the equations of linear piezoelectricity is given for the static response of a finite laminated piezoelectric cylinder with its ends simply supported the equilibrium equations and the conservation of charge equation are constructed in cylindrical coordinates the three displacement components and the electrostatic potential are expressed in terms of fourier series in the axial and circumferential directions leading to a coupled system of four ordinary differential equations in the radial coordinate the frobenious method is used to obtain the elastic and electric fields for each layer of the laminate which are a function of eight constants enforcing the boundary and continuity conditions across each interface yields the required number of equations to solve for these constants several examples are presented to study the fundamental behavior of these solids

on the operator bases underlying wigner s kirkwood s and glauber s phase space functions the hermitian operators behind wigner s phase space function 1932 are recognised to be simple ordered exponentials of the dynamical variables this operator basis is highly symmetric it supplies a perfectly unbiased formulation of operator equations in terms of phase space functions which is as close to classical physics as it possibly can be the author demonstrates how the symmetry properties of the basis can be exploited to simplify the computation of wigner functions enormously the ordered operator methods are also applicable to the phase space functions of kirkwood 1933 and glauber 1963 type both kinds are briefly discussed with emphasis on how they differ from wigner s description

symplectically entangled states and their applications to coding an angular momentum 2j 1 dimensional hilbert space h is considered symplectic transformations s on the tensor product of n of these spaces h h are studied for the case when the 2j 1 is a power of a prime galois case the corresponding operators are calculated numerically the formalism is applied to quantum coding a simple repetition code based on the space ha spanned by the direct products of n angular momentum states with the same m has distance 1 it is shown that a code based on the symplectically transformed space sha has in general larger distance an example with three qutrits is discussed in detail

free axisymmetric vibration of transversely isotropic piezoelectric circular plates abstract based on three dimensional elastic theory of piezoelectric materials the axisymmetric state space formulation of piezoelectric laminated circular plates is derived finite hankel transforms are used and the boundary variables in free terms are replaced for two kinds of boundary conditions to obtain ordinary differential equations with constant coefficients regarding the axisymmetric free vibration problem two exact solutions for two different boundary conditions are found discarding piezoelectric effect the exact solutions for transversely isotropic circular laminates are also obtained through the same procedure numerical examples are given and compared with those of finite element method fem

exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates we use reddy s third order plate theory to study buckling and steady state vibrations of a simply supported functionally gradient isotropic polygonal plate resting on a winkler pasternak elastic foundation and subjected to uniform in plane hydrostatic loads young s modulus and the poisson ratio for the material of the plate are assumed to vary only in the thickness direction effects of rotary inertia are considered the problem of determining the critical buckling load or the vibration frequency of the plate is found to be analogous to that of ascertaining the frequency of a membrane clamped at the edges and whose shape coincides with that of the plate the critical buckling load and the vibration frequency are shown to be positive some available results for plates symmetric about the mid plane can be retrieved from the present analysis

eigenvalues and eigenvectors of the finite fourier transform the eigenvalues and eigenvectors of the n n unitary matrix of finite fourier transform whose j k element is 1 n 1 2 exp 2 i n jk i 1 1 2 is determined in doing so a multitude of identities some of which may be new are encountered a conjecture is advanced

factorization in finite quantum systems unitary transformations in an angular momentum hilbert space h 2j 1 are considered they are expressed as a finite sum of the displacement operators which play the role of su 2j 1 generators with the weyl function as coefficients the chinese remainder theorem is used to factorize large qudits in the hilbert space h 2j 1 in terms of smaller qudits in hilbert spaces h 2ji 1 all unitary transformations on large qudits can be performed through appropriate unitary transformations on the smaller qudits

von neumann s hypothesis concerning coherent states an orthonormal basis of modified coherent states is constructed each member of the basis is an infinite sum of coherent states on a von neumann lattice a single state is assigned to each unit cell of area h planck constant in the phase plane the uncertainties of the coordinate x and the square of the momentum p2 for these states are shown to be similar to those for the usual coherent states expansions in the newly established set are discussed and it is shown that any function in the kq representation can be written as a sum of two fixed kq functions approximate commuting operators for x and p2 are defined on a lattice in phase plane according to von neumann s prescription

about mutually unbiased bases in even and odd prime power dimensions mutually unbiased bases generalize the x y and z qubit bases they possess numerous applications in quantum information science it is well known that in prime power dimensions n pm with p prime and m a positive integer there exists a maximal set of n 1 mutually unbiased bases in the present paper we derive an explicit expression for those bases in terms of the operations of the associated finite field galois division ring of n elements this expression is shown to be equivalent to the expressions previously obtained by ivanovic 1981 j phys a math gen 14 3241 in odd prime dimensions and wootters and fields 1989 ann phys 191 363 in odd prime power dimensions in even prime power dimensions we derive a new explicit expression for the mutually unbiased bases the new ingredients of our approach are basically the following we provide a simple expression of the generalized pauli group in terms of the additive characters of the field and we derive an exact groupal composition law between the elements of the commuting subsets of the generalized pauli group renormalized by a well chosen phase factor

symplectic transformations and quantum tomography in finite quantum systems quantum systems where the position and momentum are in the ring zd d is an odd integer are considered symplectic transformations are studied and the order of sp 2 zd is calculated quantum tomography is also discussed it is shown that measurements used in the inverse radon transform need to be made on j2 d lines where j2 d is the jordan totient function

general solutions for coupled equations for piezoelectric media abstract three general solutions are obtained for the coupled dynamic equations for a transversely isotropic piezoelectric medium these solutions are expressed in terms of the two functions and f where satisfies a second degree partial differential equation and f a sixth degree partial differential equation respectively if the terms concerning the derivatives of time are removed the results become three general solutions for the corresponding equilibrium equations in which the function f can be represented by functions fi i 1 2 3 each of which satisfies a second degree partial differential equation by utilizing a generalized almansi theorem and the solution wang and zheng int j solids structures32 105 115 1995 obtained is proved to be consistent with one case of one of the three general solutions when the constants e15 e31 e33 0 the piezo electric coupling is absent then two of the solutions reduce to the elasticity general solutions for a transversely isotropie medium one of which is the result hu acta scientia sin 2 2 145 151 1953 obtained the other one has not been published last the solution in the limiting explicit form for the problem for a half space with concentrated loads at the boundary is obtained by utilizing the general solutions

the angle angular momentum quantum phase space the angle angular momentum quantum phase space is considered and the corresponding heisenberg weyl group is studied when 2j 1 is a power of a prime z 2j 1 is a galois field and stronger results can be proved sl 2 z 2j 1 transformations are explicitly constructed and various properties of the displacement operators are studied central extensions of the abelian group by z 2j 1 are studied and they provide all the ways of constructing the heisenberg weyl group from g and z 2j 1

vibration of electro elastic versus magneto elastic circular annular plates using the chebyshev ritz method abstract the aim of this paper is to analyze three dimensional free vibration of magneto elastic electro elastic circular annular plates with different boundary conditions using the chebyshev ritz method in which a set of duplicate chebyshev polynomial series multiplied by the boundary function satisfying the boundary conditions are chosen as the trial functions of the displacement components the electric potential and the magnetic potential convergence of the method is checked using various chebyshev polynomial terms the effect of geometrical parameters and material properties of magneto elastic electro elastic circular annular plates on the eigenfrequencies of free vibration is considered

coupled thermoelastic shell equations with second sound for high frequency vibrations of temperature dependent materials guided by the three dimensional theory of coupled thermoelasticity with second sound a system of shear deformable shell equations is consistently derived in invariant differential and variational forms for the high frequency vibrations of temperature dependent materials the first part of the paper is concerned with a unified variational principle describing the fundamental equations of thermoelasticity the differential type of variational principle is presented by expressing hamilton s principle for the thermal part of a thermoelastic region and then combining it with its mechanical part in the second part the hierarchic system of non isothermal shell equations is systematically established by use of the variational principle together with mindlin s kinematic hypothesis for shells the system of two dimensional approximate equations which may take account of all the significant mechanical and thermal effects including the temperature dependency of material governs the extensional thickness shear flexural and torsional as well as coupled vibrations of shells of uniform thickness lastly in the third part emphasis is placed on certain cases involving special material geometry and kinematics besides a theorem is devised so as to enumerate the initial and boundary conditions sufficient for the uniqueness in solutions of the system of non isothermal shell equations

periodic and discrete zak bases weyl s unitary operators for displacement in position and momentum commute with one another if the product of the elementary displacements equals planck s constant then their common eigenstates constitute the zak basis with each state specified by two phase parameters accordingly the transformation function from the position basis to the zak basis maps the hilbert space on the line onto the hilbert space on the torus this mapping is one to one provided that the zak basis states are periodic functions of their phase parameters but then the mapping cannot be continuous on the whole torus with the periodicity of the zak basis enforced the basis has a double fourier series the fourier coefficients identify a discrete basis which complements the periodic zak basis to form a pair of mutually unbiased bases the discrete basis states are the common eigenstates of the two complementary partners to the two unitary displacement operators these partner operators are of angular momentum type with integer eigenvalues and generate the fundamental rotations of the torus conversely the displacement operators are the ladder operators for their partners for each consistent phase convention for the periodic zak basis and thus for the line onto torus mapping there is a corresponding discrete zak basis and a corresponding pair of partner operators examples of particular interest are the conventions that give a continuous mapping in one phase parameter or are symmetric in both phase parameters the latter emphasizes the heisenberg weyl symmetry between position and momentum we discuss briefly the relation between the zak bases and aharonov s modular operators finally as an application of the zak operators for the torus we mention how they can be used to associate with the single degree of freedom of the line a pair of genuine qubits that are potentially entangled

an initial boundary value problem for model electromagnetoelasticity system in this paper we consider an initial boundary value problem related to the electrodynamics of vibrating elastic media the aim is to prove an existence and uniqueness result for a model describing the nonlinear interactions of the electromagnetic and elastic waves we assume that the motion of the continuum occurs at velocities that are much smaller than the propagation velocity of the electromagnetic waves through the elastic medium the model under study consists of two coupled differential equations one of them is the hyperbolic equation an analog of the lame system and another one is the parabolic equation an analog of the diffusion maxwell system one stability result is proved too

an integral transform related to quantization ii some mathematical properties we study in more detail the mathematical properties of the integral transform relating the matrix elements between coherent states of a quantum operator to the corresponding classical function explicit families of hilbert spaces are constructed between which the integral transform is an isomorphism

a state space formalism for anisotropic elasticity part i rectilinear anisotropy a state space formalism for anisotropic elasticity including the thermal effect is developed a salient feature of the formalism is that it bridges the compliance based and stiffness based formalisms in a natural way the displacement and stress components and the thermoelastic constants of a general anisotropic elastic material appear explicitly in the formulation yet it is simple and clear this is achieved by using the matrix notation to express the basic equations and grouping the stress in such a way that it enables us to cast neatly the three dimensional equations of anisotropic elasticity into a compact state equation and an output equation the homogeneous solution to the state equation for the generalized plane problem leads naturally to the eigen relation and the sextic equation of stroh extension twisting bending temperature change and body forces are accounted for through the particular solution based on the formalism the general solution for generalized plane strain and generalized torsion of an anisotropic elastic body are determined in an elegant manner

group theoretical construction of mutually unbiased bases in hilbert spaces of prime dimensions mutually unbiased bases in hilbert spaces of finite dimensions are closely related to the quantal notion of complementarity an alternative proof of existence of a maximal collection of n 1 mutually unbiased bases in hilbert spaces of prime dimension n is given by exploiting the finite heisenberg group also called the pauli group and the action of on finite phase space implemented by unitary operators in the hilbert space crucial for the proof is that for prime is also a finite field

geometrical approach to the discrete wigner function in prime power dimensions we analyse the wigner function in prime power dimensions constructed on the basis of the discrete rotation and displacement operators labelled with elements of the underlying finite field we separately discuss the case of odd and even characteristics and analyse the algebraic origin of the non uniqueness of the representation of the wigner function explicit expressions for the wigner kernel are given in both cases

radial vibration of piezoelectric magnetostrictive composite hollow sphere the radial vibration of a multilayered piezoelectric magnetostrictive composite hollow sphere is investigated in terms of the gaussian equations two unknown time functions are first introduced to complete the solution of electric displacement and magnetic induction the solution for mechanical field involving two unknown time functions is obtained by means of the superposition method the state space method as well as the separation of variables method by means of the electric and magnetic boundary conditions and continuity conditions two volterra integral equations of the second kind with respect to two time functions are derived the interpolation method is employed to solve the volterra integral equations the present solution is suitable for analyzing the transient responses of composite hollow sphere composed of piezoelectric and magnetostrictive layers with arbitrary composite sequence numerical results are presented and discussed