transverse vibrations of non homogeneous orthotropic rectangular plates of variable thickness a spline technique an analysis and numerical results are presented for free transverse vibrations of non homogeneous orthotropic rectangular plates of non uniform thickness and resting on an elastic foundation of winkler type on the basis of classical plate theory the non homogeneity of the plate material is assumed to arise due to the exponential variation in young s moduli and density along one direction following levy approach i e the two parallel edges are simply supported the fourth order differential equation governing the motion of such plates of exponentially varying thickness in one direction has been solved by using the quintic splines interpolation technique for three different combinations of clamped simply supported and free boundary conditions at the other two edges effect of the non homogeneity and elastic foundation together with other plate parameters such as orthotropy aspect ratio and thickness variation on the natural frequencies of vibration is illustrated for the first three modes of vibration normalized displacements are presented for specified plates for all the three boundary conditions

translationally invariant states and the spectrum ideal in the algebra of test functions for quantum fields a class of states on borchers tensor algebra is constructed these states are invariant under the translation group and fulfill the spectrum condition this leads to a characterization of the linear span of all such states in terms of a simple continuity property

free vibration analysis of plates using least square based finite difference method in this paper we apply the two dimensional least square based finite difference lsfd method for solving free vibration problems of isotropic thin arbitrarily shaped plates with simply supported and clamped edges using the chain rule we show how the fourth order derivatives of the plate governing equation can be discretized in two or three steps as well as how the boundary conditions can be implemented directly into the governing equation by analyzing vibrating plates of various shapes and comparing the solutions obtained against existing results we clearly demonstrate the effectiveness of lsfd as a mesh free method for computing vibration frequencies of generally shaped plates accurately

free vibration and buckling analysis of clamped rectangular plates of variable thickness by the galerkin method abstract the problem of free vibration and buckling of isotropic clamped rectangular plates of variable thickness is investigated the fourth order differential equation is solved by using galerkin s variational method the thickness of the plate varies linearly along the x axis and this variation is taken to be symmetric with respect to the middle surface the parameters considered herein for buckling and free vibration behaviour of rectangular plates of variable thickness are the plate aspect ratios taper parameters and load ratios simplicity and quick convergence is the advantage of the method in comparison with other much more laborious numerical methods which require extensive computer facilities

vibrations of circular plates with variable profile galerkin s variational approach is invoked in analyzing transverse vibrations of circular plates where the thickness varies according to the functional relation h r h0 1 r a n where n is an integer the displacement function is approximated in terms of simple polynomials which identically satisfy the boundary conditions the two lowest frequency coefficients of axisymmetric modes are determined in the present paper for several combinations of the governing mechanical parameters

a search for bilinear equations passing hirota s three soliton condition ii mkdv type bilinear equations in this paper the results of a search for complex bilinear equations with two soliton solutions are presented the following basic types are discussed a the nonlinear schrodinger equation b dx g f 0 a dx dt f f gg and b the benjamin ono equation p dx f f 0 it is found that the existence of two soliton solutions is not automatic but introduces conditions that are like the usual three and four soliton conditions the search was limited by the degree of a 2 and by degree of p 4 the main results are the following 1 iad3x dxdt idy b g f 0 d2xf f gg 2 d2x ad2y idt b g f 0 dxdy f f gg 3 iad3x d2x idt f f 0 and 4 dxdt i adx bdt f f 0

four 2 1 dimensional integrable extensions of the kadomtsev petviashvili equation in this work four 2 1 dimensional nonlinear extensions of the kadomtsev petviashvili kp equation are developed the complete integrability of these models are investigated multiple soliton solutions and multiple singular soliton solutions are determined to demonstrate the compatibility of these models the resonance phenomenon does not exist for any of the derived models

axisymmetric vibrations of an isotropic elastic non homogeneous circular plate of linearly varying thickness abstract free axisymmetric vibrations of an isotropic elastic non homogeneous circular plate of linearly varying thickness have been studied on the classical theory of plates the non homogeneity of the material of the plate is assumed to arise due to the variation of young s modulus and density with the radius vector whereas poisson s ratio is assumed to remain constant the governing differential equation of motion is solved by the method of frobenius the transverse displacement of the plate has been expressed as a power series in terms of the radial co ordinate the frequency parameters corresponding to the first two modes of vibration have been computed for different values of the non homogeneity parameter and taper constant and for clamped and simply supported edge conditions of the plate a comparison between the numerical results for homogeneous and non homogeneous material of the plate is also made

multiple soliton solutions for the boussinesq equation abstract in this work we use the hirota s direct method combined with the simplified version of this method to determine the n soliton solutions for the boussinesq equation the one soliton solutions will be handled by the tanh coth method the work highlights the significant features of the employed methods

the existence of quantum fields for local nets of algebras of observables a necessary and sufficient criterion for the existence of quantum fields related to a given local net of algebras of observables is proved this criterion is written in terms of the conjugation operators so of the local algebras a o it shows that the modular structure of the local algebras essentially determines the corresponding quantum field theory in the case where the local net of algebras is conformally covariant the criterion gives the result that the existence of quantum fields depends only on the representation of the conformal group and does not depend on the concrete form of the algebras for the proof of the criterion the fact that a quantum field related to a local net of algebras can be essentially characterized by one vector is used

vibrations of clamped orthotropic rectangular plates abstract a solution in a double trigonometric series form is proposed for a forced vibration problem of a clamped orthotropic rectangular plate with the increasing number of terms of the series the solution satisfies more closely both the boundary condition and the governing equation the accuracy of the solution is discussed numerically as an example the solution is applied to the iteration method for the analysis of the free vibration problem of a clamped orthotropic rectangular plate very accurate natural frequencies are obtained for typical plates

multiple soliton solutions and fusion interaction phenomena for the 2 1 dimensional modified dispersive water wave system by means of backlund transformation and the hirota bilinear method the 2 1 dimensional modified dispersive water wave system is investigated with the aid of symbolic computation new multiple soliton solutions with arbitrary functions are derived based on the derived solutions rich coherent structures like dromions peakons and compactons can be derived and moreover the fusion interactions among different types of localized structures are graphically studied which might be helpful to understand the propagation processes for nonlinear and dispersive long gravity waves on shallow waters

the hirota s direct method and the tanh coth method for multiple soliton solutions of the sawada kotera ito seventh order equation abstract in this work the sawada kotera ito seventh order equation is studied the tanh coth method is applied to obtain soliton solution of this equation the hirota s direct method combined with the simplified hereman s method are applied to determine the n soliton solutions for this equation the study highlights the significant features of the employed methods and its capability of handling completely integrable equations

free vibration analysis of orthotropic rectangular plates with variable thickness and general boundary conditions a discrete method is developed for analyzing the free vibration problem of orthotropic rectangular plates with variable thickness the green function which is obtained by transforming the differential equations into integral equations and using numerical integration is used to establish the characteristic equation of the free vibration the effects of the aspect ratios boundary conditions the variation of the thickness on the frequencies are considered by comparing the numerical results obtained by the present method with the those previously published the efficiency and accuracy of the present method are investigated the frequency parameters are obtained for the orthotropic plates with general boundary conditions and variable thickness in one or two directions the model shapes are given for some of the square plates with three kinds of thickness variations

multiple front solutions for the burgers kadomtsev petviashvili equation abstract in this work we study a completely integrable dissipative equation the burgers equation is extended by using the sense of the kadomtsev petviashvili kp equation the new established burgers kp equation is studied by using the tanh coth method to obtain kink solutions and periodic solutions we also apply the powerful hirota s bilinear method to establish exact n soliton solutions for the derived integrable equation

scattering theory for quantum fields with indefinite metric in this work we discuss the scattering theory of local relativistic quantum fields with indefinite metric since the results of haag ruelle theory do not carry over to the case of indefinite metric 4 we propose an axiomatic framework for the construction of in and out states such that the lsz asymptotic condition can be derived from the assumptions the central mathematical object for this construction is the collection of mixed vacuum expectation values of local in and out fields called the form factor functional which is required to fulfill a hilbert space structure condition given a scattering matrix with polynomial transfer functions we then construct interpolating local relativistic quantum fields with indefinite metric which fit into the given scattering framework

solitons and singular solitons for the gardner kp equation abstract we present in this work a reliable treatment for the gardner kp gkp equation the hirota s bilinear method is used to obtain multiple soliton solutions for this completely integrable equation multiple singular soliton solutions are obtained as well the study highlights a variety of multi solitary wave and multi singular solitary solutions of the gardner kp equation

vibration of tapered thickness annular sector plates by spline element method abstract this paper deals with the determination of the vibrations of thin annular sector plates of tapered thickness by using the spline element method to demonstrate the accuracy of the present method several examples are solved and results are compared with those obtained by analytical methods and other numerical methods good accuracy is obtained frequencies of tapered annular sector plates with several boundary conditions are analyzed for the different sector angles and thickness parameters

axisymmetric vibrations of polar orthotropic mindlin annular plates of variable thickness abstract analysis and numerical results are presented for the axisymmetric vibrations of polar orthotropic annular plates with linear variation in thickness according to mindlin s shear theory of plates a chebyshev collocation technique has been employed to obtain the frequency equations for the transverse motion of such plates for three different boundary conditions frequencies mode shapes and moments for the first three modes of vibration have been computed for different plate parameters a comparison of frequencies with the corresponding values obtained by classical plate theory leads to some interesting conclusions

a 3 1 dimensional nonlinear evolution equation with multiple soliton solutions and multiple singular soliton solutions in this work a 3 1 dimensional nonlinear evolution equation is investigated the hirota s bilinear method is applied to determine the necessary conditions for the complete integrability of this equation multiple soliton solutions are established to confirm the compatibility structure multiple singular soliton solutions are also derived the resonance phenomenon does not exist for this model

vibration analysis of arbitrarily shaped plates using beam characteristic orthogonal polynomials in the semi analytical finite strip method abstract a semi analytical finite strip method mapping arbitrarily shaped plates into a natural co ordinate plane using serendipity functions is presented the product of normalized beam characteristic orthogonal polynomials and hermitian polynomials form the displacement function for the strip in the natural co ordinate domain flexural free vibration analysis of various shaped plates is performed results show that as long as the plate is modelled by high enough degree mapping functions for the specific applications requested the flexural frequencies obtained are in excellent agreement with those found in the literature

a study on kdv and gardner equations with time dependent coefficients and forcing terms abstract in this work we study the kdv equation and the gardner equation with time dependent coefficients and forcing term for each equation a generalized wave transformation is used to convert each equation to a homogeneous equation the soliton ansatz will be applied to the homogeneous equations to obtain soliton solutions

vibration analysis of non homogeneous circular plate of nonlinear thickness variation by differential quadrature method free axisymmetric vibrations of non homogeneous isotropic circular plates of nonlinear thickness variation have been analyzed on the basis of classical plate theory employing the differential quadrature dq method the non homogeneity is assumed to arise due to the variation in young s modulus and also the density of the plate material the first three natural frequencies have been obtained for clamped simply supported and free edge conditions taking grid points as zeros of chebyshev polynomials the effect of non homogeneity and thickness variation on natural frequencies of vibration has been investigated for the first three modes of vibration the results for linear as well as parabolic thickness variations have been obtained as special cases comparison studies have been carried out to establish the accuracy and versatility of the present dq method

multiple front solutions for the burgers equation and the coupled burgers equations abstract in this work multiple front solutions for the burgers equation and the coupled burgers equations are examined the tanh coth method and the cole hopf transformation are used the work highlights the power of the proposed schemes and the structures of the obtained multiple front solutions

free vibration of annular sector plates with edges possessing different degrees of rotational restraint abstract results for the natural frequencies of annular sector plates possessing different degrees of elastic restraint along the edges are presented the analysis is based on a numerical method developed by the author the functions in the circumferential direction satisfying the boundary conditions along the radial edges which are required in the analysis are indicated to the best of the author s knowledge no previous results exist for such plates

approximate solution for free vibrations of thin orthotropic rectangular plates abstract in this paper the problem of approximate evaluation of the frequencies of orthotropic plates is investigated starting from a general approximate formula for the frequency proposed by hearmon it is shown how to calculate the fundamental mode of an orthotropic rectangular plate with different restraint conditions using the proper coefficient values already available in the scientific literature for the higher modal frequencies a particular form of the rayleigh method is proposed leading to a simple procedure to calculate the fundamental frequency in fact the frequency calculation is reduced to the evaluation of the fundamental frequency of a special plate associated to the real one in order to test the accuracy of the proposed method an extensive finite element investigation was carried out the numerical results obtained show that the average difference between the values computed with the approximate new method and the finite element values is less than 0 74

on the connection between quantum fields and von neumann algebras of local operators the relationship between a standard local quantum field and a net of local von neumann algebras is discussed two natural possibilities for such an association are identified and conditions for these to obtain are found it is shown that the local net can naturally be so chosen that it satisfies the special condition of duality the notion of an intrinsically local field operator is introduced and it is shown that such an operator defines a local net with which the field is locally associated a regularity condition on the field is formulated and it is shown that if this condition holds then there exists a unique local net with which the field is locally associated if and only if the field algebra contains at least one intrinsically local operator conditions under which a field and other fields in its borchers class are associated with the same local net are found in terms of the regularity condition mentioned

transverse vibrations of a trapezoidal cantilever plate of variable thickness n atural frequencies of a trapezoidal cantilever plate of variable thickness which model an aircraft wing structure approximately are determined using energy techniques characteristic orthogonal polynomials in two variables are constructed to describe the structural deflections which are used in the rayleigh ritz method to obtain the natural frequencies the fundamental natural frequencies for different parameter values are also obtained using a deflection function containing an optimized exponent the first technique can be used to obtain the natural frequencies and corresponding mode shapes for the preliminary design of aircraft wing structures

quantum energy inequalities for the non minimally coupled scalar field in this paper we discuss local averages of the energy density for the non minimally coupled scalar quantum field extending a previous investigation of the classical field by an explicit example we show that such averages are unbounded from below on the class of hadamard states this contrasts with the minimally coupled field which obeys a state independent lower bound known as a quantum energy inequality qei nonetheless we derive a generalized qei for the non minimally coupled scalar field in which the lower bound is permitted to be state dependent this result applies to general globally hyperbolic curved spacetimes for coupling constants in the range 0 1 4 we analyse the state dependence of our qei in four dimensional minkowski space and show that it is a non trivial restriction on the averaged energy density in the sense that the lower bound is of lower order in energetic terms than the averaged energy density itself

new solitary wave solutions for two nonlinear evolution equations abstract in this paper multiple exp function method is employed to investigate exact multiple wave solutions for 2 1 dimensional potential kadomtsev petviashvili equation and 3 1 dimensional jimbo miwa equation not only already known multiple wave solutions are recovered but also several new or more general multiple wave solutions are obtained

the hirota s direct method for multiple soliton solutions for three model equations of shallow water waves abstract multiple soliton solutions for three model equations for shallow water waves are determined the three models are completely integrable the hirota bilinear method is used to determine multiple soliton solutions of sech squared type for these equations the tanh coth method is used to obtain single soliton solutions and other solutions for these three models the three models have different linear dispersion relations but possess the same coefficients for the polynomials of exponentials

two systems of two component integrable equations multiple soliton solutions and multiple singular soliton solutions abstract in this work we study two systems of two component integrable equations the cole hopf transformation and hirota s bilinear method are applied to emphasize the integrability of each system multiple soliton solutions and multiple singular soliton solutions are formally derived

classification reduction group invariant solutions and conservation laws of the gardner kp equation in this paper symmetries and group invariant solutions to the gardner kp equation are obtained by using the direct symmetry method at the same time we find the corresponding lie algebra optimal system classification and the similarity reductions to the equation respectively our exact solutions generalize the corresponding results obtained by wazwaz in addition the conservation laws of gardner kp equation are also given

positivity of wightman functionals and the existence of local nets the paper is concerned with the existence of a local net of von neumann algebras associated with a given wightman field for fields satisfying a generalizedh bound the existence of such a net is shown to be equivalent to a certain positivity property of the wightman distributions

multiple soliton solutions for the lax kadomtsev petviashvili lax kp equation a new completely integrable dispersive equation is derived the new equation is obtained by extending the lax fifth order equation using the sense of the kadomtsev petviashvili kp equation in extending the kdv equation the newly derived lax kadomtsev petviashvili lax kp equation is investigated by using the tanh coth method and the hirota bilinear method to derive single soliton solution and n soliton solutions respectively the study highlights the multiple soliton solutions of the derived completely integrable equation

transverse vibrations of an orthotropic rectangular plate of linearly varying thickness and with a free edge fil bambill diana virginia consejo nacional de investigaciones cientificas y tecnicas centro cientifico tecnologico conicet bahia blanca argentina universidad nacional del sur departamento de ingenieria argentina

on the free transverse vibration of annular and circular thin sectorial plates subject to certain complicating effects abstract the rayleigh ritz method with orthogonally generated polynomials as admissible functions is used to obtain an eigenvalue equation for the free transverse vibration of thin annular sectorial plates circular sectorial plates are treated with this equation by permitting the inner radius to become negligibly small the plates may be of isotropic or polar orthotropic material of uniform or radially and or circumferentially varying thickness and may include interior circumferential or radial line supports numerical values for the natural frequency parameters of several different plates are presented and compared with previously published values where available

free vibrations of rectangular plates of exponentially varying thickness and with a free edge abstract transverse vibrations of the structural system described in the title are analyzed by using classical plate theory and employing two different methodologies the recently developed optimized kantorovich approach and a finite element algorithmic procedure it is shown that the fundamental frequency coefficients obtained by using both techniques for a rather wide variation of the governing geometric parameters are in very good agreement lower frequency coefficients of the plate system determined by means of the finite element method are also presented

quintic splines in the study of transverse vibrations of non uniform orthotropic rectangular plates an analysis and numerical results are presented for free transverse vibrations of orthotropic rectangular plates of linearly varying thickness along one direction and resting on an elastic foundation of the winkler type on the basis of classical plate theory following the levy approach i e two parallel edges being simply supported the fourth order differential equation governing the motion of such plates has been solved by using the quintic splines interpolation technique for three different combinations of clamped simply supported and free boundary conditions at the other two edges the effect of the elastic foundation together with the orthotropy aspect ratio and thickness variation on the natural frequencies of vibration is illustrated for the first three modes of vibration normalized displacements are presented for two different values of the taper constant keeping other plate parameters fixed for all the three boundary conditions a comparison of the results with those available in literature is presented

quantum inequalities from operator product expansions quantum inequalities are lower bounds for local averages of quantum observables that have positive classical counterparts such as the energy density or the wick square we establish such inequalities in general possibly interacting quantum field theories on minkowski space using nonperturbative techniques our main tool is a rigorous version of the operator product expansion

axisymmetric vibrations of non homogeneous polar orthotropic annular plates of variable thickness in this study of the free axisymmetric vibrations of non homogeneous polar orthotropic annular plates of exponentially varying thickness on the basis of the classical theory of plates the chebyshev collocation technique has been employed to solve the differential equation governing the transverse motion of such plates the non homogeneity of the plate material is assumed to arise due to the variation of young s moduli and density which are assumed to vary exponentially with the radius vector the effect of various plate parameters such as radii ratio rigidity ratio non homogeneity and thickness variation on the vibrational characteristics of the plate have been studied for three different boundary conditions normalized displacements are presented for a specified plate for the first three modes of vibration a comparison of results with those available in the literature has been presented

euclidean invariant integral representations for schwinger functionals it is shown that if the schwinger functions of a wightman theory with a mass gap can be represented as moments of a complex measure there is also such a representation by a measure that is invariant under the euclidean group a necessary and sufficient condition is also given for the exponential of a quadratic form on the test function space to be the characteristic functional of a complex measure

the integrable kdv6 equations multiple soliton solutions and multiple singular soliton solutions abstract in this work the completely integrable sixth order nonlinear equations kdv6 are studied three distinct cases of these equations are selected for a reliable treatment multiple soliton solutions and multiple singular soliton solutions are formally derived for these equations the cole hopf transformation method combined with the hirota s bilinear sense are used to determine the two distinct structures of solutions the resonance relations for the three cases are investigated

local algebras of observables and pointlike localized fields we present a method to recover wightman fields from a haag kastler theory of local observables this may provide a basis for the comparison of different theories and for an algebraic description of high energy behaviour

vibration of non homogeneous circular mindlin plates with variable thickness free vibration analysis of non homogeneous circular plates of variable thickness has been presented using the first order shear deformation plate theory of mindlin chebyshev collocation technique has been employed to obtain the first three natural frequencies and mode shapes for clamped simply supported and free plate with four digit exactitude the effect of structural parameters such as taper non homogeneity and density and that of edge conditions on the natural frequencies has been investigated comparison of results for some special cases with published results obtained from other approximate methods has been presented which shows an excellent agreement

a class of nontrivial weakly local massive wightman fields with interpolating properties it is shown that in a quantum field theory satisfying wightman s axioms with locality replaced by weak locality and cyclicity by a weak irreducibility every unitary poincare invariant and cpt invariant operator is a scattering operator in the lsz sense the proof is given by explicit construction of a corresponding class of nontrivial weakly local massive wightman fields this result implies jost s conjecture that only locality leads to nontrivial restrictions for the scattering operator and extends corresponding results of schneider

accurate free vibration analysis of the completely free orthotropic rectangular plate by the method of superposition abstract the method of superposition is exploited to obtain highly accurate analytical type solutions for the free vibration of completely free orthotropic rectangular plates eigenvalues for 12 modes are provided for a particular set of problems representative of reinforced concrete and similar materials for a wide range of plate aspect ratios while it is recognized that data covering the entire range of possible problems cannot be tabulated it is hoped that the data provided will prove useful to some designers and provide a reference for other researchers to compare their results this appears to be the first study devoted to this problem to appear in the literature

multiple soliton solutions for the bogoyavlenskii s generalized breaking soliton equations and its extension form abstract in this work two generalized breaking soliton equations namely the bogoyavlenskii s breaking soliton equation and its extended form are examined the complete integrability of these equation are justified multiple soliton solutions and multiple singular soliton solutions are formally derived for each equation the additional terms of these equations do not kill the integrability of the typical breaking soliton equation the cole hopf transformation method and the simplified hereman s method are applied to conduct this analysis

four 2 1 dimensional integrable extensions of the kdv equation multiple soliton and multiple singular soliton solutions in this work four 2 1 dimensional nonlinear completely integrable equations generated by extending the kdv equation are developed the necessary condition for the complete integrability of these equation are formally derived multiple soliton solutions and multiple singular soliton solutions are determined to emphasize the compatability of these models the dispersion relations of these models are characterized by distinct physical structures the resonance phenomenon for these equations does not exist for any model

multiple soliton solutions and multiple singular soliton solutions for two higher dimensional shallow water wave equations two 3 1 dimensional shallow water wave equations are studied for complete integrability the hirota s bilinear method is used to determine the multiple soliton solutions for these equations moreover multiple singular soliton solutions will also be determined for each model the analysis highlights the capability of the direct method in handling completely integrable equations

continuous spectrum of automorphism groups and the infraparticle problem this paper presents a general framework for a refined spectral analysis of a group of isometries acting on a banach space which extends the spectral theory of arveson the concept of a continuous arveson spectrum is introduced and the corresponding spectral subspace is defined the absolutely continuous and singular continuous parts of this spectrum are specified conditions are given in terms of the transposed action of the group of isometries which guarantee that the pure point and continuous subspaces span the entire banach space in the case of a unitarily implemented group of automorphisms acting on a c algebra relations between the continuous spectrum of the automorphisms and the spectrum of the implementing group of unitaries are found the group of spacetime translation automorphisms in quantum field theory is analyzed in detail in particular it is shown that the structure of its continuous spectrum is relevant to the problem of existence of infra particles in a given theory

deformations of quantum field theories and integrable models deformations of quantum field theories which preserve poincare covariance and localization in wedges are a novel tool in the analysis and construction of model theories here a general scenario for such deformations is discussed and an infinite class of explicit examples is constructed on the borchers uhlmann algebra underlying wightman quantum field theory these deformations exist independently of the space time dimension and contain the recently studied warped convolution deformation as a special case in the special case of two dimensional minkowski space they can be used to deform free field theories to integrable models with non trivial s matrix

multiple soliton solutions of two extended model equations for shallow water waves abstract multiple soliton solutions for two extensions of model equations for shallow water waves presented in m j ablowitz d j kaup a c newell h segur the inverse scattering transform fourier analysis for nonlinear problems stud appl math 53 1974 249 315 r hirota j satsuma n soliton solutions of model equations for shallow water waves j phys soc jpn 40 2 1976 611 612 are obtained the two extensions possess identical dispersion relations but with different structures for the n soliton solutions for n 1 the hirota bilinear method is used to determine multiple soliton solutions of sech squared type for these extended equations the tanh coth method is used to obtain single soliton solutions

essential self adjointness of wick squares in quasi free hadamard representations on curved spacetimes we investigate whether a symmetric second order wick polynomial t of a free scalar field including derivatives is essentially self adjoint on the natural wightman domain in a quasi free i e fock space hadamard representation our results apply to arbitrary spacetime dimensions d 2 but we do restrict our attention to the case where t is smeared with a test function from a particular class s namely the class of sums of squares of test functions this class of smearing functions is smaller than the class of all non negative test functions a fact which follows hilbert s theorem combining techniques from microlocal and functional analysis we prove that t is essentially self adjoint if it is a wick square without derivatives in the presence of derivatives we prove the weaker result that t is essentially self adjoint if its compression to the one particle hilbert space is essentially self adjoint for the latter result we use wust s theorem and an application of konrady s trick in fock spac

numerical experiments on the determination of natural frequencies of transverse vibrations of rectangular plates of non uniform thickness abstract a comparison of natural frequencies of transverse vibration of thin rectangular plates of non uniform thickness with different combinations of boundary conditions is presented in this paper as obtained by using the following methodologies 1 the rayleigh ritz method with characteristic orthogonal polynomial shape functions 2 the rayleigh ritz method with a shape function which includes two exponents that are to be determined by minimizing the fundamental frequency coefficient 3 the optimized kantorovich method which has been proposed rather recently 4 the finite element method the results are presented in tabular form and discussed

homomorphisms and derivations in proper jcq triples we investigate homomorphisms in proper jcq triples and derivations on proper jcq triples associated with the 3 variable jensen functional equation begin array rcl 2f left frac x y z 2 right f x f y f z end array which was introduced and investigated by park cho and han we moreover prove the hyers ulam rassias stability of homomorphisms in proper jcq triples and of derivations on proper jcq triples this is applied to investigate isomorphisms between proper jcq triples

multiple soliton solutions for the kp equation by hirota s bilinear method and by the tanh coth method abstract in this work we use the hirota s direct method combined with the simplified version of this method to determine the n soliton solutions n 1 2 3 4 5 for the kadomtsev petviashvili kp equation the one soliton solutions will be handled by the tanh coth method the work emphasizes the power of the two methods that will be used

the cole hopf transformation and multiple soliton solutions for the integrable sixth order drinfeld sokolov satsuma hirota equation abstract the completely integrable sixth order nonlinear drinfeld sokolov satsuma hirota equation is studied three distinct methods namely the cole hopf transformation method the tanh coth method and the exp function method are used for a reliable treatment of this equation solitons multiple soliton solutions multiple singular soliton solutions and plane periodic solutions are obtained for this equations the study highlights the power of each method

an exact series solution for calculating the eigenfrequencies of orthotropic plates with completely free boundary abstract an analysis for solving boundary value problems in structural mechanics which was proposed by wang and lin 1996 journal of sound and vibration 196 285 293 1999 journal of applied mechanics 66 380 387 1 2 has been extended to the calculation of the eigenfrequencies of an orthotropic plate under all free boundary conditions the convergence of the series solution is assured and the procedure leads to pointwise exact solutions the calculated eigenfrequencies have been verified by a different approach and indicate that the present method is simple and effective

double periodic soliton solutions for the 3 1 dimensional boiti leon manna pempinelli equation in incompressible fluid abstract under investigation is the 3 1 dimensional boiti leon manna pempinelli equation in the incompressible fluid in this paper the extended homoclinic test technique ansatz functions and the bilinear form are used to construct double periodic soliton solutions of the 3 1 dimensional boiti leon manna pempinelli equation some entirely new double periodic soliton solutions are presented the properties and physical structure for these obtained solutions are discussed with some figures the ansatz functions are first used in 3 1 dimensional higher order differential equation

operator product expansions as a consequence of phase space properties the paper presents a model independent nonperturbative proof of operator product expansions in quantum field theory as an input a recently proposed phase space condition is used that allows a precise description of point field structures based on the product expansions we also define and analyze normal products in the sense of zimmermann

application of the spline element method to analyze vibration of annular sector plates abstract this paper deals with the vibrations of isotropic annular sector plates with arbitrary boundary conditions using the spline element method to demonstrate the accuracy of the methods several examples are solved and results are compared with those obtained by analytical methods and by other numerical methods good accuracy is obtained frequencies of annular sector plates with free edges and with point supports are presented

axisymmetric vibrations of polar orthotropic annular plates of variable thickness in this study of the free axisymmetric vibrations of polar orthotropic annular plates of linearly varying thickness on the basis of the classical theory of plates the chebyshev collocation technique has been employed to solve the differential equation governing the transverse motion of such plates frequencies mode shapes and moments have been computed for three different boundary conditions for various values of the rigidity ratios the radii ratio and the taper parameter for the first two modes of vibration the results for isotropic annular plates of uniform and non uniform thickness show good agreement with those available in the literature