vibration of rectangular mindlin plates by the spline strip method abstract this paper presents an analysis of the vibrations of rectangular mindlin plates by the spline strip method to demonstrate the convergence and accuracy of the method several examples are solved and results are compared with those obtained by analytical and other numerical methods stable convergence and excellent accuracy are obtained by using high order spline strip models frequencies of rectangular thick plates with several boundary conditions have been obtained and the results are presented in tabular form

free vibration analysis of functionally graded plates using the element free kp ritz method a free vibration analysis of metal and ceramic functionally graded plates that uses the element free kp ritz method is presented the material properties of the plates are assumed to vary continuously through their thickness according to a power law distribution of the volume fractions of the plate constituents the first order shear deformation plate theory is employed to account for the transverse shear strain and rotary inertia and mesh free kernel particle functions are used to approximate the two dimensional displacement fields the eigen equation is obtained by applying the ritz procedure to the energy functional of the system convergence studies are performed to examine the stability of the proposed method and comparisons of the solutions derived with those reported in the literature are provided to verify its accuracy four types of functionally graded rectangular and skew plates al al2o3 al zro2 ti 6al 4v aluminum oxide and sus304 si3n4 are included in the study and the effects of the volume fraction boundary conditions and length to thickness ratio on their frequency characteristics are discussed in detail

the fermionic signature operator in de sitter spacetime abstract the fermionic projector state is a distinguished quasi free state for the algebra of dirac fields in a globally hyperbolic spacetime we construct and analyze it in the four dimensional de sitter spacetime both in the closed and in the flat slicing in the latter case we show that the mass oscillation properties do not hold due to boundary effects this is taken into account in a so called mass decomposition the involved fermionic signature operator defines a fermionic projector state in the case of a closed slicing we construct the fermionic signature operator and show that the ensuing state is maximally symmetric and of hadamard form thus coinciding with the counterpart for spinors of the bunch davies state

subordination results on harmonic k uniformly convex mappings and related classes the main purpose of this paper is to establish some connections between certain classes of harmonic univalent functions by applying a number of convolution properties involving hypergeometric functions to be more precise we investigate such connections with harmonic k uniformly convex and a related class k st mappings in the plane

free vibration of skew sandwich plates with laminated facings this paper is concerned with the free vibration of skew sandwich plates composed of an orthotropic core and laminated facings the p ritz method has been adopted for the analysis the ritz functions are formed from the product of mathematically complete polynomials and boundary equations raised to appropriate integer powers depending on the boundary conditions the boundary equations ensure the satisfaction of the geometric boundary conditions a priori and facilitate the handling of any type of boundary conditions for generality better accuracy and ease in imposition of geometric boundary condition for the oblique edges the ritz formulation was non dimensionalized and cast in the skew co ordinates system since no vibration solutions are available for such skew sandwich plates the validity convergence and accuracy of the ritz formulation were established by comparing with other researchers vibration frequencies for various subset plate problems involving rectangular sandwich plates and skew laminated plates the paper features extensive generic vibration frequencies of these skew sandwich plates for various aspect ratios and boundary conditions lamination designs of facing material properties of core and facings

a variable kinematic ritz formulation for vibration study of quadrilateral plates with arbitrary thickness a new variable kinematic ritz method applied to free vibration analysis of arbitrary quadrilateral thin and thick isotropic plates is presented carrera s unified formulation and the versatile pb 2 ritz method are properly combined to build a powerful yet simple modeling and solution framework the proposed technique allows to generate arbitrarily accurate ritz solutions from a large variety of refined two dimensional plate theories by expanding so called ritz fundamental nuclei of the plate mass and stiffness matrices theoretical development of the present methodology is described in detail convergence and accuracy of the method are examined through several examples on thin moderately thick and very thick plates of rectangular skew trapezoidal and general quadrilateral shapes with an arbitrary combination of clamped free and simply supported edges present results are compared with existing three dimensional solutions from open literature maximum and average differences of various higher order plate theories and three dimensional results are also presented with the aim of providing useful guidelines on the choice of appropriate plate theory to get a desired accuracy on frequency parameters

vibration of thick skew plates based on mindlin shear deformation plate theory the free flexural vibration of thick skew plates is considered the total energy functional is derived based on the first order shear deformation plate theory by mindlin the newly developed pb 2 rayleigh ritz method is applied to obtain the solution the method features the versatile pb 2 ritz functions for approximating the deflection and rotation functions which comprise the product of 1 a two dimensional polynomial function p 2 and 2 a basic function b the basic function is the key to ensure the automatic satisfaction of the geometric boundary conditions at the outset since it is formed from the product of the boundary equations raised to appropriate powers natural frequency parameters for skew mindlin plates with different combinations of boundary conditions are presented the solutions where possible are verified by comparisons with those available in the open literature the effect of the poisson ratio on vibration frequencies of plates with free edges is also investigated

exact closed form frequency equations for thick circular plates using a third order shear deformation theory abstract this paper presents for the first time exact closed form frequency equations and transverse displacement for thick circular plates with free soft simply supported hard simply supported and clamped boundary conditions based on reddy s third order shear deformation theory hamiltonian and minimum potential energy principles are used to extract the equations of dynamic equilibrium and natural boundary conditions of the plate the new formulation is verified by comparing the results with their counterparts reported in open literature natural frequencies of circular plates with different boundary conditions are tabulated in dimensionless form for various values of thickness radius ratios the results presented on the basis of exact closed form frequency equations are expected to serve as reliable benchmarks

application of the spline element method to analyze vibration of skew mindlin plates with varying thickness in one direction this paper presents an application of the spline element method based on the mindlin plate theory to analyze the vibration of thick skew plates with varying thickness in the longitudinal direction to demonstrate the convergence and accuracy of the present method several examples are solved and results are compared with those obtained by other numerical methods good accuracy is obtained frequencies of skew mindlin plates with varying cross sections having arbitrary boundary conditions are analyzed for different thickness ratios aspect ratios ratios of the width to thickness and skew angles

uniqueness theorem for bms invariant states of scalar qft on the null boundary of asymptotically flat spacetimes and bulk boundary observable algebra correspondence this work concerns some features of scalar qft defined on the causal boundary mathfrak j of an asymptotically flat at null infinity spacetime and based on the bms invariant weyl algebra mathcal w mathfrak j

on a generalization of uniformly convex and related functions in this paper we define and study some subclasses of analytic functions by using the concept of k uniformly convexity several interesting properties coefficients and radius problems are investigated the behaviour of these classes under a certain integral operator is also studied we indicate the relevant connections of our results with various known ones

sufficient conditions for quasifree states and an improved uniqueness theorem for quantum fields on space times with horizons let be a state on the weyl algebra over a symplectic space we prove that if either i the liberation of is pure or ii the restriction of to each of two generating weyl subalgebras is quasifree and pure then is quasifree and pure and in case i is equal to its liberation in case ii is uniquely determined by its restrictions here we define the liberation of a sufficiently regular state to be the quasifree state with the same two point function results i and ii permit one to drop the quasifree assumption in a result due to wald and the author concerning linear scalar quantum fields on space times with bifurcate killing horizons and thus to conclude that on a large subalgebra of the field algebra for such a system there is a unique stationary state whose two point function has the hadamard form the paper contains a number of further related developments including a i implies a uniqueness result e g for the usual free field in minkowski space we compare and contrast this with other known uniqueness results for this system b a similar pair of results to i and ii is proven for quasifree states and liberations where the definition of quasifree differs from what we call here quasifree in that nonvanishing one point functions are permitted and the liberation of a state is defined to be the quasifree state with the same one and two point functions c we derive similar results for the canonical anticommutation relations

comparison of natural frequencies of laminates by 3 d theory part i rectangular plates abstract the three dimensional theory of laminated plates and shells has been developed by chao et al 10 13 62 63 with many applications to impact and shock modal analyses in this research a complete survey of the literature is made on the free vibration natural frequencies of simply supported rectangular plates various boundary conditions are composed of fixed pin hinge roller and sliding pin supported edges the lowest frequencies are obtained in the present study in comparison with those in earlier studies as a result of the close natural state reached in keeping with the three dimensional boundary and interlaminar continuity conditions via a 3 d augmented energy variational approach

on the stress energy tensor of quantum fields in curved spacetimes comparison of different regularization schemes and symmetry of the hadamard seeley dewitt coefficients we review a few rigorous and partly unpublished results on the regularisation of the stress energy in quantum field theory on curved spacetimes 1 the symmetry of the hadamard seeley dewitt coefficients in smooth riemannian a lorentzian spacetimes 2 the equivalence of the local function and the hadamard point splitting procedure in smooth static spacetimes 3 the equivalence of the dewitt schwinger and the hadamard point splitting pro cedure in smooth riemannian and lorentzian spacetimes

local causal structures hadamard states and the principle of local covariance in quantum field theory in the framework of the algebraic formulation we discuss and analyse some new features of the local structure of a real scalar quantum field theory in a strongly causal spacetime in particular we use the properties of the exponential map to set up a local version of a bulk to boundary correspondence the bulk is a suitable subset of a geodesic neighbourhood of an arbitrary but fixed point p of the underlying background while the boundary is a part of the future light cone having p as its own tip in this regime we provide a novel notion for the extended algebra of wick polynomials on the aforesaid cone and on the one hand we prove that it contains the information of the bulk counterpart via an injective homomorphism while on the other hand we associate to it a distinguished state whose pull back in the bulk is of hadamard form the main advantage of this point of view arises if one uses the universal properties of the exponential map and of the light cone in order to show that for any two given backgrounds m and m and for any two subsets of geodesic neighbourhoods of two arbitrary points it is possible to engineer the above procedure such that the boundary extended algebras are related via a restriction homomorphism this allows for the pull back of boundary states in both spacetimes and thus to set up a machinery which permits the comparison of expectation values of local field observables in m and m

stability and vibration of shear deformable plates first order and higher order analyses abstract this work presents the highly accurate numerical calculation of the natural frequencies and buckling loads for thick elastic rectangular plates with various combinations of boundary conditions the reissener mindlin first order shear deformation plate theory and the higher order shear deformation plate theory of reddy have been applied to the plate s analysis the governing equations and the boundary conditions are derived using the dynamic version of the principle of minimum of the total energy the solution is obtained by the extended kantorovich method this approach is combined with the exact element method for the vibration and stability analysis of compressed members which provides for the derivation of the exact dynamic stiffness matrix including the effect of in plane and inertia forces the large number of numerical examples demonstrates the applicability and versatility of the present method the results obtained by both shear deformation theories are compared with those obtained by the classical thin plate s theory and with published results many new results are given too

free vibration of skew mindlin plates by p version of f e m abstract accurate natural frequencies and mode shapes of skew plates with and without cutouts are determined by p version finite element method using integrals of legendre polynomials for p 1 14 the hierarchical plate element is formulated based on mindlin s plate theory including rotatory inertia effects and based on a skew co ordinate system non dimensional frequency parameter and mode shapes are presented for a range of skew angle aspect ratio a b thickness width ratio h b cutout dimensions and different boundary conditions the results were verified by comparison with those available in the open literature

the fekete szego problem for subclasses of analytic functions defined by a differential operator related to conic domains by using a linear multiplier fractional differential operator a new subclass of analytic functions generalized b uniformly convex functions denoted by b sp l m n a c is introduced for this class the fekete szego problem is completely solved various known or new special cases of our results are also pointed out

free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first order shear deformation theory in this study free vibration of laminated skew plates was investigated discrete singular convolution dsc method is used for numerical solution of vibration problems the straight sided quadrilateral domain is mapped into a square domain in the computational space using a four node element by using the geometric transformation typical results are presented for different geometric parameters and boundary conditions it is concluded from the results that the skew angle have considerable influence on the variations of the frequencies with fibre orientation angle and number of layers in the laminate the results obtained by dsc method are compared with those obtained by analytical and numerical approaches it is shown that reasonable accurate results are obtained present work also indicates that the method of dsc is a promising and potential approach for computational mechanics copyright 2009 john wiley sons ltd

on coefficient inequalities of functions associated with conic domains in this paper the concepts of janowski functions and the conic regions are combined to define a new domain which represents the conic type regions different views of this modified conic domain for specific values are shown graphically for better understanding of the behavior of this domain the class of such functions which map the open unit disk e onto this modified conic domain is defined also the classes of k uniformly janowski convex and k janowski starlike functions are defined and their coefficient inequalities are formulated the coefficient bound for a certain class of analytic functions proved by owa et al 2006 in 16 has also been improved

vibrations of skewed cantilevered triangular trapezoidal and parallelogram mindlin plates with considering corner stress singularities based on the mindlin shear deformation plate theory a method is presented for determining natural frequencies of skewed cantilevered triangular trapezoidal and parallelogram plates using the ritz method considering the effects of stress singularities at the clamped re entrant corner the admissible displacement functions include polynomials and corner functions the admissible polynomials form a mathematically complete set and guarantee the solution convergent to the exact frequencies when sufficient terms are used the corner functions properly account for the singularities of moments and shear forces at the re entrant corner and accelerate the convergence of the solution detailed convergence studies are carried out for plates of various shapes to elucidate the positive effects of corner functions on the accuracy of the solution the results obtained herein are compared with those obtained by other investigators to demonstrate the validity and accuracy of the solution copyright 2005 john wiley sons ltd

free vibration and stability of thick elastic plates subjected to in plane forces abstract natural frequencies and buckling loads of a simply supported thick plate subjected to in plane initial tensile and or compressive forces are analysed by using the method of power series expansion of displacement components a set of fundamental dynamic equations of a two dimensional higher order plate theory is derived through hamilton s principle several sets of truncated approximate theories are applied to solve the eigenvalue problems of a thick plate in order to assure the accuracy of the present theory convergence properties of the minimum natural frequency and the buckling load for the out of plane problem of a simply supported square plate are examined in detail it is noticed that the present approximate theories can predict the frequencies and buckling loads of an extremely thick plate more accurately compared to other refined theories and classical plate theory

vibration and stability of an initially stressed thick plate according to a high order deformation theory in this paper the average stress method is used to derive the governing equation for a thick rectangular plate according to a high order deformation theory the applied load is taken to be a combination of a pure bending stress plus an extensional stress in the plane of the plate the buckling loads and natural frequencies of simply supported plates are also investigated present results based on high order theory are compared with the results of brunelle s theory and reddy s theory in addition the effects of various parameters on the natural frequencies are studied more accurate results can be obtained by using the present theory than those of the other theories

in plane vibration and stability of shallow circular arches subjected to axial forces natural frequencies and buckling loads of a simply supported shallow circular arch with sufficiently small depth to radius of curvature ratio h r 1 subjected to initial axial tensile and or compressive forces are analysed by using the method of power series expansion of displacement components a set of fundamental dynamic equations of a one dimensional higher order arch theory for in plane vibration problems of shallow circular arches is derived through hamilton s principle several sets of truncated approximate theories which can take into account the effects of both shear deformations with depth changes and rotary inertia are applied to solve the eigenvalue problems of an elastic arch convergence properties of the natural frequency and the buckling load of simply supported shallow circular arches are examined in detail the present approximate theories can predict the natural frequencies and buckling loads of shallow circular arches with small length to depth ratio l h more accurately compared with previously published results

quantum field theory on spacetimes with a compactly generated cauchy horizon we prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime with a compactly generated cauchy horizon these theorems demonstrate the breakdown of the theory at certain base points of the cauchy horizon which are defined as past terminal accumulation points of the horizon generators thus the theorems may be interpreted as giving support to hawking s chronology protection conjecture according to which the laws of physics prevent one from manufacturing a time machine specifically we prove

high accuracy mixed finite element ritz formulation for free vibration analysis of plates with general boundary conditions abstract a high order accurate mixed finite element ritz method is introduced and developed to study the vibration problem of plates with general boundary conditions the finite element method fem with higher order interpolation functions is first used to discretize the spatial partial derivatives with respect to a co ordinate direction of the plate the ritz method is then employed to analogize the resulting system of ordinary differential equations a novel technique is also presented to exactly satisfy the mixed natural boundary conditions the proposed method is applied here to solve some benchmark vibration problems of plates including isotropic and anisotropic rectangular plates variable thickness rectangular plates multi span rectangular plates and skew plates comparisons with existing numerical and analytical solutions show that the proposed mixed method can yield highly accurate results for vibration problem of plates involving free edges free corners and irregular boundaries using a small number of finite elements and ritz terms

buckling loads for variable cross section members with variable axial forces abstract this work gives exact solutions for the buckling loads of variable cross section columns loaded by variable axial force for several boundary conditions both the cross section bending stiffness and the axial load can vary along the column as polynomial expressions the proposed solution is based on a new method that enables one to get the stiffness matrix for the member including the effects of the axial loading the buckling load is found as the load that makes the determinant of the stiffness matrix equal zero several examples are given and compared to published results to demonstrate the accuracy and flexibility of the method new exact results are given for several other cases

buckling of thick skew plates the paper considers the elastic buckling of thick skew plates up to now very little work has been done on this subject and the paper aspires to fill this gap based on the principle of stationary total potential energy and the recently developed pb 2 rayleigh ritz method as a solution procedure buckling solutions for skew plates of various aspect ratios skew angles and boundary conditions are determined the tabulation of these results not available thus far should be useful to designers and researchers who may use them as benchmark values to test the validity and convergence of their numerical techniques and softwares for thick plate analysis

a higher order shear deformation theory for the vibration of thick plates abstract several first order shear deformation theories for thick plates have been formulated during the past half century e g by reissner hencky mindlin and ambartsumyan the mindlin theory has been widely used for vibration analysis it is well known that consideration of shear flexibility corrects the flexural frequencies by reducing them however it has been found that first order shear deformation theories result in over correction in the present work a higher order theory is presented which provides additional freedom to the displacements through the plate thickness and essentially eliminates the over correction a complete theory is developed including energy functionals equations of motion and boundary conditions comparisons of frequencies arising from classical thin plate theory mindlin theory and the present theory are made for completely free rectangular plates of moderate and large thickness completely free boundaries rather than simply supported ones are chosen because they are more consistent with physical models in the theories used

a continuum three dimensional vibration analysis of thick rectangular plates abstract this paper presents a continuum three dimensional ritz formulation for the vibration analysis of homogeneous thick rectangular plates with arbitrary combinations of boundary constraints this model is formulated on the basis of the linear three dimensional small deformation elasticity theory to predict the vibratory responses of these thick rectangular plates the displacement fields in the transverse and in plane directions are expressed by sets of orthogonally generated polynomial functions these shape functions are intrinsically a product of a class of orthogonal polynomial functions and a basic function which are chosen to satisfy the essential geometric boundary conditions at the outset sets of frequency data for plates with various aspect ratios and thickness ratios have been presented these data are used to examine the merits and limitations of the classical plate theory and mindlin plate theory by direct comparisons finally using the three dimensional continuum approach sets of first known deformed mode shapes have been generated thus helping to understand the vibratory motion furthermore these results may also serve as the benchmark to further research into the refined plate theories

an efficient differential quadrature methodology for free vibration analysis of arbitrary straight sided quadrilateral thin plates in this paper a new differential quadrature dq methodology is employed to study free vibration of irregular quadrilateral straight sided thin plates a four nodded super element is used to map the irregular physical domain into a square domain in the computational domain second order transformation schemes with relative ease and less computation are employed to transform the fourth order governing equation of thin plates between the two domains the only degree of freedom within the domain is the displacement whereas along the boundaries the displacement as well as the second order derivative of the displacement with respect to associated normal co ordinate variable in computational domain are the two degrees of freedom implementing the method the formulation for the dq method for the free vibration analysis of plates of straight sided shapes was presented together with the implementation procedure for the different boundary conditions to demonstrate the accuracy convergency and stability of the new methodology detail studies are made on isotropic plates at acute angles with different geometries boundary and loading conditions including dq free edge boundary condition implementations accurate results even with fewer degrees of freedom than for those of comparable numerical algorithms were achieved

a new dq based method and its application to the stability of columns a numerical picard like method which combines successive approximations with differential quadrature is discussed for application to the stability of columns unlike other methods the present method satisfies all the boundary conditions without any additional computation for each iteration and it does not require any subdivision of the problem domain despite of its recursive nature the approximate solution can be expressed by operational matrices and vectors of known quantities such as the solution obtained by advanced polynomial expansions several examples show the satisfactorily behaviour of the proposed method in comparison to the existing methods both in the linear and nonlinear range

conic regions and k uniform convexity abstract let k c denote a domain such that 1 k and k is a conic section with eccentricity equal to 1 k in this paper authors introduce the class of k uniformly convex functions k ucv with the property that the values of the expression 1 zf z f z lie inside the domain k necessary and sufficient conditions for membership in k ucv as well as sharp growth and distortion theorems for k uniformly convex functions are given the obtained results generalize the concept of uniform convexity due to a w goodman ann polon math 56 1991 87 92

micro local approach to the hadamard condition in quantum field theory on curved space time for the two point distribution of a quasi free klein gordon neutral scalar quantum field on an arbitrary four dimensional globally hyperbolic curved space time we prove the equivalence of 1 the global hadamard condition 2 the property that the feynman propagator is a distinguished parametrix in the sense of duistermaat and hormander and 3 a new property referred to as the wave front set spectral condition wfssc because it is reminiscent of the spectral condition in axiomatic quantum field theory on minkowski space results in micro local analysis such as the propagation of singularities theorem and the uniqueness up toc of distinguished parametrices are employed in the proof we include a review of kay and wald s rigorous definition of the global hadamard condition and the theory of distinguished parametrices specializing to the case of the klein gordon operator on a globally hyperbolic space time as an alternative to a recent computation of the wave front set of a globally hadamard two point distribution on a globally hyperbolic curved space time given elsewhere by kohler to correct an incomplete computation in 32 we present a version of this computation that does not use a deformation argument such as that used in fulling narcowich and wald and is independent of the cauchy evolution argument of fulling sweeny and wald both of which are relied upon in kohler s proof this leads to a simple micro local proof of the preservation of hadamard form under cauchy evolution first shown by fulling sweeny and wald relying only on the propagation of singularities theorem in another paper 33 the equivalence theorem is used to prove a conjecture by kay that a locally hadamard quasi free klein gordon state on any globally hyperbolic curved space time must be globally hadamard

on k uniformly close to convex functions of complex order in this paper we define and study some subclasses of analytic functions by using fractional derivative operator some interesting properties coefficients problems and inclusion results of these classes are investigated it is also shown that these classes are closed under convolution with convex functions and some applications are given

a local to global singularity theorem for quantum field theory on curved space time we prove that if a reference two point distribution of positive type on a time orientable curved space time cst satisfies a certain condition on its wave front set the classp m g condition and if any other two point distribution i is of positive type ii has the same antisymmetric part as the reference modulo smooth function and iii has the same local singularity structure then it has the same global singularity structure in the proof we use a smoothing positivity preserving pseudo differential operator the support of whose symbol is restricted to a certain conic region which depends on the wave front set of the reference state this local to global theorem together with results published elsewhere leads to a verification of a conjecture by kay that for quasi free states of the klein gordon quantum field on a globally hyperbolic cst the local hadamard condition implies the global hadamard condition a counterexample to the local to global theorem on a strip in minkowski space is given when the classp m g condition is not assumed

classes of multivalent functions associated with a convolution operator we investigate several properties of the linear aouf silverman srivastava operator and associated classes of multivalent analytic functions which were introduced and studied by aouf et al m k aouf h silverman h m srivastava some families of linear operators associated with certain subclasses of multivalent functions comp math appl 55 2008 535 549 several theorems are extensions of earlier results of the above paper

analytic hadamard states calderon projectors and wick rotation near analytic cauchy surfaces we consider the klein gordon equation on analytic spacetimes with an analytic cauchy surface in this setting we prove the existence of pure analytic hadamard states the proof is based on considering an elliptic operator obtained by wick rotating the klein gordon operator in a neighborhood of a cauchy hypersurface the cauchy data of hadamard two point functions are constructed as calderon projectors suitably generalized if the hypersurface is non compact for the elliptic operator

vibration of shear deformable plates with variable thickness first order and higher order analyses this work presents accurate numerical calculations of the natural frequencies for elastic rectangular plates of variable thickness with various combinations of boundary conditions the thickness variation in one or two directions of the plate is taken in polynomial form the first order shear deformation plate theory of mindlin and the higher order shear deformation plate theory of reddy have been applied to the plate analysis the governing equations and the boundary conditions are derived using the dynamic version of the principle of minimum of the lagrangian function the solution is obtained by the extended kantorovich method this approach is combined with the exact element method for the vibration analysis of members with variable flexural rigidity which provides for the derivation of the exact dynamic stiffness matrix of varying cross sections strips the large number of numerical examples demonstrates the applicability and versatility of the present method the results obtained by both shear deformation theories are compared with those obtained by the classical thin plate theory and with published results

a closed form solution for the generalized euler problem euler9s problem that of buckling of a uniform column under its own weight is generalized to include columns of variable stiffness it is posed as an inverse problem namely determine the variation of the stiffness along the axis of the column so that the column has the prescribed buckling mode given as a simple polynomial function

supersymmetric field theoretic models on a supermanifold we propose the extension of some structural aspects that have successfully been applied in the development of the theory of quantum fields propagating on a general space time manifold so as to include superfield models on a supermanifold we only deal with the limited class of supermanifolds which admit the existence of a smooth body manifold structure our considerations are based on the catenacci reina teofillatto bryant approach to supermanifolds in particular we show that the class of supermanifolds constructed by bonora pasti tonin satisfies the criteria which guarantee that a supermanifold admits a hausdorff body manifold this construction is the closest to the physicist s intuitive view of superspace as a manifold with some anticommuting coordinates where the odd sector is topologically trivial the paper also contains a new construction of superdistributions and useful results on the wavefront set of such objects moreover a generalization of the spectral condition is formulated using the notion of the wavefront set of superdistributions which is equivalent to the requirement that all of the component fields satisfy on the body manifold a microlocal spectral condition proposed by brunetti fredenhagen kohler

global wave parametrices on globally hyperbolic spacetimes abstract in a recent work the first named author levitin and vassiliev have constructed the wave propagator on a closed riemannian manifold m as a single oscillatory integral global both in space and in time with a distinguished complex valued phase function in this paper first we give a natural reinterpretation of the underlying algorithmic construction in the language of ultrastatic lorentzian manifolds subsequently we show that the construction carries over to the case of static backgrounds thanks to a suitable reduction to the ultrastatic scenario finally we prove that the overall procedure can be generalised to any globally hyperbolic spacetime with compact cauchy surfaces as an application we discuss how from our procedure one can recover the local hadamard expansion which plays a key role in all applications in quantum field theory on curved backgrounds

a differential quadrature hierarchical finite element method using fekete points for triangles and tetrahedrons and its applications to structural vibration abstract a differential quadrature hierarchical finite element method dqhfem using fekete points was formulated for triangles and tetrahedrons and applied to structural vibration analyses first orthogonal polynomials on triangles and tetrahedrons that can be used as bases of the hierarchical finite element method hfem were derived and simple formulas of transforming one dimensional non uniform nodes to simplexes were presented then the non uniform nodes were used as initial guesses to solve the fekete points on simplexes through newton raphson s method together with the orthogonal polynomials new differential quadrature dq rules on simplexes were formulated using the hfem bases and the fekete points the numbers of nodes or bases on different edges and faces and inside the body of the new dq elements do not relate with each other like the hfem that can freely assign different numbers of bases on different edges and faces and inside the body so the new dq method was named as a differential quadrature hierarchical dqh method that uses either interpolation functions or orthogonal polynomials as bases inside the element its weak form was named as the dqhfem besides the dqh method and its weak form a simple method of generating high quality linear and high order triangular and tetrahedral meshes from a single nurbs patch was presented numerical tests of the dqhfem through structural vibration analyses showed that high accuracy results can be obtained using only a few nodes even on curvilinear domains using the dqh bases on both physical and geometric fields it was concluded that wide applications of the dqh method and the dqhfem to science and engineering are possible and commercial codes based on them are deserved to be developed