four non abelian groups of order p 4 as galois groups abstract let p be an odd prime and let f be arbitrary field of characteristic not p containing a primitive pth root of unity in this paper we prove a criterion giving the obstructions to realizability of p groups as galois groups over f having a factor group of the kind h c p we apply this to the non abelian groups of orders p 3 and p 4 where it is possible we give a description of all galois extensions realizing these groups we discuss also automatic realizations and local fields

on the descending central sequence of absolute galois groups let p be an odd prime number and f a field containing a primitive p th root of unity we prove a new restriction on the group theoretic structure of the absolute galois group g f of f namely the third subgroup g f 3 in the descending p central sequence of g f is the intersection of all open normal subgroups n such that g f n is 1 bbb z p 2 or the extra special group m p 3 of order p 3 and exponent p 2

vibration analysis by discrete singular convolution this paper explores the utility of a discrete singular convolution algorithm for vibration analysis a number of different realizations of singular convolution kernels are selected to illustrate the present algorithm vibration analysis of strings rods beams diatomic molecules membranes waveguides and thin plates are utilized to test numerical accuracy and speed of convergence of the present approach numerical experiments indicate that the discrete singular convolution is a simple and reliable algorithm for vibration analysis

numerical analysis of free vibrations of laminated composite conical and cylindrical shells discrete singular convolution dsc approach a numerical study on the free vibration analysis for laminated conical and cylindrical shell is presented the analysis is carried out using love s first approximation thin shell theory and solved using discrete singular convolution dsc method numerical results in free vibrations of laminated conical and cylindrical shells are presented graphically for different geometric and material parameters free vibrations of isotropic cylindrical shells and annular plates are treated as special cases the effects of circumferential wave number number of layers on frequencies characteristics are also discussed the numerical results show that the present method is quite easy to implement accurate and efficient for the problems considered

discrete singular convolution and its application to the analysis of plates with internal supports part 2 applications part 2 of this series of two papers presents the applications of the discrete singular convolution dsc algorithm the main purpose of this paper is to explore the utility test the accuracy and examine the convergence of the proposed approach for the vibration analysis of rectangular plates with internal supports both partial internal line supports and complex internal supports are considered for 21 square plates of various combinations of edge support conditions the effects of different size shape and topology of the internal supports and different boundary conditions on the vibration response of plates are investigated the partial internal line supports may vary from a central point support to a full range of cross or diagonal line supports several closed loop supports such as ring square and rhombus and their combinations are studied for complex internal supports convergence and comparison studies are carried out to establish the correctness and accuracy of the dsc algorithm the dsc results are compared with those in the available literature obtained by using other methods numerical results indicate that the dsc algorithm exhibits controllable accuracy for plate analysis and shows excellent flexibility in handling complex geometries boundary conditions and support conditions copyright 2002 john wiley sons ltd

quotients of absolute galois groups which determine the entire galois cohomology for a prime power q pd and a field f containing a root of unity of order q we show that the galois cohomology ring h g f mathbb z q is determined by a quotient g f 3 of the absolute galois group gf related to its descending q central sequence conversely we show that g f 3 is determined by the lower cohomology of gf this is used to give new examples of pro p groups which do not occur as absolute galois groups of fields

dsc ritz method for the free vibration analysis of mindlin plates this paper introduces a novel method for the free vibration analysis of mindlin plates the proposed method takes the advantage of both the local bases of the discrete singular convolution dsc algorithm and the pb 2 ritz boundary functions to arrive at a new approach called dsc ritz method two basis functions are constructed by using dsc delta sequence kernels of the positive type the energy functional of the mindlin plate is represented by the newly constructed basis functions and is minimized under the ritz variational principle extensive numerical experiments are considered by different combinations of boundary conditions of mindlin plates of rectangular and triangular shapes the performance of the proposed method is carefully validated by convergence analysis the frequency parameters agree very well with those in the literature numerical experiments indicate that the proposed dsc ritz method is a very promising new method for vibration analysis of mindlin plates copyright 2004 john wiley sons ltd

embedding problems over abelian groups and an application to elliptic curves conditions for the solvability of certain embedding problems can be given in terms of the existence of elements with certain norm properties a classical example due to witt 1936 crelle s j 174 237 245 is that of embedding a klein extension into a dihedral extension in construction de p extensions galoisiennes d un corps de caracteristique differente de p 1987 j algebra109 508 535 massy finds this type of condition for central p extensions of an abelian group of exponent p in this paper we generalize the results of massy to the case of central p extensions of any abelian group in the last section we discuss the reason for our interest in these problems they appear in the theory of elliptic q curves if one is interested in computing representatives with especially good arithmetic properties in the isogeny class of a given curve

structural properties of the one dimensional drift diffusion models for semiconductors this paper is devoted to the analysis of the one dimensional current and voltage drift diffusion models for arbitrary types of semiconductor devices and under the assumption of vanishing generation recombination we show in the course of this paper that these models satisfy structural properties which are due to the particular form of the coupling of the involved systems these structural properties allow us to prove an existence and uniqueness result for the solutions of the current driven model together with monotonicity properties with respect to the total current i of the electron and hole current densities and of the electric field at the contacts we also prove analytic dependence of the solutions on i these results allow us to establish several qualitative properties of the current voltage characteristic in particular we give the nature of the possible bifurcation points of this curve we show that the voltage function is an analytic function of the total current and we characterize the asymptotic behavior of the currents for large voltages as a consequence we show that the currents never saturate as the voltage goes to 00 contrary to what was predicted by numerical simulations by m s mock compel 1 1982 pp 165 174 we also analyze the drift diffusion models under the assumption of quasi neutral approximation we show in particular that the reduced current driven model has at most one solution but that it does not always have a solution then we compare the full and the reduced voltage driven models and we show that in general the quasi neutral approximation is not accurate for large voltages even if no saturation phenomenon occurs finally we prove a local existence and uniqueness result for the current driven model in the case of small generation recombination terms

the zassenhaus filtration massey products and representations of profinite groups abstract we consider the p zassenhaus filtration g n of a profinite group g suppose that g s n for a free profinite group s and a normal subgroup n of s contained in s n under a cohomological assumption on the n fold massey products which holds e g if g has p cohomological dimension 1 we prove that g n 1 is the intersection of all kernels of upper triangular unipotent n 1 dimensional representations of g over f p this extends earlier results by minac spira and the author on the structure of absolute galois groups of fields

plate vibration under irregular internal supports this paper studies the problem of plate vibration under complex and irregular internal support conditions such a problem has its widely spread industrial applications and has not been addressed in the literature yet partially due to the numerical difficulties a novel computational method discrete singular convolution dsc is introduced for solving this problem the dsc algorithm exhibits controllable accuracy for approximations and shows excellent flexibility in handling complex geometries boundary conditions and internal support conditions convergence and comparison studies are carried out to check the validity and accuracy of the dsc method case studies are considered to the combination of a few different boundary conditions and irregular internal supports the latter are generated by using an image processing algorithm completely independent verifications are conducted by using the established pb 2 ritz method which is available for two relatively simpler support patterns the morphology of the first few eigenmodes is found to be localized to largest support free spatial regions

numerical solution of the helmholtz equation with high wavenumbers this paper investigates the pollution effect and explores the feasibility of a local spectral method the discrete singular convolution dsc algorithm for solving the helmholtz equation with high wavenumbers fourier analysis is employed to study the dispersive error of the dsc algorithm our analysis of dispersive errors indicates that the dsc algorithm yields a dispersion vanishing scheme the dispersion analysis is further confirmed by the numerical results for one and higher dimensional helmholtz equations the dsc algorithm is shown to be an essentially pollution free scheme furthermore for large scale computation the grid density of the dsc algorithm can be close to the optimal two grid points per wavelength the present study reveals that the dsc algorithm is accurate and efficient for solving the helmholtz equation with high wavenumbers copyright 2003 john wiley sons ltd

a unified approach for the solution of the fokker planck equation this paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the fokker planck equation the unified features of the discrete singular convolution algorithm are discussed it is demonstrated that different implementations of the present algorithm such as global local galerkin collocation and finite difference can be deduced from a single starting point three benchmark stochastic systems the repulsive wong process the black scholes equation and a genuine nonlinear model are employed to illustrate the robustness and to test the accuracy of the present approach for the solution of the fokker planck equation via a time dependent method an additional example the incompressible euler equation is used to further validate the present approach for more difficult problems numerical results indicate that the present unified approach is robust and accurate for solving the fokker planck equation

on the cohomology of galois groups determined by witt rings let f denote a field of characteristic different from two in this paper we describe the mod 2 cohomology of a galois group gf called the w group of f which is known to essentially characterize the witt ring wf of anisotropic quadratic modules over f we show that h gf f2 contains the mod 2 galois cohomology of f and that its structure will reflect important properties of the field we construct a space xf endowed with an action of an elementary abelian group e such that the computation of the cohomology of gf reduces to calculating the equivariant cohomology h e xf f2 for the case of a field which is not formally real this amounts to computing the cohomology of an explicit euclidean space form an object which is interesting in its own right we provide a number of examples and a substantial combinatorial computation for the cohomology of the universal w groups

free vibration analysis of beams and rectangular plates with free edges by the discrete singular convolution in this paper free vibration of beams annular plates and rectangular plates with free boundaries are analyzed by using the discrete singular convolution dsc a novel method to apply the free boundary conditions is proposed detailed derivations are given to validate the proposed method eight examples including the free vibrations of beams annular plates and rectangular plates with free boundaries are analyzed two kernels the regularized shannon s kernel and the non regularized lagrange s delta sequence kernel are tested dsc results are compared with either analytical solutions or and differential quadrature dq data it is demonstrated that the proposed method to incorporate the free boundary conditions is simple to use and can yield accurate frequency data for beams with a free end and plates with free edges thus the proposed method for applying the boundary conditions extends the application range of the dsc

discrete singular convolution and its application to the analysis of plates with internal supports part 1 theory and algorithm this paper presents a novel computational approach the discrete singular convolution dsc algorithm for analysing plate structures the basic philosophy behind the dsc algorithm for the approximation of functions and their derivatives is studied approximations to the delta distribution are constructed as either bandlimited reproducing kernels or approximate reproducing kernels unified features of the dsc algorithm for solving differential equations are explored it is demonstrated that different methods of implementation for the present algorithm such as global local galerkin collocation and finite difference can be deduced from a single starting point the use of the algorithm for the vibration analysis of plates with internal supports is discussed detailed formulation is given to the treatment of different plate boundary conditions including simply supported elastically supported and clamped edges this work paves the way for applying the dsc approach in the following paper to plates with complex support conditions which have not been fully addressed in the literature yet

galois modules appearing as pth power classes of units of extensions of degree p we previously described the galois module structures of pth power class groups k k p where k f is a cyclic extension of degree p over a field f containing a primitive pth root of unity that description relied upon arithmetic invariants associated with k f here we construct field extensions k f with prescribed arithmetic invariants thus completing the classification of galois modules k k p

a characterization of c fields via galois groups abstract it is known that those fields f which are of class c in the sense of r ware can be characterized by their witt ring structure as well as by the behavior of their binary quadratic forms and the structure of their galois 2 extensions in this paper we show that c fields which have at least 8 square classes are characterized by the absence of a certain group dc of order 16 as a galois group over them moreover we show that the level of such a field is determined by the presence or absence of the cyclic group of order 4 and the dihedral group of order 8 as galois groups over it these results provide an interesting continuation of the work of ware in the appendix we give an explicit construction of field extensions with galois group dc

numerical convergence of simple and orthogonal polynomials for the unilateral plate buckling problem using the rayleigh ritz method unilateral buckling is a contact problem whereby buckling is confined to take place in only one lateral direction for plate structures this can occur when a thin steel plate is juxtaposed with a rigid concrete medium and the steel may only buckle locally away from the concrete core this paper investigates the use of simple and orthogonal polynomials in the rayleigh ritz method for unilateral plate buckling the orthogonal polynomials used are the classical chebyshev types 1 and 2 legrende hermite and laguerre the study presents a comparison between the efficiency of the polynomial based displacement functions with regard to elastic bilateral and unilateral plate buckling where efficiency is measured as a function of their convergence characteristics some buckling solutions for plates with varying boundary conditions and in plane shear loads are also provided as an illustration copyright 1999 john wiley sons ltd

discrete singular convolution for the prediction of high frequency vibration of plates theoretical analysis of high frequency vibrations is indispensable in a variety of engineering designs much effort has been made on this subject in the past few decades however there is no single technique which can be applied with confidence to various engineering structures for high frequency predictions at present this paper introduces a novel computational approach the discrete singular convolution dsc algorithm for high frequency vibration analysis of plate structures square plates with six distinct boundary conditions are considered to validate the proposed method a completely independent approach the levy method is employed to provide exact solutions for a comparison the proposed method is also validated by convergence studies we demonstrate the ability of the dsc algorithm for high frequency vibration analysis by providing extremely accurate frequency parameters for plates vibrating in the first 5000 modes

stiefel whitney classes of real representations of finite groups abstract we prove the existence and uniqueness of stiefel whitney classes of real representations subject to the hirzebruch axioms within the category of finite groups we also give a method of constructing and computing with these classes using multiplicative transfer and induced representations and apply our formulae in certain simple cases

on the witt equivalence of fields of characteristic 2 let e f be two fields of characteristic 2 and let w e w f be the witt rings of non singular symmetric bilinear forms over e and f in this note it is proved that if dime2 e dimf2 f 2 then e f is equivalent with w e w f

dsc analysis of rectangular plates with non uniform boundary conditions this paper introduces the discrete singular convolution dsc for the vibration analysis of rectangular plates with non uniform and combined boundary conditions a systematic scheme is proposed for the treatment of boundary conditions required in the proposed approach the validity of the dsc approach for plate vibration is tested by using a large number of numerical examples that have a combination of simply supported clamped and transversely supported with non uniform elastic rotational restraint edges the present results are in excellent agreement with those in the literature

construction of unipotent galois extensions and massey products abstract for all primes p and for all fields we find a sufficient and necessary condition of the existence of a unipotent galois extension of degree p 6 the main goal of this paper is to describe an explicit construction of such a galois extension over fields admitting such a galois extension this construction is surprising in its simplicity and generality the problem of finding such a construction has been left open since 2003 recently a possible solution of this problem gained urgency because of an effort to extend new advances in galois theory and its relations with massey products in galois cohomology

interpolation in the limit of increasingly flat radial basis functions abstract many types of radial basis functions such as multiquadrics contain a free parameter in the limit where the basis functions become increasingly flat the linear system to solve becomes highly ill conditioned and the expansion coefficients diverge nevertheless we find in this study that limiting interpolants often exist and take the form of polynomials in the 1 d case we prove that with simple conditions on the basis function the interpolants converge to the lagrange interpolating polynomial hence differentiation of this limit is equivalent to the standard finite difference method we also summarize some preliminary observations regarding the limit in 2 d

twists of symmetric bundles we establish comparison results between the hasse witt invariants w t e of a symmetric bundle e over a scheme and the invariants of one of its twists e alpha for general twists we describe the difference between w t e and w t e alpha up to terms of degree 3 next we consider a special kind of twist which has been studied by a frohlich this arises from twisting by a cocycle obtained from an orthogonal representation a simple important example of this twisting procedure is the bilinear trace form of an etale algebra which is obtained by twisting the standard sum of squares form by the orthogonal representation attached to the algebra we show how to explicitly describe the twist for representations arising from very general tame actions this involves the square root of the inverse different which serre esnault kahn viehweg and ourselves had studied before for torsors we show that in our geometric set up jardine s generalization of frohlich s formula holds namely let x g be a torsor with quotient y let e be a symmetric bundle over y let rho g rightarrow bf o e be an orthogonal representation and let e rho x be the corresponding twist of e then we verify up to degree 3 that the formula w t e rho x sp t rho w t e w t rho holds here sp t rho and w t rho are respectively the spinor invariant and the stiefel whitney class of rho the case of genuinely tamely ramified actions is geometrically more involved and leads us to introduce an invariant of ramification which in a sense gives a decomposition in terms of representations of the inertia groups of the invariant introduced by serre for curves the comparison result in the tamely ramified case proceeds by reduction to the case of a torsor the reduction is carried out by means of a partial normalisation procedure which we had introduced in a previous paper an important lemma of esnault kahn and viehweg allows us to express the difference between the invariants of bundles before and after the normalisation procedure in terms of chern classes of certain sub bundles as noted elsewhere this result can be best understood in the context of symmetric complexes and their invariants our results are new even for bundles over curves and they allow us to weaken the regularity assumptions that we had to impose in previous work of ours

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

dsc solution for flow in a staggered double lid driven cavity a benchmark quality solution is presented for flow in a staggered double lid driven cavity obtained by using the wavelet based discrete singular convolution dsc the proposed wavelet based algorithm combines local methods flexibility and global methods accuracy and hence is a promising approach for achieving the high accuracy solution of the navier stokes equations block structured grids with pseudo overlapping subdomains are employed in the present simulation a third order runge kutta scheme is used for the temporal discretization quantitative results are presented apart from the qualitative fluid flow patterns the prevalence of rich features of flow morphology such as two primary vortex patterns merged single primary vortex patterns and secondary eddies makes this problem very attractive and interesting the problem is quite challenging for the possible existence of numerically induced asymmetric flow patterns and elliptic instability important computational issues like consistence convergence and reliability of the numerical scheme are examined the dsc algorithm is tested on the single lid driven cavity flow and the taylor problem with a closed form solution the double lid driven cavity simulations are cross validated with the standard second order finite volume method copyright 2003 john wiley sons ltd

description of galois unipotent extensions abstract given an arbitrary field f we describe all galois extensions l f whose galois groups are isomorphic to the group of upper triangular unipotent 4 by 4 matrices with entries in the field of two elements

numerical analysis of generalized regularized long wave equation using the element free kp ritz method abstract a numerical analysis of the generalized regularized long wave grlw equation by application of the element free kp ritz method is performed to approximate the displacement field an element free kernel particle estimation is employed and a system of nonlinear discrete equations is achieved by using the ritz minimization procedure to the energy expressions validation of the present numerical solutions with the exact results has been conducted by numerical examples and evidenced a good agreement

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

on the computation of the trace form of some galois extensions abstract we investigate the trace form trl k l k x trl kx2of a finite galois extensionl k in particular we study 2 extensions of degree 16 using some reduction theorems these results yield a classification of nearly all trace forms of galois extensions of degree 31 finally we study the trace form of a cyclotomic extension and of its maximal real subfield

application of a series type method to vibration of orthotropic rectangular plates with mixed boundary conditions the object of this paper is to show an application of a series type method to the free vibration of an orthotropic rectangular plate with mixed boundary conditions the rectangular plate considered is elastically constrained or clamped along a few parts of its edge and simply supported on the remainder a frequency equation is derived to accommodate rectangular orthotropy of the plate by the extension of a previously developed method and subsequent algebraic manipulation leads to the improved equation yielding natural frequencies of the plate with very good accuracy the method is demonstrated for numerical examples where one two or three parts are constrained along the boundary of the square plate and the effects of varying constraint and orthotropic parameters on the natural frequencies and mode shapes are studied

consistency of semiconductor modeling an existence stability analysis for the stationary van roosbroeck system this paper examines the solution map of the stationary version of the van roosbroeck model for the flow of electrons and holes in a crystalline semiconductor thermodynamic equilibrium and the einstein relations linking mobility and diffusion are assumed to hold for this model incorporated into the model is the quantum statistical assumption that the carrier densities satisfy fermi dirac statistical laws with localization in the boltzmann tail this latter approximation which is seen to be inessential characterizes the conduction and valence bands as nondegenerate the boundary conditions are of two types and correspond to applied potential differences and doping on the contact portions of the device and insulation on the remainder the complete system then involves a coupled set of three nonlinear partial differential equations with their boundary conditions for the electrostatic potential and for the quasi fermi levels corresponding to the electron and hole concentrations in the absence of the classical nondegeneracy approximation the model remains valid but without a natural physical interpretation for two ofthe three dependent variables we demonstrate the existence ofsolutions for this system by associating a solution mapping t such that the fixed points of t define solutions of the system a priori estimates or weak maximum principles permit t to act invariantly on a naturally chosen subset of a hilbert product space the definition of t roughly follows the gummel procedure for uncoupling systems the schauder fixed point theorem is used to prove the existence of a fixed point for t uniqueness is not demonstrated and very possibly does not hold for these systems without special restrictions on the boundary conditions we also introduce a discrete version of the mapping t which is defined in terms of a family of finite difference approximations this mapping enjoys the stability property that it acts invariantly on a rectangular region in euclidean space the dimensions are the same as those specified in the pointwise bounds which define the domain of t a second existence theory framework with quasi constructive aspects is also studied this is based upon pseudomonotone operators the presentation is technology independent except for a section on mos fet devices these typically induce a breakdown ofuniform ellipticity and may be handled by modifications of the major arguments they also exemplify a class of devices for which the electrostatic field is defined on a strictly larger domain than the carriers themselves 1 introduction and model description this paper provides a mathematical analysis of a stationary system solution map which forms the basis for the highly successful computational algorithms used for the numerical solution of the semiconductor system cf bank rose and fichtner 3 our methods involve pointwise stability estimates on solution components organized in such a way that the solution map and a family of discrete approximations may be studied in parallel if desired moreover the weak solution methods do not require regularity theory hence are applicable to physical domains commonly encountered in practice such domains may include re entrant corner points etc and typically induce degenerate elliptic systems we shall also develop the model from physical principles the reason for this is not primarily to compile source material from several different references but rather to indicate clearly to the reader what the level of generality is and to facilitate the discussion of important variations in the device models the models studied herein are reaction diffusion con vection models for which the einstein relations linking carrier mobility and diffusion are assumed to hold the dependent variables of the system include one potential variable inducing an ambient field and two concentration variables for carriers whose convective movement is field dependent this suggests a fairly rich set ofpossible

postbuckling behavior of bi axially compressed arbitrarily straight sided quadrilateral functionally graded material plates abstract in this paper the problem of the postbuckling behavior of biaxial compressed straight sided functionally graded material fgm plates of quadrilateral shape is studied the plate considered is subjected to in plane loads on all four edges a computational framework based on an improved moving least squares imls approximation for the field variables is developed for the analysis the solution procedures involved a transformation from the physical domain to a computational domain and then discrete the nonlinear governing equation using the imls ritz method the first order shear deformation theory fsdt with the von karman nonlinearity is employed a nonlinear solution to the postbuckling of quadrilateral fgm plates is computed through the modified newton raphson method combined with the arc length iterative algorithm a stabilized conforming nodal integration scheme is employed to improve computational efficiency and eliminate shear and membrane locking the validity and accuracy of the numerical results are established through convergence studies to the best of the authors knowledge the problem has not been attempted in the open literature

implementation of clamped and simply supported boundary conditions in the gdq free vibration analysis of beams and plates abstract in this paper a new methodology for implementing the clamped and simply supported boundary conditions is presented for the free vibration analysis of beams and plates using the generalized differential quadrature gdq method the proposed approach directly substitutes the boundary conditions into the governing equations and is referred to as sbcge approach the sbcge approach is presented to overcome the drawbacks of previous approaches in treating the boundary conditions a comparison of the sbcge approach with the method of modifying weighting coefficient matrices mwcm is made by their application to the vibration analysis of beams and plates with combinations of simply supported and clamped boundary conditions some details of the gdq method are also described in the paper

induced orthogonal representations of galois groups abstract we prove a result showing the connection between induced orthogonal representations and corestrictions of group extensions derived from their clifford groups by the means of the corestriction map we then obtain new obstructions to the p embedding problems given by the group extensions of the modular p group and to one 2 embedding problem given by a group extension of the dihedral group

dsc ritz method for high mode frequency analysis of thick shallow shells this paper addresses a challenging problem in computational mechanics the analysis of thick shallow shells vibrating at high modes existing methods encounter significant difficulties for such a problem due to numerical instability a new numerical approach dsc ritz method is developed by taking the advantages of both the discrete singular convolution dsc wavelet kernels of the dirichlet type and the ritz method for the numerical solution of thick shells with all possible combinations of commonly occurred boundary conditions as wavelets are localized in both frequency and co ordinate domains they give rise to numerical schemes with optimal accurate stability and flexibility numerical examples are considered for mindlin plates and shells with various edge supports benchmark solutions are obtained and analyzed in detail experimental results validate the convergence stability accuracy and reliability of the proposed approach in particular with a reasonable number of grid points the new dsc ritz method is capable of producing highly accurate numerical results for high mode vibration frequencies which are hitherto unavailable to engineers moreover the capability of predicting high modes endows us the privilege to reveal a discrepancy between natural higher order vibration modes of a mindlin plate and those calculated via an analytical relationship linking kirchhoff and mindlin plates copyright 2004 john wiley sons ltd

field theory and the cohomology of some galois groups abstract we prove that two arithmetically significant extensions of a field f coincide if and only if the witt ring wf is a group ring z n g furthermore working modulo squares with galois groups which are 2 groups we establish a theorem analogous to hilbert s theorem 90 and show that an identity linking the cohomological dimension of the galois group of the quadratic closure of f the length of a filtration on a certain module over a galois group and the dimension over f 2 of the square class group of the field holds for a number of interesting families of fields finally we discuss the cohomology of a particular galois group in a topological context

construction de p extensions galoisiennes d un corps de caracteristique differente de p abstract let p be a prime number let k be a field with characteristic different from p containing the pth roots of unity and let e k be a galois extension of degree pd d n o with an abelian galois group gal e k g of exponent p the aim of this article is to state explicit formulas by which one can construct any field n of degree p over e such that n k is a galois extension soient p un nombre premier k un corps de caracteristique differente de p contenant les racines p iemes de l unite et e k une extension galoisienne de degre pd d n o de groupe de galois gal e k g abelien d exposant p le but de cet article est d etablir des formules explicites permettant de construire tous les corps n de degre p sur e tels que l extension n k soit galoisienne

a novel approach for the analysis of high frequency vibrations abstract despite much effort in the past few decades the numerical prediction of high frequency vibrations remains a challenging task to the engineering and scientific communities due to the numerical instability of existing computational methods however such prediction is of crucial importance to certain problems of pressing practical concern as pointed out by langley and bardell 1998 the aeronautical journal102 287 297 this paper introduces the discrete singular convolution dsc algorithm for the prediction and analysis of high frequency vibration of structures both a beam and two span plates are employed as test examples to demonstrate the capability of the dsc algorithm for high frequency vibration analysis a completely independent approach the levy method is employed to provide exact solutions for a cross validation of the proposed method the reliability of the dsc results is also validated by convergence studies remarkably extremely accurate and stable results are obtained in this work e g the relative dsc errors for the first 7100 modes of the beam and the first 4500 modes of the two span plates are all

flexural vibration of shear deformable circular and annular plates on ring supports this paper presents an analysis of free flexural vibration of circular and annular mindlin plates lying on multiple internal concentric ring supports the rayleigh ritz method with an admissible displacement function expressed in terms of a set of simple polynomials is used to obtain the governing eigenvalue equation the natural frequencies of circular and annular mindlin plates with one or two ring supports having inner and outer peripheries with different combinations of free simply supported and clamped conditions are determined a comprehensive set of vibration results is presented and where possible these have been verified with existing solutions published in the open literature no previous theoretical results for thick annular plates supported with internal rings are known to exist thus the study should be useful and valuable to engineers and researchers

the sign of the functional equation of the l function of an orthogonal motive we prove that the sign of the functional equation of the l function of an orthogonal motive of even weight is always positive if we admit the conjecture of the product formula for the epsilon factor of deligne d3 5 2 more precisely we define the sign independently of any conjecture by using the product formula as the definition and by working with one chosen good prime f and we prove its positivity the positivity has been established for the artin motives fr q d2 for the symmetric square of a modular elliptic curve c sc and in positive characteristic by serre fr q as in the proof in d2 we consider the second stiefel whitney class in zbr k of an orthogonal representation of the absolute galois group g of an algebraic number field k the positivity of the sign is then a consequence of the reciprocity law of the square residue symbol fixing a good prime f we work with an f adic representation and compare the local epsilon factor and the local stiefel whitney class for a prime vxr it is a theorem of deligne d2 for a prime vie we compute the stiefel whitney class assuming the representation is cristalline theorem 2 using a generalization of a theorem of fr6hlich fr to f adic representation of hodge tate type theorem 1 by combining them with an elementary computation for the hodge structures at r iot we conclude that the sign is positive theorem 3 the crucial step in the proof of theorem 2 given in section 1 is the determination by fontaine and lafaille fo l of the action of the tame inertia on the semisimplification of reduction modulo p of a cristalline representation the theory of orthogonal representations of galois group including a proof of fr6hlich s theorem is reviewed in a preliminary section 0

the classifying topos of a group scheme and invariants of symmetric bundles let y be a scheme in which 2 is invertible and let v be a rank n vector bundle on y endowed with a non degenerate symmetric bilinear form q the orthogonal group bf o q of the form q is a group scheme over y whose cohomology ring h b bf o q bf z 2 bf z simeq a y hw 1 q hw n q is a polynomial algebra over the etale cohomology ring a y h y et bf z 2 bf z of the scheme y here the hw i q s are jardine s universal hasse witt invariants and b bf o q is the classifying topos of bf o q as defined by grothendieck and giraud the cohomology ring h b bf o q bf z 2 bf z contains canonical classes mathrm det q and c q of degree 1 and 2 respectively which are obtained from the determinant map and the clifford group of q the classical hasse witt invariants w i q live in the ring a y our main theorem provides a computation of det q and c q as polynomials in hw 1 q and hw 2 q with coefficients in a y written in terms of w 1 q w 2 q in a y this result is the source of numerous standard comparison formulas for classical hasses witt invariants of quadratic forms our proof is based on computations with abelian and non abelian cech cocycles in the topos b bf o q this requires a general study of the cohomology of the classifying topos of a group scheme which we carry out in the first part of this paper

a new algorithm for solving some mechanical problems this paper explores the utility of a discrete singular convolution algorithm for solving certain mechanical problems benchmark mechanical systems including plate vibrations and incompressible flows are employed to illustrate the robustness and to test accuracy of the present algorithm numerical results indicate that the present approach is very accurate efficient and reliable for solving the aforementioned problems

a highly accurate analytical solution for free vibration analysis of simply supported right triangular plates abstract a new analytical technique is described for the free vibration analysis of simply supported right triangular plates while it is seen that the basic mathematical approach is applicable to right triangular plates with various types of boundary conditions the problem of the simply supported right triangular plate is resolved for illustrative purposes and eigenvalues are presented for the first four modes the method employed is basically that of superposition the governing differential equation is completely satisfied and by means of a judicious choise of building blocks the boundary conditions are satisfied to any desired degree of accuracy

on the one dimensional current driven semiconductor equations the steady state semiconductor equations in one dimension are examined subject to a given current through the device supplemented by dirichlet boundary conditions on one end of the device solutions to this current driven model are identified as the fixed points of a mapping t and uniqueness of solutions for the unipolar model is shown for arbitrary currents by demonstrating that t is unconditionally a contraction for both the uni and the bipolar model existence of solutions close to thermodynamic equilibrium is shown this means that for the one dimensional unipolar current driven model the situation is complementary to that for the potential driven model where it is possible to show existence of solutions for arbitrary applied potentials and uniqueness close to thermodynamic equilibrium only for the unipolar case iteration with the mapping t defines an algorithm for the solution of this model which is unconditionally convergent to the unique solution if it exists

natural frequencies of rectangular plates with free edges abstract this note presents vibration analysis of isotropic rectangular plates with free edges by the rayleigh ritz method with b spline functions to show the accuracy of the present method the results are compared with existing results based on other numerical methods and found to be in good agreement accurate frequencies of rectangular plates are analyzed for different aspect ratios and boundary conditions the effects of poisson s ratio on natural frequencies of square plates with free edges are also investigated

the kernel unipotent conjecture and the vanishing of massey products for odd rigid fields abstract a major difficult problem in galois theory is the characterization of profinite groups which are realizable as absolute galois groups of fields recently the kernel n unipotent conjecture and the vanishing n massey conjecture for n 3 were formulated these conjectures evolved in the last forty years as a byproduct of the application of topological methods to galois cohomology we show that both of these conjectures are true for odd rigid fields this is the first case of a significant family of fields where both of the conjectures are verified besides fields whose galois groups of p maximal extensions are free pro p groups we also prove the kernel unipotent conjecture for demushkin groups of rank 2 and establish various filtration results for free pro p groups provide examples of pro p groups which do not have the kernel n unipotent property compare various zassenhaus filtrations with the descending p central series and establish new type of automatic galois realization

a novel scheme for the discrete prediction of high frequency vibration response discrete singular convolution mode superposition approach abstract this study introduces a novel scheme for the discrete high frequency forced vibration analysis based on discrete singular convolution dsc and mode superposition ms approaches the accuracy of the dsc ms is validated for thin beams and plates by comparing with available analytical solutions the performance of the dsc ms is evaluated by predicting spatial distribution and discrete frequency spectra of the vibration response of thin plates with two different boundary conditions the frequency spectra of the time harmonic excitation forces are in the form of ideal and band limited white noise so that the natural modes in the frequency band are provoked the solution exposes high frequency response behaviour definitely therefore it is hoped with this paper to contribute the studies on the treatment of uncertainties in the high frequency design applications

primitives and central detection numbers in group cohomology abstract fix a prime p given a finite group g let h g denote its mod p cohomology in the early 1990s henn lannes and schwartz introduced two invariants d 0 g and d 1 g of h g viewed as a module over the mod p steenrod algebra they showed that in a precise sense h g is respectively detected and determined by h d c g v for d d 0 g and d d 1 g with v running through the elementary abelian p subgroups of g the main goal of this paper is to study how to calculate these invariants we find that a critical role is played by the image of the restriction of h g to h c where c is the maximal central elementary abelian p subgroup of g a measure of this is the top degree e g of the finite dimensional hopf algebra h c h g f p a number that tends to be quite easy to calculate our results are complete when g has a p sylow subgroup p in which every element of order p is central using the benson carlson duality we show that in this case d 0 g d 0 p e p and a similar exact formula holds for d 1 as a bonus we learn that h e g p contains nontrivial essential cohomology reproving and sharpening a theorem of adem and karagueuzian in general we are able to show that d 0 g max e c g v v g if certain cases of benson s regularity conjecture hold in particular this inequality holds for all groups such that the difference between the p rank of g and the depth of h g is at most 2 when we look at examples with p 2 we learn that d 0 g 14 for all groups with 2 sylow subgroup of order up to 64 with equality realized when g su 3 4 en route we study two objects of independent interest if c is any central elementary abelian p subgroup of g then h g is an h c comodule and we prove that the subalgebra of h c primitives is always noetherian of krull dimension equal to the p rank of g minus the p rank of c if the depth of h g equals the rank of z g we show that the depth essential cohomology of g is nonzero reproving and extending a theorem of green and cohen macauley in a certain sense and prove related structural results