an operational procedure for the symbolic analysis of the finite element method an operational procedure is presented for the symbolic analysis of different finite element discretizations which enables one to symbolically decouple the finite element equations and recover the corresponding limit differential equations which govern the finite element behavior comparison of the limit differential equations with the continuum differential equations succinctly manifests the component wise discretization effects on element behavior such as the transverse shear element locking phenomenon exhibited by thin co elements the procedure is applied to the hermitian approximation of the sturm liouville equation and to the linear approximation of the timoshenko beam

residual based methods for fluid loaded beams abstract in this paper residual based modifications to standard finite element approximations for structural acoustics are developed and analyzed results for symmetric residual based modifications for the coupled problem are presented the accuracy of symmetric and unsymmetric methods is determined in a two dimensional setting a symmetric form of the residual based modification results in lower computational costs than the other methods the inclusion of new fluid structure coupling and fluid stiffness terms arising from the consistent integration into the coupled formulation of residual modifications to the structural equations is shown to dramatically decrease the l 2 error

generating modules efficiently algebraic k theory for noncommutative noetherian rings abstract the well known forster swan theorem and the stable version of this result given by eisenbud and evans give a bound on the number of generators of a module over a commutative ring in terms of local data in this paper we generalise these results to arbitrary noetherian rings as an application we prove versions of serre s theorem and the cancellation theorem over such rings

complex wave number dispersion analysis of galerkin and galerkin least squares methods for fluid loaded plates abstract the technique of complex wave number dispersion analysis is used to examine the accuracy of discretized systems in the representation of wave propagation phenomena this technique was applied to study finite element approximations to in vacuo and fluid loaded plates considering discretizations of kirchhoff and reissner mindlin plate theories coupled to an acoustic medium the allowed evanescent waves in the finite element approximation of the in vacuo plate are obtained and compared with theory the finite element dispersion relation for the coupled plate fluid system is derived results for the galerkin structural approximation coupled to galerkin and galerkin least squares gls fluid formulations are presented quantitative errors are reported and the significance of these errors in view of an analytical solution to the problem is given

non holonomic modules over weyl algebras and enveloping algebras a number of counterexamples in the theory of enveloping algebras and noetherian rings are presented in particular we construct non holonomic simple modules over the weyl algebra a and the enveloping algebra u s1 z xs12 further we show that u s1 z x s12 is not weakly ideal invariant and that there exist simple s1 z x s12 modules m and e with e finite dimensional such that e is not artinian if m is a module over a ring r then the gelfand kirillov dimension of m written gk dim m is defined in 7 suppose that m is a simple module over a noetherian ring r and that g k d i m r oc then m is called holonomic if g k d i m m 8 9 the reason for the definition is that in the case when r is a weyl algebra or the enveloping algebra of a finite dimensional algebraic lie algebra holonomic modules have particularly nice properties

locking spurious mechanisms and pressure divergence in penalty finite element methods for stokes flow problems abstract solution locking spurious mechanisms and pressure divergence exhibited in the stokes flow calculations by the penalty finite element methods are analyzed employing a fourier analysis technique comparison of the approximate discrete operator components with the corresponding continuum ones enables one to explicitly identify the conditions for avoiding locking spurious mechanisms and pressure divergence in terms of discrete operator components which are applicable to either the finite difference or finite element discretizations a synthesis approach is explored to eliminate the solution locking spurious mechanisms and pressure divergence in uniformly reduced integrated four noded elements extensions of the present analysis and synthesis approach to navier stokes equations appear to be straightforward if one deals with a set of consistently linearized operators

violating the shannon capacity of metric graphs with entanglement the shannon capacity of a graph g is the maximum asymptotic rate at which messages can be sent with zero probability of error through a noisy channel with confusability graph g this extensively studied graph parameter disregards the fact that on atomic scales nature behaves in line with quantum mechanics entanglement arguably the most counterintuitive feature of the theory turns out to be a useful resource for communication across noisy channels recently leung d mancinska l matthews w ozols m roy a 2012 commun math phys 311 97 111 two examples of graphs were presented whose shannon capacity is strictly less than the capacity attainable if the sender and receiver have entangled quantum systems here we give natural possibly infinite families of graphs for which the entanglement assisted capacity exceeds the shannon capacity

a symbolic fourier synthesis of a one point integrated quadrilateral plate element a symbolic fourier analysis is performed on both one point and four point spatially integrated four noded c0 plate elements the analysis shows that the effects of different integration rules is characterized by a single fourier component called the directional averaging operator in addition the conditions for avoiding locking and spurious mechanisms are explicitly identified in a general plate operator expressed in fourier form encouraged by these results a c0 plate element is synthesized employing only one point integrated attributes the stiffness matrix of the new element consists of two parts the usual one point integrated part and the rank compensating part that is identified as the difference between the synthesized and one point integrated plate operators the present element achieves the same accuracy of elements employing the four point spatial integration rule which is not realized in the one point integrated elements using hour glass control techniques preliminary numerical experiments corroborate the present theoretical results and demonstrate the usefulness of the present symbolic analysis and fourier synthesis techniques

design of galerkin generalized least squares methods for timoshenko beams abstract a class of finite element methods the galerkin generalized least squares methods are developed and applied to model the steady state response of timoshenko beams an optimal method is designed using a linear interpolation of the response such that there is zero finite element dispersion error the classical method of selective reduced integration and a modified version of selective reduced integration with mass lumping are shown to fall under the galerkin generalized least squares framework numerical experiments in wave propagation demonstrate the dramatic superiority of the new optimal method over the standard approaches the goal of the new methods is to decrease the computational burden required to achieve a desired accurcy level at a particular frequency thereby enabling larger scale higher frequency computations for a given platform

zero error communication via quantum channels noncommutative graphs and a quantum lovasz number we study the quantum channel version of shannon s zero error capacity problem motivated by recent progress on this question we propose to consider a certain subspace of operators so called operator systems as the quantum generalization of the adjacency matrix in terms of which the zero error capacity of a quantum channel as well as the quantum and entanglement assisted zero error capacities can be formulated and for which we show some new basic properties most importantly we define a quantum version of lovasz famous function on general operator systems as the norm completion or stabilization of a naive generalization of we go on to show that this function upper bounds the number of entanglement assisted zero error messages that it is given by a semidefinite program whose dual we write down explicitly and that it is multiplicative with respect to the tensor product of operator systems corresponding to the tensor product of channels we explore various other properties of the new quantity which reduces to lovasz original in the classical case give several applications and propose to study the operator systems associated with channels as noncommutative graphs using the language of hilbert modules

exclusivity structures and graph representatives of local complementation orbits we describe a construction that maps any connected graph g on three or more vertices into a larger graph h g whose independence number is strictly smaller than its lovasz number which is equal to its fractional packing number the vertices of h g represent all possible events consistent with the stabilizer group of the graph state associated with g and exclusive events are adjacent mathematically the graph h g corresponds to the orbit of g under local complementation physically the construction translates into graph theoretic terms the connection between a graph state and a bell inequality maximally violated by quantum mechanics in the context of zero error information theory the construction suggests a protocol achieving the maximum rate of entanglement assisted capacity a quantum mechanical analogue of the shannon capacity for each h g the violation of the bell inequality is expressed by the one shot version of this capacity being strictly larger than the independence number finally given the correspondence between graphs and exclusivity structures we are able to compute the independence number for certain infinite families of graphs with the use of quantum non locality therefore highlighting an application of quantum theory in the proof of a purely combinatorial statement

convergence of curved shell elements based on assumed covariant strain interpolations a c0 9 node shell element based on assumed interpolations of covariant strain components defined with respect to the element natural co ordinate system has recently been proposed in this formulation the covariant strains are obtained directly from the cartesian strains by tensor transformation without any need to compute laminar co ordinate based strains in the present work the interpolated covariant strains used in this element are analysed to determine their satisfaction of the basic requirements for successful strain interpolation these basic requirements are stated as invariance to rigid body motions and ability to represent constant and linear strain states in the finite element formulation the weak form of momentum balance is expressed in terms of covariant strains and contravariant stresses the corresponding elasticity tensor is a function of the components of the metric tensor associated with the element natural co ordinate system the invariance properties of the metric tensor in the context of the finite element approximation are also discussed

state spaces finite algebras and skew group rings k goodearl gl considered the state space st r of a noetherian ring r and in joint work with r b warfield gw described the structure of the sate space of commutative rings hereditary noetherian prime rings and orders over dedekind domains in this work we give some properties of the state space of a ring in relation to the ideas of localization on noncommutative rings and of ramification in generically galois actions we show how the structure of st r depends on the property of localization at prime ideals some general results are given for the state space of a finite algebra over a commutative noetherian ring then we apply these results to st s g where s is a commutative noetherian domain g is a finite group acting faithfully as automorphisms of the ring s and 1 gi is invertible in s wc show that the state space st s g is the affine continuous image of an amalgamation of the state spaces of the ring localized at non trivial clans in particular that those arising from the ramified primes of s suffice we show that st s g is a singleton if and only if the action is g galois on s finally for s a dedekind domain we give a structure theorem for the state space of the skew group ring s g

grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics summary the spatial discretisation of a continuum by the fem introduces dispersion errors to the numerical solution of stress wave propagation errors of phase and group velocities and the scatter of wave propagation are induced when these propagating phenomena are modelled by the fem the speed of a single harmonic wave depends on its frequency parasitic effects do not exist in an ideal unbounded continuum with higher order finite elements there are optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the sharp wavefronts in principle the dispersion errors and the spurious oscillations cannot be removed from these solutions but can be suppressed to a certain extent for reliable numerical solutions by the fem the dispersion errors should be analysed and determined the dispersion properties of a plane square biquadratic serendipity finite element are examined and compared with a bilinear one dispersion analysis is carried out for the consistent and lumped mass matrices a dispersive improved lumped mass matrix for biquadratic serendipity elements is proposed the paper closes with the recommendation of a choice of permissible dimensionless wavelengths for bilinear and biquadratic serendipity finite element meshes copyright 2013 john wiley sons ltd

a study of stabilization and projection in the 4 node mindlin plate element in this paper a mindlin plate element is formulated based on the hellinger reissner principle and the technique the stiffness consists of a constant stress one point quadrature matrix and a stabilization matrix the stabilization matrix is compared with those previously proposed in addition the element uses a projection to modify the nodal displacements so that the patch test is satisfied the projection matrix is based on a mode decomposition several numerical cases are presented and it is shown that the mode decomposition projection is necessary both for satisfaction of the patch test and convergence

field consistent strain interpolations for the quadratic shear flexible beam element a shear flexible i e timoshenko quadratic isoparametric beam element with two degrees of freedom per node is critically examined from the point of view of the consistency of the constrained strain fields that arise in the thin beam limits the errors in terms of convergence of displacement fields and violent oscillations of stress fields that emerge when exactly integrated elements are used are predicted a priori and confirmed with numerical experiments the rationale behind the use of optimal stress sampling at gaussian points is also derived directly from these arguments

a uniform strain hexahedron and quadrilateral with orthogonal hourglass control the treatment of zero energy modes which arise due to one point integration of first order isoparametric finite elements is addressed a method for precisely isolating these modes for arbitrary geometry is developed two hourglass control schemes viscous and elastic are presented and examined in addition a convenient one point integration scheme which analytically integrates the element volume and uniform strain modes is presented

presentations over hnp rings with enough invertible ideals and torsionfree cancellation over neoclassical orders abstract we prove a uniqueness theorem for presentations of modules over a class of hereditary noetherian prime rings that includes the hereditary orders studied in integral representation theory the result also generalizes the elementary divisor theorem for non commutative pids a key part of the proof is an extension of a direct sum cancellation theorem of drozd to torsionfree modules over a class of non commutative rings that need not be module finite over their center

spurious reflection of elastic waves due to gradually changing finite element size summary when a homogeneous elastic continuum is modelled by a non uniform finite element grid the differences in the size of adjacent finite elements can cause a spurious wave reflection which does not exist in the continuum extending previous studies in which the spurious wave reflection was investigated for the case of two uniform grids with a sudden element size change from one grid to the other the present study deals with the case when the two uniform grids of different element sizes are separated by a transition zone through which the element size varies gradually either by a geometric progression or by an arithmetic progression the solution is carried out in complex variables and numerical plots of the results are given when the ratio of wavelength to the largest element size is as low as 4 1 the spurious wave reflection is very significant while for the ratios over 10 1 it is insignificant inserting a transition zone with gradually varying element size between the two uniform parts of the grid somewhat mitigates the phenomenon of spurious reflection but this is significant only when the ratio of element sizes in the uniform grids is small less than about 1 5 1 varying the element size throughout the transition zone in an arithmetic progression seems slightly better than in a geometric progression the spurious wave reflection is less pronounced for higher order elements in particular for linear strain elements as compared to constant strain elements the spurious reflection is also less severe for consistent mass than for lumped mass

the influence of the mass matrix on the dispersive nature of the semi discrete second order wave equation abstract the application of discrete solution methods to the second order wave equation can yield a dispersive representation of the non dispersive wave propagation problem resulting in a phase speed that depends not only upon the wavelength of the signal being propagated but also upon the direction of propagation in this work the dependence of the dispersive errors on the wave propagation direction mesh aspect ratio and wave number is investigated with the goal of understanding and hopefully reducing the phase and group errors associated with the two dimensional bilinear finite element an analysis of the dispersive effects associated with the consistent row sum lumped and higher order mass matrices has led to a reduced coupling penta diagonal mass matrix that yields improved phase and group errors with respect to wavelength and propagation direction the influence of row sum lumping the finite element mass matrix is demonstrated to always introduce lagging phase and group error while a linear combination of the lumped and consistent mass matrices i e a higher order mass matrix is shown to improve the dispersion characteristics of both the reduced and full integration element using a 2 5 phase error metric the higher order mass matrix can reduce the mesh resolution requirements relative to the lumped mass matrix by nearly a factor of two in one dimension a factor of 4 in two dimensions similarly the reduced coupling mass matrix can reduce the grid requirements by a factor of approximately four relative to the lumped mass matrix a factor of 16 in two dimensions although the reduced coupling mass matrix requires additional storage relative to the lumped mass the factor of 16 reduction in grid requirements promises tremendous overall savings for computing a fixed wavelength spectrum or alternatively for resolving shorter wavelengths with a fixed grid resolution

new separations in zero error channel capacity through projective kochen specker sets and quantum coloring we introduce two generalizations of kochen specker ks sets projective ks sets and generalized ks sets we then use projective ks sets to characterize all graphs for which the chromatic number is strictly larger than the quantum chromatic number here the quantum chromatic number is defined via a nonlocal game based on graph coloring we further show that from any graph with separation between these two quantities one can construct a classical channel for which entanglement assistance increases the one shot zero error capacity as an example we exhibit a new family of classical channels with an exponential increase

embedding noetherian rings in artinian rings abstract a criterion is presented which is easy to check in specific examples and provides information as to when a given noetherian ring is not embeddable in an artinian one on the other hand we provide sufficient conditions for artinian embeddability of several types of noetherian rings that have no nontrivial right ideals of reduced rank zero

a fourier analysis of spurious mechanisms and locking in the finite element method a fourier analysis technique is used to examine spurious mechanisms and the element locking phenomena engendered by different finite element discretizations it is shown that these phenomena can be identified by examining the uncoupled discrete fourier operators and corresponding characteristic equations and are caused in terms of discrete filter concepts by either a spurious mode carrier or by violating the unlocking condition specified in the paper the analysis is performed for two simple problems wave propagation in a bar and vibration of a timoshenko beam which when discretized by linear shape functions succinctly manifest the two phenomena as being directly traceable to specific components of the finite element discretizations

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

bell inequalities for graph states we investigate the nonlocal properties of graph states to this aim we derive a family of bell inequalities which require three measurement settings for each party and are maximally violated by graph states in turn for each graph state there is an inequality maximally violated only by that state we show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits we also discuss connections to other entanglement properties such as the positivity of the partial transpose or the geometric measure of entanglement

effects of spatial discretization on dispersion and spurious oscillations in elastic wave propagation the dispersive and spurious oscillation properties of one dimensional uniform finite element meshes are investigated using the information provided by the frequency response functions of the finite element meshes the modal superposition method in which the effects of temporal discretization are eliminated is employed to integrate the discretized equations of motion