the natural element method in solid mechanics the application of the natural element method nem 1 2 to boundary value problems in two dimensional small displacement elastostatics is presented the discrete model of the domain consists of a set of distinct nodes n and a polygonal description of the boundary in the natural element method the trial and test functions are constructed using natural neighbour interpolants these interpolants are based on the voronoi tessellation of the set of nodes n the interpolants are smooth c 1 everywhere except at the nodes where they are c 0 in one dimension nem is identical to linear nite elements the nem interpolant is strictly linear between adjacent nodes on the boundary of the convex hull which facilitates imposition of essential boundary conditions a methodology to model material discontinuities and non convex bodies cracks using nem is also described a standard displacement based galerkin procedure is used to obtain the discrete system of linear equations application of nem to various problems in solid mechanics which include the patch test gradient problems bimaterial interface and a static crack problem are presented excellent agreement with exact analytical solutions is obtained which exemplies the accuracy and robustness of nem and suggests its potential application in the context of other classes of problems crack growth plates and large deformations to name a few 1998 john wiley sons ltd

solving time dependent engineering problems with multiquadrics abstract this paper deals with the solution of time dependent problems the multiquadric radial basis function method is formulated with a new approach for transient problems one and two dimensional problems are considered the forward difference and the crank nicolson time marching schemes for parabolic cases are considered the central difference integration method of the newmark family is considered for hyperbolic problems the method proves its accuracy in four numerical examples

motivic decomposition of a compactification of a merkurjev suslin variety we provide a motivic decomposition of a twisted form of a smooth hyperplane section of gr 3 6 this twisted form is a norm variety corresponding to a symbol in the milnor k theory k3 3 as an application we construct a torsion element in the chow group of this variety msc2000 20g15 14f43

excellent algebraic groups i abstract the notion of an excellent quadratic form has been introduced by m knebusch proc london math soc 33 1976 65 93 34 1977 1 31 it has an obvious analogue for a semisimple linear algebraic group g over an arbitrary field k the group g is excellent if for any field extension k of k the anisotropic kernel of the k group g k k can be defined by a k group the aim of this paper is to investigate excellence properties of special linear and orthogonal groups

clifford algebras of hyperbolic involutions for as a central simple algebra of even degree with hyperbolic orthogonal involution we describe the canonically induced involution underline sigma on the even clifford algebra c 0 a sigma underline sigma of a sigma when deg a equiv 0 mod 8 a cong m 2 b and the interesting part of underline sigma is isomorphic to the canonical involution on an exterior power algebra of b as a corollary we get some properties of the involution on the exterior power algebra

volumetric locking in natural neighbour galerkin methods the behaviour of natural neighbour galerkin mixed approximation is described at the incompressible limit traditional natural elements based on the sibson mixed interpolation do not verify the lbb or inf sup condition here a study of the possible benefits of enriching the interpolation is considered using the partition of unity paradigm different enrichments were tested leading to different reproducing properties results concerning the numerical verification of the inf sup tests are addressed also the convenience of using different approximations developed in this work is analysed enrichment with the polynomial field 1 xy seems to verify the lbb condition its behaviour has proven to be very similar to the mini finite element widely used in the literature examples proving these results are provided copyright 2004 john wiley sons ltd

weight two motivic cohomology of classifying spaces for semisimple groups let f x to y be a torsor for a semisimple group g with y a smooth and geometrically irreducible variety over an arbitrary field we relate the etale motivic cohomology of weight two for x y and g we also compute the etale motivic cohomology groups of degree at most 4 for the classifying space of g this result was used in an another work by the author for the computation of the group of degree 3 cohomological invariants of semisimple groups with coefficients in bbb q bbb z 2

moments in infinite channel queues we consider a new approach to the problem of evaluating the moments of the steady state number of customers in system b for an infinite channel queue having general input our new approach uses the rate conservation law as a consequence we show that for a variety of g gi queues var b as long as service times have finite first moment in addition we give some ordering relations for the variance of b when comparing two alternative systems with convex ordered inter arrival time distributions

cohomological invariants and r triviality of adjoint classical groups using a cohomological obstruction we construct examples of absolutely simple adjoint classical groups of type 2a n with n equivalent to 3 mod 4 c n or 1d n with n equivalent to 0 mod 4 which are not r trivial hence not stably rational

compression for quadratic similarity queries the problem of performing similarity queries on compressed data is considered we focus on the quadratic similarity measure and study the fundamental tradeoff between compression rate sequence length and reliability of queries performed on the compressed data for a gaussian source we show that the queries can be answered reliably if and only if the compression rate exceeds a given threshold the identification rate which we explicitly characterize moreover when compression is performed at a rate greater than the identification rate responses to queries on the compressed data can be made exponentially reliable we give a complete characterization of this exponent which is analogous to the error and excess distortion exponents in channel and source coding respectively for a general source we prove that as with classical compression the gaussian source requires the largest compression rate among sources with a given variance moreover a robust scheme is described that attains this maximal rate for any source distribution

applying multiquadric quasi interpolation to solve burgers equation abstract in this paper we develop a kind of univariate multiquadric mq quasi interpolation and use it to solve burgers equation with viscosity at first we construct the mq quasi interpolation which possesses the properties of linear reproducing and preserving monotonicity next we obtain the numerical scheme by using the derivative of the quasi interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable then we verify our method for two examples with distinguishing initial value condition one example is tested for three reynolds number that is r 10 r 100 and r 10 000 from the numerical experiments we see that the presented method in this paper is valid although the accuracy of the technique is not higher than hon and mao s one another example is used to examine the travelling of the shock we can improve the accuracy by selecting an appropriate shape parameter and using a higher accurate mq quasi interpolation the advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement

r equivalence in adjoint classical groups over fields of virtual cohomological dimension 2 let f be a field of characteristic not 2 whose virtual cohomological dimension is at most 2 let g be a semisimple group of adjoint type defined over f let rg f denote the normal subgroup of g f consisting of elements r equivalent to identity we show that if g is of classical type not containing a factor of type d n g f rg f 0 if g is a simple classical adjoint group of type d n we show that if f and its multi quadratic extensions satisfy strong approximation property then g f rg f 0 this leads to a new proof of the r triviality of f rational points of adjoint classical groups defined over number fields

radial spline collocation method for static analysis of beams conventional spline collocation method scm uses equally spaced knots in the computation of approximation however when load distribution geometry material property of structure are discontinuous it will greatly reduce accuracy the goal of this paper is mainly to develop unequally spaced knots to improve the disadvantage of using equally spaced knots applying the concept of radial basis functions rbf the spline function is transformed into radial spline function rsf consequently rsf can conveniently calculate the values for unequally spaced knots so that the complicated beam problems with discontinuous characteristics can be solved accurately and efficiently by the proposed radial spline collocation method rscm in this paper the proposed rscm also can be extended to solve other structural problems such as frame plate shell etc

explicit and implicit meshless methods for linear advection diffusion type partial differential equations simple mesh grid free explicit and implicit numerical schemes for the solution of linear advection diffusion problems is developed and validated herein unlike the mesh or grid based methods these schemes use well distributed quasi random points and approximate the solution using global radial basis functions the schemes can be seen as generalized finite differences with random points instead of a regular grid system this allows the computation of problems with complex shaped boundaries in higher dimensions with no need for complex mesh grid structure and with no extra implementation difficulties

the map and blend scattered data interpolant on a sphere abstract the map and blend technique constructs a function defined over the sphere that interpolates to a discrete sample of measurements at arbitrary locations on the sphere this technique consists of two different mappings of the sphere to planar domains solving two corresponding scattered data interpolation problems on the planar domains and then the interpolant on the sphere is formed by blending these two planar interpolants if the user has software for solving the scattered data interpolation problem on a planar domain only a small programming effort is needed to implement the map and blend interpolant on the sphere although any interpolant to scattered data on a planar domain can be used in our general technique we use the multiquadric radial basis method

solving high order partial differential equations with indirect radial basis function networks this paper reports a new numerical method based on radial basis function networks rbfns for solving high order partial differential equations pdes the variables and their derivatives in the governing equations are represented by integrated rbfns the use of integration in constructing neural networks allows the straightforward implementation of multiple boundary conditions and the accurate approximation of high order derivatives the proposed rbfn method is verified successfully through the solution of thin plate bending and viscous flow problems which are governed by biharmonic equations for thermally driven cavity flows the solutions are obtained up to a high rayleigh number

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

compression for quadratic similarity queries finite blocklength and practical schemes we study the problem of compression for the purpose of similarity identification where similarity is measured by the mean square euclidean distance between vectors while the asymptotical fundamental limits of the problem the minimal compression rate and the error exponent were found in a previous work in this paper we focus on the nonasymptotic domain and on practical implementable schemes we first present a finite blocklength achievability bound based on shape gain quantization the gain amplitude of the vector is compressed via scalar quantization and the shape the projection on the unit sphere is quantized using a spherical code the results are numerically evaluated and they converge to the asymptotic values as predicted by the error exponent we then give a nonasymptotic lower bound on the performance of any compression scheme and compare to the upper achievability bound for a practical implementation of such a scheme we use wrapped spherical codes studied by hamkins and zeger and use the leech lattice as an example for an underlying lattice as a side result we obtain a bound on the covering angle of any wrapped spherical code as a function of the covering radius of the underlying lattice

asymptotically dense spherical codes ii laminated spherical codes for pt i see ibid vol 43 no 6 p 1774 85 1997 new spherical codes called laminated spherical codes are constructed in dimensions 2 49 using a technique similar to the construction of laminated lattices each spherical code is recursively constructed from existing spherical codes in one lower dimension laminated spherical codes outperform the best known spherical codes in the minimum distance sense for many code sizes the density of a laminated spherical code approaches the density of the laminated lattice in one lower dimension as the minimum distance approaches zero in particular the three dimensional laminated spherical code is asymptotically optimal in the sense that its density approaches the fejes toth 1959 upper bound as the minimum distance approaches zero laminated spherical codes perform asymptotically as well as wrapped spherical codes in those dimensions where laminated lattices are optimal sphere packings

tables of sphere packings and spherical codes the theta function of a sphere packing gives the number of centers at each distance from the origin the theta functions of a number of important packings a n d n e n the leech lattice and others and tables of the first fifty or so of their coefficients are given in this paper

unramified cohomology of degree 3 and noether s problem let g be a finite group and w be a faithful representation of g over c the group g acts on the field of rational functions c w the question whether the field of invariant functions c w g is purely transcendental over c goes back to emmy noether using the unramified cohomology group of degree 2 of this field as an invariant saltman gave the first examples for which c w g is not rational over c around 1986 bogomolov gave a formula which expresses this cohomology group in terms of the cohomology of the group g

a new spectral meshless radial point interpolation smrpi method for the two dimensional fredholm integral equations on general domains with error analysis in this article we present a numerical method to solve two dimensional fredholm integral equations of the second kind on general domains the method utilizes meshless and spectral collocation techniques but it is not traditional meshless collocation method the point interpolation method with the help of strictly positive definite radial basis functions is used to construct shape functions as a basis functions in the frame of spectral collocation methods these basis functions shape functions have kronecker delta function property since the proposed method is meshless it does not need any domain element and so it is independent of the geometry of the domain the method reduces the solution of the two dimensional integral equation to the solution of a linear system of algebraic equations convergence analysis with error estimates are given with full discussion furthermore some numerical examples are presented to show the validity and efficiency of smrpi

on the convergence analysis stability and implementation of meshless local radial point interpolation on a class of three dimensional wave equations summary in this article the meshless local radial point interpolation method is applied to analyze three space dimensional wave equations of the form utt ut u uxx uyy uzz f x y z t xt x y z rd d 2 3 t 0 subject to given initial and dirichlet boundary conditions the main difficulty of the great number of methods in full 3 d problems is the large computational costs in meshless local radial point interpolation method it does not require any background integration cells so that all integrations are carried out locally over small quadrature domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions the point interpolation method with the help of radial basis functions is proposed to construct shape functions that have kronecker delta function property a weak formulation with the heaviside step function converts the set of governing equations into local integral equations on local subdomains a two step time discretization method is employed to evaluate the time derivatives this suggests crank nicolson technique to be applied on the right hand side of the equation the convergence analysis and stability of the method are fully discussed three illustrative examples are presented and satisfactory agreements are achieved it is shown theoretically that the proposed method is unconditionally stable for the second example whereas it is not for the first and third ones copyright 2015 john wiley sons ltd

a new extension of the natural element method for non convex and discontinuous problems the constrained natural element method c nem in this paper a new extension of the mesh free natural element method nem is presented in this approach coined as constrained natural element method c nem a visibility criterion is introduced to select natural neighbours in the computation of the shape functions the computation of these shape functions is based on a modified constrained voronoi diagram with this technique some difficulties inherent to this method in non convex domains are avoided and the analysis of problems involving cracks or discontinuities are now easily performed as the nem satisfies the kronecker delta property the imposition of essential boundary conditions is trivial unlike other mesh free methods the c nem technique provides a description of integration cells that allows the use of the stabilized conforming nodal integration scni scheme instead of gauss integration to enhance computational efficiency and accuracy two numerical examples in elastostatics are reported to evaluate the potential of the proposed technique in highly non convex geometries like a crack through which the solution becomes discontinuous

examples of non rational varieties of adjoint groups let k be a field of characteristic 2 and k a separable closure of k s we say that an algebraic variety xrk is stably k rational if there exist two m n m n w x affine spaces a a and a k rational map a x f a merkurjev 9 k k gave a criterion of stable k rationality for the adjoint classical groups with absolute rank f 3 which covers the case of the variety pso q for any quadratic form qrk of rank f 6 this criterion gives examples of field k and quadratic form q of rank 6 with non trivial signed discriminant such that the variety pso q is not stably k rational the main result of this paper is the following

a radial basis function approach for the free vibration analysis of functionally graded plates using a refined theory abstract the free vibration analysis of functionally graded plates is performed by the multiquadric radial basis function method and a higher order shear deformation theory the multiquadric method is a truly meshless method allowing a fast and simple domain and boundary discretization we use an homogenization technique for material properties based on the mori tanaka scheme numerical tests show that the method is reliable and produces good results

some extensions of radial basis functions and their applications in artificial intelligence abstract radial basis functions have recently found interesting applications in artificial intelligence and in particular in the problem of learning to perform a particular task from a set of examples however in many practical cases the radial basis functions method cannot be applied in a straight forward manner because it does not take into account some features that are typical of the problem of learning from examples in this paper we show some extensions of the standard theory introduced in order to deal with a large number of examples and with problems in which different variables play very different roles we present some examples and also point out some open problems

a numerical solution of the nonlinear controlled duffing oscillator by radial basis functions in this research a new numerical method is applied to investigate the nonlinear controlled duffing oscillator this method is based on the radial basis functions rbfs to approximate the solution of the optimal control problem by using the collocation method we apply legendre gauss lobatto points for rbfs center nodes in order to use the numerical integration method more easily then the method of lagrange multipliers is used to obtain the optimum of the problems for this purpose different applications of rbfs are used the differential and integral expressions which arise in the dynamic systems the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients illustrative examples are included to demonstrate the validity and applicability of the technique

an improved reproducing kernel particle method for nearly incompressible finite elasticity the previously developed reproducing kernel particle method rkpm employs a high order quadrature rule for desired domain integration accuracy this leads to an over constrained condition in the limit of incompressibility and volumetric locking and pressure oscillation were encountered the employment of a large support size in the reproducing kernel shape function increases the dependency in the discrete constraint equations at quadrature points and thereby relieves locking however this approach consumes high cpu and it cannot effectively resolve pressure oscillation difficulty in this paper a pressure projection method is introduced by locally projecting the pressure onto a lower order space to reduce the number of independent discrete constraint equations this approach relieves the over constrained condition and thus eliminates volumetric locking and pressure oscillation without the expense of employing large support size in rkpm the method is developed in a general framework of nearly incompressible finite elasticity and therefore linear problems are also applicable to further reduce the computational cost a stabilized reduced integration method based on an assumed strain approach on the gradient matrix associated with the deformation gradient is also introduced the resulting stiffness matrix and force vector of rkpm are obtained explicitly without numerical integration

generically split projective homogeneous varieties let g be an exceptional simple algebraic group over a field k and x a projective g homogeneous variety such that g splits over k x we classify such varieties x this classification allows to relate the rost invariant of groups of type e7 and their isotropy and to give a two line proof of the triviality of the kernel of the rost invariant for such groups apart from this it plays a crucial role in the solution s08 of a problem posed by j p serre for groups of type e8

the asymptotic cardinal function of the multiquadratic ϕ r r2 c2 12as c a radial basis function approximation has the form s x j rd yj x xj 2 x rd where 0 r is some given function yj j zd are real coefficients and the centres xj j zd are points in rd it is known that radial basis function approximations using the multiquadric r r2 c2 12 possess many useful and interesting properties when the centres form an infinite regular lattice we analyse the limiting case as c and identify a class of functions that arise as uniform limits of the multiquadric interpolants in the univariate case we observe that the cardinal function for the multiquadratic becomes the sinc function as c the limit of the multivariate cardinal function is also identified

unramified cohomology of classifying varieties for exceptional simply connected groups let bg be a classifying variety for an exceptional simple simply connected algebraic group g we compute the degree 3 unramified galois cohomology of bg with values in q z 2 over an arbitrary field f combined with a paper by merkurjev this completes the computation of these cohomology groups for g semisimple simply connected over all fields these computations provide another family of examples of simple simply connected groups g such that bg is not stably rational

unramified degree three invariants for reductive groups of type a abstract let g be a reductive group over an algebraically closed field f of characteristic zero such that the dynkin diagram of g is the disjoint union of diagrams of type a we prove that the third unramified cohomology group of the classifying space of g with coefficients in q z is trivial

the arason invariant and mod 2 algebraic cycles introduction 73 1 review of the arason invariant 75 2 the special clifford group 76 3 k cohomology of split reductive algebraic groups 78 4 k cohomology of bg 86 5 gl n and cliff n n 92 6 two invariants for clifford bundles 95 7 snaking a bloch ogus differential 100 8 proof of theorem 1 101 9 application to quadratic forms 102 appendix a toral descent 104 appendix b the rost invariant 108 appendix c an amusing example 113 acknowledgements 116 references 116

degree three unramified cohomology of adjoint semisimple groups we compute degree 3 unramified cohomology of adjoint semisimple group new classes of non rational adjoint semisimple groups are found

conditions for locking free elasto plastic analyses in the element free galerkin method the use of finite elements with linear displacement fields in volume preserving elasto plastic problems can lead to volumetric locking due to the inability of the shape functions to describe certain displacement modes a response of the structure can be obtained which is much too stiff the element free galerkin efg method can provide shape functions that have an intrinsic richer nature and do not exhibit volumetric locking it is shown that the finite element fe method can be conceived as a specialisation of the efg method and that for a specific choice of the efg parameters the fe shape functions are retrieved then volumetric locking behaviour is found again however for other choices of the efg parameters shape functions are obtained that are able to describe isochoric elasto plasticity without volumetric locking

asymptotically dense spherical codes i wrapped spherical codes a new class of spherical codes called wrapped spherical codes is constructed by wrapping any sphere packing spl lambda in euclidean space onto a finite subset of the unit sphere in one higher dimension the mapping preserves much of the structure of spl lambda and unlike previously proposed maps the density of the wrapped spherical codes approaches the density of spl lambda as the minimum distance approaches zero we show that this implies that the asymptotically maximum spherical coding density is achieved by wrapped spherical codes whenever spl lambda is the densest possible sphere packing

shells of twisted flag varieties and the rost invariant we introduce two new general methods to compute the chow motives of twisted flag varieties and settle a 20 year old conjecture of markus rost about the rost invariant for groups of type e 7

a collocation meshless method based on local optimal point interpolation this paper deals with the use of the local optimal point interpolating lopi formula in solving partial differential equations pdes with a collocation method lopi is an interpolating formula constructed by localization of optimal point interpolation formulas that reproduces polynomials and verifies the delta kronecker property this scheme results in a truly meshless method that produces high quality output and accurate solutions

solution and control of pde via global optimization methods abstract based on the concept of equivalent solutions not to be confused with approximations to the exact solution a new consideration is given to ill posed 1 2 and overdetermined pde problems and to problems with nonexistent solutions 3 then a new method based on full global optimization techniques is developed for solution and control of processes described by partial differential equations the ideas are illustrated by examples and a case study is presented in comparison with the quasi reversibility method 4

isotropic trialitarian algebraic groups abstract by modifying a construction from knus et al we construct all isotropic algebraic groups of type 3 d 4 and 6 d 4 over an arbitrary field of characteristic 2 we also provide a nice isomorphism criterion for such groups the results of this paper extend the main results of allison using entirely different methods to fields of nonzero characteristic and algebraic groups

cohomological invariants of simply connected groups of rank 3 let g be a linear algebraic group defined over a field f one can define an equivalence relation called r equivalence on the group g f of points over f as follows cf 4 9 14 two points g0 g1 g f are r equivalent if there is a rational morphism f x 1 f g of algebraic varieties over f defined at points 0 and 1 such that f 0 g0 and f 1 g1 the group of r equivalence classes is denoted by g f r for example if g sl1 a is the special linear group of a central simple f algebra a then the group of r equivalence classes g f r is equal to the reduced whitehead group in algebraic k theory cf 27

fully meshless solution of the one dimensional multigroup neutron transport equation with the radial basis function collocation method abstract in this paper a fully meshless method is proposed for the numerical solution of the one dimensional multigroup neutron transport equation with anisotropic scattering both first order and even parity forms of the transport equation are studied the radial basis function collocation method is chosen for the spatial treatment and legendre polynomials are used to approximate the angular variable the selection of the legendre polynomials instead of discrete ordinates approach resulted with a fully meshless algorithm in both independent variables multiquadric is utilized as the radial function seven problems are considered to evaluate the performance of the method the results show that the method converges exponentially and it is possible to obtain high levels of accuracies for the multiplication factor and neutron flux with a good stability in both spatial and angular domains for the one group isotropic benchmark problem discrete ordinates solutions employing discontinuous linear finite elements for the spatial variable are also provided and a comparison of the methods revealed that the fully meshless method produced more accurate results than the discrete ordinates finite element scheme when the shape parameter is properly chosen

decomposable and indecomposable algebras of degree 8 and exponent 2 we study the decomposition of central simple algebras of exponent 2 into tensor products of quaternion algebras we consider in particular decompositions in which one of the quaternion algebras contains a given quadratic extension let b be a biquaternion algebra over f a with trivial corestriction a degree 3 cohomological invariant is defined and we show that it determines whether b has a descent to f this invariant is used to give examples of indecomposable algebras of degree 8 and exponent 2 over a field of 2 cohomological dimension 3 and over a field m t where the u invariant of m is 8 and t is an indeterminate the construction of these indecomposable algebras uses chow group computations provided by merkurjev in appendix

miscellaneous error bounds for multiquadric and related interpolators we establish several types of a a priori error bounds for multiquadric and related interpolators the results are stated and proven in the general multivariate case these estimates show for example that in many cases such interpolators converge very quickly and can be used in the recovery of band limited functions from discrete data we also include numerical experiments which illustrate the theoretical results

improved accuracy of multiquadric interpolation using variable shape parameters given n scattered data points we examined the problem of finding n variable multiquadric mq shape parameters or r2 values because the problem of finding the optimal r2 values is a nonlinear one we optimized these parameters numerically by minimizing the root mean square rms errors the resulting r2 values varied over many orders of magnitude we have tested this approach on a number of univariate and bivariate franke s problems and found that the rms error reduction was substantial

local radial point interpolation mlrpi method for solving time fractional diffusion wave equation with damping the purpose of the current investigation is to determine numerical solution of time fractional diffusion wave equation with damping for caputo s fractional derivative of order 1 2 a meshless local radial point interpolation mlrpi scheme based on galerkin weak form is analyzed the reason of choosing mlrpi approach is that it does not require any background integrations cells instead integrations are implemented over local quadrature domains which are further simplified for reducing the complication of computation using regular and simple shape the unconditional stability and convergence with order o 6 2 are proved where is time stepping also several numerical experiments are illustrated to verify theoretical analysis

unramified degree three invariants of reductive groups abstract we prove that if g is a reductive group over an algebraically closed field f then for a prime integer p char f the group of unramified galois cohomology h nr 3 f bg q p z p 2 is trivial for the classifying space bg of g if p is odd or the commutator subgroup of g is simple

application of the multiquadric method for numerical solution of elliptic partial differential equations abstract we have used the multiquadric mq approximation scheme for the solution of elliptic partial differential equations with dirichlet and or neumann boundary conditions the scheme has the advantage of using the data points in arbitrary locations with an arbitrary ordering two dimensional laplace poisson and biharmonic equations describing the various physical processes have been taken as the test examples the agreement is found to be very good between the computed and exact solutions the method also provides an excellent approximation with a curved boundary

imposing essential boundary conditions in the natural element method by means of density scaled shapes a new method is proposed for the exact imposition of essential boundary conditions in the context of the natural element method nem this is a new technique in the field of computational mechanics and can be considered as a meshless method unlike most of these methods the ne shape functions are strictly interpolant and the essential boundary conditions can be imposed by directly substituting the corresponding terms in the system of equations however these shape functions are not strictly linear over non convex boundaries and the approach does not make the test functions vanish over the whole essential boundary region a modification of the initial nem version is considered based on shapes and complexes which are widely used in the field of scientific visualization using shapes in the context of the nem allows the construction of models entirely in terms of nodes and also ensures the linear precision of the interpolant over convex and non convex boundaries results on some benchmark problems are presented after a theoretical description of the method copyright 2000 john wiley sons ltd

natural element approximations involving bubbles for treating mechanical models in incompressible media in this paper a new approach is proposed to address issues associated with incompressibility in the context of the meshfree natural element method nem the nem possesses attractive features such as interpolant shape functions or auto adaptive domain of influence which alleviates some of the most common difficulties in meshless methods nevertheless the shape functions can only reproduce linear polynomials and in contrast to moving least squares methods it is not easy to define interpolations with arbitrary approximation consistency in order to treat mechanical models involving incompressible media in the framework of mixed formulations the associated functional approximations must satisfy the well known inf sup or lbb condition in the proposed approach additional degrees of freedom are associated with some topological entities of the underlying delaunay tessellation i e edges triangles and tetrahedrons the associated shape functions are computed from the product of the nem shape functions related to the original nodes different combinations can be used to construct new families of nem approximations as these new approximations functions are not related to any node as they vanish at the nodes from now on we refer these shape functions as bubbles the shape functions can be corrected enforcing different reproducing conditions when they are used as weights in the moving least square mls framework in this manner the effects of the obtained higher approximation consistency can be evaluated in this work we restrict our attention to the 2d case and the following constructions will be considered a bubble functions associated with the delaunay triangles called b1 nem and b bubble functions associated with the delaunay edges called b2 nem we prove that all these approximation schemes allow direct enforcement of essential boundary conditions the bubble nem schemes are then used to approximate the displacements in the linear elasticity mixed formulation the pressure being approximated by the standard nem the numerical lbb test is passed for all the bubble nem approximations and pressure oscillations are removed in the incompressible limit

stabilized conforming nodal integration in the natural element method a stabilized conforming nodal integration scheme is implemented in the natural neighbour method in conjunction with non sibsonian interpolation in this approach both the shape functions and the integration scheme are defined through use of first order voronoi diagrams the method illustrates improved performance and significant advantages over previous natural neighbour formulations the method also shows substantial promise for problems with large deformations and for the computation of higher order gradients copyright 2004 john wiley sons ltd

locking in the incompressible limit for the element free galerkin method volumetric locking locking in the incompressible limit for linear elastic isotropic materials is studied in the context of the element free galerkin method the modal analysis developed here shows that the number of non physical locking modes is independent of the dilation parameter support of the interpolation functions thus increasing the dilation parameter does not suppress locking nevertheless an increase in the dilation parameter does reduce the energy associated with the non physical locking modes thus in part it alleviates the locking phenomena this is shown for linear and quadratic orders of consistency moreover the biquadratic order of consistency as in finite elements improves the locking behaviour although more locking modes are present in the element free galerkin method with quadratic consistency than with standard biquadratic finite elements finally numerical examples are shown to validate the modal analysis in particular the conclusions of the modal analysis are also confirmed in an elastoplastic example copyright 2001 john wiley sons ltd

the generalized even clifford algebra abstract for a central simple algebra a with an orthogonal involution over a field f of characteristic not equal to two we associate to it the generalized even clifford algebrac0 a we will present results on the structure of this algebra c0 a some of which are due to jacobson in j algebra1 1964 288 300 using a generic method we then give a formula for computing c0 a when a is decomposable as algebras with involution using these results a necessary condition for decomposability of an algebra with orthogonal involution compatible with the involution is then obtained

the parameter r2 in multiquadric interpolation the multiquadric mq method is an effective bivariate interpolant to three dimensional data xi yi zi where the xi yi are arbitrarily located in the plane the accuracy of the mq method is dependent on a user defined parameter r2 and most practitioners select r2 based upon the number of data points and the locations of the xi yi in the plane we observe that the optimal value of r2 is a strong function of the zi and that it is essentially independent of both the number and the locationsof the xi yi points contrary to some opinions we observe that the mq method can effectively interpolate to track data that is data sampled densely along tracks in the plane together with several other observations we present an algorithm that generally yields an effective value for r2

degree three invariants for semisimple groups of types b c and d abstract we determine the group of reductive cohomological degree 3 invariants of all split semisimple groups of types b c and d we also present a complete description of such cohomological invariants as an application we show that the group of degree 3 unramified cohomology of the classifying space bg is trivial for all split semisimple groups g of types b c and d

edged based smoothed point interpolation method for acoustic radiation with perfectly matched layer abstract it is known that for exterior acoustics the domain based finite element method always encounters the accuracy loss for high wavenumbers and the difficulty in dealing with the sommerfeld radiation condition in this work by using the polynomial and radial bases with specific node selection schemes the point interpolation method with the generalized gradient smoothing technique is employed to improve the accuracy for acoustic computations the appropriately softened acoustical stiffness of the discrete model is constructed based on the edge based smoothing domains via the gradient smoothing technique in addition the perfectly matched layer technique enables the smoothed point interpolation method to investigate exterior acoustics the complex coordinate transformation is utilized to determine the proper parameters for the perfectly matched layer through theoretical and numerical analyses several typical acoustic problems are analyzed revealing that better accuracy is obtained by the present method compared with the finite element method especially for high wavenumbers

gaussian source coding with spherical codes a fixed rate shape gain quantizer for the memoryless gaussian source is proposed the shape quantizer is constructed from wrapped spherical codes that map a sphere packing in spl ropf sup k 1 onto a sphere in spl ropf sup k and the gain codebook is a globally optimal scalar quantizer a wrapped leech lattice shape quantizer is used to demonstrate a signal to quantization noise ratio within 1 db of the distortion rate function for rates above 1 bit per sample and an improvement over existing techniques of similar complexity an asymptotic analysis of the tradeoff between gain quantization and shape quantization is also given