generalized multiple scale reproducing kernel particle methods abstract an approach to unify reproducing kernel methods under one large umbrella and an extension to include time and spatial shifting are proposed the study is divided into three major topics the groundwork is set by revisiting the fourier analysis of discrete systems the multiresolution concept and its significance in devising the reproducing kernel methods and its discrete counterpart reproducing kernel particle methods are explained an edge detection technique based on multiresolution analysis is developed this wavelet approach together with particle methods gives rise to a straightforward h adaptivity algorithm by using this framework a hermite reproducing kernel method is also proposed and its relation to wavelet methods is presented it is also shown that the new approach generalizes existing kernel methods and it can easily be degenerated into other widely used methods such as partition of unity moving least square interpolants smooth particle hydrodynamics scaling functions and wavelets and multiple scale analysis furthermore the hermite reproducing kernel particle method a particle based discrete version of the hermite reproducing kernel method is developed finally multiple scale methods based on frequency and wave number shifting techniques are presented a stability analysis is also presented for newmark time integration schemes for the low frequency equation numerical examples are presented throughout the paper to illustrate the flexibility and accuracy of this class of multiple scale methods

finite dimensional lie algebras of order f f lie algebras are natural generalizations of lie algebras f 1 and lie superalgebras f 2 when f 2 not many finite dimensional examples are known in this article we construct finite dimensional f lie algebras f 2 by an inductive process starting from lie algebras and lie superalgebras matrix realizations of f lie algebras constructed in this way from su n sp 2n so n and sl n m osp 2 m are given we obtain nontrivial extensions of the poincare algebra by inonu wigner contraction of certain f lie algebras with f 2

n ary algebras a review with applications this paper reviews the properties and applications of certain n ary generalizations of lie algebras in a self contained and unified way these generalizations are algebraic structures in which the two entries lie bracket has been replaced by a bracket with n entries each type of n ary bracket satisfies a specific characteristic identity which plays the role of the jacobi identity for lie algebras particular attention will be paid to generalized lie algebras which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized jacobi identity and to filippov or n lie algebras which are defined by fully antisymmetric n brackets that satisfy the filippov identity three lie algebras have surfaced recently in multi brane theory in the context of the bagger lambert gustavsson model because of this filippov algebras will be discussed at length including the cohomology complexes that govern their central extensions and their deformations it turns out that whitehead s lemma extends to all semisimple n lie algebras when the skewsymmetry of the lie or n lie algebra bracket is relaxed one is led to a more general type of n algebras the n leibniz algebras these will be discussed as well since they underlie the cohomological properties of n lie algebras the standard poisson structure may also be extended to the n ary case we shall review here the even generalized poisson structures whose generalized jacobi identity reproduces the pattern of the generalized lie algebras and the nambu poisson structures which satisfy the filippov identity and determine filippov algebras finally the recent work of bagger lambert and gustavsson on superconformal chern simons theory will be briefly discussed emphasis will be made on the appearance of the 3 lie algebra structure and on why the a4 model may be formulated in terms of an ordinary lie algebra and on its nambu bracket generalization

adjoint based optimal control using meshfree discretizations the paper at hand presents a combination of optimal control approaches for pdes with meshless discretizations applying a classical lagrangian type particle method to optimization problems with hyperbolic constraints several adjoint based strategies differing in the sequential order of optimization and discretization of the lagrangian or eulerian problem formulation are proposed and compared the numerical results confirm the theoretically predicted independence principle of the optimization approaches and show the expected convergence behavior moreover they exemplify the superiority of meshless methods over the conventional mesh based approaches for the numerical handling and optimization of problems with time dependent geometries and freely moving boundaries

filiform lie algebras of order 3 the aim of this work is to generalize a very important type of lie algebras and superalgebras i e filiform lie super algebras into the theory of lie algebras of order f thus the concept of filiform lie algebras of order f is obtained in particular for f 3 it has been proved that by using infinitesimal deformations of the associated model elementary lie algebra it can be obtained families of filiform elementary lie algebras of order 3 analogously as that occurs into the theory of lie algebras m vergne cohomologie des algebres de lie nilpotentes application a l etude de la variete des algebres de lie nilpotentes bull soc math france 98 81 116 1970 also we give the dimension using an adaptation of the sl 2 c module method and a basis of such infinitesimal deformations in some generic cases

an improved crack analysis technique by element free galerkin method with auxiliary supports in this study an improved crack analysis technique by element free galerkin method efgm with auxiliary supports is proposed to efficiently model the singularity and the discontinuity of the crack a singular basis function which varies only on the auxiliary supports is added to enrich the standard efg approximation and the discontinuous shape function is used in the vicinity of the crack surface the proposed technique improves the accuracy in the near tip field by using only an initial node arrangement without any modification until the completion of an analysis a parametric study which can guide the analyst on the reasonable choice for the formulation and modelling parameters to be used in the technique is performed on a relative stress norm error and stress intensity factor in addition some numerical examples are analysed to verify the effectiveness of the proposed technique for a crack problem copyright 2003 john wiley sons ltd

analysis of an augmented moving least squares approximation and the associated localized method of fundamental solutions abstract the localized method of fundamental solutions lmfs is an efficient meshless collocation method that combines the concept of localization and the method of fundamental solutions mfs the resultant system of linear algebraic equations in the lmfs is sparse and banded and thus drastically reduces the storage and computational burden of the mfs in the lmfs the moving least square mls approximation based on fundamental solutions is used to construct approximate solution at each node in this paper this fundamental solutions based mls approximation named as an augmented mls amls approximation is generalized to any point in the computational domain computational formulas theoretical properties and error estimates of the amls approximation are derived then taking laplace equation as an example this paper sets up a framework for the theoretical error analysis of the lmfs finally numerical results are presented to verify the efficiency and theoretical results of the amls approximation and the lmfs convergence and comparison researches are conducted to validate the accuracy convergence and efficiency

stereographic variables for multidimensional quantum group covariant q oscillators in this paper we study the unitary matrix representation of quantum group suq 2 in terms of stereographic coordinates z and z and a central unitary phase u the fractional linear transformation of z and z gives the action of suq 2 on the quantum sphere suq 2 u 1 with coordinates z and z we then extend this action to suq 2 and derive the transformation law of u finally we construct the two dimensional covariant q oscillators in terms of stereographic variables and then we generalize it to d dimensional case

modified moving least squares with polynomial bases for scattered data approximation one common problem encountered in many fields is the generation of surfaces based on values at irregularly distributed nodes to tackle such problems we present a modified robust moving least squares mls method for scattered data smoothing and approximation the error functional used in the derivation of the classical mls approximation is augmented with additional terms based on the coefficients of the polynomial base functions this allows quadratic base functions to be used with the same size of the support domain as linear base functions resulting in better approximation capability the increased robustness of the modified mls method to irregular nodal distributions makes it suitable for use across many fields the analysis is supported by several univariate and bivariate examples

an adaptive procedure based on background cells for meshless methods in practical implementations meshless methods using moving least squares mls approximation and global galerkin formulation require a background mesh for domain integration an adaptive procedure based on background mesh is developed for meshless methods using mls it comprises a cell energy error estimate and a local domain refinement technique the error estimate differs from conventional pointwise approaches in that it evaluates error based on individual cells instead of points for each cell a computed cell energy and a reference cell energy are generated based on a same stress field by using two different integration schemes the difference between the two energy values is used as the basic measure of error estimation the advantage of this strategy is that it requires only one stress field and no reference field needs to be furnished this has significance as the stress field generated by meshless methods is already very smooth and traditional error estimates based on stress smoothing techniques for finite element methods are not applicable to achieve high efficiency in domain refinement a local technique based on the delaunay algorithm is implemented in this technique each node is assigned a scaling factor to control local nodal density refinement of the neighborhood of a node is accomplished simply by adjusting its scaling factor the numerical experiments in this paper show that the proposed adaptive procedure is simple effective and efficient the limitations of the approach are also discussed

new boundary condition treatments in meshfree computation of contact problems due to the loss of kronecker delta properties in the meshfree shape functions the imposition of essential boundary conditions consumes significant cpu time in meshfree computation in this work two boundary condition treatments are proposed to enhance the computational efficiency of meshfree methods for contact problems the mixed transformation method is modified from the previous full transformation method by introducing a node partitioning and a mixed coordinate so that the matrix inversion and multiplication of coordinate transformation involves operations only on the sub degrees of freedom associated with the boundary group the boundary singular kernel method introduces singularities to the kernel functions of the essential and contact boundary nodes so that the corresponding coefficients of the singular kernel shape functions recover nodal values and consequently kinematic constraints can be imposed directly the effectiveness of the proposed methods is demonstrated in several numerical examples

non fragile observer based passive control for uncertain time delay systems subjected to input nonlinearity abstract the problem of non fragile observer based passive control for uncertain time delay systems subjected to input nonlinearity is investigated by using sliding mode control a novel control law is established such that the sliding surface in the state estimation space can be reached in a finite time and chattering reduction is obtained a sufficient condition for passivity and asymptotic stability of the combined system is derived via linear matrix inequality lmi finally a simulation example is presented to show the validity and advantages of the proposed method

a coupled element free galerkin boundary element method for stress analysis of two dimensional solids element free galerkin efg method is a newly developed meshless method for solving partial differential equations using moving least squares interpolants it is however computationally expensive for many problems a coupled efg boundary element be method is proposed in this paper to improve the solution efficiency a procedure is developed for the coupled efg be method so that the continuity and compatibility are preserved on the interface of the two domains where the efg and be methods are applied the present coupled efg be method has been coded in fortran the validity and efficiency of the efg be method are demonstrated through a number of examples it is found that the present method can take the full advantages of both efg and be methods it is very easy to implement and very flexible for computing displacements and stresses of desired accuracy in solids with or without infinite domains

enforcement of essential boundary conditions in meshless approximations using finite elements abstract a technique for easily treating essential boundary conditions for approximations which are not interpolants such as moving least square approximations in the element free galerkin method is presented the technique employs a string of elements along the essential boundaries and combines the finite element shape functions with the approximation in the resulting approximation essential boundary conditions can be treated exactly as in finite elements it is shown that the resulting approximation can exactly reproduce linear polynomials so that it satisfies the patch test numerical studies show that the method retains the high rate of convergence associated with moving least square approximations

hermite type moving least squares approximations the moving least squares approach first presented by mclain 1 is a method for approximating multivariate functions using scattered data information the method is using local polynomial approximations incorporating weight functions of different types some weights with certain singularities induce c interpolation approximation in n in this work we present a way of generalizing the method to enable hermite type interpolation namely interpolation to derivatives data as well the essence of the method is the use of an appropriate metric in the construction of the local polynomial approximations

fractional superlie algebras and groups the nth root of a lie algebra and its dual that is the fractional supergroup based on the permutation group sn invariant forms is formulated in the hopf algebra formalism detailed discussion of s3 graded sl 2 algebras is performed

robust adaptive control of a class of nonlinear systems with unknown dead zone this paper deals with the adaptive control of a class of continuous time nonlinear dynamic systems preceded by an unknown dead zone by using a new description of a dead zone and by exploring the properties of this dead zone model intuitively and mathematically a robust adaptive control scheme is developed without constructing the dead zone inverse the new control scheme ensures global stability of the adaptive system and achieves desired tracking precision simulations performed on a typical nonlinear system illustrate and clarify the validity of this approach

a perturbation method for stochastic meshless analysis in elastostatics a stochastic meshless method is presented for solving boundary value problems in linear elasticity that involves random material properties the material property was modelled as a homogeneous random field a meshless formulation was developed to predict stochastic structural response unlike the finite element method the meshless method requires no structured mesh since only a scattered set of nodal points is required in the domain of interest there is no need for fixed connectivities between nodes in conjunction with the meshless equations classical perturbation expansions were derived to predict second moment characteristics of response numerical examples based on one and two dimensional problems are presented to examine the accuracy and convergence of the stochastic meshless method a good agreement is obtained between the results of the proposed method and monte carlo simulation since mesh generation of complex structures can be a far more time consuming and costly effort than the solution of a discrete set of equations the meshless method provides an attractive alternative to finite element method for solving stochastic mechanics problems copyright 2001 john wiley sons ltd

frictional contact analysis of functionally graded materials with lagrange finite block method summary based on the one dimensional differential matrix derived from the lagrange series expansion the finite block method was recently developed to solve both the elasticity and transient heat conduction problems of anisotropic and functionally graded materials in this paper the formulation of the lagrange finite block method with boundary type in the strong form is presented and applied to non conforming contact problems for the functionally graded materials subjected to either static or dynamic loads the first order partial differential matrices are only needed both in the governing equations and in the neumann boundary condition by introducing the mapping technique a block of quadratic type is transformed from the cartesian coordinate of global system to the normalized coordinate with eight seeds time dependent partial differential equations are analyzed in the laplace transformed domain and the durbin s inversion method is applied to determine all the physical values in the time domain conforming and non conforming contacts are investigated by using the iterative algorithm with full load technique illustrative numerical examples are given and comparisons have been made with analytical solutions copyright 2015 john wiley sons ltd

a meshfree enriched finite element method for compressible and near incompressible elasticity summary in this paper a two dimensional displacement based meshfree enriched fem me fem is presented for the linear analysis of compressible and near incompressible planar elasticity the me fem element is established by injecting a first order convex meshfree approximation into a low order finite element with an additional node the convex meshfree approximation is constructed using the generalized meshfree approximation method and it possesses the kronecker delta property on the element boundaries the gradient matrix of me fem element satisfies the integration constraint for nodal integration and the resultant me fem formulation is shown to pass the constant stress test for the compressible media the me fem interpolation is an element wise meshfree interpolation and is proven to be discrete divergence free in the incompressible limit to prevent possible pressure oscillation in the near incompressible problems an area weighted strain smoothing scheme incorporated with the divergence free me fem interpolation is introduced to provide the smoothing on strains and pressure with this smoothed strain field the discrete equations are derived based on a modified hu washizu variational principle several numerical examples are presented to demonstrate the effectiveness of the proposed method for the compressible and near incompressible problems copyright 2012 john wiley sons ltd

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

reproducing kernel hierarchical partition of unity part i formulation and theory this work is concerned with developing the hierarchical basis for meshless methods a reproducing kernel hierarchical partition of unity is proposed in the framework of continuous representation as well as its discretized counterpart to form such hierarchical partition a class of basic wavelet functions are introduced based upon the built in consistency conditions the differential consistency conditions for the hierarchical kernel functions are derived it serves as an indispensable instrument in establishing the interpolation error estimate which is theoretically proven and numerically validated for a special interpolant with different combinations of the hierarchical kernels a synchronized convergence effect may be observed being different from the conventional legendre function based p type hierarchical basis the new hierarchical basis is an intrinsic pseudo spectral basis which can remain as a partition of unity in a local region because the discrete wavelet kernels form a partition of nullity these newly developed kernels can be used as the multi scale basis to solve partial differential equations in numerical computation as a p type refinement copyright 1999 john wiley sons ltd

realizing hybrid synchronization of time delay hyperchaotic 4d systems via partial variables hybrid synchronization of time delay hyperchaotic 4d systems with different initial conditions is investigated via partial variables based on the lyapunov stability theory sufficient conditions are given to get the hybrid synchronization by constructing a novel lyapunov function in the form of exponential form it is proved that some partial state variables of two time delay hyperchaotic systems are anti synchronized while other state variables are complete synchronized when one or two linear controllers are imposed on the response system simultaneously the unknown parameters in the response system are also estimated completely numerical simulation results are presented to demonstrate the effectiveness of the proposed chaos synchronization scheme

trefoil symmetry ii another clover extension we construct a novel graded extension of the poincare group with integer spin multiplets as novel generators the extension involves z4 z4 graded parameters and produce space time translations through the composition of novel symmetric vector and scalar multiplets

kinematical superalgebras and lie algebras of order 3 we study and classify kinematical algebras which appear in the framework of lie superalgebras or lie algebras of order 3 all these algebras are related through generalized inonu wigner contractions from either the orthosymplectic superalgebra or the de sitter lie algebra of order 3

hopf algebras for ternary algebras we construct a universal enveloping algebra associated with the ternary extension of lie super algebras called lie algebra of order three a poincare birkhoff witt theorem is proven is this context it this then shown that this universal enveloping algebra can be endowed with a structure of hopf algebra the study of the dual of the universal enveloping algebra enables to define the parameters of the transformation of a lie algebra of order of 3 it turns out that these variables are the variables which generate the three exterior algebra

chaos and hypercyclicity for solution semigroups to some partial differential equations abstract we investigate the solution semigroup to some partial differential equations and give some sufficient conditions for the solution semigroup to be hypercyclic or chaotic

a general scheme for q s synchronization of chaotic systems with unknown parameters and scaling functions this work investigates q s synchronization of non identical chaotic systems with unknown parameters and scaling function the sufficient conditions for achieving q s synchronization with a double desired scaling function of two different chaotic systems including different dimensional systems are derived based on the lyapunov stability theory by the adaptive control technique the corresponding parameter update laws are proposed such that the q s synchronization of non identical chaotic systems is to be obtained two illustrative numerical simulations are also given to demonstrate the effectiveness of the proposed scheme

consistent pseudo derivatives in meshless methods a meshless petrov galerkin formulation is developed in which derivatives of the trial functions are obtained as a linear combination of derivatives of shepard functions a key contribution is the development of conditions on test functions and trial functions for nonintegrable pseudo derivatives for petrov galerkin method which pass the patch test numerical results show that the resulting method is substantially more accurate than the galerkin method with shepard approximants and exceeds the rate of convergence of linear finite elements

hypersymmetry a z3 graded generalization of supersymmetry we propose a generalization of non commutative geometry and gauge theories based on ternary z3 graded structures in the new algebraic structures we define all products of two entities are left free the only constraining relations being imposed on ternary products these relations reflect the action of the z3 group which may be either trivial i e abc bca cab generalizing the usual commutativity or non trivial i e abc jbca with j e 2 i 3 the usual z2 graded structures such as grassmann lie and clifford algebras are generalized to the z3 graded case certain suggestions concerning the eventual use of these new structures in physics of elementary particles and fields are exposed

generalized exclusion and hopf algebras we propose a generalized oscillator algebra at the roots of unity with generalized exclusion and we investigate the braided hopf structure we find that there are two solutions these are the generalized exclusions of the bosonic and fermionic types we also discuss the covariance properties of these oscillators

a singularity avoiding moving least squares scheme for two dimensional unstructured meshes moving least squares interpolation schemes are in widespread use as a tool for numerical analysis on scattered data in particular they are often employed when solving partial differential equations on unstructured meshes which are typically needed when the geometry defining the domain is complex it is known that such schemes can be singular if the data points in the stencil happen to be in certain special geometric arrangements however little research has specifically addressed this issue in this paper a moving least squares scheme is presented which is an appropriate tool for use when solving partial differential equations in two dimensions and the precise conditions under which singularities occur are identified the theory is used to develop a stencil building algorithm which automatically detects singular stencils and corrects them in an efficient manner while attempting to maintain stencil symmetry as closely as possible finally the scheme is applied in a convection diffusion equation solver and an incompressible navier stokes solver and the results are shown to compare favourably with known analytical solutions and previously published results

element free galerkin methods for static and dynamic fracture abstract element free galerkin efg methods are presented and applied to static and dynamic fracture problems efg methods which are based on moving least square mls interpolants require only nodal data no element connectivity is needed the description of the geometry and numerical model of the problem consists only of a set of nodes and a description of exterior boundaries and interior boundaries from any cracks this makes the method particularly attractive for growing crack problems since only minimal remeshing is needed to follow crack growth in moving least square interpolants the dependent variable at any point is obtained by minimizing a function in terms of the nodal values of the dependent variable in the domain of influence of the point numerical examples involving fatigue crack growth and dynamic crack propagation are presented to illustrate the performance and potential of this method

anti synchronization of uncertain unified chaotic systems with dead zone nonlinearity abstract this paper addresses chaos anti synchronization of uncertain unified chaotic systems with dead zone input nonlinearity using the sliding mode control technique and lyapunov stability theory a proportional integral pi switching surface is proposed to ensure the stability of the closed loop error system in sliding mode then a sliding mode controller smc is proposed to guarantee the hitting of the switching surface even with uncertainties and the control input containing dead zone nonlinearity some simulation results are included to demonstrate the effectiveness and feasibility of the proposed synchronization scheme

poincare and sl 2 algebras of order 3 in this paper we initiate a general classification for lie algebras of order 3 and we give all lie algebras of order 3 based on sl 2 c and iso 1 3 the poincare algebra in four dimensions we then set the basis of the theory of the deformations in the gerstenhaber sense and contractions for lie algebras of order 3

dynamic fracture using element free galerkin methods the element free galerkin method for dynamic crack propagation is described and applied to several problems this method is a gridless method which facilitates the modelling of growing crack problems because it does not require remeshing the growth of the crack is modelled by extending its surfaces the essential feature of the method is the use of moving least squares interpolants for the trial and test functions in these interpolants the dependent variable is obtained at any point by minimizing a weighted quadratic form involving the nodal variables within a small domain surrounding the point the discrete equations are obtained by a galerkin method the procedures for modelling dynamic crack propagation based on dynamic stress intensity factors are also described

dynamic modeling of chaos and turbulence abstract the series diophantus introduction to mathematical philosophy kalikasan manila 1993 nonlinear anal 30 8 1997 5021 5032 nonlinear stud 5 2 1998 227 254 nonlinear anal 35 8 1999 259 285 proc second int conf tool math model st petersburg 4 1999 74 89 proceedings of third international conference on differential equations st petersburg 2000 pp 71 86 probl nonlinear anal eng syst 7 1 2001 56 78 proceedings of third international conference on dynamic systems and applications atlanta 2001 pp 201 208 nonlinear anal 47 2001 5955 5966 probl nonlinear anal eng syst 7 2 2001 30 44 indian j pure appl math 32 10 2001 1539 1551 appl math comput 130 1 2001 145 169 indian j pure appl math 33 1 2003 111 129 appl math comput 138 2003 127 149 appl math comput 139 1 2003 23 36 recent results new inventions and new cosmology accepted probl nonlinear anal eng syst the new nonstandard analysis and intuitive calculus submitted for publication the philosophical and mathematical foundations of flt s resolution rectification and extension of underlying fields and applications accepted int j nonlinear differential equations extending the reach of computation submitted for publication the theory of learning implications for math science education and research submitted for publications columbia the crossroads for science accepted int j nonlinear differential equations dynamic modeling and applications proceedings of fourth international conference on tools for mathematical modeling 2003 st petersburg state technical university nonlinear anal phenomena 1 1 2004 1 23 and nonlinear anal phenomena 2 1 2005 15 30 introduced embellished developed and elaborated dynamic modeling and its principal mathematical component qualitative mathematics and used it to resolve long standing unsolved problems of mathematics and physics such as fermat s last theorem the gravitational n body problem goldbach s conjecture and the search for the basic constituent of matter among its major achievements is the development of the flux theory of gravitation ftg anchored on 42 laws of nature the paper considers the questions of chaos and turbulence and shows that gravity is turbulence specifically the dynamics of vortex flux of dark matter consisting of its basic constituent the superstring ftg explains our universe as a super super galaxy comprised of nested fractal sequences of vortices from our universe down through galaxy clusters galaxies stars planets moons and cosmic dust as vortex each term is self similar to our universe beyond the cosmic dust is the domain of quantum gravity forming nested fractal sequences of vortices each starting from a molecule e g protein down to the atom and primum crossing the boundary of visible matter we enter dark matter and find its basic constituent of nested fractal sequence of superstrings the paper notes three new laws of nature discovered in the course of resolving the puzzles surrounding the disastrous final flight of the columbia space shuttle int j nonlinear diff equations accepted finally using hubble s law and guided by ftg the rate of expansion of our universe and its acceleration are computed

an enhanced strain error estimator for galerkin meshfree methods based on stabilized conforming nodal integration gradient averaging type a posteriori error estimators applied to the finite element method enjoy great popularity in the engineering community this is mainly because they are easy in their construction and computer implementation and usually provide constant free and sharp error estimates on the expense of losing the bounding property however it proves difficult to transfer this error estimation procedure to galerkin meshfree methods one reason is that the meshfree gradient approximation is generally rather accurate per se and difficult to improve moreover in many galerkin meshfree methods the shape functions are no interpolants as required in the original idea of constructing the recovered and thus smooth gradient field in this paper a novel error estimation procedure is presented that is based on the enhanced assumed strain eas method and applied to the reproducing kernel particle method rkpm as a representative of galerkin meshfree methods the error estimator is naturally tailored to galerkin meshfree methods if stabilized conforming nodal integration scni is employed which provides two gradient fields a globally smooth one the compatible strain and a cellwise constant one the enhanced assumed strain it is shown that the difference the enhanced strain can be used to derive an error estimator that follows the notion of gradient averaging type error estimators and resolves its issues when applied to galerkin meshfree methods in addition the enhanced strain error estimator is even easier to implement and computationally less expensive than gradient averaging type error estimators numerical examples of engineering interest illustrate the performance of the enhanced strain error estimator presented in this paper

efg approximation with discontinuous derivatives a technique for incorporating discontinuities in derivatives into meshless methods is presented the technique enriches the approximation by adding special shape functions that contain discontinuities in derivatives the special shape functions have compact support which results in banded matrix equations the technique is described in element free galerkin context but is easily applicable to other meshless methods and projections numerical results for problems in one and two dimensions are reported 1998 john wiley sons ltd

design of a fuzzy sliding mode synchronization controller for two different chaos systems this investigation presents a fuzzy sliding mode technology for synchronizing two chaotic systems a method of designing a fuzzy sliding mode control fsmc is presented which utilizes a variable normalization factor fsmc is designed to guarantee the global asymptotic synchronization of state trajectories of two different chaotic systems the chaotic systems are numerically simulated to demonstrate the validity and feasibility of the proposed control structure

observability of lag synchronization of coupled chaotic oscillators lag synchronization is a recently discovered theoretical phenomenon where the dynamical variables of two coupled nonidentical chaotic oscillators are synchronized with a time delay relative to each other we investigate experimentally and numerically to what extent lag synchronization can be observed in physical systems where noise is inevitable our measurements and numerical computation suggest that lag synchronization is typically destroyed when the noise level is comparable to the amount of average system mismatch at small noise levels lag synchronization occurs in an intermittent fashion

fractional supersymmetry and fth roots of representations a generalization of super lie algebras is presented it is then shown that all known examples of fractional supersymmetry can be understood in this formulation however the incorporation of three dimensional fractional supersymmetry in this framework needs some care the proposed solutions lead naturally to a formulation of a fractional supersymmetry starting from any representation d of any lie algebra g this involves taking the fth roots of d in an appropriate sense a fractional supersymmetry in any space time dimension is then possible this formalism finally leads to an infinite dimensional extension of g reducing to the centerless virasoro algebra when g sl 2 r

trefoil symmetry iii the full clover extension we aim to approach a trefoil symmetry involving z4 z4 q graded parameters multiplets of generators of integer spin 2 with naive dimensions in the interval 0 1 the resulting full clover extension involves as particular subalgebras the minimal clover extensions previously obtained we address the introduction of further scalar dimensionless multiplets and central charges they could provide connections among external and internal symmetries perhaps after some graded symmetry breaking

an adaptive approach with the element free galerkin method abstract the element free galerkin method may be regarded as an alternative to the finite element method especially for problems with discontinuities e g crack propagation problems the efg method differs from the fem by using the moving least squares interpolation the behaviour of this interpolation is strongly influenced by a weighting function which rules the influence of nodal variables on variables in arbitrary spatial points with an appropriate selection of the weighting function derivatives of field functions of any desired order are continuous throughout the problem domain within the mls interpolation hence gradients of stresses and strains may be calculated throughout the problem domain with a high accuracy furthermore the configuration of nodes is quite flexible as nodes are not ordered by an element connectivity nodes are easily introduced moved or discarded the latter characteristics make the efg method especially suitable for adaptive schemes a scheme based on strain gradients is discussed in this paper it is applied to several linear and physically nonlinear problems with high stress resp strain gradients and singularities continued mesh refinement in areas of high gradients is derived the convergence behaviour is investigated for cases where analytical solutions are available

a generic design methodology for sliding mode control of switched systems abstract the aim of this paper is to present a generic methodology to design sliding mode controllers for multivariable switched systems affine in control such as dc dc power converters an original formulation of the so called reachability condition suitable for this class of systems is established based on the choice of a lyapunov like function and parameterized by a single weighting matrix it allows several kinds of control strategies to be derived namely conventional piecewise continuous strategies as well as discrete boolean strategies its application to the important subclass of linear time invariant systems is investigated more specifically in the boolean case the present approach is also compared to another hybrid one called the stabilizing approach eventually its efficiency as a design methodology as well as the performance of the resulting control are shown by simulating it on non trivial examples of power converters

z3 graded algebras and the cubic root of the supersymmetry translations a generalization of supersymmetry is proposed based on z3 graded algebras introducing the objects whose ternary commutation relations contain the cubic roots of unity e2 i 3 e4 i 3 and 1 the operators whose trilinear combinations yield the supersymmetric translation generators can be constructed cubic matrices forming a ternary algebra are the generalization of pauli s matrices the general properties of z3 grading some other representations of such algebras and their possible pertinence with regard to the quark model are briefly discussed

analysis of thin shells by the element free galerkin method a meshless approach to the analysis of arbitrary kirchhoff shells by the element free galerkin efg method is presented the shell theory used is geometrically exact and can be applied to deep shells the method is based on moving least squares approximant the method is meshless which means that the discretization is independent of the geometric subdivision into finite elements the satisfaction of the c1 continuity requirements is easily met by efg since it requires only c1 weights therefore it is not necessary to resort to mindlin reissner theory or to devices such as discrete kirchhoff theory the requirements of consistency are met by the use of a polynomial basis of quadratic or higher order a subdivision similar to finite elements is used to provide a background mesh for numerical integration the essential boundary conditions are enforced by lagrange multipliers membrane locking which is due to different approximation order for transverse and membrane displacements is removed by using larger domains of influence with the quadratic basis and by using quartic polynomial basis which can prevent membrane locking completely it is shown on the obstacle course for shells that the present technique performs well

quantum group covariance and the braided structure of deformed oscillators the connection between braided hopf algebra structure and quantum group covariance of the deformed oscillators is constructed explicitly in this context we provide deformations of the hopf algebra of functions on su 1 1 quantum subgroups and their representations are also discussed

improved xfem an extra dof free well conditioning and interpolating xfem abstract although its unprecedentedly success in approximating the singular field around a crack tip independent of mesh discretization xfem still has been long hindered in engineering applications by its ill conditioning and the difficulty in mass lumping corresponding to extra dofs an improved xfem i xfem is developed to overcome those difficulties from three aspects 1 to eliminate the linear dependence and the ill conditioning issues of the standard and the corrected xfems 2 to get rid of extra dofs in crack tip enrichment to facilitate optimal mass lumping in dynamic analyses 3 to be interpolating at enriched nodes to enable direct essential contact boundary treatments the core of i xfem is a globally interpolating approximation based on local least squares fitting the new method is numerically examined with comprehensive comparisons with the standard xfem and the corrected xfem fries 2008 the new method s excellent performance in terms of accuracy convergence and conditioning stability are demonstrated

generalization of n ary nambu algebras and beyond the aim of this paper is to introduce n ary hom algebra structures generalizing the n ary algebras of lie type including n ary nambu algebras n ary nambu lie algebras and n ary lie algebras and n ary algebras of associative type including n ary totally associative and n ary partially associative algebras we provide examples of the new structures and present some properties and construction theorems we describe the general method allowing one to obtain an n ary hom algebra structure starting from an n ary algebra and an n ary algebra endomorphism several examples are derived using this process also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three dimensional hom nambu lie structures with diagonal homomorphism

group theoretical foundations of fractional supersymmetry fractional supersymmetry denotes a generalization of supersymmetry which may be constructed using a single real generalized grassmann variable n 0 for arbitrary integer n 2 3 an explicit formula is given in the case of general n for the transformations that leave the theory invariant and it is shown that these transformations possess interesting group properties it is shown also that the two generalized derivatives that enter the theory have a geometric interpretation as generators of left and right transformations of the fractional supersymmetry group careful attention is paid to some technically important issues including differentiation that arise as a result of the peculiar nature of quantities such as

a new implementation of the element free galerkin method abstract element free galerkin methods efg are methods for solving partial differential equations with moving least squares interpolants efg methods require only nodal data no element connectivity is needed in a previous implementation of the efg method lagrange multipliers were used to enforce the essential boundary condition however the use of lagrange multipliers increases the cost of solving the linear algebraic equations a new implementation is developed based on a modified variational principle in which the lagrange multipliers are replaced at the outset by their physical meaning so that the discrete equations are banded in addition weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is eliminated numerical examples show that the present implementation effectively computes stress concentrations and stress intensity factors at cracks with very irregular arrangements of nodes the latter makes it very advantageous for modelling progressive cracking

lag synchronization of structurally nonequivalent chaotic systems with time delays abstract in this paper we investigate the synchronization of a class of structurally nonequivalent chaotic systems with time delays the nonequivalence could be parameter mismatches differences in the time delays or more complicated nonequivalent structures we give a unified approach via unidirectional and impulsive control to them achieving lag synchronization then we apply this method to typical time delay chaotic systems mackey glass and ikeda models the corresponding estimations are given lastly we compare the results with existing results

i q graded lie algebraic extensions of the poincare algebra constraints on i and q the constraints on the index set i and on the function q of the i q graded lie algebras over k containing the poincare lie algebra are studied by using the single grading model particular choices for i and q consistent with the found constraints are determined for k c gradings are then found for which i i z2 z4n z4n gre with n n and gre an abelian group these gradings provide a way for algebraic extensions of the poincare lie algebra beyond the z2 gradings of supersymmetry and supergravity in these algebraic extensions each other commuting space time parameter can either commute or anticommute with the further parameters of the i q graded super manifold different field representations can have with each other generalized commutative behavior beyond commutativity and anticommutativity

voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids natural neighbours are based on the voronoi diagram which partitions space into closest point regions the sibson and the laplace non sibsonian interpolants which are based on natural neighbours have shown promise within a galerkin framework for the solution of partial differential equations in this paper we focus on the laplace interpolant with a two fold objective first to unify the previous developments related to the laplace interpolant and to indicate its ties to some well known numerical methods and secondly to propose a voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids a conservation law in integral form is discretized on voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids the proposed scheme can also be viewed as a point collocation technique a detailed study on consistency is conducted and the satisfaction of the discrete maximum principle stability is established owing to symmetry of the laplace weight a symmetric positive definite stiffness matrix is realized which permits the use of efficient linear solvers on a regular rectangular or hexagonal grid the difference scheme reduces to the classical finite difference method numerical examples for the poisson equation with dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme copyright 2003 john wiley sons ltd

parafermions for higher order extensions of the poincare algebra and their associated superspace parafermions of orders 2 and 3 are shown to be the fundamental tool to construct superspaces related to cubic and quartic extensions of the poincare algebra the corresponding superfields are constructed and some of their main properties are analyzed in detail in this context the existence problem of operators acting like covariant derivatives is analyzed and the associated operators are explicitly constructed

higher order simple lie algebras it is shown that the non trivial cocycles on simple lie algebras may be used to introduce antisymmetric multibrackets which lead to higher order lie algebras the definition of which is given their generalised jacobi identities turn out to be satisfied by the antisymmetric tensors or higher order structure constants which characterise the lie algebra cocycles this analysis allows us to present a classification of the higher order simple lie algebras as well as a constructive procedure for them our results are synthesised by the introduction of a single complete brst operator associated with each simple algebra

mls moving least square based finite elements for three dimensional nonmatching meshes and adaptive mesh refinement abstract with the aid of moving least square mls approximation a new class of three dimensional finite elements are proposed for treating nonmatching meshes and adaptive mesh refinement for which the existing finite elements are hardly efficient with a special choice of the weight function supports and the base functions the method results in useful elements with the polynomial shape function for which the c 1 continuity breaks down on the boundaries between the neighboring subdomains comprising one element the effectiveness of the new elements in handling the discontinuities due to nonmatching interfaces and automatic mesh refinement is demonstrated via three dimensional examples

new concepts in meshless methods meshless methods have been extensively popularized in literature in recent years due to their flexibility in solving boundary value problems two kinds of truly meshless methods the meshless local boundary integral equation mlbie method and the meshless local petrov galerkin mlpg approach are presented and discussed both methods use the moving least squares approximation to interpolate the solution variables while the mlbie method uses a local boundary integral equation formulation and the mlpg employs a local symmetric weak form the two methods are truly meshless ones as both of them do not need a finite element or boundary element mesh either for purposes of interpolation of the solution variables or for the integration of the energy all integrals can be easily evaluated over regularly shaped domains in general spheres in three dimensional problems and their boundaries numerical examples presented in the paper show that high rates of convergence with mesh refinement are achievable in essence the present meshless method based on the lswf is found to be a simple efficient and attractive method with a great potential in engineering applications copyright 2000 john wiley sons ltd

chaos synchronization of lu dynamical system abstract chaos synchronization of two identical lu systems is studied theoretically and numerically three methods of chaos synchronization are applied in this study pecora and carroll one way coupling and adaptive control the sufficient conditions for achieving synchronization of two identical lu systems are derived by using lyapunov stability theory numerical simulations are presented to demonstrate the effectiveness of the proposed chaos synchronization schemes

on special classes of n algebras we define n algebras as linear spaces on which the internal composition law involves n elements m v n v it is known that such algebraic structures are interesting for their applications to problems of modern mathematical physics using the notion of a commutant of two subalgebras of an n algebra we distinguish certain classes of n algebras with reasonable properties semisimple abelian nilpotent solvable we also consider a few examples of n algebras of different types and show their properties

a general scheme for q s synchronization of chaotic systems abstract this paper addresses the q s synchronization between chaotic and or hyper chaotic systems based on the lyapunov stability theorem a general scheme for q s synchronization of chaotic and or hyper chaotic systems is proposed the drive and response systems discussed in this paper can be strictly different dynamical systems including different dimensional systems four illustrative numerical simulations are also given to demonstrate the effectiveness of the proposed general scheme for q s synchronization

two dimensional fractional supersymmetry from the quantum poincare group at roots of unity a group theoretical understanding of the two dimensional fractional supersymmetry is given in terms of the quantum poincaregroup at roots of unity the fractional supersymmetry algebra and the quantum group dual to it are presented and the pseudo unitary and irreducible representations of them are obtained the matrix elements of these representations are explicitly constructed

adaptive element free galerkin method applied to the limit analysis of plates the implementation of an h adaptive element free galerkin efg method in the framework of limit analysis is described the naturally conforming property of meshfree approximations with no nodal connectivity required facilitates the implementation of h adaptivity nodes may be moved discarded or introduced without the need for complex manipulation of the data structures involved with the use of the taylor expansion technique the error in the computed displacement field and its derivatives can be estimated throughout the problem domain with high accuracy a stabilized conforming nodal integration scheme is extended for use in error estimation and results in an efficient and truly meshfree adaptive method to demonstrate its effectiveness the procedure is then applied to plates with various boundary conditions

the braided heisenberg group the braided groups and braided matrices b r for the solution r of the yang baxter equation associated to the quantum heisenberg group are computed it is also shown that a particular extension of the quantum heisenberg group is dual to the heisenberg universal enveloping algebra uq h and this result is used to derive an action of uq h on the braided groups the various covariance properties are then demonstrated using the braided heisenberg group as an explicit example in addition the braided heisenberg group is found to be self dual finally a physical application to a system of n braided harmonic oscillators is discussed an isomorphism is found between the n fold braided and unbraided tensor products and the usual free time evolution is shown to be equivalent to an action of a primitive generator of uq h on the braided tensor product

combination of the meshless finite difference approach with the monte carlo random walk technique for solution of elliptic problems abstract this paper proposes a stochastic approach for the fast and effective numerical analysis of the second order elliptic differential equations it is based upon the well known monte carlo mc method with a random walk rw technique carried out on the grid of points this method allows for accurate estimation of the solution of the differential equation at selected point s of the domain and or its boundary it extends the standard formulation of the monte carlo random walk mc rw approach by means of its appropriate combination with the meshless version of the finite difference method in this manner the proposed approach may deal with elliptic equations in more general non homogeneous form as well as boundary conditions of both essential and natural types moreover arbitrarily irregular clouds of nodes may be used with no a priori imposed nodes structure therefore the meshless mc rw approach may be applied to the significantly wider class of problems with more complex geometry this concept was examined on variety of 2d boundary value problems selected numerical results are presented and discussed a simple matlab code is included as well

at roots of unity the quantum group at roots of unity is introduced by means of duality pairings with the quantum algebra its irreducible representations corresponding to the type of the quantum algebra are constructed through the universal t matrix the irreducible representations corresponding to the type are also found an invariant integral on this quantum group is given endowed with that some properties like unitarity and orthogonality of the irreducible representations are discussed

a braided interpretation of fractional supersymmetry in higher dimensions a many variable q calculus is introduced using the formalism of braided covector algebras its properties are discussed in detail and related to fractional supersymmetry when certain of its deformation parameters are roots of unity the special cases of two dimensional supersymmetry and fractional supersymmetry are developed in detail

trefoil symmetries i clover extensions beyond coleman mandula theorem a graded minimal lie algebraic extension of the space time symmetry is constructed involving only spin 1 multiplets as novel generators the extension involves z4 z4 graded parameters and generators it provides a bosonic analog to supersymmetry since the composition of three symmetric vector charges produces a space time translation there arise three noncommutative four dimensional manifolds with pseudometric

irreducible representations of the poincare parasuperalgebra we explicitly describe all the irreducible unitary representations of the poincare parasuperalgebra i e the parasupersymmetric extension of the lie algebra of the poincare group this parasuperalgebra includes as a particular case the usual poincare superalgebra and can serve as the group theoretical foundation of parasupersymmetric quantum field theory

a coupled interpolating meshfree method for computing sound radiation in infinite domain summary in this paper the coupling of the improved interpolating element free galerkin iiefg method and the variable order infinite acoustic wave envelope element wee method is studied a coupled iiefg wee method for computing sound radiation is proposed to make use of their advantages while evading their disadvantages the coupling is achieved by constructing the hybrid shape function of continuity and compatibility on the interface between the iiefg and wee domains in the iiefg domain the improved interpolating moving least squares iimls method is employed to form the shape functions satisfying the kronecker delta condition while nonsingular weight functions can be used the impacts of the size of the influence domain and the shape parameter on the performance of this coupled method are investigated the numerical results show that the coupled iiefg wee method can take full advantage of both the iiefg and wee methods and that it not only can achieve higher accuracy but also has a faster convergence speed than the conventional method of the finite element coupled with the wee the experimental results show that the method is very flexible for acoustic radiation prediction in the infinite domain this article is protected by copyright all rights reserved

a novel meshless scheme for solving surface integral equations with flat integral domains numerical solutions for electromagnetic em integral equations rely on the discretization of integral domains and the use of meshes for geometric description meshing geometries is very tedious especially for complicated structures with many details tiny parts and geometric discontinuities corners or edges and remeshing could be required in many scenarios to reduce the costs of generating quality meshes meshless or mesh free methods were developed and they have been extensively studied in mechanical engineering though there are less obvious interests in em community the meshless methods employ discrete nodes to replace meshes in the description of geometries but the background meshes for integrations are still needed traditionally in this work we first address the traditional meshless scheme for solving em integral equations based on the moving least square mls approximation for unknown currents and the use of background meshes for integrations and then develop a novel meshless scheme by applying the green s lemma to the em surface integral equations with flat domains the novel scheme transforms a surface integral over a flat domain into a line integral along its boundaries when excluding a singular patch in the domain since only the domain boundaries are discretized and no background meshes are needed the scheme is truly meshless numerical examples for em scattering by flat surface objects are presented to demonstrate the effectiveness of the novel scheme

meshless local petrov galerkin mlpg approximation to the two dimensional sine gordon equation during the past few years the idea of using meshless methods for numerical solution of partial differential equations pdes has received much attention throughout the scientific community and remarkable progress has been achieved on meshless methods the meshless local petrov galerkin mlpg method is one of the truly meshless methods since it does not require any background integration cells the integrations are carried out locally over small sub domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions in this paper the mlpg method for numerically solving the non linear two dimensional sine gordon sg equation is developed a time stepping method is employed to deal with the time derivative and a simple predictor corrector scheme is performed to eliminate the non linearity a brief discussion is outlined for numerical integrations in the proposed algorithm some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped sg equation is investigated the final numerical results confirm the ability of proposed method to deal with the unsteady non linear problems in large domains

chaos control and synchronization of unified chaotic systems via linear control chaos control and synchronization in the unified chaotic systems is discussed in this paper based on the stability theory of a cascade connected system control laws are presented to achieve chaos control and synchronization respectively the advantage of the proposed controllers is that they are linear and have lower dimensions than that of the states simulation results for lorenz lu and chen chaotic systems are provided to illustrate the effectiveness of the proposed scheme

interpolating element free galerkin method for the regularized long wave equation and its error analysis abstract combining the simplified interpolating moving least squares imls method with the galerkin weak form an interpolating element free galerkin iefg method is presented for the numerical study of the regularized long wave rlw equation the trial function in the imls method has one less unknown coefficient than in the traditional mls approximation and the shape functions satisfy the interpolating property at nodes then the iefg method can apply the essential boundary conditions naturally and directly and has high computational accuracy and then this paper studies the error estimates of the iefg method for rlw equation the error estimate of the semi discrete iefg method for the rlw equation on the influence domain radius is first studied and then the convergence rate of the full discrete scheme of the method on the influence domain radius and time step is studied the theoretical results show that the iefg method for rlw equation has good convergence rate for the purpose of demonstration three selected numerical examples are given to demonstrate the method and the mathematical theory of this paper