development of a genetic algorithm based lookup table approach for efficient numerical integration in the method of finite spheres with application to the solution of thin beam and plate problems it is observed that for the solution of thin beam and plate problems using the meshfree method of finite spheres gaussian and adaptive quadrature schemes are computationally inefficient in this paper we develop a novel technique in which the integration points and weights are generated using genetic algorithms and stored in a lookup table using normalized coordinates as part of an offline computational step during online computations this lookup table is used much like a table of gaussian integration points and weights in the finite element computations this technique offers significant reduction of computational time without sacrificing accuracy example problems are solved which demonstrate the effectiveness of the procedure copyright 2006 john wiley sons ltd

density of monodromy actions on non abelian cohomology abstract in this paper we study the monodromy action on the first betti and de rham non abelian cohomology arising from a family of smooth curves we describe sufficient conditions for the existence of a zariski dense monodromy orbit in particular we show that for a lefschetz pencil of sufficiently high degree the monodromy action is dense

arithmetic monodromy groups pinkham 12 showed that the monodromy groups of the 14 exceptional unimodular singularities can be characterized arithmetically using results of m kneser we proved in 4 that this is true for all singularities of arnold s list with certain exceptions see below the object of this note is to show that this is even true for almost all isolated hypersurface singularities more precisely we prove the following theorem

approximated stable inversion for nonlinear systems with nonhyperbolic internal dynamics a technique to achieve output tracking for nonminimum phase nonlinear systems with nonhyperbolic internal dynamics is presented the present paper integrates stable inversion techniques that achieve exact tracking with approximation techniques that modify the internal dynamics to circumvent the nonhyperbolicity of the internal dynamics this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques the theory is developed for nonlinear systems and the method is applied to a two cart with inverted pendulum example

an element free galerkin approach for rigidflexible coupling dynamics in 2d state based on an improved element free galerkin efg method and the geometric nonlinear elastic theory an element free numerical approach for rigidflexible coupling dynamics of a rotating hubbeam system is implemented using the hamilton principle the coupled nonlinear integral differential governing equations are derived in which the dynamic stiffening effect is expressed by the longitudinal shrinking of the beam induced by the transverse displacement by the efg method where the global interpolating moving least squares imls and generalized moving least squares igmls were used for discretizing the longitudinal and transverse deformation variables respectively the spatially element free discretized dynamic equations of the system are obtained and the newmark scheme was selected as the time integration method for the numerical computation the superiority of the global interpolating property makes the ease for imposing both displacement and derivative boundary conditions the transverse bending vibration and structural dynamics of the flexible beam in non inertial system are analyzed in the numerical simulations and influence parameters of the efg method are also fully discussed simulation results verify the feasibility of the improved efg approach for rigidflexible coupling dynamics

non matching mesh gluing by meshless interpolation an alternative to lagrange multipliers rewards of using non matching meshes are great in many aspects sub meshing a complex structure in a sub structure wise manner separately and or in parallel selective local refinement unlimited scalability guarantee for generating meshes in increasingly large scale finite element simulation etc however when meshes do not match a gluing algorithm is required to enforce inter domain continuity non matching terminologically originates from mesh discretization in nature and the non matching mesh issue is therefore avoidable or does not exist in a node based or meshless discretization in meshless methods motivated by this a gluing algorithm is developed based on meshless interpolation the gluing is accomplished by continuous trial and test functions across non matching meshes constructed using nodes only the developed gluing algorithm is tested in static and wave propagation problems in two and three dimensions it is demonstrated that the gluing algorithm does not deteriorate convergence and accuracy compared with the one piece conforming mesh compared with lagrange multiplier gluing one of the most common approaches the current algorithm has two significant benefits 1 easier implementation in any dimension and 2 positive definite banded system matrices not acting against equation solvers and hence better suited for large scale finite element analysis

the deformations of the simple space curve singularities in 4 and 5 marc giusti classified the simple isolated complete intersection singularities of positive dimension he showed that besides the simple hypersurface singularities there are only simple singularities of curves in complex 3 space he gave a list of adjacencies between these singularities later v v goryunov see 6 found some additional adjacencies but the complete list remained unknown see 1 p 23 in this note we prove the following theorem theorem the following diagram shows the complete list of adjacencies between the simple space curve singularities which are not hypersurface singularities here giusti s list is completed by the deformations z10 t9 and z10 u9 s5 s6 s7 s8 s9

arithmeticity of certain symplectic hypergeometric groups we give a sufficient condition on a pair of primitive polynomials that the associated hypergeometric group monodromy group of the corresponding hypergeometric differential equation is an arithmetic subgroup of the integral symplectic group

the griffiths group of a general calabi yau threefold is not finitely generated j 2k 1 x h 2k 1 x c f k h 2k 1 x h 2k 1 x z where f k h 2k 1 x is the set ofclasses representable by a closed form in f k a 2k 1 x that is which is locally ofthe form i j i j dzi dzj with i j 2k 1 and i k griffiths 9 has defined the abel jacobi map k k x j 2k 1 x where k x is the group ofcodimension k algebraic cycles homologous to zero on x using the identification j 2k 1 x f n k 1 h 2n 2k 1 x h2n 2k 1 x z n dim x

variational multiscale element free galerkin vmefg and local discontinuous galerkin ldg methods for solving two dimensional brusselator reaction diffusion system with and without cross diffusion abstract the finite element method fem is one of the basic methods for solving deterministic and stochastic partial differential equations this method is proposed in the 19 decade and after years several modifications for this well known technique such as mortal fem discontinuous galerkin fem extended fem least squares fem spectral fem mixed fem immersed fem adaptive fem etc have been proposed also for improving the accuracy and for considering complex domain shape functions of the moving least squares approximation have been replaced with the traditional shape function of the finite element technique the name of this improved method is element free galerkin efg method which is classified in the category of meshless methods the efg method has been applied for solving many problems in engineering in the current paper we select two numerical procedures that are extracted from fem the discontinuous galerkin approach is a useful technique for solving problems that their exact solutions have discontinuity it should be noted that many enriched ideas have been explained for improving accuracy of efg method in the current paper the local discontinuous galerkin and variational multiscale efg methods are applied for obtaining numerical solution of two dimensional brusselator system with and without cross diffusion the brusselator system is a theoretical model for a type of autocatalytic reaction up to best of authors knowledge the accuracy of the obtained numerical solutions using local discontinuous galerkin method is very related to the used time discrete scheme therefore fourth order exponential time differencing method has been employed for discretizing the time variable also to achieve a full discretization scheme the local discontinuous galerkin finite element method is used moreover several test problems are given that show the acceptable accuracy and efficiency of the proposed schemes

new large rank nichols algebras over nonabelian groups with commutator subgroup z2 abstract in this article we explicitly construct new finite dimensional indecomposable nichols algebras with dynkin diagrams of type a n c n d n e 6 7 8 f 4 over any group g of order 2 l with commutator subgroup isomorphic to z 2 the construction is generic in the sense that the type just depends on the rank and center of g and thus positively answers for all groups of this class a question raised by susan montgomery in 1995 22 4 our construction uses the new notion of a covering nichols algebra as a special case of a covering hopf algebra 18 and produces non faithful nichols algebras we give faithful examples of doi twists for type a 3 c 3 d 4 c 4 f 4 over several nonabelian groups of order 16 and 32 these are hence the first known examples of nondiagonal finite dimensional indecomposable nichols algebras of rank 2 over nonabelian groups

a meshfree level set method for topological shape optimization of compliant multiphysics actuators abstract this paper proposes a topology optimization method for compliant multiphysics actuators of geometrically nonlinear structures using meshfree galerkin weak forms and level set methods the design boundary is implicitly represented as the zero level set of a higher dimensional level set function leading to a level set model capable of handling complex shape and topological changes with flexibilities a family of compactly supported radial basis functions csrbfs is firstly used to interpolate the level set function of lipschitz continuity and then augmented to construct the shape function for meshless approximation by satisfying basic requirements in particular the predetermined consistency and the kronecker delta function property a meshless galerkin method mgm with global weak forms is established to implement the discretization of the state equations the design of actuators is transformed into an easier size optimization from a more difficult shape and topology optimization the design boundary evolution is just a question of advancing the discrete level set function in time by updating the design variables of the size optimization compared to most conventional level set methods the proposed meshless level set method is able to implement the free moving boundary discontinuities without remeshing and unify two different numerical procedures in propagating the discrete level set function e g eulerian grid and approximating the state equation e g lagrangian mesh respectively this method can also avoid numerical difficulties in solving a series of complicate hamilton jacobi partial differential equations pdes with explicit time schemes two typical numerical examples are used to demonstrate the effectiveness of the proposed method

local stabilization of minimum phase nonlinear systems abstract in this note we briefly review the notion of a nonlinear minimum phase system i e a system which when constrained in such a way as to produce zero output evolves with an asymptotically stable dynamics the main purpose of the paper is to show that any minimum phase nonlinear system can always be locally stabilized by smooth state feedback

local heaviside weighted mlpg meshless method for two dimensional solids using compactly supported radial basis functions abstract compactly supported radial basis functions csrbf are employed for constructing trial functions in the local heaviside weighted meshless local petrov galerkin method for stress analysis of two dimensional solids where the heaviside step function is used as the weighting function over a local sub domain the present method is a truly meshless method based only on a number of randomly located nodes no domain integration is needed no element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions effects of the sizes of local sub domain and interpolation domain on the performance of the present method are investigated in this paper the size of the support of the basis function has been treated as a shape parameter and then the behaviour of this shape parameter has been systematically studied for six different csrbfs example problems in elastostatics are presented and compared with closed form solutions results show that the proposed method is highly accurate and possesses no numerical difficulties

indecomposable higher chow cycles on jacobians we construct some natural indecomposable elements of ch g j c 1 with trivial regulator and in particular prove that ch g ind j c 1 mb q is uncountable for c a generic curve or a generic hyperelliptic curve of genus g geq 3

on the griffiths group of the cubic sevenfold for x a smooth complex projective variety one of the important questions in algebraic geometry is the existence and the behaviour of non trivial subvarieties on x i e subvarieties that are not the intersection of x with a hypersurface in general the approach is as follows we let zd x be the free abelian group generated by the irreducible subvarieties of codimension d in x and introduce various equivalence relation on zd x the problem is then to understand the quotients of zd x under these relations the first and most obvious is homological equivalence but there are other interesting relations namely algebraic and rational equivalence the so called classical cases when d 1 divisors or d dimx 0 cycles are well understood but little is known in general in these cases homological and algebraic equivalence coincide and the group of cycles algebraically equivalent to zero modulo rational equivalence is isomorphic to an abelian variety one of the first result for general d is due to griffiths 8 who showed that homological and algebraic equivalence do not coincide if d 1 dimx the group of cycles on x of codimension d homologous to zero modulo algebraic equivalence is called the d th griffiths group of x and is denoted by gd x we will mainly consider the q vector space g6 x gd x q or equivalently the griffiths group modulo torsion clemens 5 then showed that g6 x can have infinite dimension over q clemens example is given by a general quintic hypersurface in p4 and this opened the way to the construction of other examples see 11 21 131 17

torsion algebraic cycles and complex cobordism atiyah and hirzebruch gave the first counterexamples to the hodge conjecture with integral coefficients 3 that conjecture predicted that every integral cohomology class of hodge type p p on a smooth projective variety should be the class of an algebraic cycle but atiyah and hirzebruch found additional topological properties which must be satisfied by the integral cohomology class of an algebraic cycle here we provide a more systematic explanation for their results by showing that the classical cycle map from algebraic cycles modulo algebraic equivalence to integral cohomology factors naturally through a topologically defined ring which is richer than integral cohomology the new ring is based on complex cobordism a well developed topological theory which has been used only rarely in algebraic geometry since hirzebruch used it to prove the riemann roch theorem 17 this factorization of the classical cycle map implies the topological restrictions on algebraic cycles found by atiyah and hirzebruch it goes beyond their work by giving a topological method to show that the classical cycle map can be noninjective as well as nonsurjective the kernel of the classical cycle map is called the griffiths group and the topological proof here that the griffiths group can be nonzero is the first proof of this fact which does not use hodge theory the proof here gives nonzero torsion elements in the griffiths group whereas griffiths s hodge theoretic proof gives nontorsion elements 13 this topological argument also gives examples of algebraic cycles in the kernel of various related cycle maps where few or no examples were known before thus answering some questions posed by colliot thelene and schoen 8 p 14 37 p 13 colliot thelene asked in particular whether the map ch2 x n h4 x z n is injective for all smooth complex projective varieties x here ch x is the group of codimension i algebraic cycles modulo rational equivalence the first examples where colliot thelene s map is not injective were found by kollar and van geemen see 4 p 135 very recently bloch and esnault found examples defined over number fields 7 over nonalgebraically closed fields k there are other examples of smooth projective varieties xk with ch2 xk n hg4t xk z n not injective due to colliot thelene and sansuc as reinterpreted by salberger see 9 and 8 remark 7 6 1 and parimala and suresh 31 these elements of ch2 xk n are not shown to remain nonzero in ch2 xc n however here our topological 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

lefschetz theorems for torsion algebraic cycles in codimension 2 abstract let y be a smooth projective variety over c and x be a smooth hypersurface in y we prove that the natural restriction map on chow groups of codimension two cycles is an isomorphism when restricted to the torsion subgroups provided dim y 5 we prove an analogous statement for a very general hypersurface x p 4 of degree 5 in the more general setting of a very general hypersurface x of sufficiently high degree in a fixed smooth projective four fold y under some additional hypothesis we prove that the restriction map is an isomorphism on l primary torsion for almost all primes l as a consequence we obtain a weak lefschetz theorem for torsion in the griffiths groups of codimension 2 cycles and prove the injectivity of the abel jacobi map when restricted to torsion in this griffiths group thereby providing a partial answer to a question of nori

motives and filtrations on chow groups in this paper sequential to sa we discuss a philosophy of bloch and beilinson concerning filtrations on chow groups of algebraic vareties which provides us with a good understanding on the structure of at least certain portions of chow groups let k be a fixed ground field and let c be the category of smooth projective schemes over k with a fixed suitable weil cohomology theory cf notations x in mathcal c rightsquigarrow h x mathop oplus limits i in z h i x

a local point interpolation method for static and dynamic analysis of thin beams abstract the local point interpolation method lpim is a newly developed truly meshless method based on the idea of meshless local petrov galerkin mlpg approach in this paper a new lpim formulation is proposed to deal with fourth order boundary value and initial value problems for static and dynamic analysis stability free vibration and forced vibration of beams local weak forms are developed using weighted residual method locally in order to introduce the derivatives of the field variable into the interpolation scheme a technique is proposed to construct polynomial interpolation with kronecker delta function property based only on a group of arbitrarily distributed points because the shape functions so obtained possess delta function property the essential boundary conditions can be implemented with ease as in the conventional finite element method fem the validity and efficiency of the present lpim formulation are demonstrated through numerical examples of beams under various loads and boundary conditions

stable inversion for nonlinear nonminimum phase time varying systems we extend stable inversion to nonlinear time varying systems and study computational issues the technique is applicable to minimum phase as well as nonminimum phase systems the inversion technique is new even in the linear time varying case and relies on partitioning the dichotomic split of the linearized system dynamics into time varying stable and unstable submanifolds this dichotomic split is used to build time varying filters which are in turn the basis of a contraction used to find a bounded inverse input state trajectory finding the inverse input state trajectory allows the development of exact output tracking controllers the method is local to the time varying trajectory and requires that the internal dynamics vary slowly however the method represents a significant advance relative to presently available tracking controllers present techniques are restricted to time invariant nonlinear systems and in the general case track only asymptotically

inversion of nonlinear time varying systems a procedure for inverting nonlinear systems that presents some computational advantages when applied to flexible robot arms or more generally to mechanical structures is given the procedure is presented in a general setting for nonlinear time varying systems an iterative algorithm that computes a smooth controlled invariant time varying manifold the mathematical properties of which are illustrated and exploited is also proposed an application to a flexible two link manipulator illustrates the algorithm and its computational advantages

proper orthogonal decomposition variational multiscale element free galerkin pod vmefg meshless method for solving incompressible navier stokes equation abstract recently because of simplicity of meshless methods they have been employed for solving many partial differential equations one of the meshless methods is element free galerkin technique the element free galerkin is very similar to the finite element method with this difference that the test and trial spaces of efg procedure are shape functions of moving least squares approximation using the mentioned shape functions solving a problem on a complex domain is very simple some researchers proposed several modifications and enriched approaches for improving the element free galerkin method that one of them is variational multiscale element free galerkin procedure up to the best of authors knowledge the element free galerkin method based on the shape functions of moving least squares approximation needs more cpu time than the element free galerkin method based on the shape functions of moving kriging interpolation thus in the current paper we employ the variational multiscale element free galerkin based on the shape functions of moving kriging interpolation also for reducing the cpu time of the presented numerical scheme we use the proper orthogonal decomposition pod approach therefore in the current paper we propose the proper orthogonal decomposition variational multiscale element free galerkin pod vmefg method for solving time dependent incompressible navier stokes equation moreover several test problems are given that show the acceptable accuracy and efficiency of the proposed scheme

a point interpolation method for two dimensional solids a point interpolation method pim is presented for stress analysis for two dimensional solids in the pim the problem domain is represented by properly scattered points a technique is proposed to construct polynomial interpolants with delta function property based only on a group of arbitrarily distributed points the pim equations are then derived using variational principles in the pim the essential boundary conditions can be implemented with ease as in the conventional finite element methods the present pim has been coded in fortran the validity and efficiency of the present pim formulation are demonstrated through example problems it is found that the present pim is very easy to implement and very flexible for obtained displacements and stresses of desired accuracy in solids as the elements are not used for meshing the problem domain the present pim opens new avenues to develop adaptive analysis codes for stress analysis in solids and structures copyright 2001 john wiley sons ltd

a matrix triangularization algorithm for the polynomial point interpolation method a novel matrix triangularization algorithm mta is proposed to overcome the singularity problem in the point interpolation method pim using the polynomial basis and to ensure stable and reliable construction of pim shape functions the present algorithm is validated using several examples and implemented in the local point interpolation method lpim that is a truly meshfree method based on a local weak form numerical examples demonstrate that lpim using the present mta are very easy to implement and very robust for solving problems of computational mechanics it is shown that pim with the present mta is very effective in constructing shape functions most importantly pim shape functions possess kronecker delta function properties parameters that influence the performance of them are studied in detail the convergence and efficiency of them are thoroughly investigated

numerical study of three dimensional turing patterns using a meshless method based on moving kriging element free galerkin efg approach in this paper a numerical procedure is presented for solving a class of three dimensional turing system first we discrete the spatial direction using element free galerkin efg method based on the shape functions of moving kriging interpolation then to achieve a high order accuracy we use the fourth order exponential time differencing runge kutta etdrk4 method using this discretization for the temporal dimension we obtain an explicit scheme and do not need to solve nonlinear system of equations the efg method uses a weak form of the considered equation that is similar to the finite element method with the difference that in the efg method test and trial functions are moving least squares approximation mls shape functions since the shape functions of moving least squares mls approximation do not have kronecker delta property we cannot implement the essential boundary condition directly also building shape functions of mls approximation is a time consuming procedure because of the mentioned reasons we employ the shape functions of moving kriging interpolation technique which have the mentioned property and less cpu time is required for building them for testing this method on three dimensional pdes we select some equations and system of pdes such as allen cahn gray scott ginzburg landau brusselator models predator prey model with additional food supply to predator several test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed scheme

development of a novel meshless local kriging lokriging method for structural dynamic analysis this paper presents a novel meshless approach to study the dynamic responses of structures it is called local kriging lokriging method where the kriging interpolation is employed to construct the field approximation function and meshless shape functions and the local weak form of partial differential governing equations is derived by the weighted residual technique since the shape functions constructed by this interpolation possess the delta function property even for a set of randomly distributed points the essential boundary condition can be easily imposed in implementation of local weak form the spline function with high continuity is used as the weight function no mesh is required either for integration of the local weak form or for construction of the shape functions thus the present lokriging method is a truly meshless method several numerical examinations for the free forced vibrational analysis of structures and the dynamic performance of microelectromechanical systems mems device are carried out to demonstrate the accuracy and efficiency of the lokriging method the numerical results show that the presently developed method is quite easy to implement very accurate and highly efficient for the problems considered

nonlinear inversion based output tracking an inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory in the case of minimum phase systems the trajectory produced agrees with that generated by hirschorn s inverse dynamic system however the preimage trajectory is noncausal rather than unstable in the nonminimum phase case in addition the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case with the addition of stabilizing feedback to the preimage trajectory asymptotically exact output tracking is achieved tracking is demonstrated with a numerical example and compared to the well known byrnes isidori regulator rather than solving a partial differential equation to construct a regulator the inverse is calculated using a picard like interaction when preactuation is not possible noncausal inverse trajectories can be truncated resulting in the tracking error transients found in other control schemes

cohomologie non ramifiee et conjecture de hodge entiere en nous appuyant sur la conjecture de bloch kato en k theorie de milnor nous etablissons un lien general entre le defaut de la conjecture de hodge entiere pour la cohomologie de degre 4 et le troisieme groupe de cohomologie non ramifiee a coefficients q z ceci permet de montrer que sur un solide en anglais threefold uniregle le troisieme groupe de cohomologie non ramifiee a coefficients q z s annule ce que la k theorie algebrique ne permet d obtenir que dans certains cas ceci permet a l inverse de deduire d exemples ayant leur source en k theorie que la conjecture de hodge entiere pour la cohomologie de degre 4 peut etre en defaut pour les varietes rationnellement connexes pour certaines familles a un parametre de surfaces on etablit un lien entre la conjecture de hodge entiere et l indice de la fibre generique

lawson homology for varieties with small chow groups and the induced filtration on the griffiths groups these groups form an intriguing set of invariants despite the vast literature on this subject the groups have been calculated only in very few cases such as for the projective spaces one of the goals of this note is to understand these invariants in case the variety has few cycles in the sense that rational and homological equivalence coincide for all m cycles up to a certain rank m s actually the results only deal with that part of lawson homology that is not visible in ordinary homology in that it is in the kernel of the cycle class maps cm k 2m lmhk 2m x hk 2m x

brief optimal noncausal set point regulation of scalar systems this paper presents a novel system inversion approach to the set point regulation of linear scalar minimum phase systems this approach uses closed form expressions of cause effect pairs that make possible an arbitrarily smooth transition between two given output set points the cause effect pairs are based on the introduced concept of transition polynomials simple optimization procedures are then proposed to solve the relevant optimal output synthesis and optimal input synthesis the potentiality of the method is highlighted by the examples presented namely a synthesis of elevator velocity profiles and the performance improving of a pid controller

two dimensional linear elasticity by the boundary node method abstract this paper presents a further development of the boundary node method bnm for 2 d linear elasticity in this work the boundary integral equations bie for linear elasticity have been coupled with moving least square mls interpolants this procedure exploits the mesh less attributes of the mls and the dimensionality advantages of the bie as a result the bnm requires only a nodal data structure on the bounding surface of a body a cell structure is employed only on the boundary in order to carry out numerical integration in addition the mls interpolants have been suitably truncated at corners in order to avoid some of the oscillations observed while solving potential problems by the bnm mukherjee and mukherjee 1997a numerical results presented in this paper including those for the solution of the lame and kirsch problems show good agreement with analytical solutions

a new approach to the zero dynamics assignment problem for nonlinear discrete time systems using functional equations the present research work aims at the development of a systematic method to arbitrarily assign the zero dynamics of a nonlinear discrete time real analytic system by constructing the requisite synthetic output maps the problem under consideration is motivated by the need to adequately address the control problem of nonminimum phase nonlinear discrete time systems since the latter represent a rather broad class of systems due to the well known effect of sampling on the stability of zero dynamics in the proposed approach the above control objective can be attained through i a systematic computation of synthetic output maps that induce minimum phase behavior while being statically equivalent to the original output maps both vanish on the equilibrium manifold and ii the subsequent integration into the methodological framework of currently available nonminimum phase compensation schemes for nonlinear discrete time systems that rely on output redefinition the mathematical formulation of the zero dynamics assignment problem is realized via a system of nonlinear functional equations and a rather general set of necessary and sufficient conditions for solvability is derived the solution to the above system of functional equations can be proven to be locally analytic and this enables the development of a solution method that is easily programmable with the aid of a symbolic software package the synthetic output maps that induce the prescribed zero dynamics for the original nonlinear discrete time system can be explicitly computed on the basis of the solution to the aforementioned system of functional equations

asymptotic state tracking in a class of nonlinear systems via learning based inversion describes a learning approach to asymptotic state tracking in a class of nonlinear systems the tracking problem considered concerns the case when the tracking error dynamics are described by a set of time varying nonlinear differential equations which are periodic in time with a known period our iterative update scheme is based on the specific property that the learning system tends to oscillate in steady state in fact our approach extends in a very natural manner the idea of the well known iterative learning control for the case of finite time tracking problems to the case of infinite time asymptotic tracking problems the best advantage of the proposed leaning approach is that it is computationally simple and does not require one to solve any complicated equations based on full system dynamics we explore the conditions under which a periodic nonlinear system exhibits a steady state oscillation our work also can be viewed to provide a learning based solution to the input state inversion problem the generality and practicality of our work is demonstrated through rigorous performance analysis and simulation using a robot manipulator

a meshless local kriging method for large deformation analyses in this paper a well developed meshless numerical technique local kriging lokriging method is used to develop the lokriging formulation for the large deformation problems which are geometrically nonlinear this is the first work for the geometrically nonlinear analyses by this meshless local weak form method in the lokriging method the kriging interpolation is employed to construct the meshless shape functions the spline function with high continuity is used as the weight function the discrete equations of the large deformation analysis for two dimensional solids are obtained using the local weak forms and based on the total lagrangian tl approach the presently developed lokriging method is a truly meshless method as it does not require the mesh either for the construction of the shape functions or for the integration of the local weak form several numerical examples of the two dimensional geometrically nonlinear analysis are presented to illustrate the performance of the present lokriging method the present nonlinear lokriging formulation is also used for the large deformation analysis of the microelectromechanical systems mems device the numerical results are compared with the experimental results very good results are obtained all these applications have demonstrated that the present lokriging method is very effective for the large deformation analyses because it avoids all mesh distortion issues

motivic random variables and representation stability ii hypersurface sections abstract we prove geometric and cohomological stabilization results for the universal smooth degree d hypersurface section of a fixed smooth projective variety as d goes to infinity we show that relative configuration spaces of the universal smooth hypersurface section stabilize in the completed grothendieck ring of varieties and deduce from this the stabilization of the hodge euler characteristic of natural families of local systems constructed from the vanishing cohomology we prove explicit formulas for the stable values using a probabilistic interpretation along with the natural analogs in point counting over finite fields we explain how these results provide new geometric examples of a weak version of representation stability for symmetric symplectic and orthogonal groups this interpretation of representation stability was studied in the prequel 20 for configuration spaces

a sub domain smoothed galerkin method for solid mechanics problems summary a sub domain smoothed galerkin method is proposed to integrate the advantages of mesh free galerkin method and fem arbitrarily shaped sub domains are predefined in problems domain with mesh free nodes in each sub domain based on mesh free galerkin weak formulation the local discrete equation can be obtained by using the moving kriging interpolation which is similar to the discretization of the high order finite elements strain smoothing technique is subsequently applied to the nodal integration of sub domain by dividing the sub domain into several smoothing cells moreover condensation of dof can also be introduced into the local discrete equations to improve the computational efficiency the global governing equations of present method are obtained on the basis of the scheme of fem by assembling all local discrete equations of the sub domains the mesh free properties of galerkin method are retained in each sub domain several 2d elastic problems have been solved on the basis of this newly proposed method to validate its computational performance these numerical examples proved that the newly proposed sub domain smoothed galerkin method is a robust technique to solve solid mechanics problems based on its characteristics of high computational efficiency good accuracy and convergence copyright 2014 john wiley sons ltd

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

primitive cohomology and the tube mapping let x be a smooth complex projective variety of dimension d we show that its primitive cohomology in degree d is generated by certain tube classes constructed from the monodromy in the family of all hyperplane sections of x the proof makes use of a result about the group cohomology of certain representations that may be of independent interest

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

should model based inverse inputs be used as feedforward under plant uncertainty bounds on the size of the plant uncertainties are found such that the use of the inversion based feedforward input improves the output tracking performance when compared to the use of feedback alone the output tracking error is normalized by the size of the desired output and used as a measure of the output tracking performance the worst case performance is compared for two cases 1 with the use of feedback alone and 2 with the addition of the feedforward input it is shown that inversion based feedforward controllers can lead to performance improvements at frequencies w where the uncertainty spl delta jw in the nominal plant is smaller than the size of the nominal plant g sub 0 jw divided by its condition number k sub g0 jw i e spl par spl delta jw spl par sub 2 spl par g sub 0 jw spl par sub 2 k sub g0 jw a modified feedforward input is proposed that only uses the model information in frequency regions where plant uncertainty is sufficiently small the use of this modified inverse with any feedback results in improvement of the output tracking performance when compared to the use of the feedback alone

element free galerkin methods in combination with finite element approaches element free galerkin efg methods are methods for solving partial differential equations with the help of shape functions coming from moving least squares approximation the efg method is more flexible than the finite element fe method since it requires only nodal data and no element connectivity is needed because the efg method is computationally expensive combinations of the efg method and the fe method are considered implementations based on several weak forms of the problem description are studied numerical examples in elastostatics and fracture mechanics show that the implementations are able to compute both displacement and stress fields accurately

brief iterative learning control for linear discrete time nonminimum phase systems this paper investigates iterative learning control for linear discrete time nonminimum phase systems first iterative learning control with advanced output data is considered for maximum phase systems next the results are extended to nonminimum phase systems the stability of the inverse mapping from the desired output to the input is proven based on the results for maximum phase systems the input should be updated with the output which is more advanced than the input by the sum of the relative degree of the system and the number of nonminimum phase zeros an example is given to indicate the importance of proper advances of output in the input update law

a modified algorithm for invertibility in nonlinear systems the algorithm of hirschorn 1 for the construction of inverses of nonlinear systems is modified and new sufficient conditions for invertibility and inverse system for a larger class of systems are obtained for the systems which do not satisfy the invertibility conditions a characterization of input space on which the input output map is injective is derived

generalized abel jacobi map on lawson homology we construct an abel jacobi type map on the homologically trivial part of lawson homology groups it generalizes the abel jacobi map constructed by griffiths by using a result of h clemens we answer affirmatively the question whether there exists a smooth projective complex variety with infinitely generated lawson homology groups l ph 2p k x bbb q when k0 as a corollary we find for any nonnegative integer j a smooth complex projective variety x carrying infinitely generated semi topological k groups k sst j x bbb q

an efficient rpim for simulating wave motions in saturated porous media an efficient meshless technique for simulating wave motions in saturated porous media is introduced in this paper using radial point interpolation method rpim and considering the precision requirement in wave motion simulation a lumped mass rpim for saturated porous media with clear physical concepts is derived combining explicit time integration with the lumped mass rpim leads to a decoupled radial point interpolation method decoupled rpim for dynamic analysis without solving algebra equation set a two dimensional problem is calculated by the proposed decoupled rpim the ordinary rpim and the finite element method fem the accuracy and efficiency of these methods are compared which demonstrate that the proposed decoupled rpim has comparable accuracy with the ordinary rpim and the finite element method but has high efficiency in simulating wave motions in saturated porous media

meshless analysis of timoshenko beams based on a locking free formulation and variational approaches abstract a meshless method is developed based on subdomain variational formulations and a local petrov galerkin approximation along with the locking free formulation for the analysis of bending of a thick beam the local point interpolation method is employed to construct both trial and test functions the present method is a truly meshless method based only on a number of randomly located nodes no global background integration mesh is needed no element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions effects of the sizes of local subdomain and interpolation domain on the performance of the present method are investigated problems of thick and thin beams under various loading and boundary conditions are analysed by the proposed method and the numerical results are compared with analytical solutions the contact problem for beam by means of subdomain variational inequalities and the meshless method has also been investigated

noether lefschetz locus for beilinson hodge cycles i we discuss the noether lefschetz locus for beilinson s hodge cycles here beilinson s hodge cycles mean the cohomology class of bloch s higher chow cycles on smooth varieties the main result is to give an estimate of the dimension of the maximal component of the noether lefschetz locus for the universal family of open complete intersections

an element free smoothed radial point interpolation method efs rpim for 2d and 3d solid mechanics problems abstract this paper presents a novel element free smoothed radial point interpolation method efs rpim for solving 2d and 3d solid mechanics problems the idea of the present technique is that field nodes and smoothing cells scs used for smoothing operations are created independently and without using a background grid which saves tedious mesh generation efforts and makes the pre process more flexible in the formulation we use the generalized smoothed galerkin gs galerkin weak form that requires only discrete values of shape functions that can be created using the rpim by varying the amount of nodes and scs as well as their ratio the accuracy can be improved and upper bound or lower bound solutions can be obtained by design the scs can be of regular or irregular polygons in this work we tested triangular quadrangle n sided polygon and tetrahedron as examples stability condition is examined and some criteria are found to avoid the presence of spurious zero energy modes this paper is the first time to create gs galerkin weak form models without using a background mesh that tied with nodes and hence the efs rpim is a true meshfree approach the proposed efs rpim is so far the only technique that can offer both upper and lower bound solutions numerical results show that the efs rpim gives accurate results and desirable convergence rate when comparing with the standard finite element method fem and the cell based smoothed fem cs fem

modeling transient elastodynamic problems using a novel semi analytical method yielding decoupled partial differential equations abstract in this paper a novel semi analytical method is proposed for modeling of two dimensional 2d elastodynamic problems in this regard the domain boundary of the problem is discretized by specific non isoparametric elements that are proposed for the first time in this paper in these elements special shape functions as well as higher order chebyshev mapping functions are implemented for the shape functions kronecker delta property is satisfied for displacement function and its derivatives simultaneously moreover the first derivatives of shape functions are assigned to zero at any given node finally using a weak form of weighted residual method and implementing clenshaw curtis numerical integration coefficient matrices of the system of equations are converted into diagonal ones which leads to a set of decoupled partial differential equations for solving the whole system this means that the governing partial differential equation for each degree of freedom dof becomes independent from other dofs of the domain also to assess the accuracy and efficiency of the proposed method four benchmark problems of 2d elastodynamics are solved using a few numbers of dofs the numerical results present excellent agreement with the analytical solutions and the results from other numerical methods

monodromy of the sl n and gl n hitchin fibrations we compute the monodromy of the hitchin fibration for the moduli space of l twisted sl n mathbb c and gl n mathbb c higgs bundles for any n on a compact riemann surface of genus g 1 we require the line bundle l to either be the canonical bundle or satisfy deg l 2g 2 the monodromy group is generated by picard lefschetz transformations associated to vanishing cycles of singular spectral curves we construct such vanishing cycles explicitly and use this to show that the sl n mathbb c monodromy group is a skew symmetric vanishing lattice in the sense of janssen using the classification of vanishing lattices over mathbb z we completely determine the structure of the monodromy groups of the sl n mathbb c and gl n mathbb c hitchin fibrations as an application we determine the image of the restriction map from the cohomology of the moduli space of higgs bundles to the cohomology of a non singular fibre of the hitchin fibration