algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

the steinberg curve let e and e be elliptic curves over inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i we construct non torsion 0 cycles in the kernel of the albanese mapping ch0 e x e deg 0 e x e which are not detectable by a certain class of cohomology theories including the cohomology of the analytic motivic complex involving the dilogarithm function defined by s bloch this is in contrast to the etale version of bloch s complex defined by s lichtenbaum which contains the chow group

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

synchronization in an array of linearly stochastically coupled networks with time delays abstract in this paper the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays the stochastic coupling term which can reflect a more realistic dynamical behavior of coupled systems in practice is introduced to model a coupled system and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly based on a simple adaptive feedback control scheme and some stochastic analysis techniques several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays finally an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results

synchronization based topology identification of weighted general complex dynamical networks with time varying coupling delay abstract many existing papers investigated the geometric features control and synchronization of complex dynamical networks provided with certain topology however the exact topology of a network is sometimes unknown or uncertain based on lasalle s invariance principle we propose an adaptive feedback technique to identify the exact topology of a weighted general complex dynamical network model with time varying coupling delay by receiving the network nodes evolution the topology of such a kind of network with identical or different nodes or even with varying topology can be monitored in comparison with previous methods time delay is taken into account in this simple analytical and systematic synchronization based technique particularly the weight configuration matrix is not necessarily symmetric or irreducible and the inner coupling matrix need not be symmetric illustrative simulations are provided to verify the correctness and effectiveness of the proposed scheme

on the decay of solutions of the generalized benjamin bona mahony equation on etudie le comportement des solutions du probleme aux valeurs initiales u t u x u p u x u xxt 0 x r t o u x 0 x x r p 0 entier on suppose p 4 alors il existe 0 tel que si 1 1 5 0 et x r ou a ne depend pas de x ou t

mixed finite element analysis and numerical solitary solution for the rlw equation in this paper a mixed finite element mfe formulation is proposed for the 1 d regularized long wave rlw equation u t auu x delta u xxt 0 the existence of its mixed generalized solution and semidiscrete and fully discrete mixed finite element solutions is proved error estimates based on energy methods are given and finally results of numerical experiments comparing this formulation with a galerkin method based on cubic splines are also given

delay dependent synchronization for non diffusively coupled time varying complex dynamical networks this paper investigates the delay dependent synchronization schemes for the non diffusively coupled time varying complex dynamical networks the outer coupling configuration matrix in our network model may be non diffusive time varying uncertain asymmetric and irreducible different time varying coupling delays for different nodes are also put into consideration in this paper besides the nodes may have different state dimensions furthermore only the common bound of the outer coupling coefficients cbocc is used to design the synchronization controllers if the cbocc is known our delay dependent synchronization scheme can guarantee the network achieving exponential synchronization and when the cbocc is uncertain the adaptive synchronization scheme where only one adaptive law is needed is proposed to guarantee the network realizing asymptotic synchronization simulation examples are provided to verify the effectiveness and feasibility of our theoretical results

mixed finite element analysis for dissipative srlw equations with damping term abstract in this paper a mixed finite element mfe formulation is proposed for the initial boundary value problem of dissipative symmetric regularized long wave srlw equations with damping existence and uniqueness of its generalized solution and of the fully discrete mixed finite element solution are proved error estimates based on energy methods are given numerical experiments verify the theoretical analysis

generalized synchronization in complex dynamical networks via adaptive couplings abstract this paper investigates generalized synchronization of three typical classes of complex dynamical networks scale free networks small world networks and interpolating networks the proposed synchronization strategy is to adjust adaptively a node s coupling strength based on the node s local generalized synchronization information by taking the auxiliary system approach and using the lyapunov function method we prove that for any given initial coupling strengths the generalized synchronization can take place in complex networks consisting of nonidentical dynamical systems it is demonstrated that the coupling strengths are affected by topologies of the networks furthermore it is found that there are hierarchical features in the processes of generalized synchronization in scale free networks because of their highly heterogeneous distributions of connection degree finally we discuss in detail how a network s degree of heterogeneity affects its generalization synchronization behavior

on galois structure invariants associated to tate motives we establish the equivalence of two definitions of invariants measuring the galois module structure of k groups of rings of integers in number fields due to chinburg et al on the one hand and the authors on the other we also make some remarks concerning the possibility of yet another such definition via lichtenbaum complexes

decay of solutions of some nonlinear wave equations abstract we study the large time behaviour of solutions to the initial value problem for the korteweg de vries equation and for the regularized long wave equation with a dissipative term appended using energy estimates a maximum principle and a transformation of cole hopf type sharp rates of temporal decay of certain norms of the solution are obtained

hybrid adaptive and impulsive synchronization of uncertain complex networks with delays and general uncertain perturbations this paper is concerned with the problem of asymptotic synchronization for a class of uncertain complex networks with delays and general uncertain perturbations in order to cope with the bad effects generated by the uncertain perturbations a novel hybrid adaptive and impulsive controller is designed such that the complex network can be asymptotically synchronized onto an isolate chaotic system with uncertain perturbations all the perturbations can be different from each other on the basis of a new lemma squeezing rule and lyapunov krasovskii functionals several sufficient conditions guaranteeing the realization of the synchronization goal are derived it is shown that the designed hybrid controllers exhibit powerful robustness some existing results are improved and extended numerical simulations verify the effectiveness of the theoretical results and the robustness of the new controller

cluster synchronization for nonlinearly time varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control this paper investigate the mean square exponential cluster synchronization of a class complex networks with nonlinear hybrid time varying delays and stochastic noises via periodically intermittent pinning control to be more practical the network topology can be directed and the time delay is assumed to be time varying based on the lyapunov stability theory stochastic analysis theory and linear matrix inequalities lmi the sufficient conditions are derived to guarantee the mean square exponential cluster synchronization furthermore our results can cover and extend the related ones in existing literatures some numerical simulations are provided to show the effectiveness of our theoretical results

new similarity reductions and painleve analysis for the symmetric regularised long wave and modified benjamin bona mahoney equations the author discusses similarity reductions and painleve analysis for the symmetric regularised long wave and modified benjamin bona mahoney equations 1972 both of which arise in several physical applications including shallow water waves both equations are thought to non integrable i e not solvable by inverse scattering since numerical studies show that the interaction of solitary waves in inelastic in particular we determine some new similarity reductions of the symmetric regularised long wave equation these new similarity reductions are not obtainable using the classical lie group method for finding group invariant solutions of partial differential equations they are determined using a new and direct method which involves no group theoretical techniques it is shown that every similarity reduction of both the symmetric regularised long wave and modified benjamin bona mahoney equations obtained using the classical lie group method reduces the associated partial differential equation to an ordinary differential equation of painleve type whereas the new similarity solution of the symmetric regularised long wave equation reduces it to an ordinary differential equation which is not of painleve type it is also shown that neither the symmetric regularised long wave equation nor the modified benjamin bona mahoney equation possesses the painleve property for partial differential equations as defined by weiss et al 1983

relative k_ 0 annihilators fitting ideals and stickelberger phenomena when g is abelian and l is a prime we show how elements of the relative k group k 0 bf z l g bf q l give rise to annihilator fitting ideal relations of certain associated bf z g modules examples of this phenomenon are ubiquitous particularly we give examples in which g is the galois group of an extension of global fields and the resulting annihilator fitting ideal relation is closely connected to stickelberger s theorem and to the conjectures of coates and sinnott and brumer higher stickelberger ideals are defined in terms of special values of l functions when these vanish we show how to define fractional ideals generalising the stickelberger ideals with similar annihilator properties the fractional ideal is constructed from the borel regulator and the leading term in the taylor series for the l function en route our methods yield new proofs in the case of abelian number fields of formulae predicted by lichtenbaum for the orders of k groups and etale cohomology groups of rings of algebraic integers

a decoupled and conservative difference scheme with fourth order accuracy for the symmetric regularized long wave equations in this paper a decoupled finite difference scheme with fourth order accuracy is proposed to solve the symmetric regularized long wave equation the scheme is proved to conserve the total energy in the discrete level without any restrictions on the grid ratios the convergence of the difference scheme is proved by utilizing the energy method to be of forth order in space and second order in time a numerical example is given to support the theoretical analysis

conservative schemes for the symmetric regularized long wave equations in this paper we study the symmetric regularized long wave srlw equations by finite difference method we design some numerical schemes which preserve the original conservative properties for the equations the first scheme is two level and nonlinear implicit existence of its difference solutions are proved by brouwer fixed point theorem it is proved by the discrete energy method that the scheme is uniquely solvable unconditionally stable and second order convergent for u in l norm and for n in l2 norm on the basis of the priori estimates the second scheme is three level and linear implicit its stability and second order convergence are proved both of the two schemes are conservative so can be used for long time computation however they are coupled in computing so need more cpu time thus we propose another three level linear scheme which is not only conservative but also uncoupled in computation and give the numerical analysis on it numerical experiments demonstrate that the schemes are accurate and efficient

a new synchronization tracking technique for uncertain discrete network with spatiotemporal chaos behaviors abstract we propose a novel scheme to achieve synchronization tracking of uncertain discrete network with spatiotemporal chaos behaviors in this work the traditional method of sliding mode control is firstly modified for researching conveniently the synchronization tracking of uncertain discrete network further the network sliding mode surface and control input are designed and their effectiveness are analyzed at the same time we also design the adaptive law to identify availably the uncertain configuration coefficient of the network sliding mode surface finally an example about the small world network is considered to illustrate the application and effectiveness of the proposed scheme

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

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

comparison of dualizing complexes we prove that there is a map from bloch s cycle complex to kato s complex of milnor k theory which induces a quasi isomorphism from etale sheafified cycle complex to the gersten complex of logarithmic de rham witt sheaves next we show that the truncation of bloch s cycle complex at 3 is quasi isomorphic to spiess dualizing complex

driving and synchronizing by chaotic impulses for a class of dynamical systems driven by chaotic impulses we give conditions for the occurrence of chaos locking it is shown how the concept of time discontinuous coupling of two chaotic systems may lead to generalized synchronization the method of synchronization is interpreted as a nonlinear analog of the sampling theorem furthermore we examine the effect of amplitude quantization of the driving signal on their synchronization even though two time discontinuously coupled dynamical systems are no more exactly synchronized when the driving signal is digitized their trajectories are close enough to allow correct transmission of digital information signals between them textcopyright 1996 the american physical society

synchronization of coupled reaction diffusion neural networks with time varying delays via pinning impulsive controller in this paper global exponential synchronization stability in an array of linearly diffusively coupled reaction diffusion neural networks with time varying delays is investigated by adding impulsive controller to a small fraction of nodes pinning impulsive controller in order to overcome the difficulty resulting from the fact that the impulsive controller affects only the dynamical behaviors of the controlled nodes a new analysis method is developed by using the developed method two known lemmas on stability of delayed functional differential equation with and without impulses and lyapunov stability theory several novel and easily verified synchronization criteria guaranteeing the whole network will be pinned to a homogenous solution are derived moreover the effects of the pinning impulsive controller and the dynamics of the uncontrolled nodes and the diffusive couplings on the synchronization process are explicitly expressed in the obtained criteria our results also show that we can always de

the construction of weight two arithmetic cohomology let x be a regular noetherian scheme in a letter to soul6 be beilinson conjectured for each non negative integer n the existence of complexes f n x of zariski sheaves on x whose hypercohomology should be in the same relation to algebraic k theory as classical cohomology is to topological ktheory and proposed certain properties that these complexes should satisfy this investigation was continued in l where the conjectured complexes were moved to the a at other points we work only up to 2torsion or up to torsion involving primes dividing the residue field characteristics there seems good reason to expect our complex f 2 x to in fact exactly satisfy all the axioms we now sketch the construction of f 2 x and recall the axioms let a be a regular noetherian ring let w s p e c a t z s p e c a t t t 1 let b bl b 2 b be a finite sequence of exceptional units of a i e b i and

synchronization of a complex dynamical network with coupling time varying delays via sampled data control abstract in this paper the synchronization problem of a complex dynamical network with coupling time varying delays via delayed sampled data controller is investigated in order to make full use of the sawtooth structure characteristic of the sampling input delay a discontinuous lyapunov functional is proposed based on the extended wirtinger inequality from a convex representation of the sector restricted nonlinearity in system dynamics the stability condition based on lyapunov stability theory is obtained by utilization of linear matrix inequality formulation to find the controller which achieves the synchronization of a complex dynamical network with coupling time varying delay finally two numerical examples are given to illustrate the effectiveness of the proposed methods

synchronization of nonlinear singularly perturbed complex networks with uncertain inner coupling via event triggered control this study is concerned with the synchronization problem of nonlinear singularly perturbed complex networks with time varying coupling delays in an aim to shrink the treatment of network resources event triggered control strategy is proposed to achieve the synchronization criteria by developing the novel lyapunov krasovskii functional some adequate conditions which ensure the asymptotic synchronization are obtained in the form of linear matrix inequalities besides that synchronization problem of nonlinear singularly perturbed complex networks with uncertain inner coupling are also taken into account the uncertain inner coupling is represented by making use of the interval matrix approach finally simulation results are displayed to show the efficacy of the proposed theoretical results

a bloch wigner exact sequence over local rings abstract in this article we extend the bloch wigner exact sequence over local rings where their residue fields have more than nine elements moreover we prove van der kallen s theorem on the presentation of the second k group of local rings such that their residue fields have more than four elements note that van der kallen proved this result when the residue fields have more than five elements although we prove our results over local rings all our proofs also work over semilocal rings where all their residue fields have similar properties as the residue field of local rings

crank nicolson finite difference scheme for the rosenau burgers equation abstract in this paper a crank nicolson finite difference scheme for the numerical solution of the initial boundary value problem of rosenau burgers equation is proposed existence and uniqueness of numerical solutions are derived it is proved that the finite difference scheme is convergent in the order of o 2 h 2 and stable numerical simulations show that the method is efficient

local exponential synchronization in complex dynamical networks with time varying delay and hybrid coupling in this paper the local exponential synchronization of complex dynamical networks with time varying delay and hybrid coupling is investigated we assume that the coupling configuration matrices are asymmetric and the inner coupling matrices are not restricted to be diagonal or positive definite through constructing the appropriate lyapunov krasovskii functional and applying the linear matrix inequality lmi technique several novel delay depend sufficient conditions and the decay rate are deduced for the local exponential synchronization moreover the derivative of the time varying delay is extended to any value finally the numerical simulations are given to show the effectiveness of the theoretical results

adaptive complete synchronization of the noise perturbed two bi directionally coupled chaotic systems with time delay and unknown parametric mismatch in this paper we design an adaptive feedback controller to synchronize a class of noise perturbed two bi directionally coupled chaotic systems with time delay and unknown parametric mismatch based on invariance principle of stochastic time delay differential equations some sufficient conditions of adaptive complete synchronization are given comparing with other papers here we consider the effect of internal noise time delay and parametric mismatch in the synchronized process as the illustrative examples the famous lorenz system and rossler system are considered here in order to validate the proposed scheme numerical simulations are performed and the numerical results show that our scheme is very effective

parameter identification and synchronization for uncertain network group with different structures abstract we design a novel synchronization technique to research the synchronization of network group constituted of uncertain networks with different structures based on lyapunov theorem the selection principles of the control inputs and the parameter identification laws of the networks are determined and synchronization conditions of the network group are obtained some numerical simulations are provided to verify the correctness and effectiveness of the synchronization technique we find that the network number the number of network nodes and network connections indeed will not affect the stability of synchronization of network group

adaptive control and synchronization of identical new chaotic flows with unknown parameters via single input the single input linear feedback control for synchronizing two identical new 3d chaotic flows reported by li et al x f li k e chlouverakis d l xu nonlinear dynamics and circuit realization of a new chaotic flow a variant of lorenz chen and lu nonlinear analysis rwa 10 4 2009 2357 2368 is proposed in this paper sufficient conditions of synchronization are obtained for both linear feedback and adaptive control approaches the problem of adaptive synchronization between two nearly identical chaotic systems with unknown parameters is also studied based on the lyapunov stability theory two kinds of single input adaptive synchronization controllers are designed and the adaptive parameter update laws are developed

adaptive synchronization of two novel different hyperchaotic systems with partly uncertain parameters this paper investigates adaptive synchronization between two novel different hyperchaotic systems with partly uncertain parameters based on the lyapunov stability theorem and the adaptive control theory synchronization between these two hyperchaotic systems is achieved by proposing a new adaptive controller and a parameter estimation update law numerical simulations are presented to demonstrate the analytical results