dimension of the orbit of marked subspaces given a nilpotent endomorphism we consider the manifold of invariant subspaces having a fixed segre characteristic in linear algebra appl 332 334 2001 569 the implicit form of a miniversal deformation of an invariant subspace with respect to the usual equivalence relation between subspaces is obtained here we obtain the explicit form of this deformation when the invariant subspace is marked and we use it to calculate the dimension of the orbit and in particular to characterize the stable marked subspaces those with open orbit moreover we study the rank of the endomorphisms in the quotient space by the subspaces in the miniversal deformation of the giving subspace

on chaotic simulated annealing chen and aihara 1995 proposed a chaotic simulated annealing approach to solving optimization problems by adding a negative self coupling to a network model proposed earlier by aihara et al and gradually removing this negative self coupling they used the transient chaos for searching and self organizing thereby achieving great improvement over other neural network approaches to optimization problems with or without simulated annealing in this paper we suggest a new approach to chaotic simulated annealing with guaranteed convergence and minimization of the energy function by gradually reducing the time step in the euler approximation of the differential equations that describe the continuous hopfield neural network this approach eliminates the need to carefully select other system parameters we also generalize the convergence theorems of chen and aihara to arbitrarily increasing neuronal input output functions and to less restrictive and yet more compact forms

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

bddc preconditioning for high order galerkin least squares methods using inexact solvers a high order galerkin least squares gls finite element discretization is combined with a balancing domain decomposition by constraints bddc preconditioner and inexact local solvers to provide an efficient solution technique for large scale convection dominated problems the algorithm is applied to the linear system arising from the discretization of the two dimensional advection diffusion equation and euler equations for compressible inviscid flow a robin robin interface condition is extended to the euler equations using entropy symmetrized variables the bddc method maintains scalability for the high order discretization of the diffusion dominated flows and achieves low iteration count in the advection dominated regime the bddc method based on inexact local solvers with incomplete factorization and p 1 coarse correction maintains the performance of the exact counterpart for the wide range of the peclet numbers considered

exponential stability of continuous time and discrete time cellular neural networks with delays convergence characteristics of continuous time cellular neural networks with discrete delays are studied by using lyapunov functionals we obtain delay independent sufficient conditions for the networks to converge exponentially toward the equilibria associated with the constant input sources halanay type inequalities are employed to obtain sufficient conditions for the networks to be globally exponentially stable it is shown that the estimates obtained from the halanay type inequalities improve the estimates obtained from the lyapunov methods discrete time analogues of the continuous time cellular neural networks are formulated and studied it is shown that the convergence characteristics of the continuous time systems are preserved by the discrete time analogues without any restriction imposed on the uniform discretization step size

matrix polynomials factorization via bisolvents abstract we reconsider the classification of all the factorizations of a matrix polynomial p as p q r with q a matrix polynomial and r t s a regular matrix pencil it is shown that the entire classification problem can be reduced to the simpler classification of factors r with commuting coefficients s t it is then shown that for these commuting factors s and t must satisfy a certain algebraic equation which we call the bisolvent equation this extends the generalized bezout theorem which associates monic factors i s with solutions s of a solvent equation in case p is regular the classification of commuting pairs s t of this type up to left equivalence is described in terms of enlarged standard pairs following a well known approach under a non derogatory generic condition on the roots of p the number of such pairs associated with degree minimal factorizations is finite and admits explicit description in terms of jordan chains

chaotic simulated annealing by a neural network with a variable delay design and application in this paper we have three goals the first is to delineate the advantages of a variably delayed system the second is to find a more intuitive lyapunov function for a delayed neural network and the third is to design a delayed neural network for a quadratic cost function for delayed neural networks most researchers construct a lyapunov function based on the linear matrix inequality lmi approach however that approach is not intuitive we provide a alternative candidate lyapunov function for a delayed neural network on the other hand if we are first given a quadratic cost function we can construct a delayed neural network by suitably dividing the second order term into two parts a self feedback connection weight and a delayed connection weight to demonstrate the advantage of a variably delayed neural network we propose a transiently chaotic neural network with variable delay and show numerically that the model should possess a better searching ability than chen aihara s model wang s model and zhao s model we discuss both the chaotic and the convergent phases during the chaotic phase we simply present bifurcation diagrams for a single neuron with a constant delay and with a variable delay we show that the variably delayed model possesses the stochastic property and chaotic wandering during the convergent phase we not only provide a novel lyapunov function for neural networks with a delay the lyapunov function is independent of the lmi approach but also establish a correlation between the lyapunov function for a delayed neural network and an objective function for the traveling salesman problem

a preconditioner for substructuring based on constrained energy minimization a preconditioner for substructuring based on constrained energy minimization concepts is presented the preconditioner is applicable to both structured and unstructured meshes and offers a straightforward approach for the iterative solution of second and fourth order structural mechanics problems the approach involves constraints associated with disjoint sets of nodes on substructure boundaries these constraints provide the means for preconditioning at both the substructure and global levels numerical examples are presented that demonstrate the good performance of the method in terms of iterations compute time and condition numbers of the preconditioned equations

on the use of inexact subdomain solvers for bddc algorithms the standard bddc balancing domain decomposition by constraints preconditioner is shown to be equivalent to a preconditioner built from a partially subassembled finite element model this results in a system of linear algebraic equations which is much easier to solve in parallel than the fully assembled model the cost is then often dominated by that of the problems on the subdomains an important role is also played both in theory and practice by an averaging operator and in addition exact dirichlet solvers are used on the subdomains in order to eliminate the residual in the interior of the subdomains the use of inexact solvers for these problems and even the replacement of the dirichlet solvers by a trivial extension are considered it is established that one of the resulting algorithms has the same eigenvalues as the standard bddc algorithm and the connection of another with the feti dp algorithm with a lumped preconditioner is also considered multigrid methods are used in the experimental work and under certain assumptions it is established that the iteration count essentially remains the same as when exact solvers are used while considerable gains in the speed of the algorithm can be realized since the cost of the exact solvers grows superlinearly with the size of the subdomain problems while the multigrid methods are linear

dual primal feti methods for three dimensional elliptic problems with heterogeneous coefficients in this paper certain iterative substructuring methods with lagrange multipliers are considered for elliptic problems in three dimensions the algorithms belong to the family of dual primal finite element tearing and interconnecting feti methods which recently have been introduced and analyzed successfully for elliptic problems in the plane the family of algorithms for three dimensions is extended and a full analysis is provided for the new algorithms particular attention is paid to finding algorithms with a small primal subspace since that subspace represents the only global part of the dual primal preconditioner it is shown that the condition numbers of several of the dual primal feti methods can be bounded polylogarithmically as a function of the dimension of the individual subregion problems and that the bounds are otherwise independent of the number of subdomains the mesh size and jumps in the coefficients these results closely parallel those of other successful iterative substructuring methods of primal as well as dual type

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

algebraic multigrid for stabilized finite element discretizations of the navier stokes equations abstract an algebraic multigrid method for the solution of stabilized finite element discretizations of the euler and navier stokes equations on generalized unstructured grids is described the method is based on an elemental agglomeration multigrid strategy employing a semi coarsening scheme designed to reduce grid anisotropy the viscous terms are discretized in a consistent manner on coarse grids using an algebraic galerkin coarse grid approximation in which higher order grid transfer operators are constructed from the underlying triangulation however the combination of higher order transfer operators and galerkin rediscretization diminishes the stability of stabilized inviscid operators on coarse grids and a modification is proposed to alleviate this problem a generalized line implicit relaxation scheme is also described where the lines are constructed to follow the direction of strongest coupling applications are demonstrated for convection diffusion euler and laminar navier stokes the results show that the convergence rate is largely unaffected by mesh size over a wide range of reynolds peclet numbers

lmi based criteria for global robust stability of bidirectional associative memory networks with time delay abstract in this paper several new sufficient conditions are given to ensure existence uniqueness and globally exponential robust stability of the equilibrium point for bidirectional associative memory bam networks with delays this novel approach based on the linear matrix inequality lmi technique removes some existing restrictions on the system s parameters and the derived conditions are easy to verify via the lmi toolbox in addition two examples are given to show the effectiveness and the advantage of the proposed results

delay distribution dependent exponential stability criteria for discrete time recurrent neural networks with stochastic delay this brief is concerned with the analysis problem of global exponential stability in the mean square sense for a class of linear discrete time recurrent neural networks drnns with stochastic delay different from the prior research works the effects of both variation range and probability distribution of the time delay are involved in the proposed method first a modeling method is proposed by translating the probability distribution of the time delay into parameter matrices of the transformed drnn model where the delay is characterized by a stochastic binary distributed variable based on the new method the global exponential stability in the mean square sense for the drnns with stochastic delay is investigated by using the lyapunov krasovskii functional and exploiting some new analysis techniques a numerical example is provided to show the effectiveness and the applicability of the proposed method

on the symmetric form of systems of conservation laws with entropy abstract this paper reviews the symmetrizability of systems of conservation laws which possess entropy functions symmetric formulations in conservation form for the equations of gas dynamics are presented

stabilized finite elements on anisotropic meshes a priori error estimates for the advection diffusion and the stokes problems stabilized finite elements on strongly anisotropic meshes are considered the design of the stability coefficients is addressed for both the advection diffusion and the stokes problems when using continuous piecewise linear finite elements on triangles using the polar decomposition of the jacobian of the affine mapping from the reference triangle to the current one k and from a priori error estimates a new definition of the stability coefficients is proposed our analysis shows that these coefficients do not depend on the element diameter hk but on a characteristic length associated with k via the polar decomposition a numerical assessment of the theoretical analysis is carried out

structural stability of c a marked subspaces abstract given an observable pair of matrices c a we consider the manifold of c a invariant subspaces having a fixed brunovsky kronecker structure using arnold techniques we obtain the explicit form of a miniversal deformation of a marked c a invariant subspace with respect to the usual equivalence relation as an application we obtain the dimension of the orbit and we characterize the structurally stable subspaces those with open orbit

bddc and feti dp without matrices or vectors abstract the connection between the bddc balancing domain decomposition by constraints algorithm and the feti dp finite element tearing and interconnecting dual primal algorithm is discussed in the language of function spaces operators and linear functionals

chaos and asymptotical stability in discrete time neural networks abstract this paper aims to theoretically prove by applying marotto s theorem that both transiently chaotic neural networks tcnn and discrete time recurrent neural networks drnn have chaotic structure a significant property tcnn and drnn is that they have only one bounded fixed point when absolute values of the self feedback connection weights in tcnn and the difference time in drnn are sufficiently large we show that this unique fixed point can actually evolve into a snap back repeller which generates chaotic structure if several conditions are satisfied on the other hand by using the lyapunov functions we also derive sufficient conditions on asymptotical stability for symmetrical versions of both tcnn and drnn under which tcnn and drnn asymptotically converge to a fixed point furthermore related bifurcations are also considered in this paper since both tcnn and drnn are not special but simple and general the obtained theoretical results hold for a wide class of discrete time neural networks to demonstrate the theoretical results of this paper better several numerical simulations are provided as illustrating examples

new approach to mixed h sub 2 h sub spl infin filtering for polytopic discrete time systems this paper revisits the problem of mixed h sub 2 h sub spl infin filtering for polytopic discrete time systems differing from previous results in the quadratic framework the filter design makes full use of the parameter dependent stability idea not only is the filter dependent of the parameters which are assumed to reside in a polytope and be measurable online but in addition the lyapunov matrices are different for the entire polytope domain as well as for different channels with respect to the mixed performances these ideas are realized by introducing additional slack variables to the well established performance conditions and by employing new bounding techniques which results in a much less conservative filter design method a numerical example is presented to illustrate the effectiveness and advantage of the developed filter design method

anisotropic mesh refinement in stabilized galerkin methods the numerical solution of a convection diffusion reaction model problem is considered in two and three dimensions a stabilized finite element method of galerkin least square type accomodates diffusion dominated as well as convection and or reaction dominated situations the resolution of boundary layers occuring in the singularly perturbed case is achieved using anisotropic mesh refinement in boundary layer regions in this paper the standard analysis of the stabilized galerkin method on isotropic meshes is extended to more general meshes with boundary layer refinement simplicial lagrangian elements of arbitrary order are used

hopfield network with constraint parameter adaptation for overlapped shape recognition we propose an energy formulation for homomorphic graph matching by the hopfield network and a lyapunov indirect method based learning approach to adaptively learn the constraint parameter in the energy function the adaptation scheme eliminates the need to specify the constraint parameter empirically and generates valid and better quality mappings than the analog hopfield network with a fixed constraint parameter the proposed hopfield network with constraint parameter adaptation is applied to match silhouette images of keys and results are presented

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100

robust h sub spl infin filtering for stochastic time delay systems with missing measurements in this paper the robust hinfin filtering problem is studied for stochastic uncertain discrete time delay systems with missing measurements the missing measurements are described by a binary switching sequence satisfying a conditional probability distribution we aim to design filters such that for all possible missing observations and all admissible parameter uncertainties the filtering error system is exponentially mean square stable and the prescribed hinfin performance constraint is met in terms of certain linear matrix inequalities lmis sufficient conditions for the solvability of the addressed problem are obtained when these lmis are feasible an explicit expression of a desired robust hinfin filter is also given an optimization problem is subsequently formulated by optimizing the hinfin filtering performances finally a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

finite time non fragile passivity control for neural networks with time varying delay abstract in this paper the problem of finite time non fragile passivity control for neural networks with time varying delay is studied we construct a new lyapunov krasovskii function with triple and four integral terms and then utilizing wirtinger type inequality technique the sufficient conditions for finite time boundedness and finite time passivity are derived furthermore a non fragile state feedback controller is designed such that the closed loop system is finite time passive moreover the proposed sufficient conditions can be simplified into the form of linear matrix inequalities lmis using matlab lmi toolbox finally three numerical examples are presented to illustrate the effectiveness of the proposed criteria

the continuous galerkin method is locally conservative we examine the conservation law structure of the continuous galerkin method we employ the scalar advection diffusion equation as a model problem for this purpose but our results are quite general and apply to time dependent nonlinear systems as well in addition to global conservation laws we establish local conservation laws which pertain to subdomains consisting of a union of elements as well as individual elements these results are somewhat surprising and contradict the widely held opinion that the continuous galerkin method is not locally conservative

feti dp bddc and block cholesky methods the feti dp and bddc algorithms are reformulated using block cholesky factorizations an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations instead of introducing lagrange multipliers to enforce the coarse level primal continuity constraints in these algorithms a change of variables is used such that each primal constraint corresponds to an explicit degree of freedom with the new formulation of these algorithms a simplified proof is provided that the spectra of a pair of feti dp and bddc algorithms with the same set of primal constraints are essentially the same numerical experiments for a two dimensional laplace s equation also confirm this result copyright 2005 john wiley sons ltd

new delay dependent stability criteria for neural networks with time varying delay in this letter a new method is proposed for stability analysis of neural networks nns with a time varying delay some less conservative delay dependent stability criteria are established by considering the additional useful terms which were ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

feti domain decomposition methods for scalar advection diffusion problems abstract in this paper we show that iterative substructuring methods of finite element tearing and interconnecting type can be successfully employed for the solution of linear systems arising from the finite element approximation of scalar advection diffusion problems using similar ideas as those of a recently developed neumann neumann method we propose a one level algorithm and a class of two level algorithms obtained by suitably modifying the local problems on the subdomains we present some numerical results for some significant test cases our methods appear to be optimal for flows without closed streamlines and possibly very small values of the viscosity they also show very good performances for rotating flows and moderate reynolds numbers therefore the algorithms proposed appear to be well suited for many convection dominated problems of practical interest

dual primal feti methods for linear elasticity dual primal feti methods are nonoverlapping domain decomposition methods where some of the continuity constraints across subdomain boundaries are required to hold throughout the iterations as in primal iterative substructuring methods while most of the constraints are enforced by lagrange multipliers as in one level feti methods these methods are used to solve the large algebraic systems of equations that arise in elliptic finite element problems the purpose of this article is to develop strategies for selecting these constraints which are enforced throughout the iterations such that good convergence bounds are obtained that are independent of even large changes in the stiffness of the subdomains across the interface between them the algorithms are described in terms of a change of basis that has proven to be quite robust in practice a theoretical analysis is provided for the case of linear elasticity and condition number bounds are established that are uniform with respect to arbitrarily large jumps in the young s modulus of the material and otherwise depend only polylogarithmically on the number of unknowns of a single subdomain the strategies have already proven quite successful in large scale implementations of these iterative methods 2006 wiley periodicals inc

stability analysis for stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotic stability analysis problem is considered for a class of stochastic cohen grossberg neural networks with mixed time delays which consist of both the discrete and distributed time delays based on an lyapunov krasovskii functional and the stochastic stability analysis theory a linear matrix inequality lmi approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square it is shown that the addressed stochastic cohen grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two lmis are feasible where the feasibility of lmis can be readily checked by the matlab lmi toolbox it is also pointed out that the main results comprise some existing results as special cases a numerical example is given to demonstrate the usefulness of the proposed global stability criteria

detection of synchronization between chaotic signals an adaptive similarity based approach we present an adaptive similarity based approach to detect generalized synchronization gs with n m phase synchronization ps where n and m are integers and one of them is 1 this approach is based on the similarity index si and gaussian mixture model with the minimum description length criterion the clustering method which is shown to be superior to the closeness and connectivity of a continuous function is employed in this study to detect the existence of gs with n m ps we conducted a computer simulation and a finger lifting experiment to illustrate the effectiveness of the proposed method in the simulation of a rossler lorenz system our method outperformed the conventional si and gs with 2 1 ps within the coupled system was found in the experiment of self paced finger lifting movement cortico muscular gs with 1 2 and 1 3 ps was found between the surface electromyogram signals on the first dorsal interossei muscle and the magnetoencephalographic data in the motor area the gs with n m ps n or m 1 has been simultaneously resolved from both simulation and experiment the proposed approach thereby provides a promising means for advancing research into both nonlinear dynamics and brain science

recurrent neural network as a linear attractor for pattern association we propose a linear attractor network based on the observation that similar patterns form a pipeline in the state space which can be used for pattern association to model the pipeline in the state space we present a learning algorithm using a recurrent neural network a least squares estimation approach utilizing the interdependency between neurons defines the dynamics of the network the region of convergence around the line of attraction is defined based on the statistical characteristics of the input patterns performance of the learning algorithm is evaluated by conducting several experiments in benchmark problems and it is observed that the new technique is suitable for multiple valued pattern association

spectral element feti dp and bddc preconditioners with multi element subdomains abstract the discrete systems generated by spectral or hp version finite elements are much more ill conditioned than the ones generated by standard low order finite elements or finite differences this paper focuses on spectral elements based on gauss lobatto legendre gll quadrature and the construction of primal and dual non overlapping domain decomposition methods belonging to the family of balancing domain decomposition methods by constraints bddc and dual primal finite element tearing and interconnecting feti dp algorithms new results are presented for the spectral multi element case and also for inexact feti dp methods for spectral elements in the plane theoretical convergence estimates show that these methods have a convergence rate independent of the number of subdomains and coefficient jumps of the elliptic operator while there is only a polylogarithmic dependence on the spectral degree p and the ratio h h of subdomain and element sizes parallel numerical experiments on a linux cluster confirm these results for tests with spectral degree up to p 32 thousands of subdomains and coefficient jumps up to 8 orders of magnitude

recurrent neural nets as dynamical boolean systems with application to associative memory discrete time discrete state recurrent neural networks are analyzed from a dynamical boolean systems point of view in order to devise new analytic and design methods for the class of both single and multilayer recurrent artificial neural networks with the proposed dynamical boolean systems analysis we are able to formulate necessary and sufficient conditions for network stability which are more general than the well known but restrictive conditions for the class of single layer networks 1 symmetric weight matrix with 2 positive diagonal and 3 asynchronous update in terms of design we use a dynamical boolean systems analysis to construct a high performance associative memory with this boolean memory we can guarantee that all fundamental memories are stored and also guarantee the size of the basin of attraction for each fundamental memory

versal deformations of invariant subspaces we describe a miniversal deformation of invariant subspaces with regard to a fixed endomorphism by means of a technique which can be applied to obtain explicitly miniversal deformations in a general orbit space in addition we present an application to the problem of classifying invariant subspaces

a simple mesh generator in matlab creating a mesh is the first step in a wide range of applications including scientific computing and computer graphics an unstructured simplex mesh requires a choice of meshpoints vertex nodes

a novel chaotic neural network with the ability to characterize local features and its application to provide an ability to characterize local features for the chaotic neural network cnn gauss wavelet is used for the self feedback of the cnn with the dilation parameter acting as the bifurcation parameter the exponentially decaying dilation parameter and the chaotically varying translation parameter not only govern the wavelet self feedback transform but also enable the cnn to generate complex dynamics behavior preventing the network from being trapped in the local minima analysis of the energy function of the cnn indicates that the local characterization ability of the proposed cnn is effectively provided by the wavelet self feedback in the manner of inverse wavelet transform and that the proposed cnn can achieve asymptotical stability the experimental results on traveling salesman problem tsp suggest that the proposed cnn has a higher average success rate for obtaining globally optimal or near optimal solutions

finite element methods for first order hyperbolic systems with particular emphasis on the compressible euler equations a petrov galerkin finite element formulation is presented for first order hyperbolic systems of conservation laws with particular emphasis on the compressible euler equations applications of the methodology are made to one and two dimensional steady and unsteady flows with shocks results obtained suggest the potential of the type of methods developed

how delays affect neural dynamics and learning we investigate the effects of delays on the dynamics and in particular on the oscillatory properties of simple neural network models we extend previously known results regarding the effects of delays on stability and convergence properties we treat in detail the case of ring networks for which we derive simple conditions for oscillating behavior and several formulas to predict the regions of bifurcation the periods of the limit cycles and the phases of the different neurons these results in turn can readily be applied to more complex and more biologically motivated architectures such as layered networks in general the main result is that delays tend to increase the period of oscillations and broaden the spectrum of possible frequencies in a quantifiable way simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior adaptable delays are then proposed as one additional mechanism through which neural systems could tailor their own dynamics accordingly we derive recurrent backpropagation learning formulas for the adjustment of delays and other parameters in networks with delayed interactions and discuss some possible applications

perturbed marked reduced forms of invariant subspaces abstract the classification of invariant subspaces is an open problem related to other important ones like the carlson problem here we obtain a reduced form of these invariant subspaces as a new tool to tackle these problems in particular it allows us to prove quite easily partial results already known the key point is assigning to each invariant subspace a marked one its marked type in order to partition the set of invariant subspaces in a finite number of subsets the marked classes each one containing only one marked subspace next we parametrize minimally each marked class by means of the so called pm reduced families so that representatives of an invariant subspace its pm reduced forms appear in just one of these families

mixed finite element methods with convection stabilization for the large eddy simulation of incompressible turbulent flows abstract the variational multiscale method thought as an implicit large eddy simulation model for turbulent flows has been shown to be an alternative to the widely used physical based models this method is traditionally combined with equal order velocity pressure pairs since it provides pressure stabilization in this work we consider a different approach based on inf sup stable elements and convection only stabilization in order to do so we consider a symmetric projection stabilization of the convective term using an orthogonal subscale decomposition the accuracy and efficiency of this method compared with residual based algebraic subgrid scales and orthogonal subscales methods for equal order interpolation is assessed in this paper moreover when inf sup stable elements are used the grad div stabilization term has been shown to be essential to guarantee accurate solutions hence a study of the influence of such term in the large eddy simulation of turbulent incompressible flows is also performed furthermore a recursive block preconditioning strategy has been considered for the resolution of the problem with an implicit treatment of the projection terms two different benchmark tests have been solved the taylor green vortex flow with r e 1600 and the turbulent channel flow at r e 395 and r e 590

characteristic and hyperinvariant subspaces over the field gf 2 let f be an endomorphism of a vector space v over a field k an f invariant subspace x v is called hyperinvariant respectively characteristic if x is invariant under all endomorphisms respectively automorphisms that commute with f if k 2 then all characteristic subspaces are hyperinvariant if k 2 then there are endomorphisms f with invariant subspaces that are characteristic but not hyperinvariant in this paper we give a new proof of a theorem of shoda which provides a necessary and sufficient condition for the existence of characteristic non hyperinvariant subspaces

a domain decomposition preconditioner for an advection diffusion problem abstract we propose a generalization of the neumann neumann algorithm for advection diffusion problems the neumann conditions are replaced by suitable robin conditions the method is first introduced and analysed in the case where the domain is partitioned into vertical strips then generalized to an arbitrary decomposition a coarse space procedure is proposed finally numerical results for bidimensional and tridimensional tests are given

approximation of discrete time state space trajectories using dynamic recurrent neural networks in this note the approximation capability of a class of discrete time dynamic recurrent neural networks drnn s is studied analytical results presented show that some of the states of such a drnn described by a set of difference equations may be used to approximate uniformly a state space trajectory produced by either a discrete time nonlinear system or a continuous function on a closed discrete time interval this approximation process however has to be carried out by an adaptive learning process this capability provides the potential for applications such as identification and adaptive control

bogdanov takens singularity in tri neuron network with time delay this brief reports a retarded functional differential equation modeling tri neuron network with time delay the bogdanov takens b t bifurcation is investigated by using the center manifold reduction and the normal form method we get the versal unfolding of the norm forms at the b t singularity and show that the model can exhibit pitchfork hopf homoclinic and double limit cycles bifurcations some numerical simulations are given to support the analytic results and explore chaotic dynamics finally an algorithm is given to show that chaotic tri neuron networks can be used for encrypting a color image