controller design for synchronization of an array of delayed neural networks using a controllable probabilistic pso in this paper a controllable probabilistic particle swarm optimization cppso algorithm is introduced based on bernoulli stochastic variables and a competitive penalized method the cppso algorithm is proposed to solve optimization problems and is then applied to design the memoryless feedback controller which is used in the synchronization of an array of delayed neural networks dnns the learning strategies occur in a random way governed by bernoulli stochastic variables the expectations of bernoulli stochastic variables are automatically updated by the search environment the proposed method not only keeps the diversity of the swarm but also maintains the rapid convergence of the cppso algorithm according to the competitive penalized mechanism in addition the convergence rate is improved because the inertia weight of each particle is automatically computed according to the feedback of fitness value the efficiency of the proposed cppso algorithm is demonstrated by comparing it with some well known pso algorithms on benchmark test functions with and without rotations in the end the proposed cppso algorithm is used to design the controller for the synchronization of an array of continuous time delayed neural networks

hp discontinuous galerkin method based on local higher order reconstruction we present a new adaptive higher order finite element method hp fem for the solution of boundary value problems formulated in terms of partial differential equations pdes the method does not use any information about the problem to be solved which makes it robust and equation independent it employs a higher order reconstruction scheme over local element patches which makes it faster and easier to parallelize compared to hp adaptive methods that are based on the solution of a reference problem on a globally hp refined mesh the method can be used for the solution of linear as well as nonlinear problems discretized by conforming or non conforming finite element methods and it can be combined with arbitrary a posteriori error estimators the performance of the method is demonstrated by several examples carried out by the discontinuous galerkin method

synchronization in weighted scale free networks with degree degree correlation abstract we study synchronization phenomena in scale free networks of asymmetrically coupled dynamical systems featuring degree degree correlation in the topology of the connection wiring we show that when the interaction is dominant from the high degree to the low degree or from the low degree to the high degree nodes synchronization is enhanced for assortative or disassortative degree degree correlations

multitarget error estimation and adaptivity in aerodynamic flow simulations important quantities in aerodynamic flow simulations are the aerodynamic force coefficients including the pressure induced and the viscous stress induced drag lift and moment coefficients in addition to the exact approximation of these quantities it is of increasing importance in particular in the field of uncertainty quantification to estimate the error in the computed quantities in recent years a posteriori error estimation and goal oriented refinement approaches have been developed for the accurate and efficient computation of single target quantities the current approaches are based on computing an adjoint solution related to each of the specific target quantities under consideration in this paper we extend this approach to the accurate and efficient computation of multiple target quantities instead of computing multiple adjoint solutions one for each target functional the new approach is based on the solution to one discrete adjoint problem and one discrete error problem this way only two auxiliary problems are required irrespective of the number of target functionals the practical performance of this approach is demonstrated for a laminar compressible flow in particular the proposed approach is compared to the standard approach of error estimation and goal oriented refinement as well as to residual based refinement the performance of the algorithms is measured in terms of computing resources required for meeting industrial as well as academic accuracy requirements on the computed force coefficients

synchronization in complex dynamical networks with nonsymmetric coupling based on the work of nishikawa and motter who have extended the well known master stability framework to include non diagonalizable cases we develop another extension of the master stability framework to obtain criteria for global synchronization several criteria for global synchronization are provided which generalize some previous results the jordan canonical transformation method is used in stead of the matrix diagonalization method especially we show clearly that the synchronizability of a dynamical network with nonsymmetric coupling is not always characterized by its second largest eigenvalue even though all the eigenvalues of the nonsymmetric coupling matrix are real furthermore the effects of the asymmetry of coupling on synchronizability of networks with different structures are analyzed numerical simulations are also done to illustrate and verify the theoretical results on networks in which each node is a dynamical limit cycle oscillator consisting of a two cell cellular neural network

spatio temporal intermittency in coupled map lattices abstract the transition to turbulence in a one dimensional array of maps coupled by diffusion is shown to display critical properties resembling those of directed percolation the analogy is supported by the reconstruction of a probabilistic cellular automation with closely similar statistical properties numerical results suggest however that spatio temporal intermittency does not belong to the same universality class as directed percolation

division theorems for exact sequences under certain integrability and geometric conditions we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of koszul complex by introducing a singular hermitian structure on the trivial bundle our results recover skoda s division theorem for holomorphic functions on pseudoconvex domains in complex euclidean spaces

a note on the design of hp adaptive finite element methods for elliptic partial differential equations we introduce an hp adaptive finite element algorithm based on a combination of reliable and efficient residual error indicators and a new hp extension control technique which assesses the local regularity of the underlying analytical solution on the basis of its local legendre series expansion numerical experiments confirm the robustness and reliability of the proposed algorithm

synchronous chaos in coupled oscillator systems we investigate the synchronization of chaotic oscillations in coupled oscillator systems both theoretically and in analog electronic circuits particular attention is paid to deriving and testing general conditions for the stability of synchronous chaotic behavior in cases where the coupled oscillator array possesses a shift invariant symmetry these cases include the well studied cases of nearest neighbor diffusive coupling and all to all or global coupling an approximate criterion is developed to predict the stability of synchronous chaotic oscillations in the strong coupling limit when the oscillators are coupled through a single coordinate scalar coupling this stability criterion is illustrated numerically in a set of coupled r ossler like oscillators synchronization experiments with coupled r ossler like oscillator circuits are also carried out to demonstrate the applicability of the theory to real systems

interpolation and sampling hypersurfaces for the bargmann fock space in higher dimensions we study those smooth complex hypersurfaces w in open image in new window having the property that all holomorphic functions of finite weighted lp norm on w extend to entire functions with finite weighted lp norm such hypersurfaces are called interpolation hypersurfaces we also examine the dual problem of finding all sampling hypersurfaces i e smooth hypersurfaces w in open image in new window such that any entire function with finite weighted lp norm is stably determined by its restriction to w

global exponential stability of impulsive discrete time neural networks with time varying delays this paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete time neural networks with time varying delays firstly by means of the lyapunov stability theory some inequality analysis techniques and a discrete time halanay type inequality technique sufficient conditions for ensuring global exponential stability of discrete time neural networks are derived and the estimated exponential convergence rate is provided as well the obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete time neural networks with time varying delays finally numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria

adaptive mesh strategies for the spectral element method abstract an adaptive spectral element method has been developed for the efficient solution of time dependent partial differential equations adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the one dimensional viscous burgers equation and the two dimensional navier stokes equations for driven flow in a cavity sharp gradients singularities and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used the adaptive formulation presents significant increases in efficiency flexibility and general capabilities for high order spectral methods

pseudo riddling in chaotic systems abstract previous investigations of riddling have focused in the case where the dynamical invariant set in the symmetric invariant subspace of the system is a chaotic attractor a situation expected to arise commonly in dynamical systems however is that the dynamics in the invariant subspace is in a periodic window in such a case there are both a stable periodic attractor and a coexisting non attracting chaotic saddle in the invariant subspace we show that riddling can still occur in a generalized sense in particular we argue that the basin of the periodic attractor in the invariant subspace contains both an open set and a set of measure zero with riddled holes that belong to the basin of another attractor we call such basin pseudo riddled and we argue that pseudo riddling can be more pervasive than riddling of chaotic attractors because it can occur regardless of whether the chaotic saddle in the invariant subspace is transversely stable or unstable we construct an analyzable model derive a scaling law for pseudo riddling and provide numerical support we also show that the chaotic saddle in the invariant subspace can undergo an enlargement into the full phase space when it becomes transversely unstable

some remarks on the local moduli of tangent bundles over complex surfaces using the hirzebruch s riemann roch formula for endomorphism bundles over a compact complex two fold we prove that the tangent bundle of a complex surface m of general type admits a nontrivial trace free deformation unless m is holomorphically covered by the euclidean ball it follows that the tangent bundle of the mostow siu surface which is a kahler surface with a negative definite curvature tensor does have a nontrivial trace free moduli among some other results we also point out a relationship between the kuranishi obstruction and symmetric holomorphic two tensors on a complex surface

curvature of the l2 metric on the direct image of a family of hermitian einstein vector bundles for a holomorphic family of simple hermitian einstein holomorphic vector bundles over a compact kahler manifold the locally free part of the associated direct image sheaf over the parameter space forms a holomorphic vector bundle and it is endowed with a hermitian metric given by the l 2 pairing using the hermitian einstein metrics our main result in this paper is to compute the curvature of the l 2 metric in the case of a family of hermitian holomorphic line bundles with fixed positive first chern form and under certain curvature conditions we show that the l 2 metric is conformally equivalent to a hermitian einstein metric as applications this proves the semi stability of certain picard bundles and it leads to an alternative proof of a theorem of kempf 0 introduction given a holomorphic family of simple hermitian einstein holomorphic vector bundles over a fixed compact kahler manifold and paramet rized by a complex manifold one obtains a coherent analytic sheaf over the parameter space by taking direct image the locally free part of the direct image sheaf forms a holomorphic vector bundle over a zariski open subset of the pa rameter space and is endowed with a hermitian metric given by the l 2 pairings on global holomorphic sections of the hermitian einstein bundles with respect to the hermitian einstein metrics and the kahler metric on the kahler manifold our objective in this paper is to compute the curvature of this l 2 metric this work is partly motivated by earlier works of various authors on the analogous problem of computing the curvature of the weil petersson metric on the moduli space of hermitian einstein vector bundles over a compact kahler manifold c st zt where the weil petersson metric is defined similarly by the l 2 pairing on the harmonic representatives of the kodaira spencer classes associated to tangent vectors of the moduli space in particular the approach of schumacher toma st is especially inspiring to us and their observation that the curvature form of the total space contains the harmonic representatives of the kodaira spencer classes also plays an important role in our computations in the case of a family of ample line bundles over a compact kahler manifold of semi positive ricci cuvature the curvature of the l 2 metric takes a simple form see theorem 2 when the parameter space is a compact kahler manifold the l 2 metric is conformally equivalent to a hermitian einstein metric which

l 2 metrics projective flatness and families of polarized abelian varieties we compute the curvature of the l 2 metric on the direct image of a family of hermitian holomorphic vector bundles over a family of compact kahler manifolds as an application we show that the l 2 metric on the direct image of a family of ample line bundles over a family of abelian varieties and equipped with a family of canonical hermitian metrics is always projectively flat when the parameter space is a compact kahler manifold this leads to the poly stability of the direct image with respect to any kahler form on the parameter space

adaptive synchronization of neural networks with time varying delay and distributed delay abstract in this paper the adaptive synchronization of neural networks with time varying delay and distributed delay is discussed based on the lasalle invariant principle of functional differential equations and the adaptive feedback control technique some sufficient conditions for adaptive synchronization of such a system are obtained finally a numerical example is given to show the effectiveness of the proposed synchronization method

discrete synchronization of massively connected systems using hierarchical couplings abstract we study the synchronization of massively connected dynamical systems for which the interactions come from the succession of couplings forming a global hierarchical coupling process motivations of this work come from the growing necessity of understanding properties of complex systems that often exhibit a hierarchical structure starting with a set of 2 n systems the couplings we consider represent a two by two matching process that gather them in larger and larger groups of systems providing to the whole set a structure in n stages corresponding to n scales of hierarchy this leads us naturally to the synchronization of a cantor set of systems indexed by 0 1 n using the closed open sets defined by n tuples of 0 and 1 that permit us to make the link with the finite previous situation of 2 n systems we obtain a global synchronization result generalizing this case in the same context we deal with this question when some defects appear in the hierarchy that is to say when some couplings among certain systems do not happen at a given stage of the hierarchy we prove we can accept an infinite number of broken links inside the hierarchy while keeping a local synchronization under the condition that these defects are present at the n smallest scales of the hierarchy for a fixed integer n and they be enough spaced out in those scales

numerical error estimation for nonlinear hyperbolic pdes via nonlinear error transport abstract the estimation of discretization error in numerical simulations is a key component in the development of uncertainty quantification in particular there exists a need for reliable robust estimators for finite volume and finite difference discretizations of hyperbolic partial differential equations the approach espoused here often called the error transport approach in the literature is to solve an auxiliary error equation concurrently with the primal governing equation to obtain a point wise cell wise estimate of the discretization error nonlinear time dependent problems are considered in contrast to previous work fully nonlinear error equations are advanced and potential benefits are identified a systematic approach to approximate the local residual for both method of lines and space time discretizations is developed behavior of the error estimates on problems that include weak solutions demonstrates the positive properties of nonlinear error transport

on synchronized regions of discrete time complex dynamical networks in this paper the local synchronization of discrete time complex networks is studied first it is shown that for any natural number n there exists a discrete time network which has at least disconnected synchronized regions for local synchronization which implies the possibility of intermittent synchronization behaviors different from the continuous time networks the existence of an unbounded synchronized region is impossible for discrete time networks the convexity of the synchronized regions is also characterized based on the stability of a class of matrix pencils which is useful for enlarging the stability region so as to improve the network synchronizability

synchronization in complex delayed dynamical networks with nonsymmetric coupling abstract a new general complex delayed dynamical network model with nonsymmetric coupling is introduced and then we investigate its synchronization phenomena several synchronization criteria for delay independent and delay dependent synchronization are provided which generalize some previous results the matrix jordan canonical formalization method is used instead of the matrix diagonalization method so in our synchronization criteria the coupling configuration matrix of the network does not required to be diagonalizable and may have complex eigenvalues especially we show clearly that the synchronizability of a delayed dynamical network is not always characterized by the second largest eigenvalue even though all the eigenvalues of the coupling configuration matrix are real furthermore the effects of time delay on synchronizability of networks with unidirectional coupling are studied under some typical network structures the results are illustrated by delayed networks in which each node is a two dimensional limit cycle oscillator system consisting of a two cell cellular neural network numerical simulations show that these networks can realize synchronization with smaller time delay and will lose synchronization when the time delay increase larger than a threshold

disconnected synchronized regions of complex dynamical networks this technical note addresses the synchronized region problem which is converted to a more convenient matrix stability problem for complex dynamical networks for any natural number n the existence of a network with n disconnected synchronized regions is theoretically proved and numerically demonstrated this shows the intrinsic complexity of the network synchronization problem convexity characteristic of stability for relevant matrix pencils is further discussed a smooth chua s circuit network is finally discussed as an example for illustration

on approximations and ergodicity classes in random chains we study the limiting behavior of a random dynamic system driven by a stochastic chain our interest is in the chains that are not necessarily ergodic but are decomposable into ergodic classes to investigate the conditions under which the ergodic classes of a model can be identified we introduce and study an l1 approximation and infinite flow graph of the model we show that the l1 approximations of random chains preserve certain limiting behavior using the l1 approximations we show how the connectivity of the infinite flow graph is related to the structure of the ergodic groups of the model our main result of this paper provides conditions under which the ergodicity groups of the model can be identified by considering the connected components in the infinite flow graph we provide two applications of our main result to random networks namely broadcast over time varying networks and networks with random link failure

on some properties of contracting matrices abstract the concepts of paracontracting pseudocontracting and nonexpanding operators have been shown to be useful in proving convergence of asynchronous or parallel iteration algorithms the purpose of this paper is to give characterizations of these operators when they are linear and finite dimensional first we show that pseudocontractivity of stochastic matrices with respect to is equivalent to the scrambling property a concept first introduced in the study of inhomogeneous markov chains this unifies results obtained independently using different approaches secondly we generalize the concept of pseudocontractivity to set contractivity which is a useful generalization with respect to the euclidean norm in particular we demonstrate non hermitian matrices that are set contractive for 2 but not pseudocontractive for 2 or for constant row sum matrices we characterize set contractivity using matrix norms and matrix graphs furthermore we prove convergence results in compositions of set contractive operators and illustrate the differences between set contractivity in different norms finally we give an application to the global synchronization in coupled map lattices

erratum to a nonlinear elliptic system for maps from hermitian to riemannian manifolds and rigidity theorems in hermitian geometry it is the purpose of this paper to introduce and study a nonlinear elliptic system of equations imposed on a map from a hermitian into a riemannian manifold which seems to be more appropriate to hermitian geometry than the harmonic map system thus let x be a complex manifold with hermitian metric 7 in local coordinates n a riemannian manifold with metric gij and christoffel symbols f k a harmonic map f x n then has to satisfy

synchronization of complex networks via aperiodically intermittent pinning control in this note synchronization for linearly coupled network is investigated by pinning a simple aperiodically intermittent controller nodes dynamical behaviors in the network are described by continuous time ordinary differential equations some sufficient conditions to guarantee global synchronization are presented furthermore an adaptive algorithm is designed for the pinning control gain and its validity is also proved rigorously finally numerical simulations are given to demonstrate the correctness of obtained results

an eigenvalue estimate for the bar partial laplacian we study the bar partial laplacian on forms taking values in lk a high power of a semipositive line bundle over a compact complex manifold and give an estimate of the number of eigenvalues smaller than examples show that the estimate gives the right order of magnitude in terms of the two spectral parameters k and

global synchronization for discrete time stochastic complex networks with randomly occurred nonlinearities and mixed time delays in this paper the problem of stochastic synchronization analysis is investigated for a new array of coupled discrete time stochastic complex networks with randomly occurred nonlinearities rons and time delays the discrete time complex networks under consideration are subject to 1 stochastic nonlinearities that occur according to the bernoulli distributed white noise sequences 2 stochastic disturbances that enter the coupling term the delayed coupling term as well as the overall network and 3 time delays that include both the discrete and distributed ones note that the newly introduced rons and the multiple stochastic disturbances can better reflect the dynamical behaviors of coupled complex networks whose information transmission process is affected by a noisy environment e g internet based control systems by constructing a novel lyapunov like matrix functional the idea of delay fractioning is applied to deal with the addressed synchronization analysis problem by employing a combination of the linear matrix inequality lmi techniques the free weighting matrix method and stochastic analysis theories several delay dependent sufficient conditions are obtained which ensure the asymptotic synchronization in the mean square sense for the discrete time stochastic complex networks with time delays the criteria derived are characterized in terms of lmis whose solution can be solved by utilizing the standard numerical software a simulation example is presented to show the effectiveness and applicability of the proposed results

state estimation for coupled uncertain stochastic networks with missing measurements and time varying delays the discrete time case this paper is concerned with the problem of state estimation for a class of discrete time coupled uncertain stochastic complex networks with missing measurements and time varying delay the parameter uncertainties are assumed to be norm bounded and enter into both the network state and the network output the stochastic brownian motions affect not only the coupling term of the network but also the overall network dynamics the nonlinear terms that satisfy the usual lipschitz conditions exist in both the state and measurement equations through available output measurements described by a binary switching sequence that obeys a conditional probability distribution we aim to design a state estimator to estimate the network states such that for all admissible parameter uncertainties and time varying delays the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square by employing the lyapunov functional method combined with the stochastic analysis approach several delay dependent criteria are established that ensure the existence of the desired estimator gains and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities lmis two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes

network synchronization spectral versus statistical properties we consider synchronization of weighted networks possibly with asymmetrical connections focusing on causal relations rather than the observed correlations we show that the synchronizability of networks cannot be directly inferred from their statistical properties small local changes in the network structure can sensitively affect the eigenvalues relevant for synchronization while the gross statistical network properties remain essentially unchanged consequently commonly used statistical properties including the degree distribution degree homogeneity average degree average distance degree correlation and clustering coefficient can fail to characterize the synchronizability of networks in terms of causal relations despite the observed correlations c 2006 elsevier b v all rights reserved

stability and synchronization of discrete time markovian jumping neural networks with mixed mode dependent time delays in this paper we introduce a new class of discrete time neural networks dnns with markovian jumping parameters as well as mode dependent mixed time delays both discrete and distributed time delays specifically the parameters of the dnns are subject to the switching from one to another at different times according to a markov chain and the mixed time delays consist of both discrete and distributed delays that are dependent on the markovian jumping mode we first deal with the stability analysis problem of the addressed neural networks a special inequality is developed to account for the mixed time delays in the discrete time setting and a novel lyapunov krasovskii functional is put forward to reflect the mode dependent time delays sufficient conditions are established in terms of linear matrix inequalities lmis that guarantee the stochastic stability we then turn to the synchronization problem among an array of identical coupled markovian jumping neural networks with mixed mode dependent time delays by utilizing the lyapunov stability theory and the kronecker product it is shown that the addressed synchronization problem is solvable if several lmis are feasible hence different from the commonly used matrix norm theories such as the m matrix method a unified lmi approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation where the lmis can be easily solved by using the available matlab lmi toolbox two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained

maximum performance at minimum cost in network synchronization we consider two optimization problems on synchronization of oscillator networks maximization of synchronizability and minimization of synchronization cost we first develop an extension of the well known master stability framework to the case of non diagonalizable laplacian matrices we then show that the solution sets of the two optimization problems coincide and are simultaneously characterized by a simple condition on the laplacian eigenvalues among the optimal networks we identify a subclass of hierarchical networks characterized by the absence of feedback loops and the normalization of inputs we show that most optimal networks are directed and non diagonalizable necessitating the extension of the framework we also show how oriented spanning trees can be used to explicitly and systematically construct optimal networks under network topological constraints our results may provide insights into the evolutionary origin of structures in complex networks for which synchronization plays a significant role

synchronization analysis of delayed complex networks with time varying couplings abstract in this paper a new method is presented to analyze the linear stability of the synchronized state in arbitrarily coupled complex dynamical systems with time delays the coupling configurations are not restricted to the symmetric and irreducible connections or the non negative off diagonal links the stability criteria are obtained by using lyapunov krasovskii functional method and subspace projection method these criteria reveal the relationship between coupling matrices and stability of the dynamical networks

cross correlation of instantaneous phase increments in pressure flow fluctuations applications to cerebral autoregulation we investigate the relationship between the blood flow velocities bfv in the middle cerebral arteries and beat to beat blood pressure bp recorded from a finger in healthy and post stroke subjects during the quasisteady state after perturbation for four different physiologic conditions supine rest head up tilt hyperventilation and co2 rebreathing in upright position to evaluate whether instantaneous bp changes in the steady state are coupled with instantaneous changes in the bfv we compare dynamical patterns in the instantaneous phases of these signals obtained from the hilbert transform as a function of time we find that in post stroke subjects the instantaneous phase increments of bp and bfv exhibit well pronounced patterns that remain stable in time for all four physiologic conditions while in healthy subjects these patterns are different less pronounced and more variable we propose an approach based on the cross correlation of the instantaneous phase increments to quantify the coupling between bp and bfv signals we find that the maximum correlation strength is different for the two groups and for the different conditions for healthy subjects the amplitude of the cross correlation between the instantaneous phase increments of bp and bfv is small and attenuates within 3 5 heartbeats in contrast for post stroke subjects this amplitude is significantly larger and cross correlations persist up to 20 heartbeats further we show that the instantaneous phase increments of bp and bfv are cross correlated even within a single heartbeat cycle we compare the results of our approach with three complementary methods direct bp bfv cross correlation transfer function analysis and phase synchronization analysis our findings provide insight into the mechanism of cerebral vascular control in healthy subjects suggesting that this control mechanism may involve rapid adjustments within a heartbeat of the cerebral vessels so that bfv remains steady in response to changes in peripheral bp

multiplier ideal sheaves and kahler einstein metrics of positive scalar curvature we present a method for proving the existence of kiihler einstein metrics of positive scalar curvature on certain compact complex manifolds and use the method to produce a large class of examples of compact kiihler einstein manifolds of positive scalar curvature suppose that m is a compact complex manifold of positive first chern class as is well known the existence of a kiihler einstein metric on m is equivalent to the existence of a solution to a certain complex monge ampere equation on m to solve this complex mongeampere equation by the method of continuity one needs only to establish the appropriate zeroth order a priori estimate suppose now that m does not admit a kiihler einstein metric so that the zeroth order a priori estimate fails to hold from this lack of an estimate we extract various global algebro geometric properties of m by introducing a coherent sheaf of ideals j on m called the multiplier ideal sheaf which carefully measures the extent to which the estimate fails the sheaf y is analogous to the subelliptic multiplier ideal sheaf that j j kohn introduced over a decade ago to obtain sufficient conditions for subellipticity of the d neumann problem now j is a global algebro geometric object on m and it so happens that j satisfies a number of highly nontrivial global algebro geometric conditions including a cohomology vanishing theorem in particular the complex analytic subspace v c m cut out by j is nonempty connected and has arithmetic genus zero if v is zero dimensional then it is a single reduced point while if v is one dimensional then its support is a tree of smooth rational curves the logarithmic geometric genus of m v always vanishes these considerations place nontrivial global algebro geometric restric

comparison of the bergman and szego kernels abstract the quotient of the szego and bergman kernels for a smooth bounded pseudoconvex domains in c n is bounded from above by a constant multiple of log p for any p n where is the distance to the boundary for a class of domains that includes those of d angelo finite type and those with plurisubharmonic defining functions the quotient is also bounded from below by a constant multiple of log p for any p 1 moreover for convex domains the quotient is bounded from above and below by constant multiples of

a semi implicit semi lagrangian p adaptive discontinuous galerkin method for the shallow water equations a semi implicit and semi lagrangian discontinuous galerkin method for the shallow water equations is proposed for applications to geophysical scale flows a non conservative formulation of the advection equation is employed in order to achieve a more treatable form of the linear system to be solved at each time step the method is equipped with a simple p adaptivity criterion that allows to adjust dynamically the number of local degrees of freedom employed to the local structure of the solution numerical results show that the method captures well the main features of gravity and inertial gravity waves as well as reproducing correct solutions in nonlinear test cases with analytic solutions the accuracy and effectiveness of the method are also demonstrated by numerical results obtained at high courant numbers and with automatic choice of the local approximation degree

brief paper razumikhin type stability theorems for discrete delay systems in this paper by employing the razumikhin technique and lyapunov functions razumikhin type theorems that guarantee the uniform stability uniformly asymptotic stability and uniformly exponential stability for the general discrete delay systems are established respectively moreover razumikhin type uniformly exponential stability theorem gives the estimation of the convergence speed as theoretic application the razumikhin type uniformly exponential stability result is further studied and used to show some well known stability results for some kinds of discrete delay systems finally examples are also worked through to illustrate our results

robust synchronization of an array of coupled stochastic discrete time delayed neural networks this paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete time neural networks with time varying delay the individual neural network is subject to parameter uncertainty stochastic disturbance and time varying delay where the norm bounded parameter uncertainties exist in both the state and weight matrices the stochastic disturbance is in the form of a scalar wiener process and the time delay enters into the activation function for the array of coupled neural networks the constant coupling and delayed coupling are simultaneously considered we aim to establish easy to verify conditions under which the addressed neural networks are synchronized by using the kronecker product as an effective tool a linear matrix inequality lmi approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally robustly exponentially synchronized in the mean square the lmi based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time varying delay and can be solved efficiently via the matlab lmi toolbox two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme

lp estimates and existence theorems for the operator on complete kahler manifolds abstract in this paper we establish some l p estimates and existence theorems for the operator on a holomorphic hermitian vector bundle over a complete kahler manifold as applications we prove some vanishing theorems of the l p dolbeault cohomology on complete kahler manifolds with suitable geometric conditions

entropy adjoint p adaptive discontinuous galerkin method for the under resolved simulation of turbulent flows this paper presents an approach to mesh adaptation suitable for scale resolving simulations the methodology is based on the entropy adjoint approach which corresponds to a standard output based a

the equation on a positive current we study the induced equation on a positive current in a complex manifold we extend the l 2 estimates for the equation to harmonic currents of bidimension 1 1 satisfying a frobenius type condition we also show that the l 2 estimates are satisfied for the equation on a positive closed current of bidegree 1 1 on a pseudoconvex domain in n

a posteriori error estimation for discontinuous galerkin finite element approximation it is shown that the interelement discontinuities in a discontinuous galerkin finite element approximation are subordinate to the error measured in the broken h 1 seminorm one consequence is that the dg norm of the error is equivalent to the broken energy seminorm computable a posteriori error bounds are obtained for the error measured in both the dg norm and the broken energy seminorm and are shown to be efficient in the sense that they also provide lower bounds up to a constant and higher order data oscillation terms the estimators are completely free of unknown constants and provide guaranteed numerical bounds for the error

synchronization analysis of linearly coupled networks of discrete time systems abstract in this paper we present a framework for analysis of synchronization of linearly coupled map lattices lcmls the dynamics at each node of the coupled map lattices is described by a general difference equation which can be of chaotic or others as for coupling configuration of the linearly coupled map lattices it is not assumed that the coupling matrix is symmetric and irreducible criteria are obtained for both local and global synchronization these criteria reveal that two factors influence synchronization dynamical behaviors at each node and coupling configuration by these criteria one can verify whether the lcml is synchronized which is important and useful for both understanding and interpreting synchronization phenomena and designing coupling configuration a scale d is presented to measure the synchronization capability of a linearly coupled map lattice as we show d can be regarded as a function of the smallest and the largest eigenvalues of the coupling matrix various kinds of coupling schemes including complex networks such as small world sw lattice and scale free network are studied the quantity d is carefully analyzed and calculated for each case

convergence rate for discrete time multiagent systems with time varying delays and general coupling coefficients multiagent systems mass are ubiquitous in our real world there is an increasing attention focusing on the consensus or synchronization problem of mass over the past decade although there are numerous results reported on the convergence of a discrete time mas based on the infinite products of matrices few results are on the convergence rate because of the switching topology the traditional eigenvalue analysis and the lyapunov function methods are both invalid for the convergence rate analysis of an mas with a switching topology therefore the estimation of the convergence rate for a discrete time mas with time varying delays remains a difficult problem to overcome the essential difficulty of switching topology this paper aims at developing a contractive set approach to analyze the convergence rate of a discrete time mas in the presence of time varying delays and generalized coupling coefficients using the proposed approach we obtain an upper bound of the convergence rate under the condition of joint connectivity in particular the proposed method neither requires the nonnegative property of the coupling coefficients nor the basic assumption of a uniform lower bound for all positive coupling coefficients which have been widely applied in the existing works on this topic as an application of the main results we will show that the classical vicsek model with time delays can realize synchronization if the initial topology is connected

pluriharmonic maps of maximal rank if f m p is a pluriharmonic map of a complex manifold m into a compact symmetric space p then the image of any holomorphic tangent space t xm under df x is a flat subspace of t p cp where p f x thus the maximal dimension of flat subspaces of t p cp other than t p p and t p p if p is hermitian is a bound for the rank of any non holomorphic pluriharmonic map into p we give examples of pluriharmonic maps of maximal rank when p is a complex grassmannian in fact we classify all those maps under an additional condition isotropy

global synchronization for delayed complex networks with randomly occurring nonlinearities and multiple stochastic disturbances this paper is concerned with the synchronization problem for a new class of continuous time delayed complex networks with stochastic nonlinearities randomly occurring nonlinearities interval time varying delays unbounded distributed delays as well as multiple stochastic disturbances the stochastic nonlinearities and multiple stochastic disturbances are investigated here in order to reflect more realistic dynamical behaviors of the complex networks that are affected by the noisy environment by utilizing a new matrix functional with the idea of partitioning the lower bound 1 of the time varying delay we employ the stochastic analysis techniques and the properties of the kronecker product to establish delay dependent synchronization criteria that ensure the globally asymptotically mean square synchronization of the addressed stochastic delayed complex networks the sufficient conditions obtained are in the form of linear matrix inequalities lmis whose solutions can be readily solved by using the standard numerical software a numerical example is exploited to show the applicability of the proposed results

estimates for the neumann problem and nonexistence of c 2 levi flat hypersurfaces in cp n letbe a pseudoconvex domain with c 2 boundary in cp n n 2 we prove that the neumann operator n exists for square integrable forms on furthermore there exists a number 0 0 such that the operators n n n and the bergman projection are regular in the sobolev space w for 0 and n 2 as a consequence we prove the nonexistence of c 2 levi flat hypersurfaces in cp n

a comparison of refinement indicators for p adaptive simulations of steady and unsteady flows using discontinuous galerkin methods abstract this paper presents an analysis of refinement indicators for the simulation of steady and unsteady flows by means of p adaptive algorithms for discontinuous galerkin dg methods residual error discretization error and feature based indicators are compared by studying their effect on convergence history computational gain and refinement regions selected by the adaptive algorithm the analysis is initially carried out on steady flow configurations static p adaptive simulations of the periodic flow past a cylinder at r e 100 are then performed compared to uniform p refinement a reduction between 50 and 75 in the number of degrees of freedom is obtained for all test cases considered the accuracy and efficiency observed for the small scale energy density 1 and spectral decay 2 indicators demonstrate their great potential for the adaptive simulation of unsteady flows

adaptation strategies for high order discontinuous galerkin methods based on tau estimation in this paper three p adaptation strategies based on the minimization of the truncation error are presented for high order discontinuous galerkin methods the truncation error is approximated by means of a estimation procedure and enables the identification of mesh regions that require adaptation three adaptation strategies are developed and termed a posteriori quasi a priori and quasi a priori corrected all strategies require fine solutions which are obtained by enriching the polynomial order but while the former needs time converged solutions the last two rely on non converged solutions which lead to faster computations in addition the high order method permits the spatial decoupling for the estimated errors and enables anisotropic p adaptation these strategies are verified and compared in terms of accuracy and computational cost for the euler and the compressible navier stokes equations it is shown that the two quasi a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment namely for a viscous boundary layer flow we obtain a speedup of 6 6 and 7 6 for the quasi a priori and quasi a priori corrected approaches respectively

synchronization of markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time varying delays the paper investigates the synchronization stability problem for a class of complex dynamical networks with markovian jumping parameters and mixed time delays the complex networks consist of m modes and the networks switch from one mode to another according to a markovian chain with known transition probability the mixed time delays are composed of discrete and distributed delays the discrete time delay is assumed to be random and its probability distribution is known a priori in terms of the probability distribution of the delays the new type of system model with probability distribution dependent parameter matrices is proposed based on the stochastic analysis techniques and the properties of the kronecker product delay dependent synchronization stability criteria in the mean square are derived in the form of linear matrix inequalities which can be readily solved by using the lmi toolbox in matlab the solvability of derived conditions depends on not only the size of the delay but also the probability of the delay taking values in some intervals finally a numerical example is given to illustrate the feasibility and effectiveness of the proposed method

adaptive discontinuous galerkin finite element methods for the compressible euler equations in this paper a recently developed approach for the design of adaptive discontinuous galerkin finite element methods is applied to physically relevant problems arising in inviscid compressible fluid flows governed by the euler equations of gas dynamics in particular we employ weighted type i a posteriori bounds to drive adaptive finite element algorithms for the estimation of the error measured in terms of general target functionals of the solution these error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain dual problem that must be numerically approximated this general approach leads to the design of economical finite element meshes specifically tailored to the computation of the target functional of interest as well as providing reliable and efficient error estimation the superiority of the proposed approach over mesh refinement algorithms which employ standard unweighted type ii error indicators which do not require the solution of an auxiliary problem are illustrated by a series of numerical experiments here we consider transonic flow through a nozzle as well as subsonic and supersonic flows around different airfoil geometries

stochastic synchronization in blinking networks of chaotic maps in this paper we analyze stochastic synchronization of coupled chaotic maps over blinking networks composed of a pristine static network and stochastic on off couplings between any pair of nodes we focus on mean square linear stability of the synchronized state by analyzing the time evolution of the second moment of the variation transverse to the synchronization manifold by projecting the variational equations on the eigenvectors of a higher order state matrix describing this variational dynamics we establish a necessary and sufficient condition for stochastic synchronization based on the largest lyapunov exponent of the map and the spectral radius of such matrix this condition is further simplified by computing closed form results for the spectral properties of the moments of the graph laplacian associated to the intermittent coupling and using classical eigenvalue bounds we illustrate the main results through simulations on synchronization of chaotic henon maps

chaotic synchronization in lattice of partial state coupled lorenz equations abstract in this paper we study chaotic synchronization in lattices of coupled lorenz equations with neumann or periodic boundary condition three different coupling configurations in the single x i y i or z i component are considered synchronization is affected by coupling rules we prove that synchronization occurs for either x i or y i component coupling provided the coupling coefficient is sufficiently large moreover we determine the dependence of coupling coefficients on the lattice size for the case of the z i component coupling we demonstrate by numerical experience that the synchronization cannot occur