a staggered grid lagrangian eulerian remap code for 3 d mhd simulations abstract in this paper an approach to multidimensional magnetohydrodynamics mhd which correctly handles shocks but does not use an approximate riemann solver is proposed this approach is simple and is based on control volume averaging with a staggered grid the method builds on the older and often overlooked technique of on each step taking a fully 3 d lagrangian step and then conservatively remapping onto the original grid at the remap step gradient limiters are applied so that the scheme is monotonicity preserving for euler s equations this technique combined with an appropriately staggered grid and wilkins artificial viscosity can give results comparable to those from approximate riemann solvers we show how this can be extended to include a magnetic field maintaining the divergence free condition and pressure positivity and then present numerical test results where possible a comparison with other shock capturing techniques is presented and the advantages and disadvantages of the proposed scheme are clearly explained

a new method for complete stability analysis of cellular neural networks with time delay this paper presents new complete stability results for delayed cellular neural networks dcnns a novel method is proposed for complete stability analysis of dcnns by applying the m matrix theory and introducing some new estimation techniques on the solutions of dcnns a simple and improved complete stability criterion is derived the new criterion unifies the delay dependent and delay independent complete stability conditions for dcnns moreover the obtained delay dependent criterion can give a larger upper bound of the time delay than the existing ones such that the complete stability can still be retained numerical examples are presented which show that the new complete stability results for dcnns are compared favorably with the existing results

adaptive fuzzy tracking control for a class of pure feedback nonlinear systems with time varying delay and unknown dead zone abstract this paper investigates the problem of adaptive fuzzy tracking control for a category of pure feedback nonlinear systems with time varying delay and unknown dead zone fuzzy logic systems are used to identify unknown functions existing in systems mean value theorem is introduced to overcome the difficulty arising from the pure feedback structure in designing controller based on the information of dead zone slopes dead zone is handled only one adaptive parameter needs updating online by considering the norm of membership function vectors rather than all sub vectors moreover utilizing the adaptive backstepping technique a novel adaptive fuzzy tracking control scheme is developed to guarantee all signals of the closed loop systems are semi globally uniformly ultimately bounded and the tracking error can be regulated to the origin with a small neighborhood the stability of the closed loop system is proved and simulation results are given to demonstrate the effectiveness of the proposed control approach

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

relaxed conditions for stability of time varying delay systems in this paper the problem of delay dependent stability analysis of time varying delay systems is investigated firstly a new inequality which is the modified version of free matrix based integral inequality is derived and then by aid of this new inequality two novel lemmas which are relaxed conditions for some matrices in a lyapunov function are proposed based on the lemmas improved delay dependent stability criteria which guarantee the asymptotic stability of the system are presented in the form of linear matrix inequality lmi two numerical examples are given to describe the less conservatism of the proposed methods

an improved global asymptotic stability criterion for delayed cellular neural networks a new lyapunov krasovskii functional is constructed for delayed cellular neural networks and the s procedure is employed to handle the nonlinearities an improved global asymptotic stability criterion is also derived that is a generalization of and an improvement over previous results numerical examples demonstrate the effectiveness of the criterion

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

mixed h l2 l state estimation for switched genetic regulatory networks subject to packet dropouts a persistent dwell time switching mechanism abstract in this work a kind of switched gene regulatory networks with packet dropout and uncertainties are constructed by switched coupled nonlinear difference equations in comparison a more comprehensive switching regulation persistent dwell time is employed to it the aim is to construct a mixed mode dependent and mode independent estimator for the before mentioned gene regulatory networks with a view to the loss of system modal information thereafter the augmented system is established after that the sufficient conditions of the exponential stability and mixed h l 2 l performance for the augmented system are deduced by the switching lyapunov theory finally a numerical example is employed to elucidate the validity of the estimator gains decoupled by the congruent transformation

non uniform convergence of finite volume schemes for riemann problems of ideal magnetohydrodynamics this paper presents riemann test problems for ideal magnetohydrodynamics mhd finite volume schemes the test problems place emphasis on the hyperbolic irregularities of the ideal mhd system namely the occurrence of intermediate shocks and non unique solutions we investigate numerical solutions for the test problems obtained by several commonly used methods roe hlle central scheme all methods turned out to show a non uniform convergence behavior which may be paraphrased as pseudo convergence initially the methods show convergence towards a wrong solution with irregular wave patterns only after heavy grid refinement the methods switch to converge to the true solution this behavior is most pronounced whenever the solution should be unique but its phase space trajectory lies in the vicinity of that of a non unique solution we show detailed grid convergence studies and empirical error analysis the results may be related to similar results for a 2 2 model system and to time dependent investigations of other authors the non uniform convergence is expected to be present for any diffusive finite volume method and question the reliability of coarse grid ideal mhd solutions also in higher space dimensions

new stability results for delayed neural networks this paper is concerned with the stability for delayed neural networks by more fully making use of the information of the activation function a new lyapunov krasovskii functional lkf is constructed then a new integral inequality is developed and more information of the activation function is taken into account when the derivative of the lkf is estimated by lyapunov stability theory a new stability result is obtained finally three examples are given to illustrate the stability result is less conservative than some recently reported ones

higher order godunov methods for general systems of hyperbolic conservation laws abstract we describe an extension of higher order godunov methods to general systems of hyperbolic conservation laws this extension allow the method to be applied to problems that are not strictly hyperbolic and exhibit local linear degeneracies in the wave fields the method constructs an approximation of the riemann problem from local wave information a generalization of the engquist osher flux for systems is then used to compute a numerical flux based on this approximation this numerical flux replaces the godunov numerical flux in the algorithm thereby eliminating the need for a global riemann problem solution the additional modifications to the godunov methodology that are needed to treat loss of strict hyperbolicity are described in detail the method is applied to some simple model problems for which the global analytic structure is known the method is also applied to the black oil model for multiphase flow in petroleum reservoirs

nonparametric density estimation for randomly perturbed elliptic problems i computational methods a posteriori analysis and adaptive error control we consider the nonparametric density estimation problem for a quantity of interest computed from solutions of an elliptic partial differential equation with randomly perturbed coefficients and data our particular interest are problems for which limited knowledge of the random perturbations are known we derive an efficient method for computing samples and generating an approximate probability distribution based on lion s domain decomposition method and the neumann series we then derive an a posteriori error estimate for the computed probability distribution reflecting all sources of deterministic and statistical errors finally we develop an adaptive error control algorithm based on the a posteriori estimate

delay dependent global exponential stability for delayed recurrent neural networks this paper deals with the global exponential stability for delayed recurrent neural networks drnns by constructing an augmented lyapunov krasovskii functional and adopting the reciprocally convex combination approach and wirtinger based integral inequality delay dependent global exponential stability criteria are derived in terms of linear matrix inequalities meanwhile a general and effective method on global exponential stability analysis for drnns is given through a lemma where the exponential convergence rate can be estimated with this lemma some global asymptotic stability criteria of drnns acquired in previous studies can be generalized to global exponential stability ones finally a frequently utilized numerical example is carried out to illustrate the effectiveness and merits of the proposed theoretical results

stability analysis for neural networks with time varying interval delay this letter is concerned with the stability analysis of neural networks nns with time varying interval delay the relationship between the time varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of lyapunov functional as a result some improved delay interval dependent stability criteria for nns with time varying interval delay are proposed numerical examples are given to demonstrate the effectiveness and the merits of the proposed method

further result on asymptotic stability criterion of cellular neural networks with time varying discrete and distributed delays based on a recent work and the linear matrix inequality lmi optimization approach we extend the recent work on global asymptotic stability of a class of neural networks to uncertain cellular neural networks with time varying discrete and distributed delays

robust stability analysis for stochastic neural networks with time varying delay this brief investigates the problem of mean square exponential stability of uncertain stochastic delayed neural networks dnns with time varying delay a novel lyapunov functional is introduced with the idea of the discretized lyapunov krasovskii functional lkf method then a new delay dependent mean square exponential stability criterion is derived by applying the free weighting matrix technique and by equivalently eliminating time varying delay through the idea of convex combination numerical examples illustrate the effectiveness of the proposed method and the improvement over some existing methods

estimation of domain of attraction for aperiodic sampled data switched delayed neural networks subject to actuator saturation in this paper for the case of the asynchronous switching caused by that subsystem s switching occuring during a sampling interval the domain of attraction estimation problem is investigated for aperiodic sampled data switched delayed neural networks asdsdnns subject to actuator saturation a parameters dependent time scheduled lyapunov functional consisting of a novel looped functional is constructed using segmentation technology and linear interpolation by employing this novel functional and using an average dwell time adt approach exponential stability criteria are proposed for polytopic uncertain asdsdnns subject to actuator saturation and a relationship between adt and sampling period is revealed for asdsdnns as a corollary exponential stability criteria are proposed for nominal asdsdnns subject to actuator saturation furthermore by describing the domain of attraction as a time varying ellipsoid determined by the time scheduled lyapunov matrix the proposed theoretical conditions are transformed into a linear matrix inequality lmi based multi objective optimization problem the dynamic estimates of the domain of attraction for asdsdnns are solved numerical simulation examples are provided to illustrate the effectiveness of the proposed method

admissible delay upper bounds for global asymptotic stability of neural networks with time varying delays this paper is concerned with global asymptotic stability of a neural network with a time varying delay where the delay function is differentiable uniformly bounded with delay derivative bounded from above first a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions this inequality provides a tighter bound in the form of a convex combination than some existing ones second by constructing proper lyapunov krasovskii functional global asymptotic stability of the neural network is analyzed for two types of the time varying delays depending on whether or not the lower bound of the delay derivative is known third noticing that sufficient conditions on stability from estimation on the derivative of some lyapunov krasovskii functional are affine both on the delay function and its derivative allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study finally two numerical examples are given to substantiate the effectiveness of the proposed method

global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays by employing the lyapunov krasovskii functional and linear matrix inequality lmi approach the problem of global asymptotical stability is studied for recurrent neural networks with both discrete time varying delays and distributed time varying delays some sufficient conditions are given for checking the global asymptotical stability of recurrent neural networks with mixed time varying delay the proposed lmi result is computationally efficient as it can be solved numerically using standard commercial software two examples are given to show the usefulness of the results

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

high order numerical method for magnetohydrodynamic control of shock induced separation magnetic fields significantly affect the flow of ionized gases and may be exploited for the control of separation transition and turbulence the wave structure of ionized gas high speed flows under the influence of magnetic fields is more involved than the waves of ordinary gas dynamics and high resolution is required to accurately compute the complex wave interactions of such flows with discontinuities numerical solutions of the nonlinear ideal and viscous magnetohydrodynamic equations are obtained with a high order accurate shock capturing scheme the numerical method is tested for flows containing strong magnetohydrodynamic discontinuities and smooth flow features to ensure that it maintains high order accuracy for the smooth parts of the flow it preserves numerical stability and eliminates nonphysical features that result from the violation of the divergence free condition for the magnetic field problems with exact solutions such as the convection of smooth waves caused by magnetic fields are also solved numerically to validate the method the numerical method is applied to simulate separation control at the interaction region of an oblique shock with a laminar boundary layer under the influence of magnetic fields

complete delay decomposing approach to asymptotic stability for neural networks with time varying delays this paper is concerned with the problem of stability of neural networks with time varying delays a novel lyapunov krasovskii functional decomposing the delays in all integral terms is proposed by exploiting all possible information and considering independent upper bounds of the delay derivative in various delay intervals some new generalized delay dependent stability criteria are established which are different from the existing ones and improve upon previous results numerical examples are finally given to demonstrate the effectiveness and the merits of the proposed method

a simple and accurate riemann solver for isothermal mhd a new approximate riemann solver for the equations of magnetohydrodynamics mhd with an isothermal equation of state is presented the proposed method of solution draws on the recent work of miyoshi and kusano in the context of adiabatic mhd where an approximate solution to the riemann problem is sought in terms of an average constant velocity and total pressure across the riemann fan this allows the formation of four intermediate states enclosed by two outermost fast discontinuities and separated by two rotational waves and an entropy mode in the present work a corresponding derivation for the isothermal mhd equations is presented it is found that the absence of the entropy mode leads to a different formulation which is based on a three state representation rather than four numerical tests in one and two dimensions demonstrate that the new solver is robust and comparable in accuracy to the more expensive linearized solver of roe although considerably faster

an implicit scheme for nonideal magnetohydrodynamics a new implicit algorithm is developed for solving the time dependent nonideal magnetohydrodynamic equations it can also be used as an efficient relaxation scheme for steady state solutions the algorithm is a finite volume scheme that uses an approximate riemann solver for the hyperbolic fluxes and central differencing applied on nested control volumes for the parabolic fluxes that arise from the non ideal terms i e resistivity and viscosity in one dimension the scheme is second order accurate in space and time in two or three dimensions the accuracy is between first and second order for the class of problems considered the implicit formulation is stable for any size time step thus allowing efficient tracking of slower transients the implicit operator is inverted using a lower upper symmetric gauss seidel iteration results from several test cases are presented that show good agreement with analytical solutions and illustrate the advantages of the scheme

notes on the eigensystem of magnetohydrodynamics the eigenstructure of the equations governing one dimensional ideal magnetohy drodynamics is examined motivated by the wish to exploit it for construction of high resolution computational algorithms the results are given in simple forms that avoid indeterminacy or degeneracy whenever possible the unavoidable indeterminacy near the magnetosonic or triple umbilic state is analysed and shown to cause no difficulty in evaluating a numerical flux function the structure of wave paths close to this singularity is obtained and simple expressions are presented for the structure coefficients that govern wave steepening

stability analysis of distributed delay neural networks based on relaxed lyapunov krasovskii functionals this paper revisits the problem of asymptotic stability analysis for neural networks with distributed delays the distributed delays are assumed to be constant and prescribed since a positive definite quadratic functional does not necessarily require all the involved symmetric matrices to be positive definite it is important for constructing relaxed lyapunov krasovskii functionals which generally lead to less conservative stability criteria based on this fact and using two kinds of integral inequalities a new delay dependent condition is obtained which ensures that the distributed delay neural network under consideration is globally asymptotically stable this stability criterion is then improved by applying the delay partitioning technique two numerical examples are provided to demonstrate the advantage of the presented stability criteria

simulating diffusions with piecewise constant coefficients using a kinetic approximation using a kinetic approximation of a linear diffusion operator we propose an algorithm that allows one to deal with the simulation of a multi dimensional stochastic process in a media which is locally isotropic except on some surface where the diffusion coefficient presents some discontinuities numerical examples are given in dimensions one to three on pdes or stochastic pdes with or without source terms

a computational measure theoretic approach to inverse sensitivity problems ii a posteriori error analysis in part one of this paper t butler and d estep siam j numer anal to appear we develop and analyze a numerical method to solve a probabilistic inverse sensitivity analysis problem for a smooth deterministic map assuming that the map can be evaluated exactly in this paper we treat the situation in which the output of the map is determined implicitly and is difficult and or expensive to evaluate e g requiring the solution of a differential equation and hence the output of the map is approximated numerically the main goal is an a posteriori error estimate that can be used to evaluate the accuracy of the computed distribution solving the inverse problem taking into account all sources of statistical and numerical deterministic errors we present a general analysis for the method and then apply the analysis to the case of a map determined by the solution of an initial value problem

nonparametric density estimation for randomly perturbed elliptic problems ii applications and adaptive modeling nonparametric density estimation for randomly perturbed elliptic problems ii applications and adaptive modeling

extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics an extension of the piecewise parabolic method to treat multidimensional ideal magnetohydrodynamical equations is presented in this paper the multidimensional scheme is constructed from a one dimensional functioning code based on the dimensional splitting method originally suggested by strang the functioning code is built upon a nonlinear riemann solver for ideal mhd equations recently developed by the authors the correctness of the scheme is tested in the steepening of waves in both one and two dimensional situations and in various mhd shock tube problems which involve all the discontinuities in ideal mhd the robust character of the scheme is demonstrated in the shock tube problems and in the interaction between mhd shocks and a cloud the results of these problems show that the scheme keeps the principal advantages of a high order godunov scheme robust operation in the presence of very strong waves thin shock fronts with little attendant noise generation and thin contact discontinuity

further results on delay dependent stability criteria of neural networks with time varying delays in this brief paper an augmented lyapunov functional which takes an integral term of state vector into account is introduced owing to the functional an improved delay dependent asymptotic stability criterion for delayed neural networks nns is derived in term of linear matrix inequalities lmis it is shown that the obtained criterion can provide less conservative result than some existing ones when linear fractional uncertainties appear in nns a new robust delay dependent stability condition is also given numerical examples are given to demonstrate the applicability of the proposed approach

cost effective robust stabilization and bifurcation suppression a novel technique of robust stabilization and bifurcation suppression is proposed the proposed method the center probe method stabilizes an equilibrium point of a delay differential equation at

generalizations and accelerations of lions nonoverlapping domain decomposition method for linear elliptic pde in this paper a one parameter generalization of lions nonoverlapping domain decomposition method for linear elliptic pdes is proposed and studied the generalized methods are shown to be descent direction methods for minimizing an interface bias functional iteration convergence of both the continuous and finite element versions of the proposed methods is established it is theoretically and numerically demonstrated that for generic choices of the parameter the generalized methods converge faster than lions original method algorithms are given and numerical results are presented

hierarchical stability conditions for a class of generalized neural networks with multiple discrete and distributed delays this brief investigates the analysis issue for global asymptotic stability of a class of generalized neural networks with multiple discrete and distributed delays to tackle delays arising in different neuron activation functions we employ a generalized model with multiple discrete and distributed delays which covers various existing neural networks we then generalize the bessel legendre inequalities to deal with integral terms with any linearly independent functions and nonlinear function of states based on these inequalities we design the lyapunov krasovskii functional and derive hierarchical linear matrix inequality stability conditions finally three numerical examples are provided to demonstrate that the proposed method is less conservative with a reasonable numerical burden than the existing results

a staggered mesh algorithm using high order godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations the equations of magnetohydrodynamics mhd have been formulated as a hyperbolic system of conservation laws in that form it becomes possible to use higher order godunov schemes for their solution this results in a robust and accurate solution strategy however the magnetic field also satisfies a constraint that requires its divergence to be zero at all times this is a property that cannot be guaranteed in the zone centered discretizations that are favored in godunov schemes without involving a divergence cleaning step in this paper we present a staggered mesh strategy which directly uses the properly upwinded fluxes that are provided by a godunov scheme the process of directly using the upwinded fluxes relies on a duality that exists between the fluxes obtained from a higher order godunov scheme and the electric fields in a plasma by exploiting this duality we have been able to construct a higher order godunov scheme that ensures that the magnetic field remains divergence free up to the computer s round off error we have even presented a variant of the basic algorithm that uses multidimensional features in the flow to design an upwinded strategy that aligns itself with the predominant upwinded direction in the flow we have devised several stringent test problems to show that the scheme works robustly and accurately in all situations in doing so we have shown that a scheme that involves a collocation of magnetic field variables that is different from the one traditionally favored in the design of higher order godunov schemes can nevertheless offer the same robust and accurate performance of higher order godunov schemes provided the properly upwinded fluxes from the godunov methodology are used in the scheme s construction

lmi based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures global asymptotic stability problem is studied for a class of recurrent neural networks with distributed delays satisfying lebesgue stieljies measures on the basis of linear matrix inequality the concerned network model includes many neural network models with various delays and structures as its special cases such as the delays covering the discrete delays and distributed delays and the network structures containing the neutral type networks and high order networks therefore many new stability criteria for the above neural network models have also been derived from the present stability analysis method all the obtained stability results have similar matrix inequality structures and can be easily checked three numerical examples are used to show the effectiveness of the obtained results

fault detection for discrete time linear systems based on descriptor observer approach this paper investigates the problem of actuator fault detection filter design for discrete time linear systems with output disturbance by using the descriptor observer method an h fault detection filter is designed to guarantee the residual system is admissible and satisfies the h performance by utilizing lyapunov function approach a sufficient condition for the admissible of the residual system is obtained in the form of linear matrix inequality lmi the desired fault detection filter can be designed by solving a set of lmis finally a numerical example is proposed to illustrate the effectiveness of the developed method

stability analysis for delayed neural networks with an improved general free matrix based integral inequality this paper revisits the problem of stability analysis for neural networks with a time varying delay an improved general free matrix based fmb integral inequality is proposed with an undetermined number m compared with the conventional fmb ones the improved inequality involves a much smaller number of free matrix variables in particular the improved fmb integral inequality is expressed in a concrete form for any value of m by employing the new inequality with a properly constructed lyapunov krasovskii functional a new stability condition is derived for neural networks with a time varying delay two commonly used numerical examples are given to show strong competitiveness of the proposed approach in both the conservatism and computation burdens

new lyapunov krasovskii functionals for global asymptotic stability of delayed neural networks this brief deals with the problem of global asymptotic stability for a class of delayed neural networks some new lyapunov krasovskii functionals are constructed by nonuniformly dividing the delay interval into multiple segments and choosing proper functionals with different weighting matrices corresponding to different segments in the lyapunov krasovskii functionals then using these new lyapunov krasovskii functionals some new delay dependent criteria for global asymptotic stability are derived for delayed neural networks where both constant time delays and time varying delays are treated these criteria are much less conservative than some existing results which is shown through a numerical example

exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays this paper is concerned with exponential estimates and stabilization for a class of uncertain singular systems with discrete and distributed delays a sufficient condition which does not only guarantee the exponential stability and admissibility but also gives the estimates of decay rate and decay coefficient is established in terms of the linear matrix inequality lmi technique and a new lyapunov krasovskii functional the estimating procedure is implemented by solving a set of lmis which can be checked easily by effective algorithms under the proposed condition the algebraic subsystems possess the same decay rate as the differential ones moreover a state feedback stabilizing controller which makes the closed loop system exponentially stable and admissible with a prescribed lower bound of the decay rate is designed numerical examples are provided to illustrate the effectiveness of the theoretical results

stochastic computation based on orthogonal expansion of random fields abstract in solving stochastic differential equations recently a random variable based polynomial chaos rv pc method has been developed as a major numerical solver for many realistic random media problems the rv pc method however confronts a critical challenge of curse of dimensionality since a random field is represented by random variables the use of various optimal sampling techniques and conventional high dimensional methods still faces the curse of dimensionality distinguished from all the random variable based methods in this study a novel random field based orthogonal expansion rf oe method is proposed in aim to circumvent the curse of dimensionality for many physical systems whereas the input information is represented as random fields or stochastic processes e g seismic ocean wave wind load shock wave and geophysical media multiscale modeling of random media problems is selected as the benchmark problem to test the rf oe method especially the rf oe method provides a perfect matching with the higher order mehler s formula by replacing high dimensional random variable representations with a series of orthogonal expansion terms about an underlying random field process the rf oe method reduces the number of dimensions of a stochastic differential equation exponentially in the first example the rf oe method is verified with monte carlo simulation on a lognormal random media flow transport problem in the second example the rf oe method is applied to a time domain problem involving orthogonal expansion of random excitations in the conclusion the items for further development of the rf oe method are identified

a new criterion of delay dependent asymptotic stability for hopfield neural networks with time delay in this brief the problem of global asymptotic stability for delayed hopfield neural networks hnns is investigated a new criterion of asymptotic stability is derived by introducing a new kind of lyapunov krasovskii functional and is formulated in terms of a linear matrix inequality lmi which can be readily solved via standard software this new criterion based on a delay fractioning approach proves to be much less conservative and the conservatism could be notably reduced by thinning the delay fractioning an example is provided to show the effectiveness and the advantage of the proposed result

adaptive variational multiscale methods based on a posteriori error estimation energy norm estimates for elliptic problems we develop a new adaptive multiscale finite element method using the variational multiscale framework together with a systematic technique for approximation of the fine scale part of the solution the fine scale is approximated by a sum of solutions to decoupled localized problems which are solved numerically on a fine grid partition of a patch of coarse grid elements the sizes of the patches of elements may be increased to control the error caused by localization we derive an a posteriori error estimate in the energy norm which captures the dependency of the crucial discretization parameters the coarse grid mesh size the fine grid mesh size and the sizes of the patches based on the a posteriori error estimate we present an adaptive algorithm that automatically tunes these parameters finally we show how the method works in practice by presenting various numerical examples

improved delay dependent asymptotic stability criteria for delayed neural networks this brief is concerned with asymptotic stability of neural networks with uncertain delays two types of uncertain delays are considered one is constant while the other is time varying the discretized lyapunov krasovskii functional lkf method is integrated with the technique of introducing the free weighting matrix between the terms of the leibniz newton formula the integrated method leads to the establishment of new delay dependent sufficient conditions in form of linear matrix inequalities for asymptotic stability of delayed neural networks dnns a numerical simulation study is conducted to demonstrate the obtained theoretical results which shows their less conservatism than the existing stability criteria

stability analysis for delayed neural networks considering both conservativeness and complexity this paper investigates delay dependent stability for continuous neural networks with a time varying delay this paper aims at deriving a new stability criterion considering tradeoff between conservativeness and calculation complexity a new lyapunov krasovskii functional with simple augmented terms and delay dependent terms is constructed and its derivative is estimated by several techniques including free weighting matrix and inequality estimation methods then the influence of the techniques used on the conservativeness and the complexity is analyzed one by one moreover useful guidelines for improving criterion and future work are briefly discussed finally the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples

shock capturing approach and nonevolutionary solutions in magnetohydrodynamics shock capturing methods have become an effective tool for the solution of hyperbolic partial differential equations both upwind and symmetric tvd schemes in the framework of the shock capturing approach are thoroughly investigated and applied with great success to a number of complicated multidimensional gasdynamic problems the extension of these schemes to magnetohydrodynamic mhd equations is not a simple task first the exact solution of the mhd riemann problem is too multivariant to be used in regular calculations on the other hand the extensions of roe s approximate riemann problem solvers for mhd equations in general case are nonunique and need further investigation that is why some simplified approaches should be constructed in this work the second order of accuracy in time and space high resolution lax friedrichs type scheme is suggested that gives a drastic simplification of the numerical algorithm comparing to the precise characteristic splitting of jacobian matrices the necessity is shown to solve the full set of mhd equations for modeling of multishocked flows even when the problem is axisymmetric to obtain evolutionary solutions for the numerical example the mhd riemann problem is used with the initial data consisting of two constant states lying to the right and to the left from the centerline of the computational domain if the problem is solved as purely coplanar a slow compound wave appears in the self similar solution obtained by any shock capturing scheme if the full set of mhd equations is used and a small uniform tangential disturbance is added to the magnetic field vector a rotational jump splits from the compound wave and it degrades into a slow shock the reconstruction process of the nonevolutionary compound wave into evolutionary shocks is investigated presented results should be taken into account in the development of shock capturing methods for mhd flows

finite time state estimation for coupled markovian neural networks with sensor nonlinearities this paper investigates the issue of finite time state estimation for coupled markovian neural networks subject to sensor nonlinearities where the markov chain with partially unknown transition probabilities is considered a luenberger type state estimator is proposed based on incomplete measurements and the estimation error system is derived by using the kronecker product by using the lyapunov method sufficient conditions are established which guarantee that the estimation error system is stochastically finite time bounded and stochastically finite time stable respectively then the estimator gains are obtained via solving a set of coupled linear matrix inequalities finally a numerical example is given to illustrate the effectiveness of the proposed new design method

stability and dissipativity analysis of distributed delay cellular neural networks in this brief the problems of delay dependent stability analysis and strict q s dissipativity analysis are investigated for cellular neural networks cnns with distributed delay first by introducing an integral partitioning technique two new forms of lyapunov krasovskii functionals are constructed and improved distributed delay dependent stability conditions are established in terms of linear matrix inequalities based on this criterion a new sufficient delay and dependent condition is given to guarantee that the cnns with distributed delay are strictly q s dissipative the results developed in this brief can tolerate larger allowable delay than existing ones in the literature which is demonstrated by several examples

a measure theoretic computational method for inverse sensitivity problems i method and analysis we consider the inverse sensitivity analysis problem of quantifying the uncertainty of inputs to a deterministic map given specified uncertainty in a linear functional of the output of the map this is a version of the model calibration or parameter estimation problem for a deterministic map we assume that the uncertainty in the quantity of interest is represented by a random variable with a given distribution and we use the law of total probability to express the inverse problem for the corresponding probability measure on the input space assuming that the map from the input space to the quantity of interest is smooth we solve the generally ill posed inverse problem by using the implicit function theorem to derive a method for approximating the set valued inverse that provides an approximate quotient space representation of the input space we then derive an efficient computational approach to compute a measure theoretic approximation of the probability measure on the input space imparted by the approximate set valued inverse that solves the inverse problem

stability analysis of quaternion valued neural networks with both discrete and distributed delays abstract the existence uniqueness and stability of the equilibrium of quaternion valued neural networks qvnns with both discrete and distributed delays are investigated in this paper the considered model is managed as a single entirety without decomposition based on homeomorphic mapping theorem and linear matrix inequality several sufficient criteria are derived to ascertain the aforementioned qvnns to be globally asymptotically stable and exponentially stable moreover provided criteria can be verified by the linear matrix inequality lmi toolbox in matlab finally one simulation example is demonstrated to verify the effectiveness of obtained results

global asymptotic stability for a class of generalized neural networks with interval time varying delays this paper is concerned with global asymptotic stability for a class of generalized neural networks nns with interval time varying delays which include two classes of fundamental nns i e static neural networks snns and local field neural networks lfnns as their special cases some novel delay independent and delay dependent stability criteria are derived these stability criteria are applicable not only to snns but also to lfnns it is theoretically proven that these stability criteria are more effective than some existing ones either for snns or for lfnns which is confirmed by some numerical examples

new passivity analysis for neural networks with discrete and distributed delays in this brief the problem of passivity analysis is investigated for a class of uncertain neural networks nns with both discrete and distributed time varying delays by constructing a novel lyapunov functional and utilizing some advanced techniques new delay dependent passivity criteria are established to guarantee the passivity performance of nns essentially different from the available results when estimating the upper bound of the derivative of lyapunov functionals we consider and best utilize the additional useful terms about the distributed delays which leads to less conservative results these criteria are expressed in the form of convex optimization problems which can be efficiently solved via standard numerical software numerical examples are provided to illustrate the effectiveness and less conservatism of the proposed results

central finite volume methods with constrained transport divergence treatment for ideal mhd two and three dimensional finite volume extensions of the lax friedrichs lf and nessyahu tadmor one dimensional difference schemes were previously presented and successfully applied to several problems for nonlinear hyperbolic systems and in particular to typical test cases for both inviscid and viscous compressible flows these central schemes by pass the resolution at the cell interfaces of the riemann problems thanks to the use of the staggered lf scheme which serves as the base scheme on which high order finite volume methods can be constructed using van leer s muscl type limited reconstruction principle for this purpose two dual grids are used at alternate time steps these methods are extended here to several problems in one and multi dimensional ideal compressible magnetohydrodynamics using a modified version of the first author s central methods with oblique diamond shaped dual cells in two dimensions the system has eight equations and solving the corresponding riemann problem is an elaborate and time consuming process central methods lead to significant computing time reductions and the numerical experiments presented here suggest the accuracy is quite satisfactory in order to satisfy the physical constraint b 0 we have constructed a strategy ctcs inspired from the constrained transport method of evans and hawley the validity of our base scheme and our ctcs approach is clearly confirmed by the results

producing stable periodic solutions of switched impulsive delayed neural networks using a matrix based cubic convex combination approach this article is dedicated to designing a novel periodic impulsive control strategy for producing globally exponentially stable periodic solutions for switched neural networks with discrete and finite distributed time varying delays first tunable parameters and cubic convex combination approach are proposed to study the globally exponential convergence of switched neural networks second a sufficient criterion for the existence uniqueness and globally exponential stability of a periodic solution is demonstrated by using contraction mapping theorem and the impulse delay dependent lyapunov krasovskii functional method it is worth emphasizing that the addressed lyapunov krasovskii functional covers both triple integral terms and novel quadruple integral terms which makes the conservatism of the above criteria decrease even if the original neural network models are unstable or the impulsive effects are strong the addressed neural network model can produce a globally exponentially stable periodic solution these results here which include boundedness globally uniformly exponential convergence and globally exponentially stability of the periodic solution generalize and improve the earlier publications finally two numerical examples and their computer simulations are given to show the effectiveness of theoretical results

h state estimation for neural networks with general activation function and mixed time varying delays this article deals with h state estimation of neural networks with mixed delays in order to make full use of delay information novel delay product lyapunov krasovskii functional lkf by using parameterized delay interval is first constructed then generalized free weighting matrix integral inequality is used to estimate the derivative of lkf to reduce the conservatism also a more general activation function is further applied by combining with parameterized delay interval in order to obtain a more accurate estimator model finally sufficient conditions are derived to confirm that the estimation error system is asymptotically stable with a prescribed h performance numerical examples are simulated to show the benefits of our proposed method