(r, s)-STABILITY OF UNFOLDING OF г-EQUIVARIANT BIFURCATION PROBLEM

In this paper,the (?)-equivariant (s, t)-equivalence relation and (?)-equivariant infinitesimally (r, s)-stability of (?)-equivariant bifurcation problem are defined. The criterion for (?)-equivariant infinitesimally (r, s)-stability is proven when (?) is a compact finite Lie group .Transversality condition is used to characterize the stability.

NNGP_G-STABILITY OF LINEAR MULTISTEP METHODS FOR SYSTEMS OF GENERALIZED NEUTRAL DELAY DIFFERENTIAL EQUATIONS

The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.

Practical φ_0-stability of stochastic differential equations and corresponding stochastic perturbation theory

The notions of practical φ0-stability were introduced for stochastic differential equations. Sufficient conditions on such practical properties were obtained by using the comparison principle and the cone-valued Lyapunov function methods. Based on an extended comparison theorem, a perturbation theory of stochastic differential systems was given.

Integral <i>Φ</i>₀-Stability of Impulsive Differential Equations

In this paper, the notions of integral Φ0-stability of ordinary impulsive differential equations are introduced. The definition of integral Φ0-stability depends significantly on the fixed time impulses. Sufficient conditions for integral Φ0-stability are obtained by using comparison principle and piecewise continuous cone valued Lyapunov functions. A new comparison lemma, connecting the solutions of given impulsive differential system to the solution of a vector valued impulsive differential system is also established.

μ-stability of multiple equilibria in Cohen-Grossberg neural networks and its application to associative memory

In this paper, the μ-stability of multiple equilibrium points(EPs) in the Cohen-Grossberg neural networks(CGNNs) is addressed by designing a kind of discontinuous activation function(AF). Under some criteria, CGNNs with this AF are shown to possess at least 5^(n)EPs, of which 3^(n)EPs are locally μ-stable. Compared with the saturated AF or the sigmoidal AF, CGNNs with the designed AF can produce many more total/stable EPs. Therefore, when CGNNs with the designed discontinuous AF are applied to associative memory, they can store more prototype patterns. Moreover, the AF is expanded to a more general version to further increase the number of total/stable equilibria. The CGNNs with the expanded AF are found to produce(2k+3)^(n)EPs, of which (k+2)^(n)EPs are locally μ-stable. By adjusting two parameters in the AF, the number of sufficient conditions ensuring the μ-stability of multiple equilibria can be decreased. This finding implies that the computational complexity can be greatly reduced.Two numerical examples and an application to associative memory are illustrated to verify the correctness of the obtained results.

THE l^1-STABILITY OF A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH DISCONTINUOUS POTENTIALS

We study the l^1-stability of a Haxniltonian-preserving scheme, developed in [Jin and Wen, Comm. Math. Sci., 3 （2005）, 285-315], for the Liouville equation with a discontinuous potential in one space dimension. We prove that, for suitable initial data, the scheme is stable in the l^1-norm under a hyperbolic CFL condition which is in consistent with the l^1-convergence results established in [Wen and Jin, SIAM J. Numer. Anal., 46 （2008）, 2688-2714] for the same scheme. The stability constant is shown to be independent of the computational time. We also provide a counter example to show that for other initial data, in particular, the measure-valued initial data, the numerical solution may become l^1-unstable.

Frequency-domain L2-stability conditions for time-varying linear and nonlinear MIMO systems

The paper deals with the g2-stability analysis of multi-input-multi-output （MIMO） systems, governed by integral equations, with a matrix of periodic/aperiodic time-varying gains and a vector of monotone, non-monotone and quasi-monotone nonlin- earities. For nonlinear MIMO systems that are described by differential equations, most of the literature on stability is based on an application of quadratic forms as Lyapunov-function candidates. In contrast, a non-Lyapunov framework is employed here to derive new and more general g2-stability conditions in the frequency domain. These conditions have the following features： i） They are expressed in terms of the positive definiteness of the real part of matrices involving the transfer function of the linear time-invariant block and a matrix multiplier function that incorporates the minimax properties of the time-varying linear/nonlinear block, ii） For certain cases of the periodic time-varying gain, they contain, depending on the multiplier function chosen, no restrictions on the normalized rate of variation of the time-varying gain, but, for other periodic/aperiodic time-varying gains, they do. Overall, even when specialized to periodic-coefficient linear and nonlinear MIMO systems, the stability conditions are distinct from and less restrictive than recent results in the literature. No comparable results exist in the literature for aperiodic time-varying gains. Furthermore, some new stability results concerning the dwell-time problem and time-varying gain switching in linear and nonlinear MIMO systems with periodic/aperiodic matrix gains are also presented. Examples are given to illustrate a few of the stability theorems.

Practical ф_0 -stability of switched stochastic nonlinear systems and corresponding stochastic perturbation theory

The aim of this paper is to study the practical φ0-stability in probability （Pφ0 SiP） and practical ~o-stability in pth mean （Pφ0SpM） of switched stochastic nonlinear systems. Sufficient conditions on such practical properties are obtained by using the comparison principle and the cone-valued Lyapunov function methods. Also, based on an extended comparison principle, a perturbation theory of switched stochastic systems is given.

On the l_2-stability of time-varying linear and nonlinear discrete-time MIMO systems

New conditions are derived for the l2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput （MIMO） systems, having a linear time time-invariant block with the transfer function F（z）, in negative feedback with a matrix of periodic/aperiodic gains A（k）, k = 0,1, 2,... and a vector of certain classes of non-monotone/monotone nonlinearities φp（-）, without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features： i） They involve the positive definiteness of the real part （as evaluated on ｜z｜ = 1） of the product of Г （z） and a matrix multiplier function of z. ii） For periodic A（k）, one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A（k）, but for aperiodic A（k）, which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of （A（k ＋ 1）,A（k））, k = 1, 2 iii） They are distinct from and less restrictive than recent results in the literature.

Synthesis of Nafion^(■)-stabilized Pt nanoparticles to improve the durability of proton exchange membrane fuel cell

Nafion-stabilized Pt nanoparticle colloidal solution is synthesized through ethylene glycol reduction.Pt/Nafion added with carbon black as electric conduction material（labeled Pt/Nafion-XC72） shows excellent electrochemical property compared with Pt/C.After a 300-cycle discharging durability test,the cell performance of membrane electrode assembly（MEA） with the Pt/Nafion-XC72 and Pt/C catalysts indicates a 29.9% and 92.2% decrease,respectively.The charge transfer resistances of Pt/Nafion-XC72 and Pt/C increase by 27.2% and 101.9%,respectively.The remaining electrochemically active surface area of Pt is about 61.7% in Pt/Nafion-XC72 and about 38.1% in Pt/C after the durability test.The particle size of Pt/C increases from about 5.1 nm to about 10.8 nm but only from 3.6 nm to 5.8 nm in the case of Pt/Nafion-XC72.These data suggest that Pt/Nafion-XC72 as a catalyst can enhance the durability of PEMFCs compared with Pt/C.

Integral Event-Triggered Attack-Resilient Control of Aircraft-on-Ground Synergistic Turning System With Uncertain Tire Cornering Stiffness

This article proposes an integral-based event-triggered attack-resilient control method for the aircraft-on-ground(AoG) synergistic turning system with uncertain tire cornering stiffness under stochastic deception attacks. First, a novel AoG synergistic turning model is established with synergistic reverse steering of the front and main wheels to decrease the steering angle of the AoG fuselage, thus reducing the steady-state error when it follows a path with some large curvature. Considering that the tire cornering stiffness of the front and main wheels vary during steering, a dynamical observer is designed to adaptively identify them and estimate the system state at the same time.Then, an integral-based event-triggered mechanism(I-ETM) is synthesized to reduce the transmission frequency at the observerto-controller end, where stochastic deception attacks may occur at any time with a stochastic probability. Moreover, an attackresilient controller is designed to guarantee that the closed-loop system is robust L2-stable under stochastic attacks and external disturbances. A co-design method is provided to get feasible solutions for the observer, controller, and I-ETM simultaneously. An optimization program is further presented to make a tradeoff between the robustness of the control scheme and the saving of communication resources. Finally, the low-and high-probability stochastic deception attacks are considered in the simulations. The results have illustrated that the AoG synergistic turning system with the proposed control method follows a path with some large curvature well under stochastic deception attacks. Furthermore,compared with the static event-triggered mechanisms, the proposed I-ETM has demonstrated its superiority in saving communication resources.

Delay-dependent stability analysis of Runge-Kutta methods for neutral delay differential equations

The aim of this paper is to study the asymptotic stability properties of Runge Kutta(R-K) methods for neutral differential equations(NDDEs) when they are applied to the linear test equation of the form: y′(t)=ay(t)+by(t-τ)+cy’(t-τ), t>0, y(t)=g(t), -τ≤t≤0, with a,b,c∈[FK(W+3mm\.3mm][TPP129A,+3mm?3mm,BP], τ>0 and g(t) is a continuous real value function. In this paper we are concerned with the dependence of stability region on a fixed but arbitrary delay τ. In fact, it is one of the N.Guglielmi open problems to investigate the delay dependent stability analysis for NDDEs. The results that the 2,3 stages non natural R-K methods are unstable as Radau IA and Lobatto IIIC are proved. And the s stages Radau IIA methods are unstable, however all Gauss methods are compatible.

去杠杆:由虚拟经济转向实体经济的关键一役

以"去产能、去库存、去杠杆、降成本、补短板"为重点内容的供给侧结构性改革,经稳步推进取得了阶段性成效。在实体经济结构逐步优化,去产能、去库存有效进行的同时,各类资产价格却轮番出现大涨大跌的现象。文本从再平衡与信息技术革命导致传统制造业回报阶段性走弱,凯恩斯逆周期调控理论引发货币政策的"流动性陷阱",以及金融自由化单兵突进诱发制度套利三点阐述金融市场"脱实向虚"的原因,并提出在去杠杆过程中需要审慎处理的三大博弈风险和需要坚持的三大原则。我国要通过坚定不移的去杠杆创造稳健的金融市场,进一步深化供给侧结构性改革,确保我国经济稳中求进,以振兴实体经济,培育壮大新功能。

SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA

In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the un-derlying problem. Unconditional L2-stability and error estimate of order O？τr＋1＋hk＋1/2？ are obtained when polynomials of degree at most r and k are used for the temporal dis-cretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r＋1 in temporal variable t.

ON THE ASYMPTOTIC DYNAMICS OF THE VLASOV-YUKAWA-BOLTZMANN SYSTEM NEAR VACUUM

In this pape,~ we study uniform L1-stability and asymptotic completeness of the Vlasov-Yukawa-Boltzmann （V-Y-B） system. For a sufficiently small rand smooth initial data, we show that classical solutions exist globally and satisfy dispersion estimates, uniform L1-stability with respect to initial data and scattering type estimate. We show that the short range nature of interactions due to the Yukawa potential enables us to construct robust Lyapunov type functional to derive scattering states. In the zero mass limit of force carrier particles, we also show that the classical solutions to the V-Y-B system converge to that of the Vlasov-Poisson-Boltzmann （V-P-B） system in any finite time interval

Stability of equivariant bifurcation problems with two types of state variables and their unfoldings in presence of parameter symmetry

Based on the contact equivalent relation of smooth map-germs in singularity theory, the stability of equivariant bifurcation problems with two types of state variables and their unfoldings in the presence of parameter symmetry is discussed. Some basic results are obtained. Transversality condition is used to characterize the stability of equavariant bifurcation problems.

A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations

A high-order full-discretization method （FDM） using Hermite interpolation （HFDM） is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.

当代青藏地区民族和谐交往与社会稳定之建构

和谐社会涵盖了政治、经济、文化等各个领域。青藏地区民族关系的和谐程度不仅是我国民族关系整体和谐进程的一个重要组成部分,也是全社会民族关系和谐的风向标。改革开放以来,青藏地区经济迅速发展,为社会主义和谐社会的形成奠定了坚实的物质基础。但是,由于诸多原因,青藏地区的民族交往过程中尚存在一些问题,这些问题不仅有碍于民族团结,而且也关系着当地社会稳定之建构。

Implicit DG Method for Time Domain Maxwell’s Equations Involving Metamaterials

An implicit discontinuous Galerkin method is introduced to solve the timedomain Maxwell’s equations in metamaterials.The Maxwell’s equations in metamaterials are represented by integral-differential equations.Our scheme is based on discontinuous Galerkin method in spatial domain and Crank-Nicolson method in temporal domain.The fully discrete numerical scheme is proved to be unconditionally stable.When polynomial of degree at most p is used for spatial approximation,our scheme is verified to converge at a rate of O(τ^(2)+h^(p)+1/2).Numerical results in both 2D and 3D are provided to validate our theoretical prediction.

A Mixed Finite Element Scheme for Biharmonic Equation with Variable Coefficient and von Kármán Equations

In this paper,a new mixedfinite element scheme using element-wise stabilization is introduced for the biharmonic equation with variable coefficient on Lipschitz polyhedral domains.The proposed scheme doesn’t involve any integration along mesh interfaces.The gradient of the solution is approximated by H(div)-conforming BDMk+1 element or vector valued Lagrange element with order k+1,while the solution is approximated by Lagrange element with order k+2 for any k≥0.This scheme can be easily implemented and produces symmetric and positive definite linear system.We provide a new discrete H^(2)-norm stability,which is useful not only in analysis of this scheme but also in C^(0) interior penalty methods and DG methods.Optimal convergences in both discrete H^(2)-norm and L^(2)-norm are derived.This scheme with its analysis is further generalized to the von K´arm´an equations.Finally,numerical results verifying the theoretical estimates of the proposed algorithms are also presented.