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Search Results: 1 - 10 of 28532 matches for " Hongjie Zhu "
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Research on Digital Signature in Electronic Commerce
Hongjie Zhu,Daxing Li
Lecture Notes in Engineering and Computer Science , 2008,
Observer-Type Consensus Protocol for a Class of Fractional-Order Uncertain Multiagent Systems
Hongjie Li
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/672346
Abstract: This paper investigates the consensus problem for a class of fractional-order uncertain multiagent systems with general linear node dynamics. Firstly, an observer-type consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on property of the Kronecker product and stability theory of fractional-order system, some sufficient conditions are presented for robust asymptotical stability of the observer-based fractional-order control systems. Thirdly, robust stabilizing controllers are derived by using linear matrix inequality approach and matrix’s singular value decomposition. Our results are in the form of linear matrix inequalities which can easily be solved by LMI toolbox in MATLAB. Finally, a numerical simulation is performed to show the effectiveness of the theoretical results.
Event-Triggered State Estimation for a Class of Delayed Recurrent Neural Networks with Sampled-Data Information
Hongjie Li
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/731453
Abstract: The paper investigates the state estimation problem for a class of recurrent neural networks with sampled-data information and time-varying delays. The main purpose is to estimate the neuron states through output sampled measurement; a novel event-triggered scheme is proposed, which can lead to a significant reduction of the information communication burden in the network; the feature of this scheme is that whether or not the sampled data should be transmitted is determined by the current sampled data and the error between the current sampled data and the latest transmitted data. By using a delayed-input approach, the error dynamic system is equivalent to a dynamic system with two different time-varying delays. Based on the Lyapunov-krasovskii functional approach, a state estimator of the considered neural networks can be achieved by solving some linear matrix inequalities, which can be easily facilitated by using the standard numerical software. Finally, a numerical example is provided to show the effectiveness of the proposed event-triggered scheme.
State Estimation for Fractional-Order Complex Dynamical Networks with Linear Fractional Parametric Uncertainty
Hongjie Li
Abstract and Applied Analysis , 2013, DOI: 10.1155/2013/178718
Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness
Hongjie Dong
Mathematics , 2007,
Abstract: We study the critical and super-critical dissipative quasi-geostrophic equations in $\bR^2$ or $\bT^2$. Higher regularity of mild solutions with arbitrary initial data in $H^{2-\gamma}$ is proved. As a corollary, we obtain a global existence result for the critical 2D quasi-geostrophic equations with periodic $\dot H^1$ data. Some decay in time estimates are also provided.
Solvability of second-order equations with hierarchically partially BMO coefficients
Hongjie Dong
Mathematics , 2010, DOI: 10.1090/S0002-9947-2011-05453-X
Abstract: By using some recent results for divergence form equations, we study the $L_p$-solvability of second-order elliptic and parabolic equations in nondivergence form for any $p\in (1,\infty)$. The leading coefficients are assumed to be in locally BMO spaces with suitably small BMO seminorms. We not only extend several previous results by Krylov and Kim [14]-[18] to the full range of $p$, but also deal with equations with more general coefficients.
On elliptic equations in a half space or in convex wedges with irregular coefficients
Hongjie Dong
Mathematics , 2012, DOI: 10.1016/j.aim.2013.02.004
Abstract: We consider second-order elliptic equations in a half space with leading coefficients measurable in a tangential direction. We prove the $W^2_p$-estimate and solvability for the Dirichlet problem when $p\in (1,2]$, and for the Neumann problem when $p\in [2,\infty)$. We then extend these results to equations with more general coefficients, which are measurable in a tangential direction and have small mean oscillations in the other directions. As an application, we obtain the $W^2_p$-solvability of elliptic equations in convex wedge domains or in convex polygonal domains with discontinuous coefficients.
Parabolic equations with variably partially VMO coefficients
Hongjie Dong
Mathematics , 2008,
Abstract: We prove the $W^{1,2}_{p}$-solvability of second order parabolic equations in nondivergence form in the whole space for $p\in (1,\infty)$. The leading coefficients are assumed to be measurable in one spatial direction and have vanishing mean oscillation (VMO) in the orthogonal directions and the time variable in each small parabolic cylinder with the direction depending on the cylinder. This extends a recent result by Krylov [17] for elliptic equations and removes the restriction that $p>2$.
On a multi-dimensional transport equation with nonlocal velocity
Hongjie Dong
Mathematics , 2014, DOI: 10.1016/j.aim.2014.07.028
Abstract: We study a multi-dimensional nonlocal active scalar equation of the form $u_t+v\cdot \nabla u=0$ in $\mathbb R^+\times \mathbb R^d$, where $v=\Lambda^{-2+\alpha}\nabla u$ with $\Lambda=(-\Delta)^{1/2}$. We show that when $\alpha\in (0,2]$ certain radial solutions develop gradient blowup in finite time. In the case when $\alpha=0$, the equations are globally well-posed with arbitrary initial data in suitable Sobolev spaces.
Hessian equations with elementary symmetric functions
Hongjie Dong
Mathematics , 2005,
Abstract: We consider the Dirichlet problem for two types of degenerate elliptic Hessian equations . New results about solvability of the equations in the $C^{1,1}$ space are provided.
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