ESTIMATION OF ATTRACTION DOMAIN AND EXPONENTIAL CONVERGENCE RATE OF CONTINUOUS FEEDBACK ASSOCIATIVE MEMORY

Analytical techniques and Liapunov method were used for the estimation of the attraction domain of memory patterns and local exponential stability of neural networks. The results were used to design efficient continuous feedback associative memory neural networks. The neural network synthesis procedure ensured the gain of large exponential convergence rate without reduction of the attraction domain.

Local Bifurcation Analysis of a Delayed Fractional-order Dynamic Model of Dual Congestion Control Algorithms

In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay, the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results. © 2017 Chinese Association of Automation.

BOUNDARY INTEGRAL EQUATIONS FOR THE BENDING PROBLEM OF PLATES ON TWO-PARAMETER FOUNDATION

By means of Fourier integral transformation of generalized function, the fundamental solution for the bending problem of plates on two-parameter foundation is derived in this paper, and the fundamental solution is expanded into a uniformly convergent series. On the basis of the above work, two boundary integral equations which are suitable to arbitrary shapes and arbitrary boundary conditions are established by means of the Rayleigh-Green identity. The content of the paper provides the powerful theories for the application of BEM in this problem.

Optimization of Additively Decomposed Function with Constraints

We propose a modified evolutionary computation method to solve the optimization problem of additively decomposed function with constraints. It is based on factorized distribution instead of penalty function and any transformation to a linear model or others. The feasibility and convergence of the new algorithm are given. The numerical results show that the new algorithm gives a satisfactory performance.

Perturbation Analysis of the Attached Water Mass Effect on Offshore Platform Dynamic Response

Theoretically speaking, it is impossible to make the differential equation of motion uncoupled for the natural modes of a system in consideration of the attached water. The hydro-elastic structure is equal to the non-proportional damping system. In this paper a perturbation analysis method is put forward. The structure motion equation is strictly solved mathematically, and the non-proportional damping problem is transformed into a series of proportional damping ones in the superposition form. The paper also presents the calculation formula of the dynamic response of the structure being subjected to harmonic and arbitrary load. The convergence of the proposed method is also studied in this paper, and the corresponding convergence conditions are given. Finally, the proposed method is used to analyze the displacement response of a real offshore platform. The calculation results show that this method has the characteristics of high accuracy and fast convergence.

PGOPO Approach to Design Linear Servomechanism of Time-Varying Systems with Time-Delay

Based on a new linear, continuous and bounded operator (PGOPO), a more effective approach and optimal control algorithm than by the block-pulse functions and Walsh functions to design the linear servomechanism of time-varying systems with time-delay is proposed in the paper. By means of the operator, the differential equation is transferred to a more explicit algebraic form which is much easier than the numerical integration of nonlinear TPBVP derived from Pantryagin's maximum principle method. Furthermore, the method is established strictly based on the theory of convergence in the mean square and it is convenient and simple in computation. So the method can be applied to industry control and aeronautics and astronautics field which is frequently mixed with time varying and time delay. Some illustrative numerical examples are interpreted to support the technique.

P-FEMOL ANALYSIS OF PLATE BENDING PROBLEMS

In this paper, the p- version of the finite element method of lines (FEMOL) for the analysis of the Mindlin-Reissner plate bending problems is presented and a class of p-FEMOL elements with polynomial degrees as high as nine is developed. Numerical examples given in this paper show tremendous performance of the present method: namely, rapid convergence rate, high accuracy for both displacements and stress resultants, removal of shear-locking trouble, capability of dealing with difficult problems such as the boundary layer behavior near a free edge and stress concentration around a hole.

Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings

We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.

Synthesis and Stability of Hydroxyfasudil Derivatives as Prodrugs

Fasudil (HA-1077) is the first small-molecule inhibitor of Rho-kinase and has been employed for clinical treatment of cerebral vasospasm. Hydroxyfasudil, as a metabolite of fasudil, exhibited better activity than fasudil. However, it also suffered from quick metabolisation, weak lipotropy and worse penetration of the blood–brain barrier. Thus, some hydroxyfasudil derivatives such as hydroxyfasudil acetate, hydroxyfasudil phosphate and 1-methoxyfasudil as the prodrugs of hydroxyfasudil were designed and synthesised. Meanwhile, the stability of these three compounds was also investigated. Furthermore, the reason and mechanism of hydrolysis of these compounds were discussed. This work could provide a useful guide for future research. © 2016, Tianjin University and Springer-Verlag Berlin Heidelberg.

Neural Network inverse Adaptive Controller Based on Davidon Least Square

General neural network inverse adaptive controller has two flaws: the first is the slow convergence speed; the second is the invalidation to the non-minimum phase system. These defects limit the scope in which the neural network inverse adaptive controller is used. We employ Davidon least squares in training the multi-layer feedforward neural network used in approximating the inverse model of plant to expedite the convergence, and then through constructing the pseudo-plant, a neural network inverse adaptive controller is put forward which is still effective to the nonlinear non-minimum phase system. The simulation results show the validity of this scheme.

SPECTRAL-FINITE ELEMENT METHOD FOR COMPRESSIBLE FLUID FLOW

In this paper, a combined Fourier spectral-finite element method is proposed for solving n-dimensional (n = 2,3), semi-periodic compressible fluid flow problems. The strict error estimation as well as the convergence rate, is presented.

NONLINEAR GALERKIN METHOD FOR THE EXTERIORNONSTATIONARY NAVIER-STOKES EQUATIONS

A new algorithm combining nonlinear Galerkin method and coupling method of finite element and boundary element is introduced to solve the exterior nonstationary Navier-Stokes equations. The regularity of the coupling variational formulation and the convergence of the approximate solution corresponding to the algorithm are proved. If the fine mesh h is chosen as coarse mesh H-square, the nonlinear Galerkin method, nonlinearity is only treated on the coarse grid and linearity is treated on the fine grid. Hence, the new algorithm can save a large amount of computational time.

NUMERICAL STUDY OF TURBULENT FLOW AROUND TWIN PLATE AT LARGE ATTACK ANGLE

The fluid dynamic force on the twin plate in a turbulent flow has been studied by using the SIMPLE approach. The multiple time scale turbulent k-Ε model was employed to determine the eddy viscosity of turbulent flow. The turbulent model was used with a restriction for the kinetic energy of smaller turbulent scale to achieve numerical stability. The lengths of recirculation zone were in good agreement with the experimental data under condition of attack angle AOA=50° and constant flow blockage ratio 10%. The results of multiple time scale k-Ε model were compared with single time scale. It is found that the drag force and distribution of wall pressure are influenced by the arrangement of twin plate. The multiple k-Ε model with the kinetic energy restriction can be applied to even more complex turbulent shear flow simulation.

Optimal Approach to SAR Image Despeckling

Speckle filtering of synthetic aperture radar (SAR) images while preserving the spatial signal variability (texture and fine structures) still remains a challenge. Many algorithms have been proposed for the SAR imagery despeckling. However, simulated annealing (SA) methods is one of excellent choices currently. A critical problem in the study on SA is to provide appropriate cooling schedules that ensure fast convergence to near-optimal solutions. This paper gives a new necessary and sufficient condition for the cooling schedule so that the algorithm state converges in all probability to the set of global minimum cost states. Moreover, it constructs an appropriate objective function for SAR image despeckling. An experimental result of the actual SAR image processing is obtained.

NUMERICAL STUDY FOR NONLINEAR EVOLUTION OF VORTEX SHEET AND ITS APPLICATIONS: PART I. APPROACH AND PERIODICAL EVOLUTION OF VORTEX SHEET

The superconvergence of Multhopp′s discretization for the solution to the normal wash integral equation for the flow past a curved plate was theoretically analyzed and numerically examined. The Multhopp′s discretization also has a superconvergence behavior in simulating the vortex sheet evolution. An improved Multhopp′s method was suggested and applied to the numerical simulation of a periodical evolution of a flat vortex sheet. To validate the results obtained by the inviscid vortex method, the initial-value problem for the development of a shear layer at large Reynolds number was numerically investigated by solving the two-dimensional incompressible Navier-Stokes equations.

ON THE L_∞ CONVERGENCE AND THE EXTRAPOLATION METHOD OF A DIFFERENCE SCHEME FOR NONLOCAL PARABOLIC EQUATION WITH NATURAL BOUNDARY CONDITIONS

In paper (J. Comput. Appl. Math., 76 (1996), 137-146), a difference scheme for a class of nonlocal parabolic equations with natural boundary conditions was derived by the method of reduction of order and the unique solvability and second order convergence in L2-norm are proved. In this paper, we prove that the scheme is second order convergent in L∞ norm and then obtain fourth order accuracy approximation in L∞ norm by extrapolation method. At last, one numerical example is presented.

GENERALIZED COMPLEMENTARITY PROBLEMS FOR FUZZY MAPPINGS

In this paper we introduce a new class of generalized complementarity problems for the fuzzy mappings and construct a new iterative algorithm. We also discuss the existence of solutions for the generalized complementarity problems and the convergence of tterative sequence.

Finite element beam propagation method for analysis of plasmonic waveguide

The basic idea of the finite element beam propagation method （FE-BPM） is described. It is applied to calculate the fundamental mode of a channel plasmonic polariton （CPP） waveguide to confirm its validity. Both the field distribution and the effective index of the fundamental mode are given by the method. The convergence speed shows the advantage and stability of this method. Then a plasmonic waveguide with a dielectric strip deposited on a metal substrate is investigated, and the group velocity is negative for the fundamental mode of this kind of waveguide. The numerical result shows that the power flow direction is reverse to that of phase velocity.

FINITE DIFFERENCE METHOD WITH NONUNIFORM MESHES FOR QUASILINEAR PARABOLIC SYSTEMS

The analysis of the finite difference schemes with nonuniform meshes for the problems of partial differential equations is extremely rare even for very simple problems and even for the method of fully heuristic character. In the present work the boundary value problem for quasilinear parabolic system is solved by the finite difference method with nonuniform meshes. By using of the interpolation formulas for the spaces of discrete functions with unequal meshsteps and the method of a priori estimation for the discrete solutions of finite difference schemes with nonuniform meshes, the absolute and relative convergence of the discrete solutions of the finite defference scheme are proved. The limiting vector function is just the unique generalized solution of the original problem for the parabolic system.

MUSCL TYPE SCHEMES AND DISCRETE ENTROPY CONDITIONS

In this paper, the semi-discrete entropy conditions with so called the proper discrete entropy flux of a class of high resolution MUSCL type schemes are discussed for genuinely nonlinear scalar conservation laws. It is shown that the high resolution schemes satisfying such;semi-discrete entropy conditions cannot preserve second order accuracy in the rarefaction region.