ABOUT HYBRID BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH DISCRETE DELAYS

In this paper, hybrid bidirectional associative memory neural networks with discrete delays is considered. By ingeniously importing real parameters di > 0(i = 1,2,···,n) which can be adjusted, we establish some new sufficient conditions for the dynamical characteristics of hybrid bidirectional associative memory neural networks with discrete delays by the method of variation of parameters and some analysis techniques. Our results generalize and improve the related results in [10,11]. Our work is significant...     

Stability analyses on dynamic control for a moving body levitated magnetically over elastic guideways

Based on the Floquet theory on ordinary differential equations with periodically variable coefficients and the bifurcation approach to nonlinear equations, a numerical approach to determining the stability region of control parameters is established for a dynamic control system composed of a moving body levitated magnetically over flexible guideways. The system is nonlinearly coupled among the elastic deformation of guideways, disturbance the levitation position of the body and electromagnetic control forces. The numerical simulation is given for the system in the case in which the control parameters are taken within and out of the stability region respectively. Results show that this approach is reliable. This project is supported by NSFC(No. 19725207), the Pre-research Project of the Committee of Science and Technology for Defence of China and the Science Foundation of Education Ministry of China for Ph. D. Programmes.     

Application of the sequential gradient-restoration algorithm to thermal convective instability problems

The problem of the thermal stability of a horizontal incompressible fluid layer with linear and nonlinear temperature distributions is solved by using the sequential gradient-restoration algorithm developed for optimal control problems. The hydrodynamic boundary conditions for the layer include a rigid or free upper surface and a rigid lower surface. The resulting disturbing equations are solved as a Bolza problem in the calculus of variations. The results of the study are compared with the existing works in the literature.The authors acknowledge valuable discussions with Dr. A. Miele.     

Algebras of Approximation Sequences: Finite Sections of Band-Dominated Operators

We develop the stability theory for the finite section method for general band-dominated operators on l ^p spaces over Z ^k . The main result says that this method is stable if and only if each member of a whole family of operators – the so-called limit operators of the method – is invertible and if the norms of these inverses are uniformly bounded.     

Metal Chelates of Hydrazo-Dimedon Dyes. Chelating Tendencies of 5,5-Dimethylcyclohexane-2-(2-Carboxyphenyl,and 3-Carboxyphenyl)-Hydrazono 1,3-Dione (DC-2-CPHD and DC-3-CPHD)

The consecutive stepwise formation constants of 1:1 and 1:2 chelate species formed by the interaction of DC-2-CPHD and DC-3-CPHD anions with tripositive lanthanon and divalent copper, nickel, cobalt, zinc, manganese, and cadmium cations were determined potentiometrically at ionic strengh of 0.1 (KNO₃) and 30°C. The results indicate that two different coordination modes, one tridentate (DC-2-CPHD), and one bidentate (DC-3-CPHD), are in evidence.     

Asymptotic stability of traveling waves in a discrete convolution model for phase transitions

In a recent paper [P. Bates, A. Chmaj, A discrete convolution model for phase transition, Arch. Rational Mech. Anal. 150 (1999) 281-305], a discrete convolution model for Ising-like phase transition has been derived, and the existence, uniqueness of traveling waves and stability of stationary solution have been studied. This nonlocal model describes l₂-gradient flow for a Helmholts free energy functional with general range interaction. In this paper, by using the comparison principle and the squeezing technique, we prove that the traveling wavefronts with nonzero speed is globally asymptotic stable with phase shift.     

Effect of boundary vorticity discretization on explicit stream‐function vorticity calculations

The numerical solution of the time‐dependent Navier–Stokes equations in terms of the vorticity and a stream function is a well tested process to describe two‐dimensional incompressible flows, both for fluid mixing applications and for studies in theoretical fluid mechanics. In this paper, we consider the interaction between the unsteady advection–diffusion equation for the vorticity, the Poisson equation linking vorticity and stream function and the approximation of the boundary vorticity, examining from a practical viewpoint, global iteration stability and error. Our results show that most schemes have very similar global stability constraints although there may be small stability gains from the choice of method to determine boundary vorticity. Concerning accuracy, for one model problem we observe that there were cases where the boundary vorticity discretization did not propagate to the interior, but for the usual cavity flow all the schemes tested had error close to second order. Copyright © 2005 John Wiley & Sons, Ltd.     

The delay of transition of a laminar boundary layer over compliant wall

In a previous paper^[1], a method has been developed to study the stability characteristics of laminar boundary layers over compliant walls. In this paper, the effect of double layered compliant wall and Kramer type compliant wall on delaying the transition is investigated, and it is shown that there does exist the possibility to delay the transition by applying such compliant walls. The project supported by the National Natural Science Foundation of China.     

Structure,stability, and aromaticity of M?SubPc (MB,Al, and Ga): Computational study

A theoretical investigation on the structure, stability, and aromaticity of M‐subphthalocyanine (M? SubPc; M?B, Al, and Ga) was performed at the B3LYP/6‐31+G*//B3LYP/6‐31G* level. The comparison between M? SubPc and the corresponding M? phthalocyanine (M? Pc) was considered. The geometry optimization of the M? SubPc shows that in the Al? SubPc and Ga? SubPc, the steric repulsions among the three azacoupled isoindole moieties increase, as to their macrocycles tend to be far from planarity. The binding energies of Cl? M … aza‐coupled isoindole corrected by the basis set superposition error (BSSE), and the nucleus‐independent chemical shift (NICS) values at the ring center, which are a simple and effective local aromaticity probe, were calculated. The results show that Al? SubPc is less stable than both B? SubPc and Al? Pc for larger steric repulsion, smaller binding energy, and weaker aromaticity. In the same way, Ga? SubPc is less stable than both B? SubPc and Ga? Pc. In addition, the ring expansion reactivity occurring in B? SubPc was confirmed by the global aromaticity mirrored by the electrophilicity index ω values. Therefore, the Al? SubPc and Ga? SubPc remain unknown, while the corresponding compounds Al? Pc and Ga? Pc are known experimentally. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Mean-square stability of Milstein method for linear hybrid stochastic delay integro-differential equations

In this paper we study the mean-square (MS) stability of the Milstein method for linear stochastic delay integro-differential equations (SDIDE) with Markovian switching by extending the techniques of [Z. Wang, C. Zhang, An analysis of stability of Milstein method for stochastic differential equations with delay, Computers and Mathematics with Applications 51 (2006) 1445–1452; L. Ronghua, H. Yingmin, Convergence and stability of numerical solutions to SDDEs with Markovian switching, Applied Mathematics and Computation 175 (2006) 1080–1091]. It is established that the Milstein method is MS-stable for linear stochastic delay differential equations (Wang and Zhang (2006); in the above reference). Here we prove that it is MS-stable for linear SDIDE with Markovian switching also under suitable conditions on the integral term. A numerical example is provided to illustrate the theoretical results.