Robust asymptotic state estimation of Takagi–Sugeno fuzzy Markovian jumping Hopfield neural networks with mixed interval time‐varying delays

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the state estimation of uncertain Markovian jumping Hopfield neural networks with mixed interval time‐varying delays. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time delays, the dynamics of the estimation error are globally asmptotically stable in the mean square. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, several delay‐dependent robust state estimators for such T–S fuzzy Markovian jumping Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. Finally a numerical example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Delay-range dependent stability criteria for neural networks with Markovian jumping parameters

The paper is concerned with a stability analysis problem for neural networks with Markovian jumping parameters. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process, which are governed by a Markov process with discrete and finite state space. A new type of Markovian jumping matrix P_i is introduced in this paper. The discrete delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the lower conservatism and the effectiveness of the proposed LMI conditions.     

On heat kernel estimates and parabolic Harnack inequality for jump processes on metric measure spaces

In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality.     

Index computations in FJRW theory

We compute the index of the real Cauchy–Riemann operator defined in FJRW theory in case of the smooth metric.For the cylindrical metric,we study the relation between the index of the linearized operator of Witten map and weights in weighted Sobolev spaces.     

Constancy regions of mixed multiplier ideals in two‐dimensional local rings with rational singularities

The aim of this paper is to study mixed multiplier ideals associated with a tuple of ideals in a two‐dimensional local ring with a rational singularity. We are interested in the partition of the real positive orthant given by the regions where the mixed multiplier ideals are constant. In particular we reveal which information encoded in a mixed multiplier ideal determines its corresponding jumping wall and we provide an algorithm to compute all the constancy regions, and their corresponding mixed multiplier ideals, in any desired range.     

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基于人-板系统的数学模型分析跳板跳水起跳阶段的各个过 程. 提出了以增大起跳能量为目标提高跳板跳水质量的观点,解释了当前采用的各项跳板跳 水起跳技术的力学原理.     

State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

In this Letter, we investigate the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters as well as mode-dependent mixed time-delays. The parameters of the discrete-time neural networks are subject to the switching from one mode to another at different times according to a Markov chain, and the mixed time-delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. New techniques are developed to deal with the mixed time-delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time-delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A numerical example is exploited to show the usefulness of the derived LMI-based conditions.     

Swirling turbulent wake behind a self-propelled body

The development of the swirling turbulent axisymmetric wake of a self-propelled body is modeled numerically. The flow pattern is calculated within the framework of the thin shear layer approach for nonclosed system of the motion and continuity equations. The closed system of equations is written for two different formulations of the closure relations. The numerical solution of the problem is performed with the use of the finite-difference algorithm realised on moving grids. The algorithm is conservative with respect to the laws of conservation of the momentum and the angular momentum. The experimentally measured distributions are used as the initial conditions. Both the models described agree well with the experimental data of Gavrilov N., Demenkov A., Kostomakha V., Chernykh G. (2000), Experimental and numerical modelling of turbulent wake behind self-propelled body, J. Appl. Mech. Tech. Phys., 41 (4), 619–627. It is demonstrated that at the large distances downstream from the body the solution of the problem approaches the self-similar one.     

Optimization of the take-off movement of ski jumping with the method of mathematical programming

This paper is based on the finite and dispersed data which were obtained from the experiments of the wind tunnel and of the force measurement and from the high-speed photography. It analyses and optimizes the take-off movement of ski jumping with the theory of dynamics of systems of rigid bodies and with the method of mathematical programming. The paper describes the optimal take-off movement of ski jumping. Furthermore, it presents an example and compares the result with those of other papers published at home and abroad. The comparison shows that our computation and optimization are reasonable and well-grounded.