A novel mixed-synchronization phenomenon in coupled Chua's circuits via non-fragile linear control

Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme. In this paper, a non-fragile linear feedback control strategy with multiplicative controller gain uncertainties is proposed for realizing the mixed-synchronization of Chua＇s circuits connected in a drive-response configuration. In particular, in the mixed-synchronization regime, different state variables of the response system can evolve into complete synchronization, anti-synchronization and even amplitude death simultaneously with the drive variables for an appropriate choice of scaling matrix. Using Lyapunov stability theory, we derive some sufficient criteria for achieving global mixed-synchronization. It is shown that the desired non-fragile state feedback controller can be constructed by solving a set of linear matrix inequalities （LMIs）. Numerical simulations are also provided to demonstrate the effectiveness of the proposed control approach.

English Sentence Recognition Based on HMM and Clustering

For English sentences with a large amount of feature data and complex pronunciation changes contrast to words, there are more problems existing in Hidden Markov Model (HMM), such as the computational complexity of the Viterbi algorithm and mixed Gaussian distribution probability. This article explores the segment-mean algorithm for dimensionality reduction of speech feature parameters, the clustering cross-grouping algorithm and the HMM grouping algorithm, which are proposed for the implementation of the speaker-independent English sentence recognition system based on HMM and clustering. The experimental result shows that, compared with the single HMM, it improves not only the recognition rate but also the recognition speed of the system.

The construction of generalized B-spline low-pass filters related to possibility density

Starting from piecewise constant functions, a novel family of generalized symmetric B-splines, with realizable ideal low-pass filters, are constructed. The first order generalized B-spline low-pass filter is closely related to functions analytic in a neighborhood of the unit disc and the generalized sinc functions. The properties of this kind of low-pass filters are investigated. The behavior of the generalized B-spline low-pass filter related to normalized Gaussian distribution is considered.

A Constructive Proof of Beurling-Lax Theorem

This paper deals with an alternative proof of Beurling-Lax theorem by adopting a constructive approach instead of the isomorphism technique which was used in the original proof.

Shannon-type sampling for multivariate non-bandlimited signals

In this paper, starting from a function analytic in a neighborhood of the unit disk and based on Bessel functions, we construct a family of generalized multivariate sinc functions, which are radial and named radial Bessel-sinc (RBS) functions being time-frequency atoms with nonlinear phase. We obtain a recursive formula for the RBS functions in R d with d being odd. Based on the RBS function, a corresponding sampling theorem for a class of non-bandlimited signals is established. We investigate a class of radial functions and prove that each of these functions can be extended to become a monogenic function between two parallel planes, where the monogencity is taken to be of the Clifford analysis sense.

New Kamenev-type Oscillation Criteria for Half-linear Partial Differential Equations

We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping div（A（x）｜｜ u｜｜^p-2 u）＋〈b（x）,｜｜ u｜｜^p-2 u〉＋c（x）｜u｜^p-2u=0（E）under quite general conditions. These results are extensions of the recent results developed by Sun [Y.C. Sun, New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 （2004） 341-351] for second order ordinary differential equations in a natural way, and improve some existing results in the literature. As applications, we illustrate our main results using two different types of half-linear partial differential equations.