Stability analysis of a class of uncertain switched systems on time scale using Lyapunov functions

This paper deals with the stability analysis of a class of uncertain switched systems on non-uniform time domains. The considered class consists of dynamical systems which commute between an uncertain continuous-time subsystem and an uncertain discrete-time subsystem during a certain period of time. The theory of dynamic equations on time scale is used to study the stability of these systems on non-uniform time domains formed by a union of disjoint intervals with variable length and variable gap. Using the concept of common Lyapunov function, sufficient conditions are derived to guarantee the asymptotic stability of this class of systems on time scale with bounded graininess function. The proposed scheme is used to study the leader–follower consensus problem under intermittent information transmissions.     

Coordination Polymers. 9. Chelate Polymers Derived from Bisphenolic Complexes and Propylenediamine

Chelate polymers derived from bis(2,4-dihydroxybenzaldehyde)propyl-enediimine M and bis(2,4-dihydroxyacetophenone)propylenediimine M (M = Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺) with aromatic acid chlorides were prepared by interfacial polycondensation. Also, chelate polysiloxanes were obtained from the same monomers and α,ω-dichloropolydimethyl-siloxane. The spectral, thermal, magnetic, and electrical properties of the polychelates were studied.     

Incompatibility networks as models of scale-free small-world graphs

We make a mapping from Sierpinski fractals to a new class of networks, the incompatibility networks, which are scale-free, small-world, disassortative, and maximal planar graphs. Some relevant characteristics of the networks such as degree distribution, clustering coefficient, average path length, and degree correlations are computed analytically and found to be peculiarly rich. The method of network representation can be applied to some real-life systems making it possible to study the complexity of real networked systems within the framework of complex network theory.     

完备布尔代数商格的注

本文研究了完备布尔代数L的商格Q(L),建立 L上q-集构成的集合Q′(L)与Q(L)之间的同构,得出了完备布尔代数的商格仍是完备布尔代数,并给出了完备布尔代数范畴的某些性质.     

Bool阵的逆阵

We give a characterization of a regular Boolean matrix and prove that AB = I Implies that BA = I, where A and B are Boolean matrices whose elements belong to a Boolean algebra of a set with more than two elements.     

Simultaneous Determination of Multicomponents in Air Toxic Organic Compounds Using Artificial Neural Networks in Ftir Spectroscopy

The application of Artificial Neural Networks (ANNs) for nonlinear multivariate calibration using simulated FTIR data was demonstrated in this paper. Neural networks consisting of three layers of nodes were trained by using the back-propagation learning rule. Since parameters affect the performance of the network greatly, simulated data were used to train the network in order to get a satisfactory combination of all parameters. The mixtures of four air toxic organic compounds whose FTIR spectra are overlapped were chosen to evaluate the calibration and prediction ability of the network. The relative standard error (RSD%), the percent standard error of prediction samples (%SEP) and the percent standard error of calibration samples (%SEC) are used for evaluating the ability of the neural network.     

A limited resource model of fault-tolerant capability against cascading failure of complex network

We propose a novel capacity model for complex networks against cascading failure. In this model, vertices with both higher loads and larger degrees should be paid more extra capacities, i.e. the allocation of extra capacity on vertex i will be proportional to k_i ^γ , where k_i is the degree of vertex i and γ > 0 is a free parameter. We have applied this model on Barabási-Albert network as well as two real transportation networks, and found that under the same amount of available resource, this model can achieve better network robustness than previous models.     

Martin's Axiom is consistent with the existence of nowhere trivial automorphisms

Martin's Axiom does not imply that all automorphisms of are somewhere trivial. An alternate method for obtaining models where every automorphism of is somewhere trivial is explained.