Thermal rearrangement of 7,7-dichloro-[a,c]-dibenzo-[4,1,0]-bicycloheptane (1) to 5,6-dichloro-5Hdibenzo-[a,c]-cycloheptene (2) was studied in the solid phase and in solvents with different polarities. Thefirst-order constants at various temperatures for the rearrangement process were evaluated from theabsorption time data. The activation parameters for this rearrangement were obtained from the...

We propose a method of estimating the fast-scale stability margin of dc–dc converters based on Filippov’s theory—originally developed for mechanical systems with impacts and stick-slip motion. In this method one calculates the state transition matrix over a complete clock cycle, and the eigenvalues of this matrix indicate the stability margin. Important components of this matrix are the state t...

The transition matrix of the Markov chain describing card shuffling (“shuffle matrix”) is studied. The authors propose a method to compute (a subset of) the eigenvalues of a shuffle matrix, which is a generalization of a method proposed by Doner and Uppuluri [2]. The method works by defining Markov chains with smaller state spaces than the original state space, the transition matrices of which ...

This paper shows how the eigenstructure of the adjacency matrix can be used for the purposes of robust graph-matching. We commence from the observation that the leading eigenvector of a transition probability matrix is the steady state of the associated Markov chain. When the transition matrix is the normalised adjacency matrix of a graph, then the leading eigenvector gives the sequence of node...

The model A hidden Markov model is characterized by a set of M states, by an initial probability distribution for the first state, by a transition probability matrix linking successive states, and by a state-dependent probability distribution on the outputs. We represent the state at time t as a multinomial random variable qt, with components q t, for i = 1, . . . ,M . Thus q t is equal to one ...

X nx1 system state matrix A nxn state transition matrix (possible time varying) Bnxm input matrix (possibly time varying) U mx1 input of system inputs Uideal mx1 matrix defining the input required to force perfect tracking. Xref nx1 matrix defining the path the states are to follow, periodic in time T. T The period of the repetitive motion: Xref(t)=Xref(t+T) W(t) Basis function for determining ...

The reaction mechanism between (H2C) and (7, 0), zigzag single-walled carbon nanotubes(ZSWCNTs) on two different orientation of C-C have been studied by semi empirical AM!method. The activation barriers of (H2C) adding to (7, 0) ZSWCNT are computed and compared.The effects of diameters of zigzag SWCNT on their binding energies were studied