The finite-lattice method of series expansions has been combined with a new extrapolation procedure to extend the low-temperature series for the specific heat, spontaneous magnetisation and susceptibility of the spin-1 Ising model on the square lattice. The extended series were derived by directly calculating the series to order 99 (in the variable u = exp[−J/k B T ]) and using the new extrapol...

We consider time series models of the MA (moving average) family, and deal with the estimation of the residual variance. Results are known for maximum likelihood estimates under normality, both for known or unknown mean, in which case the asymptotic biases depend on the number of parameters (including the mean), and do not depend on the values of the parameters. For moment estimates the situati...

The purpose of this paper is to give complete proofs of several fundamental results about modular forms. Modular forms are complex functions with certain analytic properties, and that transform nicely under a certain group of transformations of the complex upper half plane. It turns out that modular forms can be used to study number theory, by investigating the coefficients in series expansions...

In the paper, algorithms for disturbance observers are newly presented in the time-domain. Attention is paid to observing a ramp disturbance by introducing an integral term to the output equation of a constant disturbance observer. In order to reduce the sensitivity to the measurement noise, the disturbance observer is combined with the state observer. It will be shown that the estimation dynam...

In this paper, a suitable numerical method based on block pulse functions is introduced to approximate the Wiener integrals which the exact solution of them is not exist or it may be so hard to find their exact solutions. Furthermore, the error analysis of this method is given. Some numerical examples are provided which show that the approximation method has a good degree of accuracy. The main ...

In this chapter we present an innovative approach to combine common results of Markov decision theory and series expansions for optimization. We call our algorithm the series expansion optimization algorithm. Our algorithm efficiently determines the optimal policy of continuous-time Markov decision processes exactly or alternatively up to an arbitrarily small precision. We prove its convergence...

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

Continuous and discrete variations in material properties lead to substantial difficulties for most mesh-based methods for modeling and analysis of physical fields. The meshfree method described in this paper relies on distance fields to boundaries and to material features in order to represent variations of material properties as well as to satisfy prescribed boundary conditions. The method is...