In this paper, we establish a residue theorem for Malcev-Neumann series that requires few constraints, and includes previously known combinatorial residue theorems as special cases. Our residue theorem identifies the residues of two formal series that are related by a change of variables. We obtain simple conditions for when a change of variables is possible, and find that the two related forma...

Improving the order of accuracy for any numerical method remains a continuing quest. For a large class of computational uid dynamics (CFD) problems, the discrete approximate solution error is viewed as truncation of a Taylor series expansion. In this paper, a weak statement Galerkin matrix perturbation (GMP) method is utilized yielding simple tridiagonal forms that reduce, or annihilate in spec...

In this study, the KLME approach, a momentequation approach based on the Karhunen–Loeve decomposition developed by Zhang and Lu (Comput Phys 194(2):773–794, 2004), is applied to unconfined flow with multiple random inputs. The log-transformed hydraulic conductivity F, the recharge R, the Dirichlet boundary condition H, and the Neumann boundary condition Q are assumed to be Gaussian random field...

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...

In this paper we review some of the state of the art techniques for parasitic interconnect extraction in the presence of random geometrical variations due to uncertainties in the manufacturing processes. We summarize some of the most recent development in both sampling based (non-intrusive) and expansion based (intrusive) algorithms for the extraction of both general impedance and capacitance i...

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 ...