Let where 1 and n, ..., are integers 1. For 1 ≤ ≤ k, let and , and suppose that is a nontrivial involution; i.e., . Let , and denote = ). If , let be its binary expansion. We say that is (-symmetric if ; thus, we are considering matrices with levels of block structure and an involutory...

Let be a nontrivial unitary involution; i.e., . We say that is -symmetric (-skew symmetric) if = = −A). Let be one of the following subsets of : (i) hermitian matrices; (ii) hermitian -symmetric matrices; (iii) hermitian -skew symmetric matrices. Given , we characterize the matrices in that...

We consider a model of margin trading based on the hyperfinite timeline. Using only elementary nonstandard analysis we are able to derive explicit formulas for the expected margin call time and loss. Further margin trading strategy is studied and an application to pricing barrier option is...

A Laplacian matrix, , has nonpositive off-diagonal entries and zero row sums. As a matrix associated with a weighted directed graph, it generalizes the Laplacian matrix of an ordinary graph. A standardized Laplacian matrix is a Laplacian matrix with at . We study the spectra of Laplacian...

A new design approach of observer is proposed for generalized dynamical systems with unknown input disturbances. By introducing proportional gain, derivative gain and multiple-integral gains, the estimation error dynamics can be guaranteed to be internally proper stable and the disturbance can...

The objective of the paper is to obtain results on the behavior of a specific plane discontinuous dynamical system in the neighbourhood of the singular point. A new technique of investigation is presented. Conditions for existence of the foci and centres are proposed. The focus-centre problem...

In this paper we establish asymptotic (biasymptotic) equivalence between spaces of solutions of a given linear homogeneous system and a perturbed system. The perturbations are of either linear or weakly linear characters. Existence of a homeomorphism between subspaces of almost periodic and...

“This sentence is short” is true of itself and we use it to assert that fact. That leads to the loss of its entire syntactic links to other sentences including its negation in normal use, “This sentence is not short”, which attributes a different property to a different string if it...

This paper presents simulation results on the robustness of normal parametric inference in non-linear mixed models. A linearization approach to inference is compared with two two-stage methods (standard two-stage, STS, and global two-stage, GTS). When the assumptions of normality of the...

Plouffe studied the recurrences , and (defined below). Plouffe's constant [1] arises from the recurrence . We present a closely related constant, ç, arising from the recurrence and like Plouffe's constant it has a feasible algorithm (more efficient) for its th digit and can be constructed by a...