The purpose of this paper is to investigate the real quadratic number fields $Q(sqrt{d})$ which contain the specific form of the continued fractions expansions of integral basis element  where $dequiv 2,3( mod  4)$ is a square free positive integer. Besides, the present paper deals with determining the fundamental unit$$epsilon _{d}=left(t_d+u_dsqrt{d}right) 2left.right > 1$$and  $n_d$ and $m_d...

Let $n_q(k,d)$ denote the smallest value of $n$ for which there exists a linear $[n,k,d]$-code over the Galois field $GF(q)$. An $[n,k,d]$-code whose length is equal to $n_q(k,d)$ is called {em optimal}. In this paper we present some matrix generators for the family of optimal $[n,3,d]$ codes over $GF(7)$ and $GF(11)$. Most of our given codes in $GF(7)$ are non-isomorphic with the codes pre...

This paper describes the mathematical modelling of selfexcited induction generators (SEIGs) with are improved electronic load controller (IELC) for microhydel applications supplying variety of loads. In small hydro plants, governor unit of turbine can be eliminated using IELC, which is simple and cost effective. The improved electronic load controller is a combination of a three-phase insulated...

We deal with the following eigenvalue optimization problem: Given a bounded domain D ⊂ R, how to place an obstacle B of fixed shape within D so as to maximize or minimize the fundamental eigenvalue λ1 of the Dirichlet Laplacian on D \ B. This means that we want to extremize the function ρ 7→ λ1(D \ ρ(B)), where ρ runs over the set of rigid motions such that ρ(B) ⊂ D. We answer this problem in t...

Let S be a fixed finite symmetric subset of SLd(Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of πq(G) with respect to the generating set πq(S) form a family of expanders, where πq is the projection map Z → Z/qZ.

Quantitative measurements of fluorescein in the eye are widely used in studying the function of the bloodretinal barrier, but they also can be of value in measuring the flow rate of the tears and aqueous humor and the barriers offered by the corneal layers and the other anterior structures of the eye. Concentrations down to 10~ g/ml can be determined in the ocular humors, and this allows measur...

lnvestigaltons into the nature of desiccation-sensitive, or recalcitant, seed behavior have as yet failed to identify exact causes of this phenomenon. Experiments with Quercus nigra L. and Quercus alba L. were conducted to examine physiological and biochemical changes brought about by seed desiccation and to determine if there were predictable changes in seed moisture content, m enthalpy (heat ...

Abstract We consider a quiver with potential (QP) $(Q(D),W(D))$ and an iced (IQP) $(\overline {Q}(D), F(D), \overline {W}(D))$ associated Postnikov Diagram D prove that their mutations are compatible the geometric exchanges of . This ensures we may define QP $(Q,W)$ IQP {Q},F,\overline {W})$ for Grassmannian cluster algebra up to mutation equivalence. It shows is always rigid (thus nondegenerat...