For k even, let Pk denote the vector space of polynomials in 2 real variables of degree at most k. A linear functional L : Pk −→ R is positive if p ∈ Pk, p|R2 ≥ 0 =⇒ L(p) ≥ 0. Hilbert’s theorem on sums of squares (cf. [15]) implies that L : P4 −→ R is positive if and only if the moment matrix associated to L is positive semidefinite. In this note, using k = 6, we exhibit the first families of p...

he linear exponential distribution is a very well-known distribution for modeling lifetime data in reliability and medical studies.We introduce in this paper a new four-parameter generalized version of the transmuted generalized linear exponential distribution.We provide a comprehensive account of the mathematical properties of the new distributions. In particular, A closed-form expressions for...

The problem of tracking a vessel modelled at a distance by an equivalent magnetic dipole is investigated. Tracking a magnetic dipole from magnetic field measurements is a complex non-linear problem. The determination of target position, velocity and magnetic moment is formulated as an optimal stochastic estimation problem, which could be solved using the non-linear Kalman filtering methods. The...

Nanosystems are devices that are in the size range of a billionth of a meter (1×10−9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of th...

Document mentioned in title of this article was published in first version in 2004. In moment research was started version revised on 16.01.2006 was available and this article refers mainly to that version. At this moment newer version revised on 16.10.2006 is available, but main idea is same. This article contains formulation of TSP 2 problem. Then problem is modeled as Integer Linear Programm...