The Ellipsoid algorithm was developed by (formerly) Soviet mathematicians (Shor (1970), Yudin and Nemirovskii (1975)). Khachian (1979) proved that it provides a polynomial time algorithm for linear programming. The average behavior of the Ellipsoid algorithm is too slow, making it not competitive with the simplex algorithm. However, the theoretical implications of the algorithm are very importa...

An ellipsoid farrowing crate was designed and compared to the conventional rectangular crate with regard to its effect on sows' production traits. The main features of this crate are its oval horizontal frame and bowed vertical bars. Thirty-two sows farrowed in each system. Those in the ellipsoid crates raised 318 pigs and those in the rectangular crates raised 304. Stillbirth rate was lower in...

PURPOSE To compare estimated prostate volume (PV) based on computed tomography (CT) scan and transrectal ultrasonography (TRUS) in patients with lower urinary tract symptoms (LUTS). MATERIALS AND METHODS Between January 2010 and October 2012, 107 consecutive patients with LUTS were analyzed, retrospectively. PV measures were performed by the means of ellipsoid formula (PV = π/6 [width (cm) th...

This thesis deals with a method to obtain the ejection fraction of the left ventricle of the heart from a gated set of planar myocardial perfusion images. Ejection fraction is defined as the ratio of the fully contracted left-ventricular volume to the fully expanded left-ventricular volume and is known as an effective gauge of cardiac function. This method is proposed as a safer and more cost e...

Let S denote the convex hull of m full-dimensional ellipsoids in Rn. Given > 0 and δ > 0, we study the problems of computing a (1 + )-approximation to the minimum volume covering ellipsoid of S and a (1 + δ)n-rounding of S. We extend the first-order algorithm of Kumar and Yıldırım that computes an approximation to the minimum volume covering ellipsoid of a finite set of points in Rn, which, in ...

Chronometric geodesy applies general relativity to study the problem of the shape of celestial bodies including the earth, and their gravitational field. The present paper discusses the relativistic problem of construction of a background geometric manifold that is used for describing a reference ellipsoid, geoid, the normal gravity field of the earth and for calculating geoid’s undulation (hei...

In high bit rate optical fiber communication systems, Polarization mode dispersion (PMD) is one of the main factors to signal distortion and needs to be compensated. PMD monitoring system is the key integral part of an adaptive PMD compensator. The degree of polarization (DOP) ellipsoid obtained by using a polarization scrambler can be used as a feedback signal for automatic PMD compensation. G...