In this paper generalizations of Heilbronn's triangle problem are considered. By using results on the independence number of linear hypergraphs, for xed integers k 3 and any integers n k a o(n6k 4) time deterministic algorithm is given, which nds distributions of n points in the unit square [0; 1]2 such that, simultaneously for j = 3; : : : ; k, the areas of the convex hulls determined by any j...

This note outlines an algorithm for solving the complex “matrix Procrustes problem”. This is a least-squares approximation over the cone of positive semi-definite Hermitian matrices, which has a number of applications in the areas of Optimization, Signal Processing and Control. The work generalises the method of [J.C. Allwright, “Positive semidefinite matrices: Characterization via conical hull...

We consider linearly independent families of Hermitian matrices {A1, . . . , Am} so thatWk(A) is convex. It is shown that m can reach the upper bound 2k(n− k) + 1. A key idea in our study is relating the convexity of Wk(A) to the problem of constructing rank k orthogonal projections under linear constraints determined by A. The techniques are extended to study the convexity of other generalized...

We consider the person re-identification problem, assuming the availability of a sequence of images for each person, commonly referred to as video-based or multi-shot reidentification. We approach this problem from the perspective of learning discriminative distance metric functions. While existing distance metric learning methods typically employ the average feature vector as the data exemplar...

This paper is devoted to the hydroforming performances of toroidal pressure hulls with octagonal cross-sections, together buckling hydroformed hulls. The cross-sections preforms are inscribed from circular perfect shells a 150 mm major radius, 75 section and 1.058 wall thickness. nonlinear finite-element method was employed study under various pressures. To verify numerical findings, three nomi...

Planing hulls, commonly used in many areas, have different hydrodynamic behavior than the displacement even calm water. Therefore, this makes calculation of maneuvering parameters these hulls appealing. In present study, a planing hull's numerical static drift analyses are performed using unsteady RANS approach to evaluate sway force and yaw moment at angles attack advance velocities. The resul...