The goal of this project is to investigate constant properties (called the Liouville-type Problem) for a p-stable map as a local or global minimum of a p-energy functional where the domain is a Euclidean space and the target space is a closed half-ellipsoid. The First and Second Variation Formulas for a p-energy functional has been applied in the Calculus Variation Method as computation techniq...

The motion of a heavy rigid ellipsoidal particle settling in an infinitely long circular tube filled with an incompressible Newtonian fluid has been studied numerically for three categories of problems, namely, when both fluid and particle inertia are negligible, when fluid inertia is negligible but particle inertia is present, and when both fluid and particle inertia are present. The governing...

In this problem, one of the primaries of mass m1 is a Roche Ellipsoid filled with a homogeneous incompressible fluid of density ρ1. The smaller primary of mass m2 is a point mass outside the Ellipsoid. The third and the fourth bodies (of mass m3 and m4 respectively) are small solid spheres of density ρ3 and ρ4 respectively inside the Ellipsoid, with the assumption that the mass and the radius o...

Let S = Sg,n be a connected, orientable surface of genus g ≥ 0 with n ≥ 0 punctures. Let Teich(S) denote the corresponding Teichmüller space, and let Mod(S) denote the mapping class group of S. Understanding the analogy of Teich(S) with symmetric spaces is a wellknown theme. Recall that a complete Riemannian manifold X is symmetric if it is symmetric at each point x ∈ X: the map γ(t) 7→ γ(−t) w...

In this paper, the concepts of L-concave structures, concave Linterior operators and concave L-neighborhood systems are introduced. It is shown that the category of L-concave spaces and the category of concave Linterior spaces are isomorphic, and they are both isomorphic to the category of concave L-neighborhood systems whenever L is a completely distributive lattice. Also, it is proved that th...

The thinnest coverings of ellipsoids are studied in the Euclidean spaces of an arbitrary dimension n. Given any ellipsoid, our goal is to find the minimum number of unit balls needed to cover this ellipsoid. A tight asymptotic bound on the logarithm of this number is obtained. © 2006 Elsevier Inc. All rights reserved.

The difference between the way in which binocular disparity scales with viewing distance and the way in which motion parallax scales with viewing distance introduces a potential indirect cue for viewing distance: the viewing distance is the only distance at which disparity and motion specify the same depth. The present study examines whether this information is used. Two simulated ellipsoids we...

BACKGROUND Navigation through the environment requires a working memory for the chosen target and path integration facilitating an approach when the target becomes temporarily hidden. We have previously shown that this visual orientation memory resides in the ellipsoid body, which is part of the central complex in the Drosophila brain. Former analysis of foraging and ignorant mutants have revea...

1. Abstract This paper focuses on the use of minimum norm ellipsoids in stress-based fatigue criteria. We consider both the theoretical issues involved in constructing mathematical models for high cycle fatigue endurance limits and the computational features concerning the application of the resulting fatigue criteria. In the present approach, the macroscopic level of continuum is enhanced with...

We propose an unsupervised “local learning” algorithm for learning a metric in the input space. Geometrically, for a given query point, the algorithm finds the minimum volume ellipsoid (MVE) covering its neighborhood which characterizes the correlations and variances of its neighborhood variables. Algebraically, the algorithm maximizes the determinant of the local covariance matrix which amount...