In this paper, we prove the energy diminishing of a normalized gradient flow which provides a mathematical justification of the imaginary time method used in physical literatures to compute the ground state solution of Bose-Einstein condensates (BEC). We also investigate the energy diminishing property for the discretization of the normalized gradient flow. Two numerical methods are proposed fo...

A volume-normalized formulation of the Lp-Minkowski problem is presented. This formulation has the advantage that a solution is possible for all p ≥ 1, including the degenerate case where the index p is equal to the dimension of the ambient space. A new approach to the Lp-Minkowski problem is presented, which solves the volume-normalized formulation for even data and all p ≥ 1. The Minkowski pr...

‎let $g$ be a graph without an isolated vertex‎, ‎the normalized laplacian matrix $tilde{mathcal{l}}(g)$‎‎is defined as $tilde{mathcal{l}}(g)=mathcal{d}^{-frac{1}{2}}mathcal{l}(g) mathcal{d}^{-frac{1}{2}}$‎, where ‎$‎mathcal{‎d}‎$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎g‎$‎‎. ‎the eigenvalues of‎‎$tilde{mathcal{l}}(g)$ are ‎called ‎ ‎ as ‎the ‎normalized laplacian ...

In this note, we would like to explore some of the issues suggested by the discussion paper of Pizlo et. al. The context is the study of image of planar objects taken with calibrated cameras. However, in this note, we shall consider the question using notation that has become somewhat standard in the literature of computer vision, particularly in the study of uncalibrated cameras. The projectio...

nowadays, because of the growing numbers of vehicles on streets and roads, the use of intelligent controlsystems to improve driving safety and health has become a necessity. to design and implement suchcontrol systems, having information about traffic light colors is essential. there are the wide variety oftraffic lights in terms of light intensity and color. therefore it seems that design and ...