We study the problem of how to detect \interesting objects" appeared in a given image, I. Our approach is to treat it as a function approximation problem based on an over-redundant basis. Since the basis (a library of image templates) is over-redundant, there are innnitely many ways to decompose I. To select the \best" decomposition we rst propose a global optimization procedure that considers ...

In this paper we prove the unobstructedness of the deformation of integral coisotropic submanifolds in symplectic manifolds, which can be viewed as a natural generalization of results of Weinstein [4] for Lagrangian submanifolds. Let (X,ω) be a symplectic manifold. A submanifold Y ⊂ (X,ω) is coisotropic if rank(ω|Y ) = 2 dim(Y ) − dimX . The closedness of ω implies that ker(ω|Y ) defines an int...

Concave gold nanoplates are obtained in hexagonal liquid crystal (LLC) made of SDS (sodium dodecyl sulfate)/glycine/HAuCl(4) aqueous solution system where glycine plays the key role. All plates are single-crystals, characterized by {111} facets, with concave centers of regular hexagonal or triangular shapes, and with better electrocatalytic activity than gold nanoplates.

In the last decades, many efforts have been made to solve multimodal optimization problems using Particle Swarm Optimization (PSO). To produce good results, these PSO algorithms need to specify some niching parameters to define the local neighborhood. In this paper, our motivation is to propose the novel neighborhood structures that remove undesirable niching parameters without sacrificing perf...

In the real world, many problems are continuous in nature. In some cases, finding the global solutions for these problems is difficult. The reason is that the problem’s objective function is non convex, nor concave and even not differentiable. Tackling these problems is often computationally too expensive. Although the development in computer technologies are increasing the speed of computation...

A class of linear operators L+λI between suitable function spaces is considered, when 0 is an eigenvalue of L with constant eigenfunctions. It is proved that L + λI satisfies a strong maximum principle when λ belongs to a suitable pointed left-neighborhood of 0, and satisfies a strong uniform antimaximum principle when λ belongs to a suitable pointed right-neighborhood of 0. Applications are gi...

For the Kuramoto Sivashinsky equation with L-periodic boundary conditions we show that the radius of space analyticity on the global attractor is lowersemicontinuous function at the stationary solutions, and thereby deduce the existence of a neighborhood in the global attractor of the set of all stationary solutions in which the radius of analyticity is independent of the bifurcation parameter ...

Question 1. Let f(z1, . . . , zn) be a holomorphic function on an open set U ⊂ C. For which t ∈ R is |f |t locally integrable? The positive values of t pose no problems, for these |f |t is even continuous. If f is nowhere zero on U then again |f |t is continuous for any t ∈ R. Thus the question is only interesting near the zeros of f and for negative values of t. More generally, if h is an inve...