Related papers: A maximal energy pointset configuration problem
We consider the Max Unique Coverage problem, including applications to the data stream model. The input is a universe of $n$ elements, a collection of $m$ subsets of this universe, and a cardinality constraint, $k$. The goal is to select a…
We consider eigenvalue problems for general elliptic operators of arbitrary order subject to homogeneous boundary conditions on open subsets of the euclidean N-dimensional space. We prove stability results for the dependence of the…
A mesh condition is developed for linear finite element approximations of anisotropic diffusion-convection-reaction problems to satisfy a discrete maximum principle. Loosely speaking, the condition requires that the mesh be simplicial and…
Specific data compression techniques, formalized by the concept of coresets, proved to be powerful for many optimization problems. In fact, while tightly controlling the approximation error, coresets may lead to significant speed up of the…
We revisit a version of the classic occupancy scheme, where balls are thrown until almost all boxes receive a given number of balls. Special cases are widely known as coupon-collectors and dixie cup problems. We show that as the number of…
In this paper we analyze a continuous version of the maximal covering location problem, in which the facilities are required to be interconnected by means of a graph structure in which two facilities are allowed to be linked if a given…
Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures. The technique interpolates between standard statistical energy…
We study an inverse design problem for the linear multiple fragmentation equation arising in particle dynamics. Our objective is to reconstruct an unknown initial size distribution that evolves, under a prescribed fragmentation law, into a…
The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N = 1054. In the predecessor to this paper…
A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…
Begin with a set of four points in the real plane in general position. Add to this collection the intersection of all lines through pairs of these points. Iterate. Ismailescu and Radoi\v{c}i\'{c} (2003) showed that the limiting set is dense…
We consider the stationary problem for a diffusive logistic equation with the homogeneous Dirichlet boundary condition. Concerning the corresponding Neumann problem, Wei-Ming Ni proposed a question as follows: Maximizing the ratio of the…
Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…
The finite element solution of two-dimensional anisotropic diffusion problems is considered. A Delaunay-type mesh condition is developed for linear finite element approximations to satisfy a discrete maximum principle. The condition is…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
In this paper, we consider a maximizing problem associated with the Sobolev type embedding on the space of bounded variation. We show that, although the maximizing problem suffers from both of the non-compactness of vanishing and…
For the heat equation on a bounded subdomain $\Omega$ of $\mathbb{R}^d$, we investigate the optimal shape and location of the observation domain in observability inequalites. A new decomposition of $L^2(\mathbb{R}^d)$ into heat packets…
In this work, we consider a method of searching of the direction of a wireless network development (the places of new access points or base stations etc.) optimized with criteria of coverage of important territories and minimum cost of…
We investigate the optimal stopping problems involving the supremum of a diffusion. The starting point is the link between works of Peskir and Meilijson, which we describe in a unified manner. The description developped follows mainly the…
Minimum energy configurations in celestial mechanics are investigated. It is shown that this is not a well defined problem for point-mass celestial mechanics but well-posed for finite density distributions. This naturally leads to a…