相关论文: Generalizations of the Hanoi Towers Problem

We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…

Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…

We begin development of a method for studying dynamical systems using concepts from computational complexity theory. We associate families of decision problems, called telic problems, to dynamical systems of a certain class. These decision…

In the classical facility location problem we consider a graph $G$ with fixed weights on the edges of $G$. The goal is then to find an optimal positioning for a set of facilities on the graph with respect to some objective function. We…

We analyze Solo Chess puzzles, where the input is an $n \times n$ board containing some standard Chess pieces of the same color, and the goal is to make a sequence of capture moves to reduce down to a single piece. Prior work analyzes this…

This work is devoted to the investigation of possibility of controlling of ions motion inside Paul trap. It has been shown that by proper selection of the parameters of controlling electric fields, stable localization of ions inside Paul…

A method to determine the admissibility of symbolic sequences and to find the unstable periodic orbits corresponding to allowed symbolic sequences for the diamagnetic Kepler problem is proposed by using the ordering of stable and unstable…

In p-median location interdiction the aim is to find a subset of edges in a graph, such that the objective value of the p-median problem in the same graph without the selected edges is as large as possible. We prove that this problem is…

(Talk presented at the 7th Marcel Grossmann Meeting on General Relativity, Stanford, CA, July 24-30, 1994) We study the semi-classical limit of the solution of the Dirac equation in a background electromagnetic/gravitational plane wave. We…

We consider the problem of placing n small balls of given radius in a certain domain subject to a force f in order to minimize the compliance of the configuration. Then we let n tend to infinity and look at the asymptotics of the…

We study the problem of covering a given set of $n$ points in a high, $d$-dimensional space by the minimum enclosing polytope of a given arbitrary shape. We present algorithms that work for a large family of shapes, provided either only…

We present a novel feasibility criteria for the finite intersection of convex sets given by inequalities. This criteria allows us to easily assert the feasibility by analyzing the unconstrained minimum of a speci?fic convex function, that…

The general position problem for graphs asks for the largest number of vertices in a subset $S \subseteq V(G)$ of a graph $G$ such that for any $u,v \in S$ and any shortest $u,v$-path $P$ we have $S \cap V(P) = \{ u,v\} $, whereas the…

The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a…

In the problem "Localization and trilateration with the minimum number of landmarks", we faced the 3-Guard and classic Art Gallery Problems. The goal of the art gallery problem is to find the minimum number of guards within a simple polygon…

The polygon retrieval problem on points is the problem of preprocessing a set of $n$ points on the plane, so that given a polygon query, the subset of points lying inside it can be reported efficiently. It is of great interest in areas such…

We prove the existence of dark monopole solutions in a recently formulated Yang--Mills--Higgs theory model with technical features similar to the classical monopole problems. The solutions are obtained as energy-minimizing static…

In a wide class of the so called Obstacle Problems of parabolic type it is shown how to improve the optimal regularity of the solution and as a consequence how to obtain space-time regularity of the corresponding free boundary.

We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only…

The Heilbronn triangle problem asks for the placement of $n$ points in a unit square that maximizes the smallest area of a triangle formed by any three of those points. In $1972$, Schmidt considered a natural generalization of this problem.…