منابع مشابه
Topology of random linkages
Betti numbers of configuration spaces of mechanical linkages (known also as polygon spaces) depend on a large number of parameters – the lengths of the bars of the linkage. Motivated by applications in topological robotics, statistical shape theory and molecular biology, we view these lengths as random variables and study asymptotic values of the average Betti numbers as the number of links n t...
متن کاملStabilizing a Multi-Agent System to an Equilateral Polygon Formation
The problem of stabilizing a group of agents in the plane to a stationary formation is analyzed. A local control scheme is proposed to stabilize the agents to the vertices of an equilateral polygon. The centroid of the agents is stationary during the evolution. For three agents a full stability analysis is performed: If three agents start in distinct and non-collinear locations, they converge t...
متن کاملLaplace’s Equation in the Exterior of a Convex Polygon. the Equilateral Triangle
A general method for studying boundary value problems for linear and for integrable nonlinear partial differential equations in two dimensions was introduced in [3]. For linear equations in a convex polygon [2,4,5], this method: (a) Expresses the solution q(x,y) in the form of an integral (generalized inverse Fourier transform) in the complex k-plane involving a certain function q̂(k) (generaliz...
متن کاملLaplace’s Equation in the Exterior of a Convex Polygon. the Equilateral Triangle
A general method for studying boundary value problems for linear and for integrable nonlinear partial differential equations in two dimensions was introduced in Fokas, 1997. For linear equations in a convex polygon (Fokas and Kapaev (2000) and (2003), and Fokas (2001)), this method: (a) expresses the solution q(x, y) in the form of an integral (generalized inverse Fourier transform) in the comp...
متن کاملPacking and Covering a Unit Equilateral Triangle with Equilateral Triangles
Packing and covering are elementary but very important in combinatorial geometry , they have great practical and theoretical significance. In this paper, we discuss a problem on packing and covering a unit equilateral triangle with smaller triangles which is originated from one of Erd˝ os' favorite problems.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1996
ISSN: 0166-8641
DOI: 10.1016/0166-8641(96)00046-6