This paper addresses the problem of searching for a located target in the plane by using one searcher starting its motion from the point . The searcher moves along parabolic spiral curve. The position of the target has a known distribution. We show that the distance between the target position and the searcher starting point depends on the number of revolutions, where the complete revolution is done when . Furthermore, we study this technique in the one-dimensional case (i.e., when the searcher moves with linear search technique). It is desired to get the expected value of the time for detecting the target. Illustrative examples are given to demonstrate the applicability of this technique assuming circular normal distributed estimates of the target position.
In tlıis paper we derive sufficient coııditioııs for strict convexity of subsets iıı a complete siınply connectcd smooth Riemannian manifold witlıout focal points in terms of local and global exposed points.
A set A in Euclidean n-space E n , is called an m-convex set if for every m distinct points of A at least one of the line segments joining two points of them lies in A. In this article we study some geometrical and topological properties of these sets in E n .
Mathematics Subject Classification: 53C42, 52A05
In this paper the uniform convexity as well as stıict uniform convexity have been defined for Riemannian manifolds. Necessary and sufficient conditions are established for a Riemannian manifold without conjugate points to be free from focal points in terms of the uniform convexity concept.
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