Controlled Flight Into Terrain (CFIT) accidents continue to be a major source of loss of aircraft and aircrew in both military and civil aviation (Cooper, 1995; Miller, Price, and Darrah, 1987; Proctor, 1997). These accidents usually occur in reduced-visibility conditions, and with no prior awareness of impending collision on the part of the flight crew (Scott, 1996). While warning and automate...

For Euclidean space (`2), there exists the powerful dimension reduction transform of Johnson and Lindenstrauss [26], with a host of known applications. Here, we consider the problem of dimension reduction for all `p spaces 1 ≤ p ≤ 2. Although strong lower bounds are known for dimension reduction in `1, Ostrovsky and Rabani [40] successfully circumvented these by presenting an `1 embedding that ...

We introduce a new approach to approximate generalized 3D Voronoi diagrams for different site shapes (points, spheres, segments, lines, polyhedra, etc) and different distance functions (Euclidean metrics, convex distance functions, etc). The approach is based on an octree data structure denoted Voronoi-Octree (VO) that encodes the information required to generate a polyhedral approximation of t...

We have developed simple algorithms that allow adjacency and proximity searching in Google and the Science Citation Index (SCI). The SCI algorithm exploits the fact that SCI stopwords in a search phrase function as a placeholder. Such a phrase serves effectively as a fixed adjacency condition determined by the number n of adjacent stopwords (i.e., retrieve all records where word A and word B ar...

In this work we investigate a class of admitting center maps on a metric space. We state and prove some fixed point and best proximity point theorems for them. We obtain some results and relevant examples. In particular, we show that if $X$ is a reflexive Banach space with the Opial condition and $T:Crightarrow X$ is a continuous admiting center map, then $T$ has a fixed point in $X.$ Also, we ...

in this paper, we establish and prove the existence of best proximity points for multivalued cyclic $f$- contraction mappings in complete metric spaces. our results improve and extend various results in literature.

In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we sho...