This paper presents BSR-parallel algorithms for three geometrical problems : point location, convex hull and smallest enclosing rectangle. These problems are solved in constant time using the BSR model introduced by S. Akl in (21. The first algorithm uses O ( N ) processors ( N is the number of edges of the polygon R). The second uses O ( N " ) processors (N ' is the nuniber of points) and the ...

Western musicians traditionally classify pitch sequences by disregarding the effects of five musical transformations: octave shift, permutation, transposition, inversion, and cardinality change. We model this process mathematically, showing that it produces 32 equivalence relations on chords, 243 equivalence relations on chord sequences, and 32 families of geometrical quotient spaces, in which ...

Fisher's geometrical model amounts to a description of mutation and selection for individuals characterised by a number of quantitative traits. In the present work the fitness landscape is not assumed to be spherically symmetric, hence different points, i.e. phenotypes, on a surface of constant fitness generally have different curvatures. We investigate two different approximations of Fisher's ...

In the past decades, central limit theorem (CLT) has been generalized to non-Euclidean data spaces. Some years ago, it was found that for some random variables on circle, sample Fréchet mean fluctuates around population asymptotically at a scale n−τ with exponent τ<1/2 non-normal distribution if probability density antipodal point of is 12π. The author and his collaborator recently discovered τ...

many earthquakes occur in iran every year and some of these earthquakes cause loss of life and property. consequently earthquake is one of challenging topics not only in iran but also in other active tectonic regions in the world. investigating the mechanism of earthquake as a natural disaster is the first and important step. to study earthquakes, different information such as geometry and beha...