Spherical Distribution of 5 Points with Maximal Distance Sum

Spherical Distribution of 5 Points with Maximal Distance Sum

In this paper, we mainly consider the problem of spherical distribution of 5 points, that is, how toconfigure 5 points on a sphere such that the mutual distance sum attains the maximum. It is conjecturedthat the sum of distances is maximal if 5 points form a bipyramid configuration in which case two pointsare positioned at two poles of the sphere and the other three are position...

Fixed Points Theorems with respect to \fuzzy w-distance

In this paper, we shall introduce the fuzzyw-distance, then prove a common fixed point theorem with respectto fuzzy w-distance for two mappings under the condition ofweakly compatible in complete fuzzy metric spaces.

Small Maximal Sum-Free Sets

Let G be a group and S a non-empty subset of G. If ab / ∈ S for any a, b ∈ S, then S is called sum-free. We show that if S is maximal by inclusion and no proper subset generates 〈S〉 then |S| ≤ 2. We determine all groups with a maximal (by inclusion) sum-free set of size at most 2 and all of size 3 where there exists a ∈ S such that a / ∈ 〈S \ {a}〉.

On Maximal Spherical Codes I

We investigate the possibilities for attaining two Levenshtein upper bounds for spherical codes. We find the distance distributions of all codes meeting these bounds. Then we show that the fourth Levenshtein bound can be attained in some very special cases only. We prove that no codes with an irrational maximal scalar product meet the third Levenshtein bound. So in dimensions 3 ≤ n ≤ 100 exactl...

Distribution of Rational Points: A Survey