New sets with large Borsuk numbers

New sets with large Borsuk numbers

We construct finite sets in Rn, n ≥ 298, which cannot be partitioned into n + 11 parts of smaller diameter thus decreasing the smallest dimension in which Borsuk’s conjecture is known to be false.

Sets with a Large Numbers of Nuclei on a Conic

For large q we characterize the (q + 1)-sets in PG(2, q), q odd, having more than 0.326q nuclei on a conic. In the process more information about the structure of (q + 1)-sets having a large number of nuclei on a conic is obtained.

Laws of Large Numbers for Random Linear

The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the...

Computations with Large Numbers

Since any personal computer has a limited range of integer values, therefore, it will result in an integer overflow when a program tries to compute a value larger than machine’s maximum value. We will discuss a workable algorithm that will be able to deal with any large numbers without getting an integer overflow.

A Note on Strong Laws of Large Numbers for Dependent Random Sets and Fuzzy Random Sets