Set Theory and Logic

1410 Submissions

[2] viXra:1410.0131 [pdf] submitted on 2014-10-22 17:37:47

Roughness of Neutrosophic Sets

Authors: A. A. Salama, Said Broumi
Comments: 5 Pages.

Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. In this paper we define rough neutrosophic sets and study their properties. Some propositions in this notion are proved. Possible application to computer sciences is touched upon.
Category: Set Theory and Logic

[1] viXra:1410.0022 [pdf] submitted on 2014-10-04 20:57:05

A Note on the Length of Maximal Arithmetic Progressions in Random Subsets

Authors: Yilun Shang
Comments: 6 Pages.

Let $U^{(n)}$ denote the maximal length arithmetic progression in a non-uniform random subset of $\{0,1\}^n$, where $1$ appears with probability $p_n$. By using dependency graph and Stein-Chen method, we show that $U^{(n)}-c_n\ln n$ converges in law to an extreme type distribution with $\ln p_n=-2/c_n$. Similar result holds for $W^{(n)}$, the maximal length aperiodic arithmetic progression (mod $n$).
Category: Set Theory and Logic