We give a new upper bound for the rectilinear crossing number cr(n) of the complete geometric graph Kn. We prove that cr(n) ≤ 0.380559 ¡n 4 ¢ + Θ(n3 ) by means of a new const...
We give a new insight into the upper bounding of the 3-SAT threshold by the first moment method. The best criteria developed so far to select the solutions to be counted discrimina...
We present a new general upper bound on the number of examples required to estimate all of the expectations of a set of random variables uniformly well. The quality of the estimat...
Let P(n) denote the largest prime divisor of n, and let (x, y) be the number of integers n x with P(n) y. In this paper we present improvements to Bernstein's algorithm, whi...
The main contribution of this work is an analytical model for finding the upper bound on the temperature difference among various locations on the die. The proposed model can be u...