In Hans Christian Andersen's folktale, The Emperor's New Clothes, when a child cries out that the emperor is naked, he isn't revealing a secret. Everyone already knows it. What changes in that instant ...

What if machines could not only learn but also teach themselves to become better with each iteration? This isn’t the plot of a sci-fi movie—it’s the reality unfolding in artificial intelligence ...

Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians. Simple, yes, but ...

ABSTRACT: In this paper, we investigate the solutions of the system of difference equations xn+1=xn-1/ynxn-1-1,yn+1=yn-1/xnyn-1-1,zn+1=xn/ynzn-1 where x0,x-1,y0,y-1 ...

In this note, we will give the recursive formulas for sample mean and sample variance, and their generalized forms for batch updates.

Abstract We give arithmetic formulas for the coefficients of Hauptmoduln of higher level as analogues of Kaneko’s formula for the 𝑗-invariant. We also obtain their asymptotic formulas by employing ...

In this paper we propose a new formula to divide power series. We develop two versions of the formula: a recursive and a non-recursive one, the latter aiming to reduce the computational cost for ...

Abstract: Ensemble of metamodels is an effective way to overcome the deficiency of stand-alone metamodel. A new ensemble technique with Recursive arithmetic average ...