Let Cn and Cn(q) be the nth Catalan number and the nth q-Catalan number, respectively. In this paper, we show that the Diophantine equation Cn = Cm(q) has only finitely many integer solutions (m,n, q) with m > 1, n > 1, q > 1. Moreover, they are all effectively computable. – To Professor Carl Pomerance on his 65th birthday

In this note we show that the nth Morava E-cohomology group of a finite spectrum with action of the nth Morava stabilizer group can be recovered from the (n + 1)st Morava Ecohomology group with action of the (n + 1)st Morava stabilizer group.

the nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. using the leray-schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.

In this paper an equalization technique for colour images is introduced. The method is based on n th root and n th power equalization approach but with optimization of the mean of the image in different colour channels such as RGB and HSI. The performance of the proposed method has been measured by the means of peak signal to noise ratio. The proposed algorithm has been compared with convention...

Stronger light intensity fluctuations are pursued by related applications such as optical resolution, image enhancement, and beam positioning. In this paper, an Nth-order fluctuation amplifier is proposed, which was demonstrated a four-wave mixing process with different statistical distribution coupling lights. Firstly, its amplification mechanism revealed both theoretically experimentally. The...