conformational properties of n-aryl-1-azacyclooctan-5- ones with a p-methyl, m-methyl, and p-methoxy group as a substituent have been studied by 1h-nmr, 13c-nmr and ir spectroscopies. transannular interaction of the two functional groups have been examined from the ring inversion barriers and the carbonyl vibrational frequencies with reference to the corresponding data of the respective monofun...

Crohn's disease (CD) and ulcerative colitis (UC) make up the so-called chronic inflammatory bowel disease (IBD). Advances in the understanding of IBD pathophysiologic mechanisms in the last few years have allowed the development of novel therapies such as biologic therapies, which at least theoretically represent a more specific management of this disease with fewer side effects. Currently, the...

ardy and Littlewood conjectured that every large integer $n$ that is not a square is the sum of a prime and a square. They believed that the number $mathcal{R}(n)$ of such representations for $n = p+m^2$ is asymptotically given by begin{equation*} mathcal{R}(n) sim frac{sqrt{n}}{log n}prod_{p=3}^{infty}left(1-frac{1}{p-1}left(frac{n}{p}right)right), end{equation*} where $p$ is a prime, $m$ is a...