Mathematics and Applications

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Proceedings of the National Academy of Sciences (PNAS), a peer reviewed journal of the National Academy of Sciences (NAS) - an authoritative source of high-impact, original research that broadly spans the biological, physical, and social sciences.

We introduce a method for showing that there exist prime numbers which are very close together. The method depends on the level of distribution of primes in arithmetic progressions. Assuming the Elliott-Halberstam conjecture, we prove that there are infinitely often primes differing by 16 or less. Even a much weaker c…

• CEM YALÇIN YILDIRIM

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A generalization of the famous KdV and BBM equation are considered with a new nonlinear term. Sufficient conditions of solvability, existence and uniqueness are established.

• CAN MURAT DİKMEN

A generalization of the famous KdV and BBM equation are considered with a new nonlinear term. Sufficient conditions of solvability, existence and uniqueness are established.

• HASAN ÖĞÜNMEZ

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We prove that $ \mathop{ \lim \inf}\limits_{n \rightarrow \infty} \frac{p_{n+1}-p_{n}}{\sqrt{\log p_{n}} \left(\log \log p_{n}\right)^{2}}< \infty, $where pn denotes the nth prime. Since on average pn+1−pn is asymptotically log n, this shows that we can always find pairs of primes much closer together than the average…

• CEM YALÇIN YILDIRIM

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• OSMAN ZEKİ OKUYUCU

A special Frenet motion with a one parameter has been given by Bottema [5] in E 3. In this study, we have given a generalization of [5] to Bishop motion in Euclidean 3-space. Firstly, Bishop motion is defined for space curve α and then Darboux vector of this motion is calculated for fixed and moving spaces in E 3.The…

• MURAT KEMAL KARACAN