Explication of Dio 3 -Tuples from Truncated Octahedral Number-I

3 dio Efikasnost.p65

3 dio Modno.p65

Primes in tuples I

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 conjecture implies that there are infinitely often primes a bounded distance ap...

A truncated octahedral nanocage for fluorescent detection of nucleoside.

A truncated octahedral nanocage containing amide and quinoline groups has been synthesized as an artificial chemosensor for selectively fluorescent detection of uridine over other RNA-based nucleosides.

On the number of Diophantine m-tuples

A set of m positive integers is called a Diophantine m-tuple if the product of any two of them is one less than a perfect square. It is known that there does not exist a Diophantine sextuple and that there are only finitely many Diophantine quintuples. On the other hand, there are infinitely many Diophantine m-tuples for m = 2, 3 and 4. In this paper, we derive asymptotic extimates for the numb...