We study the space of all d-tuples unitaries u = ( 1 , … d ) using dilation theory and matrix ranges. Given two such v generating, respectively, C*-algebras A B, we seek minimal constant c that ≺ by which mean there exist faithful ∗-representations π : → B H ρ K with ⊆ for i, i is equal to compression P | H. This gives rise a metric D log max { } on set equivalence classes ∗-isomorphic tuples u...

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...

Relational database is a collection of relations. Duplicate tuple existence is common in many real time relational databases. In a relational database, if the same real-world entity is represented by more than one tuple, then such tuples are called duplicate tuples. Finding duplicate tuples and then replacing them by one best tuple is called a fusion operation. Whenever duplicate tuples are fou...