More and Less than Equal

ATANASSOV'S INTUITIONISTIC FUZZY GRADE OF I.P.S. HYPERGROUPS OF ORDER LESS THAN OR EQUAL TO 6

In this paper we determine the sequences of join spaces and Atanassov's intuitionistic fuzzy sets associated with all i.p.s. hypergroups of order less than or equal to 6, focusing on the calculation of their lengths.

When some are more equal than others.

Turbulence in more than two and less than three dimensions.

We investigate the behavior of turbulent systems in geometries with one compactified dimension. A novel phenomenological scenario dominated by the splitting of the turbulent cascade emerges both from the theoretical analysis of passive scalar turbulence and from direct numerical simulations of Navier-Stokes turbulence.

Saying More (or Less) than One Thing

In a paper called Definiteness and Knowability, Timothy Williamson investigates the question of whether one must accept that vagueness is an epistemic phenomenon if one adopts classical logic and a disquotational principle for truth. Some have thought that one must not, and have argued that classical logic and the disquotational principle can be preserved without accepting that vagueness is an ...

ON THE NUMBER OF PRIMES LESS THAN OR EQUAL x

(3) Z I"—1 log p = x log x + 0{x). r-ix\-pJ Since [x/^>]= [[#]/£], it is clear that (3) then holds for all real x>0. We propose to show in this note that the order of w(x) =the number of primes less than or equal x (a result originally due to Tschebyschef, cf. [l]) may be derived very quickly from (3) as a consequence of a general theorem which has no particular relationship to prime numbers. T...