Hopfian Boolean algebras of power less than or equal to continuum

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.

Rank-width is less than or equal to branch-width

We prove that the rank-width of the incidence graph of a graph G is either equal to or exactly one less than the branch-width of G, unless the maximum degree of G is 0 or 1. This implies that rank-width of a graph is less than or equal to branch-width of the graph unless the branch-width is 0. Moreover, this inequality is tight.

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.

Continuum Cardinals Generalized to Boolean Algebras

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...