There exist irreducible exact covering systems (ECS). These are ECS which are not a proper split of a coarser ECS. However, an ECS admiting a maximal modulus which is divisible by at most two distinct primes, primely splits a coarser ECS. As a consequence, if all moduli of an ECS A are divisible by at most two distinct primes, then A is natural. That is, A can be formed by iteratively splitting...

A fuzzy queuing coherent hierarchical location-allocation model is developed for congested systems. The parameters of the model are approximately evaluated and stated as fuzzy-numbers. The coverage of demand nodes is also considered in an approximate manner and is stated by the degree of membership. Using the queuing theory and fuzzy conditions, a coherent hierarchical model is developed for th...

Most people will store smartphone waste or give it to others; this is due inadequate collection facilities in all cities/regencies Indonesia. In Yogyakarta Province, there no electronic facility. Therefore, an e-waste network needed cover potential the province of Yogyakarta. This study aims design a provide easy access for users, which includes number and location each center route transportin...

Let J (M) denote the σ-ideal associated with two-dimensional Miller forcing. We show that it is relatively consistent with ZFC that the additivity of J (M) is bigger than the covering number of the ideal of the meager subsets of ω. We also show that Martin’s Axiom implies that the additivity of J (M) is 2. Finally we prove that there are no analytic infinite maximal antichains in any finite pro...

Article history: Received 15 April 2014 Received in revised form 29 September 2014 Accepted 28 October 2014 Available online 4 November 2014

Let F denote the class of all functions univalent in the unit disk and convex in the direction of the real axis. In the paper we discuss the functions of the class F which are n-fold symmetric, where n is positive even integer. For the class of such functions we find the Koebe set as well as the covering set, i.e. T f2F f ðDÞ and S f2F f ðDÞ. Moreover, the Koebe constant and the covering consta...

For every fixed graph H, we determine the H-covering number of Kn, for all n > n0(H). We prove that if h is the number of edges of H, and gcd(H) = d is the greatest common divisor of the degrees of H, then there exists n0 = n0(H), such that for all n > n0, C(H,Kn) = d dn 2h dn− 1 d ee, unless d is even, n = 1 mod d and n(n− 1)/d+ 1 = 0 mod (2h/d), in which case C(H,Kn) = d ( n 2 ) h e+ 1. Our m...