We investigate the irregularity strength (s(G)) and total vertex irregularity strength (tvs(G)) of circulant graphs Cin(1, 2, . . . , k) and prove that tvs(Cin(1, 2, . . . , k)) = ⌈ n+2k 2k+1 ⌉ , while s(Cin(1, 2, . . . , k)) = ⌈ n+2k−1 2k ⌉ except if either n = 2k + 1 or if k is odd and n ≡ 2k + 1(mod4k), then s(Cin(1, 2, . . . , k)) = ⌈ n+2k−1 2k ⌉ + 1.

In this paper we prove that if φ : C → C is a K-quasiconformal map, with K > 1, and E ⊂ C is a compact set contained in a ball B, then Ċ 2K 2K+1 , 2K+1 K+1 (E) diam(B) 2 K+1 ≥ c−1 ( γ(φ(E)) diam(φ(B)) ) 2K K+1 , where γ stands for the analytic capacity and Ċ 2K 2K+1 , 2K+1 K+1 is a capacity associated to a non linear Riesz potential. As a consequence, if E not K-removable, it has positive capac...

ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...

In this paper we introduce a new algorithm for division in residue number system, which can be applied to any moduli set. Simulation results indicated that the algorithm is faster than the most competitive published work. To further improve this speed, we customize this algorithm to serve two specific moduli sets: (2k, 2k −1, 2k−1 −1) and (2k +1, 2k, 2k −1). The customization results in elimina...