Abstract: In this paper, we compute number of fuzzy subgroups of some dihedral groups such as D2pn where p is a prime number and D2p1×p2×···×pn where p1, p2, ..., pn are distinct prime numbers. We use their chain diagram to determine the number of their fuzzy subgroups and present an explicit recursive formula to D2pn and at the result in specially case D2n and finally a formula to count number...

Let pn denote the nth prime. The prime number graph is the set of lattice points (n, pn), n = 1, 2.We show that for every k there are k such points that are collinear. By considering the convex hull of the prime number graph, we show that there are infinitely many n such that 2pn < pn_¡ + Pn+Ifor all positive i < n. By a similar argument, we show that there are infinitely many n for which pn > ...

We consider the class Pn of labeled posets on n elements which avoid certain three-element induced subposets. We show that the number of posets in Pn is (n+1) by exploiting a bijection between Pn and the set of regions of the arrangement of hyperplanes in R of the form xi&xj=0 or 1 for 1 i< j n. It also follows that the number of posets in Pn with i pairs (a, b) such that a<b is equal to the nu...

The endgame of Lines of Action (LOA) is problematic because (1) LOA evaluation functions are not good predictors in the case of forced wins and (2) the state-space complexity of the LOA endgame is too large to use endgame databases. Because of the frequency of forced moves and the mobility component in the LOA endgame the utility of proof-number (PN) search is investigated in this paper. Also t...

Given a monotone property P of graphs, write Pn for the set of graphs with vertex set [n] having property P. Building on recent results in the enumeration of graphical properties, we prove numerous results about the structure of graphs in Pn and the functions |Pn|. We also examine the measure eP (n), the maximum number of edges in a graph of Pn.

where Pn,0(x) denotes the limit of Pn,r (x) as r → 0+ and where qi > 0, 1≤ i≤n, are positive real numbers with ∑n i=1qi = 1 and x = (x1,x2, . . . ,xn). In this note, we let q =minqi and always assume n≥ 2 and 0≤ x1 <x2 < ···<xn. We define An(x) = Pn,1(x), Gn(x) = Pn,0(x), and Hn(x) = Pn,−1(x) and we will write Pn,r for Pn,r (x), An for An(x), and similarly for other means when there is no risk ...

Let pn/qn be the n-th convergent of a real irrational number α, and let εn = αqn−pn. In this paper we investigate various sums of the type ∑ m εm, ∑ m |εm|, and ∑ m εmx m. The main subject of the paper is bounds for these sums. In particular, we investigate the behaviour of such sums when α is a quadratic surd. The most significant properties of the error sums depend essentially on Fibonacci nu...