In this paper, we frequently use the notation from [S1]. A “rational semigroup” G is a semigroup generated by non-constant rational maps g : CI → CI, where CI denotes the Riemann sphere, with the semigroup operation being functional composition. For a rational semigroup G, we set F (G) := {z ∈ CI | G is normal in a neighborhood of z} and J(G) := CI \ F (G). F (G) is called the Fatou set of G an...

Data envelopment analysis (DEA) is a method to evaluate the relative efficiency of decision making units (DMUs). In this method, the issue has always been to determine a set of weights for each DMU which often caused many problems. Since the DEA models also have the multi-objective linear programming (MOLP) problems nature, a rational relationship can be established between MOLP and DEA problem...

In this paper, we investigate algorithms for finding centers of a given collection $$\mathcal N$$ sets. particular, focus on metric rational set similarities, broad class similarity measures including Jaccard and Hamming. A S is called if $$D=1-S$$ distance function. We study the 1-center problem these spaces. The consists C that minimizes maximum to any . present general framework computes $$(...

A natural number is a non-negative whole number. We use the set of natural numbers, IN, for counting. It is useful to know that the sum or product of two natural numbers is again a natural number. We say that IN is closed with respect to addition and multiplication. However IN is not closed with respect to subtraction, since for example 2 − 4 = −2 and −2 is not a non-negative whole number. An i...

We present two infinite families of sequences that are analogous to the Stern sequence. Sequences in the first family enumerate the set of positive rational numbers, while sequences in the second family enumerate the set of positive rational numbers with either an even numerator or an even denominator.

A new method for structural topology optimization is introduced which employs the Isogeometric Analysis (IA) method. In this approach, an implicit function is constructed over the whole domain by Non-Uniform Rational B-Spline (NURBS) basis functions which are also used for creating the geometry and the surface of solution of the elasticity problem. Inspiration of the level set method zero level...

Let be m ∈ Z>0 and a, q ∈ Q. Denote by APm(a, q) the set of rational numbers d such that a, a + q, . . . , a + (m − 1)q form an arithmetic progression in the Edwards curve Ed : x2 +y2 = 1+d x2y2. We study the set APm(a, q) and we parametrize it by the rational points of an algebraic curve.