Abstract: Cubic ideals, cubic bi-ideals and cubic quasi-ideals of
a Γ-semiring are introduced and various properties of these ideals
are investigated. Among all other results, some characterizations of
regular Γ-semirings are achieved.
Abstract: A lattice network is a special type of network in
which all nodes have the same number of links, and its boundary
conditions are periodic. The most basic lattice network is the ring, a
one-dimensional network with periodic border conditions. In contrast,
the Cartesian product of d rings forms a d-dimensional lattice
network. An analytical expression currently exists for the clustering
coefficient in this type of network, but the theoretical value is valid
only up to certain connectivity value; in other words, the analytical
expression is incomplete. Here we obtain analytically the clustering
coefficient expression in d-dimensional lattice networks for any link
density. Our analytical results show that the clustering coefficient for
a lattice network with density of links that tend to 1, leads to the
value of the clustering coefficient of a fully connected network. We
developed a model on criminology in which the generalized clustering
coefficient expression is applied. The model states that delinquents
learn the know-how of crime business by sharing knowledge, directly
or indirectly, with their friends of the gang. This generalization shed
light on the network properties, which is important to develop new
models in different fields where network structure plays an important
role in the system dynamic, such as criminology, evolutionary game
theory, econophysics, among others.
Abstract: The notions of prime(semiprime) fuzzy h-ideal(h-biideal,
h-quasi-ideal) in Γ-hemiring are introduced and some of their
characterizations are obtained by using "belongingness(∈)" and
"quasi - coincidence(q)". Cartesian product of prime(semiprime)
fuzzy h-ideals of Γ-hemirings are also investigated.
Abstract: In a graph G, a cycle is Hamiltonian cycle if it contain all vertices of G. Two Hamiltonian cycles C_1 = 〈u_0, u_1, u_2, ..., u_{n−1}, u_0〉 and C_2 = 〈v_0, v_1, v_2, ..., v_{n−1}, v_0〉 in G are independent if u_0 = v_0, u_i = ̸ v_i for all 1 ≤ i ≤ n−1. In G, a set of Hamiltonian cycles C = {C_1, C_2, ..., C_k} is mutually independent if any two Hamiltonian cycles of C are independent. The mutually independent Hamiltonicity IHC(G), = k means there exist a maximum integer k such that there exists k-mutually independent Hamiltonian cycles start from any vertex of G. In this paper, we prove that IHC(C_n × C_n) = 4, for n ≥ 3.
Abstract: The purpose of this research is to study the concepts
of multiple Cartesian product, variety of multiple algebras and to
present some examples. In the theory of multiple algebras, like other
theories, deriving new things and concepts from the things and
concepts available in the context is important. For example, the first
were obtained from the quotient of a group modulo the equivalence
relation defined by a subgroup of it. Gratzer showed that every
multiple algebra can be obtained from the quotient of a universal
algebra modulo a given equivalence relation.
The purpose of this study is examination of multiple algebras and
basic relations defined on them as well as introduction to some
algebraic structures derived from multiple algebras. Among the
structures obtained from multiple algebras, this article studies submultiple
algebras, quotients of multiple algebras and the Cartesian
product of multiple algebras.
Abstract: This paper presents three new methodologies for the
basic operations, which aim at finding new ways of computing union
(maximum) and intersection (minimum) membership values by
taking into effect the entire membership values in a fuzzy set. The
new methodologies are conceptually simple and easy from the
application point of view and are illustrated with a variety of
problems such as Cartesian product of two fuzzy sets, max –min
composition of two fuzzy sets in different product spaces and an
application of an inverted pendulum to determine the impact of the
new methodologies. The results clearly indicate a difference based on
the nature of the fuzzy sets under consideration and hence will be
highly useful in quite a few applications where different values have
significant impact on the behavior of the system.
Abstract: The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.
Abstract: The notions of intuitionistic fuzzy h-ideal and normal
intuitionistic fuzzy h-ideal in Γ-hemiring are introduced and some
of the basic properties of these ideals are investigated. Cartesian
product of intuitionistic fuzzy h-ideals is also defined. Finally a
characterization of intuitionistic fuzzy h-ideals in terms of fuzzy
relations is obtained.
Abstract: The balanced Hamiltonian cycle problemis a quiet new topic of graph theorem. Given a graph G = (V, E), whose edge set can be partitioned into k dimensions, for positive integer k and a Hamiltonian cycle C on G. The set of all i-dimensional edge of C, which is a subset by E(C), is denoted as Ei(C).