Revistas académicas de la Universidad Católica del Norte
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(Completely) weak simple semigroups and (Completely) weak 0-simple semigroups
No full textThe structure theorems for (Completely) simple semigroups and (Completely) 0-simple semigroups have proved a powerful tool in the investigation of such semigroups. In this paper, first of all, we define weak simple semigroups and weak 0-simple semigroups and compare them with simple semigroups and 0-simple semigroups respectively.
Then we give examples of these semigroups and describe the structure of them. Also, we define completely weak simple semigroup and completely weak 0-simple semigroup. Finally, by using Green’s equivalences, we prove some results and give equivalences, for these semigroups
Minimal connected restrained monophonic sets in graphs
No full textFor a connected graph G = (V,E) of order at least two, a connected restrained monophonic set S of G is a restrained monophonic set such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected restrained monophonic set of G is the connected restrained monophonic number of G and is denoted by mcr(G). A connected restrained monophonic set S of G is called a minimal connected restrained monophonic set if no proper subset of S is a connected restrained monophonic set of G. The upper connected restrained monophonic number of G, denoted by m+cr(G), is defined as the maximum cardinality of a minimal connected restrained monophonic set of G. We determine bounds for it and certain general properties satisfied by this parameter are studied. It is shown that, for positive integers a, b such that 4≤ a ≤ b , there exists a connected graph G such that mcr(G) = a and m+cr(G) = b.
On a maximal subgroup of the orthogonal group O⁺₈ (3)
No full textThe orthogonal simple group 0 (3) has three conjugacy classes of maximal subgroups of the form 36:L4(3). These groups are all isomorphic to each other and each group has order 4421589120 with index 1120 in 0 (3). In this paper, we will compute the ordinary carácter table of one of these classes of maximal subgroups using the technique of Fischer-Clifford matrices. This technique is very efficient to compute the ordinary character table of an extension group Ḡ = N.G and especially where the normal subgroup N of Ḡ is an elementary abelian p-group. The said technique reduces the computation of the ordinary character table of Ḡ to find a handful of so-called Fischer-Clifford matrices of Ḡ and the ordinary or projective character tables of the inertia factor groups of the action of Ḡ on N
Periodic parabolic problem with discontinuous coefficients: Mathematical analysis and numerical simulation
No full textThis work presents a new approach for the mathematical analysis and numerical simulation of a class of periodic parabolic equations with dis- continuous coefficients. Our technique is based on the minimization of a least-squares cost function. By the means of variational calculus, we prove that the considered optimization problem admits an optimal solution. Using the Lagrangian method, we compute the gradient of the cost function associated with our problem. Finally, we give several numerical simulations that show the efficiency and robustness of our method
Implications of Some Types of Pairwise Closed Graphs
No full textThe main goal of this paper is to introduce and look into some of the fundamental properties of pairwise strongly closed, pairwise strongly -closed and pairwise quasi -closed graphs. Some characterizations and several properties concerning these graphs are obtained. We also investigate relationships between (i,j)-strongly alpha -closed graph G(f) and (i,j)-weakly alpha -continuous. We study relationships between (i,j) strongly alpha -closed (i,j)-quasi alpha-closed graphs with covering properties. The concepts of pairwise -closed and pairwise quasi H-closed relatively are stated
Spatial fuzzy topological space
No full textThe concept of spatial fuzzy set is introduced in this article. We have established some fundamental conclusions on the spatial fuzzy set and the spatial fuzzy topological space. Because fuzziness is an internal feature of spatial objects, we used topological relations to build internal properties and relationships between them
Some open questions about line arrangements in the projective plane
No full textDespite that the study of line arrangements in the projective plane is old and elemental, there is still a long list of intriguing open questions and applications to modern mathematics. Our goal is to discuss part of that list, focusing on the connection with Chern invariants and pointing towards configurations of rational curves
A new proof of Fillmore’s theorem for integer matrices
No full textFillmore’s theorem is a matrix completion problem that states that if A is a nonscalar matrix over a field F and ϒ1,..., ϒ n ∈ F so that ϒ 1 +...+ ϒ n = tr(A) then there is a matrix similar to A with diagonal (ϒ1,..., ϒn). Borobia [1] extended Fillmore’s Theorem to the matrices over the ring of integers and Soto, Julio and Collao [3] studied it with the nonnegativity hypothesis. In this paper we prove the same result by modifying the initial proof of Fillmore, a subsequent new algorithm is proposed and some new information about the final matrix will be given
Uniqueness of fixed point for sum of operators in ordered Banach spaces and application
No full textIn this article, we are concerned by existence and uniqueness of a fixed point for the sum of two operators A and B, defined on a closed convex subset of an ordered Banach space, where the order is induced by a normal and minihedral cone. In such a structure, an absolute value function is generated by the order and this provide the ability to introduce new versions of the concepts of lipschitzian and expansive mappings. Therefore we prove that if A is expansive and B is contractive, then the sum A + B has a unique fixed point
Existence of coincidence points for Feng-Liu type multivalued contractions with a singlevalued mapping
No full textIn this paper we establish coincidence point results for multivalued Feng-Liu type contractions with a singlevalued mapping. There is a supporting example. Several other existing results are contained in our Theorems