Revistas académicas de la Universidad Católica del Norte
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Enumeration of spanning trees in prisms of some graphs
No full textIn graph theory, a prism over a graph G is the cartesian product of the graph G with P₂. The purpose of this work is to investigate the complexity of the prisms of some path and cycle-related graphs. In particular, we obtain simpler and more explicit formulas for the complexity of a special class of prisms of path-related graphs: fan graph, ladder graph, the composition Pn[P₂] graph, and book graph. Moreover, we obtain straightforward formulas for the complexity of a special class of prisms of cycle-related graphs: wheel graph, gear graph, prism graph, n−crossed prism graph, mirror graph M(Cn) of even cycle Cn, twisted prism, total graph T(Cn) of the cycle Cn, the friendship graph, the flower graph, and planner sunflower graph. These closed formulas are deduced using some basic properties of block matrix, recurrence relation, eigenvalues of circulant matrices, and orthogonal polynomials
On some P-Q modular equations of degree 45
No full textOn page 330 of his second notebook, Srinivasa Ramanujan recorded a P-Q modular equation of degree 45, proof of which has been given by Bruce C. Berndt via theory of modular forms. We in this paper, give a simple proof of the same using the identities of Ramanujan and also establish few new P-Q modular equations of degree 45. Further using these, we establish certain new modular equations of signature 3
Nonlocal partial fractional evolution equations with state dependent delay
No full textIn this work, we propose sufficient conditions guaranteeing an existence result of mild solutions by using the nonlinear Leray-Schauder alternative in Banach spaces combined with the semigroup theory for the class of Caputo partial semilinear fractional evolution equations with finite state-dependent delay and nonlocal conditions
A theoretical approach on intuitionistic Fuzzy Hausdorff space
No full textThe object of this paper is to introduce a new definition for intuitionistic fuzzy Hausdorff space (IFHS). We investigate some of its characterizations and discuss it with some necessary counter examples. In addition, we compared the new notion with the existing notions. Finally we point out the significance of Hausdorffness in digital image processing
Hermite–Hadamard type inequalities via weighted integral operators
No full textIn this paper, we consider general convex functions of various type. We establish some new integral inequalities of Hermite--Hadamard type for -convex and -convex functions, using generalized integrals. We also investigate differentiable functions with general convex derivative. The proven results generalize many results previously known from the literature
Note on modified generalized Bessel function
No full textAn attempt is made to define Modified Generalized Bessel Function, and Modified Generalized Bessel Matrix Function. Some properties have also been discussed
On universal realizability in the left half-plane
No full textA list Λ = {λ1, λ2,..., λn} of complex numbers is said to be realizable if it is the spectrum of a nonnegative matrix. Λ is said to be universally realizable (UR) if it is realizable for each possible Jordan canonical form allowed by Λ. In this paper, using companion matrices and applying a procedure by Šmigoc, we provide sufficient conditions for the universal realizability of left half-plane spectra, that is, spectra Λ = {λ1,...,λn} with λ1 > 0, Re λi ≤ 0, i = 2, . . . , n. It is also shown how the effect of adding a negative real number to a not UR left half-plane list of complex numbers, makes the new list UR, and a family of left half-plane lists that are UR is characterized
Commuting graph of CA−groups
No full textA group G is called a CA−group, if all the element centralizers of G are abelian and the commuting graph of G with respect to a subset A of G, denoted by Γ(G, A), is a simple undirected graph with vertex set A and two distinct vertices a and b are adjacent if and only if ab = ba. The aim of this paper is to generalize results of a recently published paper of F. Ali, M. Salman and S. Huang [On the commuting graph of dihedral group, Comm. Algebra 44 (6) (2016) 2389—2401] to the case that G is an CA−group
A kind of characterization of homeomorphism and homeomorphic spaces by Core fundamental groupoid: a good invariant
No full textIn this paper, we give new topological invariants and a complete characterization to homeomorphisms. The finding a sufficient condition for homeomorphism and classifying topological spaces up to homeomorphism is the open problemin topology [1, 9, 14]. In this article, the main results are Propositions 3.24, 4.40 and 4.41, and Propositions 4.40 is about complete characterization of homeomorphisms i.e. "f : M -->N is a homeomorphism if and only if f# : pi1M --> pi1N is a groupoid iso-homeomorphism". this is the answer to the open problem [1, 9, 14] mentioned. First, we characterize the homeomorphisms completely. In addition, we resolve the open issue [1, 9, 14] of finding sufficient conditions for two topological spaces to be homeomorphic by giving an invariant. The entire result will be obtained by constructing a new notion, that is an extension of fundamental groups; which is already a topological invariant but not a sufficient one. We extend new theory by defining an algebraic sense of fundamental groupoid by establishing such algebraic structure and a unique topology on it. This fundamental groupoid is different from the fundamental groupoid in [16] and also these two different groupoids (one is algebraic sense and another is category theoretic) are not equivalent. We have an explicit description for algebraic structure groupoid and a unique topological structure on fundamental groupoid. And also we will discuss their topological properties also possibility of smooth structures
Path-connectedness and topological closure of some sets related to the non-compact Stiefel manifold
No full textIf H is a Hilbert space, the non-compact Stiefel manifold St(n, H) consists of independent n-tuples in H. In this article, we contribute to the topological study of non-compact Stiefel manifolds, mainly by proving two results on the path-connectedness and topological closure of some sets related to the non-compact Stiefel manifold. In the first part, after introducing and proving an essential lemma, we prove that ∩j∈J (U(j) + St(n, H)) is path-connected by polygonal paths under a condition on the codimension of the span of the components of the translating J-family. Then, in the second part, we show that the topological closure of St(n, H)∩S contains all polynomial paths contained in S and passing through a point in St(n, H). As a consequence, we prove that St(n, H) is relatively dense in a certain class of subsets which we illustrate with many examples from frame theory coming from the study of the solutions of some linear and quadratic equations which are finite-dimensional continuous frames. Since St(n, L2(X, μ; F)) is isometric to, FF(X, μ), n, this article is also a contribution to the theory of finite-dimensional continuous Hilbert space frames