Revistas académicas de la Universidad Católica del Norte
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Some characterizations of frames in ℓ²(I; H) and topological applications
No full textWe propose in this article some characterizations of the notion of frame in ℓ²(I; H). The first one is general, and depends on a procedure of inserting a family of vectors instead of x in the definition of a frame. This allows us to define the analysis, synthesis and frame operator on the space ℓ²(I; H) instead of H. The second one is specific to ℓ² (I; Ck) and relate it to the freeness of the finite set of components of the frame. The third one concerns normalised tight frames in ℓ²(I; Ck). Afterwards, we give an example of a frame in ℓ²(I; C²) using another sufficient condition in dimension 2. We conclude with some topological applications of these characterizations
Energy of commuting graph of finite AC- groups
No full textLet Γ be a graph with the adjacency matrix A. The energy of Γ is the sum of the absolute values of the eigenvalues of A. In this article we compute the energies of the commuting graphs of some finite groups and discuss some consequences regarding hyperenergetic and borderenergetic graphs
The Holder continuity of the solutions to quasi-linear system of elliptic partial differential equations with singular coefficients
No full textThis article establishes the Holder continuity of the solutions to a quasi-linear system of elliptic partial differential equations with singular coefficients under the assumption of its form-boundary
Stability and instability analysis for the standing waves for a generalized Zakharov-Rubenchik system
No full textIn this paper, we analyze the stability and instability of standing waves for a generalized Zakharov-Rubenchik system (or the Benney-Roskes system) in spatial dimensions N = 2, 3. We show that the standing waves generated by the set of minimizers for the associated variational problem are stable, for N = 2 and σ (p − 2) > 0. We also show that the standing waves are strongly unstable, for N = 3 and if either σ < 0 and 4/3 <p< 4, or σ > 0 and 0 <p< 2. Results follow by using the variational characterization of standing waves, the concentration compactness principle due to J. Lions and the compactness lemma due to E. Lieb to solve the associated minimization problem
On the isotopic characterizations of generalized Bol loops
No full textIn this study, the notion of isotopy of generalized Bol loop is characterized. A loop isotope of a σ-generalized Bol loop is shown to be a σ'-generalized Bol loop if σ' fixes its (isotope) identity element where σ' is some conjugate of σ. A loop isotope of a σ-generalized Bol loop is shown to be a σ'-generalized Bol loop if and only if the image of the isotope’s identity element under σ' is right nuclear (where σ' is some conjugate of σ). It is shown that a generalized Bol loop can be constructed using a group and a subgroup of it. A right conjugacy closed σ-generalized Bol loop is shown to be a σ-generalized right central loop
On fuzzy γµ-open sets in generalized fuzzy topological spaces
No full textIn this paper, we explore the existence of operation approach on open sets in a generalized fuzzy topological space. We introduce the concept of fuzzy γµ-open set and study some basic properties of it. We obtain an interesting result that the intersection of two fuzzy γµ-open sets may not be a fuzzy γµ-open set, but if the operation is regular then the intersection becomes a fuzzy γµ-open set. We also initiate the notions of fuzzy minimal γµ-open set and fuzzy γµ-locally finite space and establish various results related to these
Stratonovich-Henstock integral for the operator-valued stochastic process
No full textIn this paper, we introduce the Stratonovich-Henstock integral of an operator-valued stochastic process with respect to a Q-Wiener process. We also formulate a version of Ito's formula for this integral
Weak forms of double fuzzy α-continuous multifunctions
No full textIn this paper, we introduce and study the concept of double fuzzy upper (lower) almost α-continuous multifunctions and double fuzzy upper (lower) weakly α-continuous multifunctions
Equitable chromatic number of weak modular product of Some graphs
No full textAn equitable coloring of a graph G is a proper coloring of the vertices of G such that the number of vertices in any two color clases differ by at most one. The equitable chromatic number χ=(G) of a graph G is the minimum number of colors needed for an equitable coloring of G. In this paper, we obtain the equitable chromatic number of weak modular product of two graphs G and H, denoted by G o H.
First, we consider the graph G o H, where G is the path graph, and H be any simple graph like the path, the cycle graph, the complete graph. Secondly, we consider G and H as the complete graph and cycle graph respectively. Finally, we consider G as the star graph and H be the complete graph and star graph
Aα and Lα-spectral properties of spider graphs
No full textLet G be a graph with adjacency matrix A(G) and let D(G) be the diagonal matrix of the degrees of G. For every real α ∈ [0, 1], Nikiforov [21] and Wang et al. [26] defined the matrices Aα(G) and Lα(G), respectively, as Aα(G) = αD(G)+(1−α)A(G) and Lα(G) = αD(G)+(α − 1)A(G). In this paper, we obtain some relationships between the eigenvalues of these matrices for some families of graphs, a part of the Aα and Lα-spectrum of the spider graphs, and we display the Aα and Lα-characteristic polynomials when their set of vertices can be partitioned into subsets that induce regular subgraphs. Moreover, we determine some subfamilies of spider graphs that are cospectral with respect to these matrices