Revistas académicas de la Universidad Católica del Norte
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Existence and multiplicity of solutions for a class of nonlocal elliptic transmission systems
No full textBy using the approach based on variationnel methods and critical point theory, more precisely, the symmetric mountain pass theorem, we study the existence and multiplicity of weak solutions for a class of elliptic transmision system with nonlocal term
Paranormed Norlund Nᵗ- difference sequence spaces and their α-, β- and γ-duals
No full textKizmaz [4] defined some difference spaces viz., ℓ∞ (∆), c(∆) and c0(∆) and studied by Et and Colak [1] thoroughly. In this paper, Norlund Nt- difference sequence spaces Nt(c0, p, ∆), Nt(c, p, ∆) and Nt(ℓ∞, p, ∆) contain the sequences whose Nt∆-transforms in c0, c and ℓ∞ are defined and the paranormed linear structures are developed on these spaces. It has been shown that the spaces Nt(c0, p, ∆), Nt(c, p, ∆) & Nt(ℓ∞, p, ∆) are linearly isomorphic and are of non-absolute type. Further, it is verified that Nt(c, p, ∆), Nt(c0, p, ∆)and Nt(l∞, p, ∆) of non-absolute form are isomorphic to Nt(c0, p), Nt(c, p) and Nt(ℓ∞, p), respectively. Topological properties such as the completeness and the isomorphism are also discussed. Some inclusion relations among these spaces are also verified. Finally, the α-, β- and γ- dual of these spaces are determined and constructed the Schauder-basis of Nt(c0, p, ∆) and Nt(c, p, ∆)
A neutrosophic approach to the transportation problem using single-valued trapezoidal neutrosophic numbers
No full textIn general, a fuzzy set can’t handle situations of inconsistencies and inexact data, however, the Neutrosophic Set (NS) has been used to address such types of issues in all real world problems. The neutrosophic set is an extension of the fuzzy set and the intuitionistic fuzzy set, that can deal with imperfect, inconsistent, and indeterminate data in all the related problems. This article proposed a conventional neutrosophic approach using a ranking function for the transportation problem. This approach has considered a single-valued neutrosophic set for the entire transportation problem with the numerical illustration.
Single valued trapezoidal neutrosophic numbers are well-known and used in solving the transportation problem and its extension. Besides, a novel ranking function is proposed with the help of membership functions, which gives the best optimal solution. Moreover, the obtained optimal solution has been compared with recent new approaches. This research will help to get the best optimal solution for the transportation problem under uncertainty
A correction on “Some remarks on fuzzy infi-topological spaces”
No full textIn [3], the authors present a weak fuzzy topological structure called “fuzzy infi topological space” and studied some of its consequences. In this paper, we show that some of the results in [3] are incorrect and provide the correct versions of them
Spectra of (M, ℳ)-corona-join of graphs
No full textIn this paper, we introduce the (M, ℳ)-corona-join of G and ℋk constrained by vertex subsets ?, which is the union of two graphs: one is the M-generalized corona of a graph G and a family of graphs ℋk constrained by vertex subset ? of the graphs in ℋk, where M is a suitable matrix; and the other one is the ℳ -join of ℋk, where ℳ is a collection of matrices. We determine the spectra of the adjacency, the Laplacian, the signless Laplacian and the normalized Laplacian matrices of some special cases of the (M, ℳ)-corona-join of G and ℋk constrained by vertex subsets ?. These results enable us to deduce the spectra of all the existing variants of extended corona of graphs. Further, by using this graph operation, we construct infinitely many graphs which are simultaneously cospectral with respect to the above mentioned four type of matrices
Graph folding and chromatic number
No full textGiven a connected graph G, identify two vertices if they have a common neighbor and then reduce the resulting multiple edges to simple edges. Repeat the process until the result is a complete graph. This process is called folding a graph.
We show here that any connected graph G which is not complete folds onto the connected graph Kp where p = χ(G), the chromatic number of G. Furthermore, the set of all integers p such that G folds onto Kp consist of consecutive integers, the smallest of which is χ(G).
One particular result of this study is that a sharp upper bound was obtained on the largest complete graph which a graph can be folded onto
Aα-spectrum of duplicate and corona operations in graphs
No full textLet G be a graph of order n, A(G) its adjacency matrix and D(G) the diagonal matrix of degrees of G. In 2017, for every α in [0; 1], Nikiforov defined the matrix Aα(G) = αD(G)+ (1-α)A(G). In this paper, we investigate the Aα-spectrum of graphs obtained from the duplicate and corona operations. As an application of our results, we provide conditions for the construction of some pairs of non isomorphic Aα-cospectral graphs
Total absolute difference edge irregularity strength of Tp-tree graphs
No full textA total labeling ξ is defined to be an edge irregular total absolute difference k-labeling of the graph G if for every two different edges e and f of G there is wt(e) 6= wt(f) where weight of an edge e = xy is defined as wt(e) = |ξ(e) − ξ(x) − ξ(y)|. The minimum k for which the graph G has an edge irregular total absolute difference labeling is called the total absolute difference edge irregularity strength of the graph G, tades(G). In this paper, we determine the total absolute difference edge irregularity strength of the precise values for Tp-tree related graphs
On approximation of double Fourier series and its conjugate series for functions in mixed Lebesgue space Lp→,p ∈ [1,∞]2
No full textIn this paper, we study the approximation of double Fourier series and its conjugate series for functions in mixed Lebesgue space Lp, p ∈ [1,∞]2 using double Karamata Kλ,μ means.
A remark about mirror symmetry of elliptic curves and generalized complex geometry
No full textIn this short note we describe the isomorphism of generalized complex structure between T-dual manifolds introduced by Cavalcanti-Gualtieri, in the case of elliptic curves. We also compare this isomorphism with the mirror map for elliptic curves described by Polishchuk and Zaslow