Revistas académicas de la Universidad Católica del Norte
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Existence of weak solutions for some quasilinear degenerated elliptic systems in weighted Sobolev spaces
No full textWe consider, for a bounded open domain Ω in Rn; (n ≥ 1) and a function u : Ω → ℝm; (m ≥ 1) the quasilinear elliptic system:
(0.1)
Which is a Dirichlet problem. Here, v belongs to the dual space , f and g satisfy some stan- dard continuity and growth conditions. we will show the existence of a weak solution of this problem in the four following cases: σ is mono- tonic, σ is strictly monotonic, σ is quasi montone and σ derives from a convex potential
Bounds for absolute values and imaginary parts of matrix eigenvalues via traces
No full textLet λ1(A), λ2(A), ..., λn(A) be the eigenvalues of an n × n-matrix A taken with their algebraic multiplicities. We suggest new bounds for |λj (A) − trace(A)/ n | and |Im λj (A) − Im trace(A)/n | (j = 1, ..., n), which refine the previously published results.
Soft separation axioms and functions with soft closed graphs
No full textSeveral notions on soft topology are studied and their basic properties are investigated by using the concept of soft open sets and soft closure operators which are derived from the basics of soft set theory established by Molodtsov [7]. In this paper we introduce some soft separation axioms called Soft R0 and soft R1 in soft topological spaces which are defined over an initial universe with a fixed set of parameters. Many characterizations and properties of these spaces are found.
Necessary and sufficient conditions for a soft topological space to be a soft Ri for i = 0, 1 space are also presented. Furthermore, the concept of functions with soft closed graph and soft cluster sets are defined.
Many results on theses two concepts are proved also it is proved that a function has a soft closed graph if and only if its soft cluster set is degenerate
Fixed point theorems for a class of extended JS contraction mappings over a generalized metric space with an application to fixed circle problema
No full textIn this paper we prove some generalized fixed point theorems for a class of contractive mappings over an extended JS-generalized metric space. Notions of weakly sensitive and strongly sensitive coefficient functions have been used here in proving fixed point theorems. Examples are given in strengthening the hypothesis of our established theorems. Moreover an application is given to fixed circle problem
Powers of cycle graph which are k-self complementary and k-co-self complementary
No full textE. Sampath Kumar and L. Pushpalatha [4] introduced a generalized version of complement of a graph with respect to a given partition of its vertex set. Let G = (V,E) be a graph and P = {V₁, V₂,...,Vk} be a partition of V of order k ≥ 1. The k-complement GPk of G with respect to P is defined as follows: For all Vi and Vj in P, i ≠ j, remove the edges between Vi and Vj , and add the edges which are not in G. Analogues to self complementary graphs, a graph G is k-self complementary (k-s.c.) if GPk ≅ G and is k-co-self complementary (k-co.s.c.) if GPk ≅ Ġ with respect to a partition P of V (G). The mth power of an undirected graph G, denoted by Gm is another graph that has the same set of vertices as that of G, but in which two vertices are adjacent when their distance in G is at most m. In this article, we study powers of cycle graphs which are k-self complementary and k-co-self complementary with respect to a partition P of its vertex set and derive some interesting results. Also, we characterize k-self complementary C2n and the respective partition P of V (C2n). Finally, we prove that none of the C2n is k-co-self complementary for any partition P of V (C2n)
An extension of biconservative timelike hypersurfaces in Einstein space
No full textA well-known conjecture of Bang-Yen Chen says that the only biharmonic Euclidean submanifolds are minimal ones, which affirmed by himself for surfaces in 3-dimensional Euclidean space, E³. We consider an extended version of Chen conjecture (namely, Lk-conjecture) on Lorentzian hypersurfaces of the pseudo-Euclidean space E⁴₁ (i.e. the Einstein space). The biconservative submanifolds in the Euclidean spaces are submanifolds with conservative stress-energy with respect to the bienergy functional. In this paper, we consider an extended condition (namely, Lk-biconservativity) on non-degenerate timelike hypersurfaces of the Einstein space E⁴₁ . A Lorentzian hypersurface x : M³₁ → E⁴₁ is called Lk-biconservative if the tangent part of L²k x vanishes identically. We show that Lk-biconservativity of a timelike hypersurface of E⁴₁ (with constant kth mean curvature and some additional conditions) implies that its (k + 1) th mean curvature is constant
k-super cube root cube mean labeling of some corona graphs
No full textLet G be a graph with |V (G)| = p and |E (G)| = q and f : V (G) → {k, k+1, k+2,..., p+q+k − 1 } be an one-to-one function. The induced edge labeling f ∗, for a vertex labeling f is defined by
f ∗(e) =
for all e = uv ∈ E(G) is bijective. If f(V (G)) ∪ {f ∗(e) : e ∈ E(G)} = {k, k+1, k+2,..., p+q+k − 1}, then f is known as a k-super cube root cube mean labeling. If such labeling exists, then G is a k-super cube root cube mean graph. In this paper, I prove that Tn ʘ K1, A(Tn) ʘ K1, A(Tn) ʘ 2K1, A(Qn) ʘ K1, Pn ʘ K1,2 and Pn ʘ K1,3 are k-super cube root cube mean graphs.
Some open questions in real algebraic geometry
No full textMany interesting problems arise on the borderline between real algebraic geometry and topology. We focus on 12 open questions. Some of them come from regulous geometry, which emerged as a subfield of real algebraic geometry less than 15 years ago
On maximum degree (signless) Laplacian matrix of a graph
No full textLet G be a simple graph on n vertices and v1, v2, . . . , vn be the vertices ofG. We denote the degree of a vertex vi in G by dG(vi) = di. The maximumdegree matrix of G, denoted by M(G), is the real symmetric matrix withits ijth entry equal to max{di, dj} if the vertices vi and vj are adjacent inG, 0 otherwise. In analogous to the definitions of Laplacian matrix andsignless Laplacian matrix of a graph, we consider Laplacian and signlessLaplacian for the maximum degree matrix, called the maximum degreeLaplacian matrix and the maximum degree signless Laplacian matrix,respectively. Also, we introduce maximum degree Laplacian energy andmaximum degree signless Laplacian energy of a graph. Then we determinethe maximum degree (signless) Laplacian energy of some graphs in termsof ordinary energy, and (signless) Laplacian energy. We compute themaximum degree (signless) Laplacian spectra of some graph compositions.A lower and upper bound for the largest eigenvalue of the (signless) Laplacianmatrix is established and also we determine an upper bound for the secondsmallest eigenvalue of maximum degree Laplacian matrix in terms of vertexconnectivity. We also determine bounds for the maximum degree (signless)Laplacian energy in terms of first Zagreb index
Decomposition dimension of corona product of some classes of graphs
No full textFor an ordered k-decomposition D = {G1, G2,...,Gk} of a connected graph G = (V,E), the D-representation of an edge e is the k-tuple γ(e/D)=(d(e, G1), d(e, G2), ...,d(e, Gk)), where d(e, Gi) represents the distance from e to Gi. A decomposition D is resolving if every two distinct edges of G have distinct representations. The minimum k for which G has a resolving k-decomposition is its decomposition dimension dec(G). In this paper, the decomposition dimension of corona product of the path Pn and cycle Cn with the complete graphs K1 and K2 are determined