Revistas académicas de la Universidad Católica del Norte
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Lyapunov stability and weak attraction for control systems
No full textIn this paper we deal with Lyapunov stability and weak attraction for control systems. We give characterizations of the stability and asymptotical stability of a compact set by means of its components. We also study the asymptotical stability of the prolongation of a compact weak attractor
On the cohomological equation of a linear contraction
No full textIn this paper, we study the discrete cohomological equation of a contracting linear automorphism A of the Euclidean space Rd. More precisely, if δ is the cobord operator defined on the Fréchet space E = Cl (Rd) (0 ≤ l ≤ ∞) by: δ(h) = h − h ◦ A, we show that:
If E = C0(Rd), the range δ (E) of δ has infinite codimension and its closure is the hyperplane E0 consisting of the elements of E vanishing at 0. Consequently, H1 (A, E) is infinite dimensional non Hausdorff topological vector space and then the automorphism A is not cohomologically C0-stable.
If E = Cl (Rd), with 1 ≤ l ≤ ∞, the space δ (E) coincides with the closed hyperplane E0. Consequently, the cohomology space H1 (A, E) is of dimension 1 and the automorphism A is cohomologically Cl-stable
Dynamics of a second order three species nonlinear difference system with exponents
No full textIn this paper, we study the persistence, boundedness, convergence, invariance and global asymptotic behavior of the positive solutions of the second order difference system
xn+1 = α1 + ae−xn−1 + byne−yn−1 ,
(0.1) yn+1 = α2 + ce−yn−1 + dzne−zn−1,
zn+1 = α3 + he−zn−1 + jxne−xn−1, n = 0, 1, 2,....
Here xn, yn, zn can be considered as population densities of three species such that the population density of xn, yn, zn depends on the growth of yn, zn, xn respectively with growth rate b, d, j respectively. The positive real numbers α1, α2, α3 are immigration rate of xn, yn, zn respectively, while a, c, h denotes the growth rate of xn, yn, zn respectively, and the initial values x−1, y−1, z−1, x0, y0, z0 are nonnegative numbers
Fractional metric dimension of generalized prism graph
No full textFractional metric dimension of connected graph was introduced by Arumugam et al. in [Discrete Math. 312, (2012), 1584-1590] as a natural extension of metric dimension which have many applications in different areas of computer sciences for example optimization, intelligent systems, networking and robot navigation. In this paper fractional metric dimension of generalized prism graph is computed using combinatorial criterion devised by Liu et al. in [ Mathematics, 7(1), (2019), 100]
Lie (Jordan) centralizers on alternative algebras
No full textIn this article, we study Lie (Jordan) centralizers on alternative algebras and prove that every multiplicative Lie centralizer has proper form on alternative algebras under certain assumptions
Semi-commutativity of graded rings and graded modules
No full textA ring R is said to be semi-commutative if whenever a, b ∈ R such that ab = 0, then aRb = 0. In this article, we introduce the concepts of g−semi-commutative rings and g−N−semi-commutative rings and we introduce several results concerning these two concepts. Let R be a G-graded ring and g ∈ supp(R, G). Then R is said to be a g−semi-commutative if whenever a, b ∈ R with ab = 0, then aRgb = 0. Also, R is said to be a g − N−semi-commutative if for any a ∈ R and b ∈ N(R) ⋂ Ann(a), bRg ⊆ Ann(a). We introduce an example of a G-graded ring R which is g − N-semi-commutative for some g ∈ supp(R, G) but R itself is not semi-commutative. Clearly, if R is a g−semi-commutative ring, then R is a g − N−semi-commutative ring, however, we introduce an example showing that the converse is not true in general. Several results and examples are investigated. Also, we introduce the concept of g − NE−semi-commutative rings and we introduce several results concerning g−NE−semi-commutative rings.
Let R be a G-graded ring and g ∈ supp(R, G). Then R is said to be a g−NE− semi-commutative ring if whenever a ∈ N(R) and b ∈ E(R) such that ab = 0, then aRgb = 0. Clearly, g−semi-commutative rings are g −NE−semi-commutative, however, we introduce an example ..
Existence of periodic or nonnegative periodic solutions for totally nonlinear neutral differential equations with infinite delay
No full textIn this work, we investigate the existence of periodic or nonnegative periodic solutions for a totally nonlinear neutral differential equation with infinite delay. In the process, we convert the given neutral differential equation into an equivalent integral equation. Then, we employ Krasnoselskiǐ-Burton’s fixed point theorem to prove the existence of periodic or nonnegative periodic solutions. Two examples are provided to illustrate the obtained results
Ulam type stability of second-order linear differential equations with constant coefficients having damping term by using the Aboodh transform
No full textThe main aim of this paper is to investigate various types of Ulam stability and Mittag-Leffler stability of linear differential equations of second order with constant coefficients having damping term using the Aboodh transform method. We also obtain the Hyers-Ulam stability constants of these differential equations using the Aboodh transform and some examples to illustrate our main results are given
25 open questions about vector bundles and their moduli
No full textWe present 25 open questions about moduli spaces of vector bundles and related topics, and discuss some longstanding conjectures. We hope to inspire young researchers to engage in this area of research
Laurent polynomials in mirror symmetry: why and how?
No full textWe survey the approach to mirror symmetry via Laurent polynomials, outlining some of the main conjectures, problems, and questions related to the subject. We discuss: how to construct Landau–Ginzburg models for Fano varieties; how to apply them to classification problems; and how to compute invariants of Fano varieties via Landau–Ginzburg models