Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 40 num. 6 lang. pt <![CDATA[SciELO Logo]]> <![CDATA[Linear maps on ℬ(ℋ) preserving some operator properties]]> Abstract In this paper, for a complex Hilbert space ℋ with dim ℋ ≥ 2, we study the linear maps on ℬ(ℋ), the bounded linear operators on ℋ, that preserves projections and idempotents. As a result, we characterize the linear maps on ℬ(ℋ) that preserves involutions in both directions. <![CDATA[The impact of time delay in the transmission of Japanese encephalitis without vaccination]]> Abstract In this manuscript, the influence of time delay in the transmission of Japanese encephalitis without vaccination model has been studied. The time delay is because of the existence of an incubation period during which the Japanese encephalitis virus reproduces enough in the mosquitoes with the goal that it tends to be transmitted by the mosquitoes to people. The motivation behind this manuscript is to assess the influence of the time delay it takes to infect susceptible human populations after interacting with infected mosquitoes. The steadystate and the threshold value R0 of the delay model were resolved. This value assists with setting up the circumstance that ensures the asymptotic stability of relating equilibrium points. Utilizing the delay as a bifurcation parameter, we built up the circumstance for the presence of a Hopf bifurcation. Moreover, we infer an express equation to decide the stability and direction of Hopf bifurcation at endemic equilibrium by using center manifold theory and normal structure strategy. It has been seen that delay plays a vital role in stability exchanging. Furthermore, the presence of Hopf bifurcation is affected by larger values of virus transmission rate from an infected mosquito to susceptible individuals and the natural mortality of humans in a model. Finally, to understand some analytical outcomes, the delay framework is simulated numerically. <![CDATA[Domination in the entire nilpotent element graph of a module over a commutative ring]]> Abstract Let R be a commutative ring with unity and M be a unitary R module. Let Nil(M) be the set of all nilpotent elements of M. The entire nilpotent element graph of M over R is an undirected graph E(G(M)) with vertex set as M and any two distinct vertices x and y are adjacent if and only if x + y ∈ Nil(M). In this paper we attempt to study the domination in the graph E(G(M)) and investigate the domination number as well as bondage number of E(G(M)) and its induced subgraphs N(G(M)) and Non(G(M)). Some domination parameters of E(G(M)) are also studied. It has been showed that E(G(M)) is excellent, domatically full and well covered under certain conditions. <![CDATA[Laplacian integral graphs with a given degree sequence constraint]]> Abstract Let G be a graph on n vertices. The Laplacian matrix of G, denoted by L(G), is defined as L(G) = D(G) −A(G), where A(G) is the adjacency matrix of G and D(G) is the diagonal matrix of the vertex degrees of G. A graph G is said to be L-integral if all eigenvalues of the matrix L(G) are integers. In this paper, we characterize all Lintegral non-bipartite graphs among all connected graphs with at most two vertices of degree larger than or equal to three. <![CDATA[New Hermite-Hadamard type inequalities for m and (α, m)-convex functions on the coordinates via generalized fractional integrals]]> Abstract In this paper, we obtained a new Hermite-Hadamard type inequality for functions of two independent variables that are m-convex on the coordinates via some generalized Katugampola type fractional integrals. We also established a new identity involving the second order mixed partial derivatives of functions of two independent variables via the generalized Katugampola fractional integrals. Using the identity, we established some new Hermite-Hadamard type inequalities for functions whose second order mixed partial derivatives in absolute value at some powers are (α, m)-convex on the coordinates. Our results are extensions of some earlier results in the literature for functions of two variables. <![CDATA[Stationary Boltzmann Equation: an approach via Morse theory]]> Abstract In this paper we study the unidimensional Stationary Boltzmann Equation by an approach via Morse theory. We define a functional J whose critical points coincide with the solutions of the Stationary Boltzmann Equation. By the calculation of Morse index of J’’0(0)h and the critical groups C2(J, 0) and C2(J, ∞) we prove that J has two different critical points u1 and u2 different from 0, that is, solutions of Boltzmann Equation. <![CDATA[Instantaneous sentinel for the identification of the pollution term in Navier-Stokes system]]> Abstract The aim of this paper is about presenting some results of the Sentinel Theory in Connection with Control Theory of Distributed Systems. There is of course a large variety of models where the results to follow could be applied. What we have particularly in mind is the classical set of Navier-Stokes equations. We shall denote here by the velocity field and the pressure, which is a quite unusual notation in the ”Turbulence” circle. The reason is simply that in all what is following that we think of as the state of our system, this state depends on control functions, these control functions are being either ”artificial” or ”natural”. Also in this work we are(trying) working to get instantaneous information at fixed instant ”T” on pollution term in Navier-Stokes system in which the initial condition is incomplete. The best method which can solve this problem is the sentinel one; it allows the estimation of the pollution term at which we look for information independently of the missing term that we do not want to identify. So, we prove the existence of such instantaneous sentinel by solving a problem of controllability with a constraint on the control. <![CDATA[P-adic discrete semigroup of contractions]]> Abstract Let A ∈ B(X) be a spectral operator on a non-archimedean Banach space over Cp. In this paper, we give a necessary and sufficient condition on the resolvent of A so that the discrete semigroup consisting of powers of A is contractions. <![CDATA[Controllability of impulsive neutral stochastic integro-differential systems driven by fractional Brownian motion with delay and Poisson jumps]]> Abstract In this paper the controllability of a class of impulsive neutral stochastic integro-differential systems driven by fractional Brownian motion and Poisson process in a separable Hilbert space with infinite delay is studied. The controllability result is obtained by using stochas- tic analysis and a fixed-point strategy. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result. <![CDATA[Spectral analysis of Hahn-Dirac system]]> Abstract In this paper, we study some spectral properties of the one-dimensional Hahn-Dirac boundary-value problem, such as formally self-adjointness, the case that the eigenvalues are real, orthogonality of eigenfunctions, Green’s function, the existence of a countable sequence of eigenvalues, eigenfunctions forming an orthonormal basis of L2 ω,q((ω0, a); E). <![CDATA[Fixed point theorems in the study of positive strict set-contractions]]> Abstract The author uses fixed point index properties and Inspired by the work in Benmezai and Boucheneb (see Theorem 3.8 in [3]) to prove new fixed point theorems for strict set-contraction defined on a Banach space and leaving invariant a cone. <![CDATA[On the domination polynomial of a digraph: a generation function approach]]> Abstract Let G be a directed graph on n vertices. The domination polynomial of G is the polynomial D(G, x) =∑n i=0 d(G, i)xi, where d(G, i) is the number of dominating sets of G with i vertices. In this paper, we prove that the domination polynomial of G can be obtained by using an ordinary generating function. Besides, we show that our method is useful to obtain the minimum-weighted dominating set of a graph. <![CDATA[A note on convolution operators on Riesz Bounded variation spaces]]> Abstract We show some estimates and approximation results of operators of convolution type defined on Riesz Bounded variation spaces in R n. We also state some embedding results that involve the collection of generalized absolutely continuous functions. <![CDATA[On asymptotic behavior of solution to a nonlinear wave equation with Space-time speed of propagation and damping terms]]> Abstract In this paper, we consider the asymptotic behavior of solution to the nonlinear damped wave equation utt - div(a(t, x)∇u) + b(t, x)ut = −|u|p−1u t ∈ [0, ∞), x ∈ R n u(0, x) = u0(x), ut(0, x) = u1(x) x ∈ R n with space-time speed of propagation and damping potential. We obtained L2 decay estimates via the weighted energy method and under certain suitable assumptions on the functions a(t, x) and b(t, x). The technique follows that of Lin et al.[8] with modification to the region of consideration in R n. These decay result extends the results in the literature. <![CDATA[Power domination in splitting and degree splitting graph]]> Abstract A vertex set S is called a power dominating set of a graph G if every vertex within the system is monitored by the set S following a collection of rules for power grid monitoring. The power domination number of G is the order of a minimal power dominating set of G. In this paper, we solve the power domination number for splitting and degree splitting graph. <![CDATA[The paradox of heat conduction, influence of variable viscosity, and thermal conductivity on magnetized dissipative Casson fluid with stratification models]]> Abstract The boundary layer flow of temperature-dependent variable thermal conductivity and dynamic viscosity on flow, heat, and mass transfer of magnetized and dissipative Casson fluid over a slenderized stretching sheet has been studied. The model explores the Cattaneo-Christov heat flux paradox instead of the Fourier’s law plus the stratifications impact. The variable temperature-dependent plastic dynamic viscosity and thermal conductivity were assumed to vary as a linear function of temperature. The governing systems of equations in PDEs were transformed into non-linear ordinary differential equations using the suitable similarity transformations, hence the approximate solutions were obtained using Chebyshev Spectral Collocation Method (CSCM). Effects of pertinent flow parameters on concentration, temperature, and velocity profiles are presented graphically and tabled, therein, thermal relaxation and wall thickness parameters slow down the distribution of the flowing fluid. A rise in Casson parameter, temperature-dependent thermal conductivity, and velocity power index parameter increases the skin friction thus leading to a decrease in energy and mass gradient at the wall, also, temperature gradient attain maximum within 0.2 - 1.0 variation of Casson parameter. <![CDATA[The structure of Cayley graphs of dihedral groups of Valencies 1, 2 and 3]]> Abstract Let G be a group and S be a subset of G such that e ∉ S and S−1 ⊆ S. Then Cay(G, S) is a simple undirected Cayley graph whose vertices are all elements of G and two vertices x and y are adjacent if and only if xy−1 ∈ S. The size of subset S is called the valency of Cay(G, S). In this paper, we determined the structure of all Cay(D2n, S), where D2n is a dihedral group of order 2n, n ≥ 3 and |S| = 1, 2 or 3.