CUBO, A Mathematical Journal 2019-10-04T16:42:53-03:00 Mauricio Godoy Molina Open Journal Systems <p align="justify">CUBO, A Mathematical Journal is a scientific journal founded in 1985 by the Universidad de La Frontera, Temuco - Chile. The journal publishes original papers containing substantial results in areas of pure and applied mathematics. CUBO appears in three issues per year and is indexed in ZentralBlatt Math., Mathematical Reviews, MathSciNet, Latin Index and SciELO-Chile.</p> On algebraic and uniqueness properties of harmonic quaternion fields on 3d manifolds 2019-10-04T16:42:53-03:00 M.I. Belishev A.F. Vakulenko <p>Let Ω be a smooth compact oriented 3-dimensional Riemannian manifold with boundary. A quaternion field is a pair q = {α, u} of a function α and a vector field u on Ω. A field q is harmonic if α, u are continuous in Ω and ∇α = rot u, div u = 0 holds into Ω. The space 𝒞(Ω) of harmonic fields is a subspace of the Banach algebra 𝒬 (Ω) of continuous quaternion fields with the point-wise multiplication qq′ = {αα′ − u · u ′ , αu′ + α ′u + u ∧ u ′ }. We prove a Stone-Weierstrass type theorem: the subalgebra ∨𝒞(Ω) generated by harmonic fields is dense in 𝒬 (Ω). Some results on 2-jets of harmonic functions and the uniqueness sets of harmonic fields are provided. Comprehensive study of harmonic fields is motivated by possible applications to inverse problems of mathematical physics.</p> 2019-04-01T00:00:00-03:00 Copyright (c) Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions 2019-09-11T01:25:53-03:00 Yogesh J. Bagul Christophe Chesneau <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>The prime goal of this paper is to establish sharp lower and upper bounds for useful functions such as the exponential functions, with a focus on exp(−x<sup>2</sup>), the trigonometric functions (cosine and sine) and the hyperbolic functions (cosine and sine). The bounds obtained for hyperbolic cosine are very sharp. New proofs, refinements as well as new results are offered. Some graphical and numerical results illustrate the findings.</p> </div> </div> </div> 2019-04-01T00:00:00-03:00 Copyright (c) 2019 CUBO, A Mathematical Journal Commutator criteria for strong mixing II. More general and simpler 2019-09-11T01:26:11-03:00 S. Richard R. Tiedra de Aldecoa <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>We present a new criterion, based on commutator methods, for the strong mixing property of unitary representations of topological groups equipped with a proper length function. Our result generalises and unifies recent results on the strong mixing property of discrete flows {Uᴺ}N∈ℤ and continuous flows {e-itH}t∈ℝ induced by unitary operators U and self-adjoint operators H in a Hilbert space. As an application, we present a short alternative proof (not using convolutions) of the strong mixing property of the left regular representation of σ-compact locally compact groups.</p> </div> </div> </div> 2019-04-01T00:00:00-03:00 Copyright (c) Certain integral Transforms of the generalized Lommel-Wright function 2019-09-11T01:26:30-03:00 S. Haq K.S. Nisar A.H. Khan D.L. Suthar <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>The aim of this article is to establish some integral transforms of the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function. Some integrals involving trigonometric, generalized Bessel and Struve functions are also indicated as special cases of our main results.</p> </div> </div> </div> 2019-04-01T00:00:00-03:00 Copyright (c) On Fractional Integro-differential Equations with State-Dependent Delay and Non-Instantaneous Impulses 2019-09-11T01:26:51-03:00 Khalida Aissani Mouffak Benchohra Nadia Benkhettou <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In this paper, we prove the existence of mild solution of the fractional integro-differential equations with state-dependent delay with not instantaneous impulses. The existence results are obtained under the conditions in respect of Kuratowski’s measure of non- compactness. An example is also given to illustrate the results.</p> </div> </div> </div> 2019-04-01T00:00:00-03:00 Copyright (c) Positive periodic solutions of functional discrete systems with a parameter 2019-09-11T01:27:11-03:00 Youssef N. Raffoul Ernest Yankson <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>The existence of multiple positive periodic solutions of the system of difference equations with a parameter</p> <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>x(n + 1) = A(n, x(n))x(n) + λf(n, x<sub>n</sub>),</p> <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>is studied. In particular, we use the eigenvalue problems of completely continuous operators to obtain our results. We apply our results to a well-known model in population dynamics.</p> </div> </div> </div> </div> </div> </div> </div> </div> </div> 2019-04-01T00:00:00-03:00 Copyright (c)