Revistas académicas de la Universidad Católica del Norte
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On topological properties of Skorokhod's integral
No full textWe study continuity properties of Skorokhod's integral following the definition of such an integral in [4]
The fixed point and the common fixed point properties in finite pseudo-ordered sets
No full textIn this paper, we first prove that every finite nonempty pseudo-ordered with a least element has the least fixed point property and the least common fixed point property for every finite commutative family of self monotone maps. Dually, we establish that a finite nonempty pseudo-ordered with a greatest element has the greatest fixed point property and the greatest common fixed point property for every finite commutative family of self monotone maps. Secondly, we prove that every monotone map ƒ defined on a nonempty finite pseudo-ordered (X, ⊵) has at least a fixed point if and only if there is at least an element ɑ of X such that the subset of X defined by {ƒn(ɑ) : n ∈ ℕ } has a least or a greatest element. Furthermore, we show that the set of all common fixed points of every finite commutative family of monotone maps defined on a finite nonempty complete trellis is also a nonempty complete trellis
Extensión
No full textDurante el año académico 1982 el Departamento de Matemáticas de nuestra Universidad ha realizado una vasta labor de Extensión, que le ha permitido estar en permanente contacto con la comunidad
Algebraic Markov processes
No full textIn this chapter we describe the abstract definiton and the basic facts on algebraic Markov processes (see [5]). The main goal is to show that the fundamental definitions and properties of Markov processes are easiy formulated in an algebraic languaje suitable for the study of Markov processes appearing in quantum theory. Moreover, we discuss in detail the notion of complete positivity which turns out to be the natural generalisation of positivity for commutative (classical) case and a non-commutative version of the Feynman-Kac formula which is the basic ingredient in the construction of Markov cocycles and processes
Quantum flows
No full textWe develop a rather general framework for constructing quantum Markov processes through Markov operator cocycles (see Chapter 2, Section 3) that satisfy a quantum stochastic differential equation.In order to achieve this goal we first recall the basic facts of Boson Fock quantum stochastic calculus and then give the fundamental results in the theory of quantum stochastic differential equations concerning existence, uniqueness, time reversal, isometricity and coisometricity of solutions. Next we construct the quantum flow associated with a Markov operator cocycle, and give a condition that guarantees that the restriction to a commutative subalgebra is a commutative flow
Solutions and stability of a variant of Wilson’s functional equation
No full textIn this paper we will investigate the complex-valued solutions and stability of the generalized variant of Wilson’s functional equation
(E) : f(xy) + χ(y)f(σ(y)x) = 2f(x)g(y), x, y ∈ G,
where G is a group, σ is an involutive morphism of G and χ is a character of G. (a) We solve (E) when σ is an involutive automorphism, and we obtain some properties about solutions of (E) when σ is an involutive anti-automorphism. (b) We obtain the Hyers Ulam stability of equation (E). As an application, we prove the superstability of the functional equation f(xy) + χ(y)f(σ(y)x) = 2f(x)f(y), x, y ∈ G
A computer verification for the value of the Topological Entropy for some special subshifts in the Lexicographical Scenario
No full textThe Lorenz Attractor has been a source for many mathematical studies. Most of them deal with lower dimensional representations of its first return map. An one dimensional scenario can be modeled by the standard two parameter family of contracting Lorenz maps. The dynamics, in this case, can be modeled by a subshift in the Lexicographical model. The Lexicographical model is the set of two symbols with the topology induced by the lexicographical metric and with the lexicographical order. These subshifts are the maximal invariant set for the shift map in some interval. For some of them, the extremes of the interval are a minimal periodic sequence and a maximal periodic sequence which is an iteration of the lower extreme (by the shift map). For some of these subshifts the topological entropy is zero. In this case the dynamics (of the respective Lorenz map) is simple.Associated to any of these subshifts (let call it Λ) we consider an extension (let call it Γ) that contains Λ which also can be constructed by using an interval whose extremes can be defined by the extremes of Λ. For these extensions we present here a computer verification of the result that compute its topological entropy. As a consequence, of our results, we can say: the longer the period of the periodic sequence is then the lower complexity in the dynamics of the extension the associated map has
Some new triple sequence spaces over n-normed space
No full textTriple sequence spaces were introduced by Sahiner et al. The main objective of this paper is to define some new classes of triple sequences over n-normed space by means of Museiak-Orlicz function and difference operators. We also study some algebraic and topological properties of these new sequence spaces
Star edge coloring of corona product of path and wheel graph families
No full textA star edge coloring of a graph G is a proper edge coloring without bichromatic paths and cycles of length four. In this paper, we obtain the star edge chromatic number of the corona product of path with cycle, path with wheel, path with helm and path with gear graphs, denoted by Pm ◦ Cn, Pm ◦ Wn, Pm ◦ Hn, Pm ◦ Gn respectively
Dual third-order Jacobsthal quaternions
No full textIn 2016, Yüce and Torunbalcı Aydın (18) defined dual Fibonacci quaternions. In this paper, we defined the dual third-order Jacobsthal quaternions and dual third-order Jacobsthal-Lucas quaternions. Also, we investigated the relations between the dual third-order Jacobsthal quaternions and third-order Jacobsthal numbers. Furthermore, we gave some their quadratic properties, the summations, the Binet’s formulas and Cassini-like identities for these quaternions