Revistas académicas de la Universidad Católica del Norte
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Yet another variant of the Drygas functional equation on groups
No full textLet G be a group and C the field of complex numbers. Suppose σ1, σ 2 : G → G are endomorphisms satisfying the condition σi(σi(x)) = x for all x in G and for i = 1, 2. In this paper, we find the central solution f : G → C of the equation f (xy) + f (σi(y)x) =2f (x) + f (y) + f (σ2(y)) for all x,y ∈ G which is a variant of the Drygas functional equation with two involutions. Further, we present a generalization the above functional equation and determine its central solutions. As an application, using the solutions ofthe generalized equation, we determine the solutions f, g, h, k : GxG → C ofthefunc-tional equation f (pr, qs) + g(sp, rq) = 2f (p, q) + h(r, s) + k(s, r) when f satisfies the condition f (pr, qs) = f (rp, sq) for all p, q, r, s ∈ G
Numerical quenching for a semilinear parabolic equation with a potential and general nonlinearities
No full textThis paper concerns the study of the numerical approximation a semilinear parabolic equation subject to Neumann boundary conditions and positive initial data. We find some conditions under which the solution of a semidiscrete form of the above problem quenches in a fi- nite time and estimate its semidiscrete quenching time. We also prove that the semidiscrete quenching time converges to the real one when the mesh size goes to zero. A similar study has been also investigated taking a discrete form of the above problem. Finally, we give some numerical experiments to illustrate our analysis.
The uniform boundedness principle for arbitrary locally convex spaces
No full textWe establish uniform boundedness principle for pointwise bounded families of continuous linear operators between locally convex spaces which require no assumptions such as barrelledness on the domain space of the operators. We give applications of the result to separately continuous bilinear operators between locally convex spaces
Reversibility For Semigroup Actions
No full textLet Q be a topological space and S a semigroup of local homeomorphisms of Q. The purpose of this paper is to generalize the notion of reversibility and to introduce the reversible sets. And furthermore, it is established a relation between these sets and the control sets for S and it is studied reversibility of semigroup actions on fiber bundles
Topologies polaires compatibles avec une dualité séparante sur un corps value non-archiméedien
No full textIn this paper, we deal with polar topologies in separated dual pair hX, Y i of vector spaces over a non-archimedean valued field. We study compatible polar topologies, and we give some results characterizing specific subsets of X related to these topologies, especially if the field K is spherically complete or the compatible topology is polar or strongly polar. Furthermore, we investigate some topological properties in the duality hX, Y i such as barreldness and reflexivity
Conjugacies classes of some numerical methods
No full textWe study the dynamics of some numerical root finding methods such as the Newton, Halley, K¨onig and Schröder methods for three and four degree complex polynomials
Characterization of Lallement order on a regular semigroup
No full textIn this paper a study of properties of the Mitsch order relation ’µ’ on a regular semigroup and Nambooripads order ’ν’ on any arbitrary regular semigroup is made. Mainly a characterization of Lallement order on a regular semigroup is obtained. The necessary and sufficient condition for the restriction of Lallement order ’λ’ to B(S) to be usual order on an orthodox semigroup is also obtained
Functions of bounded (φ, p) mean oscillation
No full textIn this paper we extend a result of Garnett and Jones to the case of spaces of homogeneous type
A Birkhoff type theorem for strong varieties
No full textAlgebraic systems with partial operations have different ways to interpret equality between two terms of the language. A strong identity is a formula which says that two terms are equal in the algebra if the existence of one of them implies the existence of the other one and in the case of existence their values are equal. A class of partial algebras defined by a set of strong identities is called a strong variety. In the characterization of strong varieties in the case of partial algebras by means of a Birkhoff-type theorem there appeared a new concept, regularity of partial homomorphisms and partial subalgebras. Here we define and study these operators from two different perspectives.Firstly, in their relation with other well known concecpts of partial homomorphisms and partial subalgebras, as well as with the po-monoid of Pigozzi for the H, S and P operators. Secondly, in regard to the preservation of the different types of formulae that represent equality in the case of partial algebras for these operators. Finally, we give a characterization of the strong varieties as classes closed under regular homomorphisms, regular subalgebras, direct products and that satisfy a closure condition
Une remarque sur la trace de la torsion et le tenseur de Ricci
No full textOn donne une formule qui raccorde la trace de la torsion, le tenseur de Ricci et l’application exponentielle d’une connexion pour laquelle une forme volume est a dérivée covariante nulle. Ce résultat élémentaire répond a une question souvent posée