Revistas académicas de la Universidad Católica del Norte
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On the local hypercenter of a group
No full textWe introduce a local hypercenter of an arbitrary group and study its basic properties. With this concept, it turns out that classical theorems of Baer, Mal’cev and McLain on locally nilpotent groups can be obtained as special cases of statements which are valid in any group. Furthermore, we investigate the connection between the local hypercenter of a group and the intersection of its maximal locally nilpotent subgroups
Asymptotics for second order delayed differential equations
No full textIn this work we present a way to find asymptotic formulas for some solutions of second order linear differential equations with a retarded functional perturbation
S??compactness in L-topological spaces
No full textIn this paper, the notion of S??compactness is introduced in L-topological spaces by means of open ?a?cover. It is a generalization of Lowen’s strong compactness, but it is different from Wang’s strong compactness. Ultra-compactness implies S??compactness. S??compactness implies fuzzy compactness. But in general N-compactness and Wang’s strong compactness need not imply S??compactness
Sur le problème additif de cousin basique
No full textL’objet de ce travail est l’étude du problème additif de Cousin basique pour un feuilletage transversalement holomorphe. Plusieurs exemples ont été examinés et plus particulièrement les feuilletages obtenus par suspension d’un groupe de biholomorphismes d’une variété analytique complexe. Pendant l’élaboration de ce travail, le second auteur a effectué une série de séjours à l’Université de Valenciennes au sein du LAMATH. Il remercie cette institution pour son hospitalité ainsi que le CIES qui a organisé ces séjours et le Ministère Fran¸cais des Affaires Etrangères pour les avoir financés
Diagonals and eigenvalues of sums of hermitian matrices. Extreme cases
No full textThere are well known inequalities for Hermitian matrices A and B that relate the diagonal entries of A+B to the eigenvalues of A and B. These inequalities are easily extended to more general inequalities in the case where the matrices A and B are perturbed through congruences of the form UAU? + V BV ? , where U and V are arbitrary unitary matrices, or to sums of more than two matrices. The extremal cases where these inequalities and some generalizations become equalities are examined here
Non - autonomous inhomogeneous boundary cauchy problems and retarded equations
No full textIn this paper we prove the existence and the uniqueness of the classical solution of non-autonomous inhomogeneous boundary Cauchy problems, and that this solution is given by a variation of constants formula. This result is applied to show the existence of solutions of a retarded equation
Differentiability of solutions of the abstract cauchy problem
No full textIn this note we establish a result of differentiability for the mild solution of the inhomogeneous abstract Cauchy problem when the underlying space is reflexive
On the representation type of certain trivial extensions
No full textLet A ?= kQ/I be a basic and connected finite dimension algebra over closed field k. In this note show that in case B = A[M] is a tame one-point extension of a tame concealed algebra A by an indecomposable module M, then the trivial extension T(B) = B ? DB is tame if and only if the module M is regular
A gliding hump property and banach-mackey spaces
No full textWe consider the Banach–Mackey property for pairs of vector spaces E and E0 which are in duality. Let A be an algebra of sets and assume that P is an additive map from A into the projection operators on E. We define a continuous gliding hump property for the map P and show that pairs with this gliding hump property and another measure theoretic property are Banach-Mackey pairs, i. e., weakly bounded subsets of E are strongly bounded. Examples of vector valued function spaces, such as the space of Pettis integrable functions, which satisfy these conditions are given
On the levi problem with singularities
No full textIn section 1, we show that if X is a Stein normal complex space of dimension n and D ?? X an open subset which is the union of an increasing sequence D1 ? D2 ? ... ? Dn ?? ... of domains of holomorphy in X, then D is a domain of holomorphy. In section 2, we prove that a domain of holomorphy D which is relatively compact in a 2-dimensional normal Stein space X itself is Stein. In section 3, we show that if X is a Stein space of dimension n and D ? X an open subspace which is the union of an increasing sequence D1 ? D2 ? ... ? Dn ? ... of open Stein subsets of X, then D itself is Stein, if X has isolated singularities