Revistas académicas de la Universidad Católica del Norte
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On some infinitesimal automorphisms of Riemannian foliation
No full textIn Riemannian foliation, a transverse affine vector field preserves the curvature and its covariant derivatives. In this paper we solve the converse problem. Actually, we show that an infinitesimal automorphism of a Riemannian foliation which preserves the curvature and its covariant derivatives induces a transverse almost homothetic vector field. If in addition the manifold is closed and the foliation is irreducible harmonic, then a such infinitesimal automorphism induces a transverse killing vector field
About Decay Of Solution Of The Wave Equation With Dissipation
No full textIn this work, we consider the problem of existence of global solutions for a scalar wave equation with dissipation. We also study the asymptotic behaviour in time of the solutions. The method used here is based in nonlinear techniques. Key words: wave equation, evolution model, decay of solution, asymptotic behaviour
Topological classification of compact surfaces with nodes of genus 2
No full textWe associate to each Riemann or Klein surface with nodes a graph that classifies it up homeomorphism. We obtain that, for surfaces of genus two, there are 7 topological types of stable Riemann surfaces, 33 topological types of stable Klein surfaces and 35 topological types of symmetric stable Riemann surfaces (this last type of surfaces corresponds to the new surfaces appearing in the compactification of the Moduli space of real algebraic curves, see [Se] and [Si])
Une propriété du groupe á 168 éléments
No full textLet e be an affine space of dimension n over a field the affine group of e, G the corresponding linear group. To each point corresponds a section of the canonical map to the linear map corresponds the affine map wich has as associated linear map and a as fixed point. We proove that every section is of this type, except in the only one case where K = F2 and n = 3
A note on polynomial characterizations of asplund spaces
No full textIn this note we obtain several characterizations of Asplund spaces by means of ideals of Pietsch integral and nuclear polynomials, extending previous results of R. Alencar and R. Cilia-J. Gutiérrez
Spectral properties of a non selfadjoint system of differential equations with a spectral parameter in the boundary condition
No full textIn this paper we investigated the spectrum of the operator L(?) generated in Hilbert Space of vector-valued functions L2 (R+, C2) by the system iy0 1 + q1 (x) y2 = ?y1, ?iy0 2 + q2 (x) y1 = ?y2 (0.1) , x ?R+ := [0,?), and the spectral parameter- dependent boundary condition (a1? + b1) y2 (0, ?) ? (a2? + b2) y1 (0, ?)=0, where ? is a complex parameter, qi, i = 1, 2 are complex-valued functions ai 6= 0, bi 6= 0, i = 1, 2 are complex constants. Under the condition sup x?R+ {exp ?x |qi (x)|} < ?, i = 1, 2,?> 0, we proved that L(?) has a finite number of eigenvalues and spectral singularities with finite multiplicities. Furthermore we show that the principal functions corresponding to eigenvalues of L(?) belong to the space L2 (R+, {C2) and the principal functions corresponding to spectral singularities belong to a Hilbert space containing L2 (R+, C2)
Some results on prime and primary submodules
No full textThis article is devoted to study some properties of prime and primary submodules. First we characterize prime submodules of free modules and give a primality condition for certain submodules in terms of associated prime ideals. Furthermore, by using symmetric algebra of modules we describe Rees algebras associated to prime submodules and provide a computational method to check if some primary submodules of a free module have prime radical
A multiplier gliding hump property for sequence 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
Existence of solutions of semilinear systems in ℓ²
No full textLet Q : ℓ² → ℓ² be a symmetric and positive semi-definite linear operator and fj : R → R (j = 1, 2, ...) be real functions so that, fj(0) = 0 and, for every x = (x1, x2, ....) ∈ ℓ², it holds that f(x) := (f1(x1), f2(x2), ...) ∈ ℓ². Sufficient conditions for the existence of non-trivial solutions to the semilinear problem Qx = f(x) are provided. Moreover, if G is a group of orthogonal linear automorphisms of ℓ² which commute with Q, then such sufficient conditions ensure the existence of non-trivial solutions which are invariant under G. As a consequence, sufficient conditions to ensure solutions of nonlinear partial difference equations on finite degree graphs with vertex set being either finite or infinitely countable are obtained. We consider adaptations to graphs of both Matukuma type equations and Helmholtz equations and study the existence of their solutions
On the local convergence of a Newton-type method in Banach spaces under a gamma—type condition
No full textWe provide a local convergence analysis for a Newton-type method to approximate a locally unique solution of an operator equation in Banach spaces. The local convergence of this method was studied in the elegant work by Werner in [11], using information on the domain of the operator. Here, we use information only at a point and a gamma-type condition [4], [10]. It turns out that our radius of convergence is larger, and more general than the corresponding one in [10]. More over the same can hold true when our radius is compared with the ones given in [9] and [11]. A numerical example is also provided