Revistas académicas de la Universidad Católica del Norte
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Lê constant families of singular hypersurfaces
No full textWe investigate the constancy of the Le numbers of one parameter deformations F :(C X Cn, 0) — (C, 0) of holomorphic germs of functions f :(Cn, 0) — (C, 0) which have singular set with any dimension s > 1. WecharacterizeLe constant deformations in terms of the non-splitting of the polar varieties and also from the integral closure of the ideal Jz (F) in On+1 generated by the partial derivatives of F with respect to the variables z = (z!,...,zn
Equitable Graph of a Graph
No full textA subset D of V is called an equitable dominating set if for every v ∈ V — D there exists a vertex u ∈ D such that uv ∈ E(G) and |d(u) — d(v)| ≤ 1,where d(u) denotes the degree of vertex u and d(v) denotes the degree of vertex v. The minimum cardinality of such a dominating set is denoted by γe and is called the equitable domination number of G. Degree Equitable domination on Graphs were introduced in [10].This Paper aims at the study of a new concept called equitable graph ofa graph introduced by Prof. E. Sampathkumar. In this paper we show that there is relation between γ(Ge) and γe(G). Further results on the new parameter γ(Ge) are discussed
Difference inequalities of fractional order
No full textIn this paper, we establish some new difference inequalities of fractional order which provide explicit bounds on unknown functions and can be used as an effective tool in the development of the theory of fractional order difference equations
Caracterisation des classes de (≤ 3)-hypomorphie a l’aide d’interdits
No full textG. Lopez a démontréla(<6)-reconstructibilitédes relationsbi-naires finies (1972) (voir [1] et [2]) résolvant ainsi un probleme de Roland Fraissé (voir[3]). Sa preuve repose sur la notion de classe de difference. Depuis, la notion de classe de difference est un outil ma-jeur dans bien des travaux en reconstruction et demi-reconstruction notammenten[4], [5] et [6]etpermet dedefinir la notion de classe d'hypomorphie. La caracterisation des classes de (<k)-hypomorphie finies, pour k>6, a été obtenue par Hagendorf et Lopez en 1994 (voir [4]). La caracterisation des classes de (<4)-hypomorphie finies a ete obtenue par G. Lopez et C. Rauzy (1992) (voir [6]). Ensuite, celle des classes de (<5)-hypomorphie finies a etetrouvee par Y. Boudabbous (2000) (voir [7]). Dans cet article nous obtenons une caracterisation, par interdits, des classes de (<3)-hypomorphie finies, puis infinies dans un prochain article. Ces deux articles sont resumes en [8]. La reconstruction infinie a ete en particulier etudiee en [4], [9] et [11]. D'autres utilisations des classes de difference ou des liens avec elles se trouvent par exemple dans [12] a [21]
A geometric proof of the Lelong-Poincaré fórmula
No full textWe propose a geometric proof of the fundamental Lelong-Poincaré formula : ddc log |ƒ| = [ƒ = 0] where f is any nonzero holomorphic function defined on a complex analytic manifold V and [ƒ = 0] is the integration current on the divisor of the zeroes of ƒ
Matrix representations of the q-Jacobsthal numbers
No full textIn this paper, we consider a q-Jacobsthal sequence {Jq,n},with initial conditions Jq0 = 0 and Jq1 = l. Then give a generating matrix for the terms of sequence {Jq,kn} for a positive integer k.With the aid of this matrix, we derive some new identities for the sequence
Prime Submodules of Graded Modules
No full textLet G be a group, R be a G-graded ring and M be a G-graded R-module. Suppose P is a prime ideal of Reand g G G. In this article, we defineMg (P) = {m G Mg : Am C PMg for some ideal A of Re satisfying A C P}that is an Re-submodule of Mg, and we investigate some results on this submodule. Also, we introduce a situation where if N is a gr-prime R-submodule of M ,then (Ng : Mg) is a maximal ideal of Re. We close this article by introducing a situation where if N is a gr- R-submodule ofM such that Ne is a weakly prime Re-submodule ofMe,thenNg is a prime Re-submodule of Mg
Fixed points and common fixed points theorems in pseudo-ordered sets
No full textUnder suitable conditions, we establish the existence of the greatest and the least fixed points of monotone maps defined on nonempty pseudo-ordered sets. Also, we prove that the set of all common fixed points of two categories of finite commutative family F of monotone maps f defined on a nonempty complete trellis is also a nonempty complete trellis
Some results on global dominating sets
No full textA dominating set is called a global dominating set if it is a dominating set for a graph G and its complement G. We investigate some general results for global dominating sets corresponding to the graphs Pn, Cn and Wn
A convergence result for unconditional series in Lp(μ)
No full textWe give sufficient conditions for the convergence almost everywhere of the expansion with respect to an unconditional basis for functions in Lp p > 2. This result extends the classical theorem of Menchoff and Rademacher for orthogonal series in L2