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Hypersurfaces in ${\mathbb{S}}^4$ that are of $L_k$-2-type
Pascual Lucas,H\'ector-Fabi\'an Ram\'\i rez-Ospina 대한수학회 2016 대한수학회보 Vol.53 No.3
In this paper we begin the study of $L_k$-2-type hypersurfaces of a hypersphere $\S^{n+1}\subset\R^{n+2}$ for $k\geq 1$. Let $\psi:\M\rightarrow\S^{4}$ be an orientable $H_k$-hypersurface, which is not an open portion of a hypersphere. Then $\M$ is of $L_k$-2-type if and only if $\M$ is a Clifford tori $\S^1(r_1)\times\S^2(r_2)$, $r_1^2+r_2^2=1$, for appropriate radii, or a tube $T^r(V^2)$ of appropriate constant radius $r$ around the Veronese embedding of the real projective plane $\R P^2(\sqrt3)$.
Bertrand curves in non-flat 3-dimensional (Riemannian or Lorentzian) space forms
Pascual Lucas,Jose Antonio Ortega-Yagues 대한수학회 2013 대한수학회보 Vol.50 No.4
Let M3 q(c) denote the 3-dimensional space form of index q = 0, 1, and constant curvature c 6= 0. A curve α immersed in M3 q(c) is said to be a Bertrand curve if there exists another curve β and a one-to-one correspondence between α and β such that both curves have common principal normal geodesics at corresponding points. We obtain characterizations for both the cases of non-null curves and null curves. For non-null curves our theorem formally agrees with the classical one: nonnull Bertrand curves in M3 q(c) correspond with curves for which there exist two constants λ 6= 0 and μ such that λκ + μ = 1, where τ and stand for the curvature and torsion of the curve. As a consequence, non-null helices in M3 q(c) are the only twisted curves in M3 q(c) having infinite non-null Bertrand conjugate curves. In the case of null curves in the 3-dimensional Lorentzian space forms, we show that a null curve is a Bertrand curve if and only if it has non-zero constant second Frenet curvature. In the particular case where null curves are parametrized by the pseudo-arc length parameter, null helices are the only null Bertrand curves.
SLANT HELICES IN THE THREE-DIMENSIONAL SPHERE
Pascual Lucas,Jose Antonio Ortega-Yagues 대한수학회 2017 대한수학회지 Vol.54 No.4
A curve $\gamma$ immersed in the three-dimensional sphere $\S3$ is said to be a slant helix if there exists a Killing vector field $V(s)$ with constant length along $\gamma$ and such that the angle between $V$ and the principal normal is constant along $\gamma$. In this paper we characterize slant helices in $\S3$ by means of a differential equation in the curvature $\kappa$ and the torsion $\tau$ of the curve. We define a helix surface in $\S3$ and give a method to construct any helix surface. This method is based on the Kitagawa representation of flat surfaces in $\S3$. Finally, we obtain a geometric approach to the problem of solving natural equations for slant helices in the three-dimensional sphere. We prove that the slant helices in $\S3$ are exactly the geodesics of helix surfaces.
Pascual Javier,Rodríguez Alejandro,Delgado Clara Elena,Rizo-Patróe;n Alejandra,Porcar Manuel,Vilanova Cristina 한국미생물·생명공학회 2022 한국미생물·생명공학회지 Vol.50 No.1
The effluents from industries processing vegetable oils are extremely rich in sulfates, often exceeding the maximum concentration allowed to release them to the environment. Biological sulfate reduction is a promising alternative for the removal of sulfates in this type of wastewater, which has other particularities such as an acidic pH. The ability to reduce sulfates has been widely described for a particular bacterial group (SRB: sulfate-reducing bacteria), although the reports describing its application for the treatment of sulfate-rich industrial wastewaters are scarce. In this work, we describe the use of a natural SRB-based consortium able to remove above 30% of sulfates in the wastewater from one of the largest edible oil industries in Peru. Metataxonomic analysis was used to analyse the interdependencies established between SRB and the native microbiota present in the wastewater samples, and the performance of the consortium was quantified for different sulfate concentrations in laboratory-scale reactors. Our results pave the way towards the use of this consortium as a low-cost, sustainable alternative for the treatment of larger volumes of wastewater coming from this type of industries.
좌절의 학습 ( El aprendizaje de la decepcion ) 에 있어서 문학과 예술
(Clara Pascual Escudero) 한국스페인어문학회 1999 스페인어문학 Vol.14 No.1
시, 소설 그리고 산문에 걸친 F. de Azu`a의 모든 글들은 한 테마로 특징지어질 수 있다 : 예술, 예술의 본질, 예술을 창조하는 인물, 지식인. 이 모든 것에서 Azu`a는 부르조아를 자극했던 전위작가들의 문체를 떠오르게하는 작가이다. 어떤면에 있어서 예술 비평가로서의 역할을 한다. 그는 $quot;유럽의 지적 지도층$quot;의 몰락, 현대 예술의 끝, $quot;예술 혁명$quot;의 도래등을 예견한다. 18세기말부터 풍미되었던 예술의 개념에 대한 그의 통렬한 비판은 세기초 전위작가들과는 상이한 면을 보인다. 예술을 부르조아의 사회 역사적 산유물이라고 비판함에도 불구하고, 그가 보여주는 혁신은 보수성을 지닌다:그는 200년동안 지배되어온 백과전서파에 의해 보급된 현대적 예술 체제를 복원하려한다. 작가는 $quot;예술은 그 성과가 너무 짐스러워 죽어버렸다$quot;고 말하면서, 천재적 예술가들의 출현과 헤겔의 역사 이성의 미학이 현대예술의 자기파멸의 두 요인이 되었다고 주장한다. 따라서 작가는, 예외적 인물도 아니고 역사도 아닌, 하나의 주관적이고 반역사적인 예술을 부활시킨다. 이를 위한 그 원천으로서, 미, 정확성, 진실에 가치를 둔 지적경향에 대립하여, 풍부한 경험에 기초한 자연주의적 개념을 도입한다. 이에 따라, 인간의 현실적 요구들을 외면하는 스콜라적인 학문 예술의 경향에 대한 그의 반작용은 소설의 개념을 $quot;기억의 예술$quot;로서 설명한다. 그러나 그의 생각은 과거를 지워버릴수는 없다는 것을 의식하는데서 오는 모호성으로 특징지어질 수 있다. 그러므로 그의 자연주의적 제시는 좌절되며, 예술언어로서만 흡수되어버린다.
HYPERSURFACES IN 𝕊<sup>4</sup> THAT ARE OF L<sub>k</sub>-2-TYPE
Lucas, Pascual,Ramirez-Ospina, Hector-Fabian Korean Mathematical Society 2016 대한수학회보 Vol.53 No.3
In this paper we begin the study of $L_k$-2-type hypersurfaces of a hypersphere ${\mathbb{S}}^{n+1}{\subset}{\mathbb{R}}^{n+2}$ for $k{\geq}1$ Let ${\psi}:M^3{\rightarrow}{\mathbb{S}}^4$ be an orientable $H_k$-hypersurface, which is not an open portion of a hypersphere. Then $M^3$ is of $L_k$-2-type if and only if $M^3$ is a Clifford tori ${\mathbb{S}}^1(r_1){\times}{\mathbb{S}}^2(r_2)$, $r^2_1+r^2_2=1$, for appropriate radii, or a tube $T^r(V^2)$ of appropriate constant radius r around the Veronese embedding of the real projective plane ${\mathbb{R}}P^2({\sqrt{3}})$.