Analytic invariants for the 1:−11:-1 resonance

Associated to analytic Hamiltonian vector fields in $\mathbb{C}^4$ having an equilibrium point satisfying a non semisimple $1:-1$ resonance, we construct two universal constants that are invariant with respect to local analytic symplectic changes of coordinates. These invariants vanish when the Hamiltonian is integrable. We also prove that one of these invariants does not vanish on an open and dense set.Comment: 48 pages, 5 figure

Influencia de la secularización en la valoración de la asignatura de teología por los estudiantes de último semestre de la Carrera de Ingeniería en Turismo y Hotelería de la Universidad Católica de Santiago de Guayaquil. Diseño de un modelo de actividades pastorales y sociales de vinculación Universidad-Comunidad.

La presente investigación es un estudio para determinar la influencia que ejerce la secularización en los estudiantes de último semestre de la carrera de Ingeniería en Turismo y Hotelería de la Universidad Católica de Santiago de Guayaquil, en la valoración de la asignatura de Teología, del semestre B ¿ 2013. Refiriéndose al tema en mención, S.S. Juan Pablo II expresó: ¿El secularismo que por su misma naturaleza y definición es un movimiento de ideas y costumbres, defensor de un humanismo que hace total abstracción de Dios, y se concentra totalmente en el culto del hacer y del producir, a la vez que embriagado por el consumo y el placer, sin preocuparse por el peligro de perder la propia alma¿, no puede menos de minar el sentido del pecado. (Reconciliatio et paenitentia, N° 18). De alguna manera se puede decir que el secularismo es una expresión cultural o de anticultura del pecado del ser humano, como dice Juan Pablo II, al ser desobediencia de la creatura respecto a su fuente de vida, es un ¿acto suicida¿. Por lo tanto, la consecuencia del secularismo es el suicidio del mismo hombre que le da la espalda a Dios; en este caso será la muerte del espíritu humano. La carrera de Ingeniería en Turismo y Hotelería, tiene estudiantes que en el abordaje del pensum académico de su carrera aprenden la materia de Teología, la cual les permite conocen mejor a Dios y relacionarse más profundamente con él en muchos momentos de su vida, convirtiéndose en creyentes, lo que sin lugar a dudas les ayuda a vivir mejor su vida personal y profesional. Esta investigación está dividida en cinco capítulos: El primero, explica el planteamiento del problema, los objetivos generales y específicos, las preguntas de la investigación, además de la justificación y pertinencia que ésta tiene tanto para la Universidad Católica de Santiago de Guayaquil, como para la sociedad ecuatoriana. El segundo capítulo, abarca los antecedentes, objetivo general y específicos y lo que concierne a la gestión administrativa. El tercer capítulo se refiere a la fundamentación teórica. El cuarto capítulo abarca la modalidad de investigación, población y muestra de los involucrados en la investigación. El quinto capítulo se refiere al análisis e interpretación de resultados, las conclusiones y recomendaciones. El trabajo propuesto, contribuirá al Departamento de Pastoral y por lo consiguiente a la Universidad Católica de Santiago de Guayaquil, como un documento o material bibliográfico, que puede servir de referente para futuras investigaciones sobre el tema; así mismo incluirá algunas recomendaciones que puedan ayudar a contrarrestar este fenómeno que afecta la Fe cristiana que es patrimonio de la universidad y de la sociedad ecuatoriana

inter and intra tumoral heterogeneity in dna damage evaluated by comet assay in early breast cancer patients

Abstract There are no clinical tools to functionally assess degree of DNA damage in breast cancer. The comet assay is an accepted research tool for assessing DNA damage, however, most cancer studies have assessed lymphocytes as surrogate cells. The aim of this pilot study was to use the comet assay in early breast cancer directly in tumor tissue to compare DNA damage between and within traditionally defined subgroups, and to explore intra-tumoral heterogeneity. Scrapings of tumor and healthy breast tissue were obtained at primary surgery from 104 women. Comet assay was applied to quantitatively assess DNA damage, revealing substantial inter- and intra-subgroup variation. Marked intra-tumoral heterogeneity was evident across all subgroups. The degree of DNA damage for an individual could not be predicted by breast cancer subgroup. Comet assay warrants further study as a potential clinical tool for identification of tumoral DNA damage and ultimately, individualised use of DNA damaging therapy

Red seaweeds Grateloupia turuturu and Porphyra umbilicalis as nutraceuticals and functional food: nutritional/chemical composition and immunostimulatory activity

1st Natural Products Application: health, cosmetic and food - International online conference, 4-5 February 2021The number of nutraceuticals and functional foodsfrom marine origin is increasing in the worldwide market. Specifically, the red seaweeds Grareloupia turuturu and Porphyra umbilicalis have shown their potential considering relevant bioactive compounds and nutritional value [1,2]. Nevertheless, it is pertinent to explore knowledge gaps regarding their nutritional/chemical composition and bioactivities. Hence firstly G. turuturu and P. umbilicalis proximate composition and lipid classes were determined; secondly, after preparing hydroethanolic and aqueous infusion and decoction) seaweed extracts, mycosporine-like ami no acids (MAAs) and carbohydrates were quantified. and the immunomodulatory potential was assessed using RAW 264.7 cell line. Results show that dietary fibre was the most abundant nutritional parameter for both seaweed species, followed by relevant ash and protein contents. Free fatty acids were the main lipid class in both seaweed species, whereas tocopherols exhibited residual contentsby RP-HPLC-FLD. For hydroethanolic and aqueous extracts, several MAAs were quantified by RP-HPLC-DAD and LC-DAD ESI-MS. P. umbilicalis extracts demonstrated greater MAAs content than G. turuturu, and porphyra-334 was the main MAA. The aqueous extracts of both seaweeds showed higher carbohydrate contents than the hydroethanolic, with P. umbilicalis decoction exhibiting the highest level. Concerning the immunomodulatory activity, for 0.02 mg/mL, the exposure to P. umbilicalis aqueous extracts resulted in the most accentuated 'NO production by RAW 264.7 cells, showing immunostimulatory potential. MAAs and carbohydrates are believed to be responsible for the immunostimulatory activity [3,4]. G. turuturu and P. umbilicalis potential as functional food and nutraceuticals, relying on their relevance as sources of bioactive compounds to the food, pharmaceutical and cosmetic industries, is thus reinforcedThis work was financed by European Funds FEDER/COMPETE/POCI under project POCI-01-0145-FEDER-006958 (CITAB), and by FCT to CECAV (UIDB/CVT/00772/2020), CITAB (UlDB/04033/2020) and CESAM (UIDP/5001712020+UIDB/50017/2020). FCT is also acknowledged for a doctoral grant to Joao Ferreira (SFRH/BD/144882/2019)N

Annual Report 2004

13 pages, 2 figuresLet $0<\lambda<1$ and $I_1=[a_0,a_1),\ldots,I_{k}= [a_{k-1},a_k)$ be a partition of the interval $I=[0,1)$ into $k\ge1$ subintervals. Let $f:I\to I$ be a map where each restriction $f|_{I_i}$ is an increasing $\lambda$-Lipschitz function for $i=1,\ldots,k$. We prove that any piecewise increasing contraction $f$ admits at most $k$ periodic orbits, where the upper bound is sharp. Our second result concerns piecewise $\lambda$-affine maps. Let $b_1,\ldots,b_k$ be real numbers. Let $F_\lambda: I\to \mathbb{R}$ be a family of piecewise $\lambda$-affine functions, where each restriction $F_\lambda|_{I_i}(x)=\lambda x +b_i$. Under a generic assumption on the parameters $a_1,\ldots,a_{k-1},b_1,\ldots,b_k$ which define $F_\lambda$, we prove that, up to a zero Hausdorff dimension set of slopes $0<\lambda<1$, the $\omega$-limit set of the piecewise $\lambda$-affine map $f_\lambda:x\in I \to F_\lambda(x)\pmod{1}$ at every point equals a periodic orbit and there exist at most $k$ periodic orbits

Dissipative outer billiards: A case study

We study dissipative polygonal outer billiards, i.e. outer billiards about convex polygons with a contractive reflection law. We prove that dissipative outer billiards about any triangle and the square are asymptotically periodic, i.e. they have finitely many global attracting periodic orbits. A complete description of the bifurcations of the periodic orbits as the contraction rates vary is given. For the square billiard, we also show that the asymptotic periodic behaviour is robust under small perturbations of the vertices and the contraction rates. Finally, we describe some numerical experiments suggesting that dissipative outer billiards about regular polygon are generically asymptotically periodic

Dynamics of piecewise increasing contractions

13 pages, 2 figuresLet $0<\lambda<1$ and $I_1=[a_0,a_1),\ldots,I_{k}= [a_{k-1},a_k)$ be a partition of the interval $I=[0,1)$ into $k\ge1$ subintervals. Let $f:I\to I$ be a map where each restriction $f|_{I_i}$ is an increasing $\lambda$-Lipschitz function for $i=1,\ldots,k$. We prove that any piecewise increasing contraction $f$ admits at most $k$ periodic orbits, where the upper bound is sharp. Our second result concerns piecewise $\lambda$-affine maps. Let $b_1,\ldots,b_k$ be real numbers. Let $F_\lambda: I\to \mathbb{R}$ be a family of piecewise $\lambda$-affine functions, where each restriction $F_\lambda|_{I_i}(x)=\lambda x +b_i$. Under a generic assumption on the parameters $a_1,\ldots,a_{k-1},b_1,\ldots,b_k$ which define $F_\lambda$, we prove that, up to a zero Hausdorff dimension set of slopes $0<\lambda<1$, the $\omega$-limit set of the piecewise $\lambda$-affine map $f_\lambda:x\in I \to F_\lambda(x)\pmod{1}$ at every point equals a periodic orbit and there exist at most $k$ periodic orbits

Rotation number of 2-interval piecewise affine maps

We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps f_{\p} are parametrized by a quintuple \p of real numbers satisfying inequations. Viewing f_{\p} as a circle map, we show that it has a rotation number \rho(f_{\p}) and we compute \rho(f_{\p}) as a function of \p in terms of Hecke-Mahler series. As a corollary, we prove that \rho(f_{\p}) is a rational number when the components of \p are algebraic numbers

Évaluation économique de la pollution de l'environnement par une activité industrielle. Application aux centrales électriques

SCOPUS: ar.jinfo:eu-repo/semantics/publishe

The attractor of piecewise expanding maps of the interval

We consider piecewise expanding maps of the interval with finitely many branches of monotonicity and show that they are generically combinatorially stable, i.e. the number of ergodic attractors and their corresponding mixing components do not change under small perturbations of the map. Our methods provide a topological description of the attractor and give an elementary proof of the density of periodic orbits