A new bound on the Morse index of constant mean curvature tori of revolution in S3

In this work we give a new lower bound on the Morse index for constant mean curvature tori of revolution immersed in the three-sphere S3, by computing some explicit negative eigenvalues for the corresponding Jacobi operator.Ministerio de Educación y Ciencia MTM2007-6191

The maximum relative diameter for multi-rotationally symmetric planar convex bodies

In this work we study the maximum relative diameter functional dM in the class of multi-rotationally symmetric planar convex bodies. A given set C of this class is k-rotationally symmetric for k 2 {k1, . . . , kn} N, and so it is natural to consider the standard ki-partition Pki associated to C (which is a minimizing ki-partition for dM when ki > 3) and the corresponding value dM(Pki ). We establish the relation among these values, characterizing the particular sets for which all these values coincide.Ministerio de Economía y Competitividad MTM2013-48371-C2-1-PJunta de Andalucía FQM-32

Compact stable hypersurfaces with free boundary in convex solid cones with homogeneous densities

We consider a smooth Euclidean solid cone endowed with a smooth homogeneous density function used to weight Euclidean volume and hypersurface area. By assuming convexity of the cone and a curvature-dimension condition, we prove that the unique compact, orientable, second order minima of the weighted area under variations preserving the weighted volume and with free boundary in the boundary of the cone are intersections with the cone of round spheres centered at the vertex.Ministerio de Ciencia y Tecnología MTM2010-21206-C02-01Junta de Andalucía FQM-325Junta de Andalucía P09-FQM-508

Bisections of centrally symmetric planar convex bodies minimizing the maximum relative diameter

In this paper we study the bisections of a centrally symmetric planar convex body which minimize the maximum relative diameter functional. We give necessary and sufficient conditions for being a minimizing bisection, as well as analyzing the behavior of the so-called standard bisection.Ministerio de Economía e Innovación MTM2013-48371-C2-1-PJunta de Andalucía FQM-32

On the isodiametric and isominwidth inequalities for planar bisections

For a given planar convex body K, a bisection of K is a decomposition of K into two closed sets A,B so that A∩B is an injective continuous curve connecting exactly two boundary points of K. Consider a bisection of K minimizing, over all bisections, the maximum diameter (resp., maximum width) of the sets in the decomposition. In this note, we study some properties of these minimizing bisections and prove inequalities extending the classical isodiametric and isominwidth inequalities. Furthermore, we address the corresponding reverse optimization problems and establish inequalities similar to the reverse isodiametric and reverse isominwidth inequalities.Ministerio de Ciencia, Innovación y Universidades MTM2017-84851-C2-1-PJunta de Andalucía FQM-325Fundación Séneca 19901/GERM/15Ministerio de Ciencia, Innovación y Universidades PGC2018-094215-B-I0

Subdivisions of rotationally symmetric planar convex bodies minimizing the maximum relative diameter

In this work we study subdivisions of k-rotationally symmetric planar convex bodies that minimize the maximum relative diameter functional. For some particular subdivisions called k-partitions, consisting of k curves meeting in an interior vertex, we prove that the so-called standard k-partition (given by k equiangular inradius segments) is minimizing for any k 2 N, k > 3. For general subdivisions, we show that the previous result only holds for k 6 6. We also study the optimal set for this problem, obtaining that for each k 2 N, k > 3, it consists of the intersection of the unit circle with the corresponding regular k-gon of certain area. Finally, we also discuss the problem for planar convex sets and large values of k, and conjecture the optimal k-subdivision in this case.Ministerio de Educación y Ciencia MTM2010-21206-C02-01Ministerio de Economía e Innovación MTM2013-48371-C2-1-PJunta de Andalucía FQM-325Junta de Andalucía P09-FQM-508

Changes in the requirement for early surgery in inflammatory bowel disease in the era of biological agents

This is the peer reviewed version of the following article: Changes in the requirement for early surgery in inflammatory bowel disease in the era of biological agents. Journal of Gastroenterology and Hepatology (2020): 29 April, which has been published in final form at https://doi.org/10.1111/jgh.15084. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived VersionsBiological therapies may be changing the natural history of inflammatory bowel diseases, reducing the need for surgical intervention. We aimed to assess whether the availability of anti‐TNF agents impacts the need for early surgery in Crohn's disease (CD) and ulcerative colitis (UC). Methods Retrospective, cohort study of patients diagnosed within a 6‐year period before and after the licensing of anti‐TNFs (1990‐1995 and 2007‐2012 for CD; 1995‐2000 and 2007‐2012 for UC) were identified in the ENEIDA Registry. Surgery‐free survival curves were compared between cohorts. Results A total of 7,370 CD patients (2,022 in Cohort 1 and 5,348 in Cohort 2) and 8,069 UC patients (2,938 in Cohort 1 and 5,131 in Cohort 2) were included. Immunosuppressants were used significantly earlier and more frequently in both CD and UC post‐biological cohorts. The cumulative probability of surgery was lower in CD following anti‐TNF approval (16% and 11%, 22% and 16%, and 29% and 19%, at 1, 3 and 5 years, respectively p<0.0001), though not in UC (3% and 2%, 4% and 4%, and 6% and 5% at 1, 3 and 5 years, respectively; p=0.2). Ileal involvement, older age at diagnosis and active smoking in CD, and extensive disease in UC, were independent risk factors for surgery, whereas high‐volume IBD centres (in both CD and UC) and immunosuppressant use (in CD) were protective factors. Conclusions Anti‐TNF availability was associated with a reduction in early surgery for CD (driven mainly by earlier and more widespread immunosuppressant use) but not in U

Innovación en las enseñanzas universitarias: experiencias presentadas en las III Jornadas de Innovación Educativa de la ULL

En este libro se recoge un conjunto de experiencias de innovación educativa desarrolladas en la ULL en el curso 2011-12. Se abordan distintos ámbitos y ramas del conocimiento, y ocupan temáticas variadas que han sido desarrolladas con rigor, y con un claro potencial para su extrapolación a efectos de la mejora educativa en el ámbito universitario. Esta publicación constituye una primera edición de una serie que irá recogiendo las experiencias de innovación educativa de la ULL. Este es un paso relevante para su impulso en nuestra institución, como lo es el de su vinculación con la investigación educativa, para potenciar su publicación en las revistas científicas en este ámbito cada vez más pujante y relevante para las universidades. Sobre todo representan el deseo y el compromiso del profesorado de la ULL para la mejora del proceso educativo mediante la investigación, la evaluación y la reflexión compartida de nuestras prácticas y planteamientos docentes

Cheeger sets for rotationally symmetric planar convex bodies

In this note we obtain some properties of the Cheeger set CΩ associated to a k-rotationally symmetric planar convex body Ω. More precisely, we prove that CΩ is also k-rotationally symmetric and that the boundary of CΩ touches all the edges of Ω.Ministerio de Ciencia, Innovación y Universidades MTM2017-84851-C2-1-PJunta de Andalucía FQM-32