Curvature Coupling and Accelerated Expansion of the Universe

A new exactly solvable model for the evolution of relativistic kinetic system interacting with an internal stochastic reservoir under the influence of a gravitational background expansion is established. This model of self-interaction is based on the relativistic kinetic equation for the distribution function defined in the extended phase space. The supplementary degree of freedom is described by the scalar stochastic variable (Langevin source), which is considered to be the constructive element of the effective one-particle force. The expansion of the Universe is shown to be accelerated for the suitable choice of the non-minimal self-interaction force.Comment: 12 pages, no figure

Ideal webs, moduli spaces of local systems, and 3d Calabi-Yau categories

A decorated surface S is an oriented surface with punctures and a finite set of marked points on the boundary, such that each boundary component has a marked point. We introduce ideal bipartite graphs on S. Each of them is related to a group G of type A, and gives rise to cluster coordinate systems on certain spaces of G-local systems on S. These coordinate systems generalize the ones assigned to ideal triangulations of S. A bipartite graph on S gives rise to a quiver with a canonical potential. The latter determines a triangulated 3d CY category with a cluster collection of spherical objects. Given an ideal bipartite graph on S, we define an extension of the mapping class group of S which acts by symmetries of the category. There is a family of open CY 3-folds over the universal Hitchin base, whose intermediate Jacobians describe the Hitchin system. We conjecture that the 3d CY category with cluster collection is equivalent to a full subcategory of the Fukaya category of a generic threefold of the family, equipped with a cluster collection of special Lagrangian spheres. For SL(2) a substantial part of the story is already known thanks to Bridgeland, Keller, Labardini-Fragoso, Nagao, Smith, and others. We hope that ideal bipartite graphs provide special examples of the Gaiotto-Moore-Neitzke spectral networks.Comment: 60 page

Carpology and phermatology of Gomortega (Gomortegaceae): Systematic and evolutionary implications

Carpología y morfología de la cubierta de la semilla de Gomortega (Gomortegaceae): implicaciones sistemáticas y evolutivas. En un esfuerzo de clarificar la posición sistemática del género Gomortega, en el presente trabajo se estudia la morfología y anatomía de los frutos y semillas de Gomortega keule (Mol.) Baill., perteneciente al género monotípico anteriormente citado, de la monogenérica familia Gomortegaceae Reiche. Los frutos son drupas cenocárpicas carnosas, que ofrecen la apariencia de frutos sincárpicos bi- o triloculares, o más raramente uniloculares, debido a la concrescencia lateral de los 2æ6 carpelos que lo componen y que se encuentran espiraladamente dispuestos. Las semillas son aplanadas, desprovistas de arilo, con albúmen abundante y embrión pequeño, originadas a partir de primordios seminales bitégmicos, anátropos y crasinucelados. La cubierta de la semilla es endotestal-endotégmica; la endotesta (sólo la base testal se preservó en la espermodermis madura) es de tipo traqueotestal, presentando la peculiaridad de poseer mumerosas proyecciones anulares o espiraladas que penetran en las cavidades celulares. Las evidencias encontradas, fundamentalmente en base a la morfología y anatomía de las semillas, apoyan la relación filogenética existente entre Gomortega, con frutos ínferos aberrates, y Monimiaceae s.l. o, más correctamente, con el grupo de las familias Monimiaceae s. str., Amborellaceae, Hortoniaceae, Siparubaceae y Atherospermataceae, que comparten un tipo similar de cubierta seminal endotestal y traqueotestal, semillas albuminadas, con embrión pequeño, similar número de cromosomas, morfologia de los plastidios de los elementos cribosos del floema, morfología polínica, anatomía del xilema, los apéndices de los estaminodios y la dehiscencia valvar de las anteras. Con la aportación de una mayor cantidad de datos sobre la morfología y anatomía de los frutos y semillas de Atherospermataceae, las interrelaciones existentes entre Gomortega y Atherospermataceae podrían ser definidas de manera más precis

Electrodynamics of a Cosmic Dark Fluid

Cosmic Dark Fluid is considered as a non-stationary medium, in which electromagnetic waves propagate, and magneto-electric field structures emerge and evolve. A medium - type representation of the Dark Fluid allows us to involve into analysis the concepts and mathematical formalism elaborated in the framework of classical covariant electrodynamics of continua, and to distinguish dark analogs of well-known medium-effects, such as optical activity, pyro-electricity, piezo-magnetism, electro- and magneto-striction and dynamo-optical activity. The Dark Fluid is assumed to be formed by a duet of a Dark Matter (a pseudoscalar axionic constituent) and Dark Energy (a scalar element); respectively, we distinguish electrodynamic effects induced by these two constituents of the Dark Fluid. The review contains discussions of ten models, which describe electrodynamic effects induced by Dark Matter and/or Dark Energy. The models are accompanied by examples of exact solutions to the master equations, correspondingly extended; applications are considered for cosmology and space-times with spherical and pp-wave symmetries. In these applications we focused the attention on three main electromagnetic phenomena induced by the Dark Fluid: first, emergence of Longitudinal Magneto-Electric Clusters; second, generation of anomalous electromagnetic responses; third, formation of Dark Epochs in the Universe history.Comment: 39 pages, 0 figures, replaced by the version published in MDPI Journal "Symmetry" (Special Issue: Symmetry: Feature Papers 2016); typos correcte

The Catholic Core of a Celebrated Composition

Despite an undeviating opinion on the subject, his greatest work The Lord of the Rings, is replete with free-floating allegory to Christian characters. Characters and situations that suggest Biblical situations, both narratively and on the level of spirituality and ethics. Each character within biblical text correlates with one or more characters in Tolkien’s work, thus free floating. Tolkien is a devoutly religious author who processes the world, including his own fantasies, through the lens of his faith. While Tolkien draws from different elements of theology in several different ways—such as interchanging his characters to represent various aspects of key Biblical figures—it is clear that Tolkien assigned a moral, free-flowing, yet religious allegorical backbone to his work

The Melianthaceous seed and its Rhamnaceous affinity

. La semilla de Melianthaceae y su afinidad con Rhamnaceae. En el presente trabajo, se ha estudiado la anatomia y morfología de la semilla de Bersama (Bersamataceae) y Melianthus (Melianthaceae) con el objeto de clarificar su posición sistemática. La exotesta de Bersama y Melianthus, con una empalizada de células de Malpighi bien diferenciada, abundante endosperma y embrión recto y escasamente diferenciado, muestra ciertas afinidades con la exotesta albuminosa de las semillas de Rhamnaceae y Elaeagnaceae. Utilizando también datos carpológicos, florales y morfológico-vegetativos adicionales, se sugiere que Bersamataceae, junto con Melianthaceae y Rhamnaceae/Elaeagnaceae constituyen una ramificación lateral relíctica de un ancestro roside exo-mesotestado. La morfología y anatomía de las semillas evidencian la anómala y tradicional inclusión de Bersama y Melianthus en el orden Sapindales, cuyas semillas presentan diferente pautas en la estructura de la espermodermis y en la vascularización de la misma. La anatomía de la semilla, no confirma ninguna de las relaciones que se han sugerido, alternativamente, con Lardizabalaceae exo-mesotestales ni con Malvales exotegmicos. Por otra parte, consideramos insostenibles las afinidades con Celastrales exotégmicos, que han sido consideradas como una posible conexión entre Rosales arcaicos exo-mesotestados y Rhamnales/Elaeagnales exotestados. Se sugiere que ambas familias, Bersamataceae y Melianthaceae, constituyen el orden Melianthales que, junto con Rhamnaceae (Rhamnales, s. e.) y Elaeagnaceae (Elaeagnales) representan remanentes avanzados de un phyllum profusamente ramificado, cuyas relaciones se remontan directamente hacia Fabales, pasando por Rosales, Sapindales, Icacinales y Celastrales

Wreath Products in the Unit Group of Modular Group Algebras of 2-groups of Maximal Class

We study the unit group of the modular group algebra KG, where G is a 2-group of maximal class. We prove that the unit group of KG possesses a section isomorphic to the wreath product of a group of order two with the commutator subgroup of the group G.Comment: 12 pages, LaTe