La propiedad de Radon-Nikodym en espacios de Banach duales

In this note we refine some classical characterizations of the Radon-Nikodým property (briefly RNP) for dual Banach spaces. We prove that the dual space $X^\ast$, of a given Banach space (X,\parallel\mbox{ }\parallel), has the RNP if, and only if, for every probability space ($\Omega,\Sigma,\mu)$ and for every $\mu$-Bochner measurable function $f :\Omega\rightarrow X$ there exists a $\mu$-Bochner measurable function $g : \Omega\rightarrow X^\ast$ such that $\parallel f(\omega)\parallel =$ for every $\omega$ in $\Omega$. In the process we point out that spaces of $X$-valued Bochner integrable functions have properties similar to those of spaces of scalar integrable functions if, and only if, the RNP holds inthe dual $X^\ast$ of the range Banach space. We also show what is requiered for a Banach space not containing $\ell^1$ to have a dual with the RNP

Domination by second countable spaces and Lindelöf Σ-property

AbstractGiven a space M, a family of sets A of a space X is ordered by M if A={AK:K is a compact subset of M} and K⊂L implies AK⊂AL. We study the class M of spaces which have compact covers ordered by a second countable space. We prove that a space Cp(X) belongs to M if and only if it is a Lindelöf Σ-space. Under MA(ω1), if X is compact and (X×X)\Δ has a compact cover ordered by a Polish space then X is metrizable; here Δ={(x,x):x∈X} is the diagonal of the space X. Besides, if X is a compact space of countable tightness and X2\Δ belongs to M then X is metrizable in ZFC.We also consider the class M⁎ of spaces X which have a compact cover F ordered by a second countable space with the additional property that, for every compact set P⊂X there exists F∈F with P⊂F. It is a ZFC result that if X is a compact space and (X×X)\Δ belongs to M⁎ then X is metrizable. We also establish that, under CH, if X is compact and Cp(X) belongs to M⁎ then X is countable

Measurable selectors and set-valued Pettis integral in non-separable Banach spaces

AbstractKuratowski and Ryll-Nardzewski's theorem about the existence of measurable selectors for multi-functions is one of the keystones for the study of set-valued integration; one of the drawbacks of this result is that separability is always required for the range space. In this paper we study Pettis integrability for multi-functions and we obtain a Kuratowski and Ryll-Nardzewski's type selection theorem without the requirement of separability for the range space. Being more precise, we show that any Pettis integrable multi-function F:Ω→cwk(X) defined in a complete finite measure space (Ω,Σ,μ) with values in the family cwk(X) of all non-empty convex weakly compact subsets of a general (non-necessarily separable) Banach space X always admits Pettis integrable selectors and that, moreover, for each A∈Σ the Pettis integral ∫AFdμ coincides with the closure of the set of integrals over A of all Pettis integrable selectors of F. As a consequence we prove that if X is reflexive then every scalarly measurable multi-function F:Ω→cwk(X) admits scalarly measurable selectors; the latter is also proved when (X∗,w∗) is angelic and has density character at most ω1. In each of these two situations the Pettis integrability of a multi-function F:Ω→cwk(X) is equivalent to the uniform integrability of the family {supx∗(F(⋅)):x∗∈BX∗}⊂RΩ. Results about norm-Borel measurable selectors for multi-functions satisfying stronger measurability properties but without the classical requirement of the range Banach space being separable are also obtained

D6-branes and torsion

The D6-brane spectrum of type IIA vacua based on twisted tori and RR background fluxes is analyzed. In particular, we compute the torsion factors of the (co)homology groups H_n and describe the effect that they have on D6-brane physics. For instance, the fact that H_3 contains Z_N subgroups explains why RR tadpole conditions are affected by geometric fluxes. In addition, the presence of torsional (co)homology shows why some D6-brane moduli are lifted, and it suggests how the D-brane discretum appears in type IIA flux compactifications. Finally, we give a clear, geometrical understanding of the Freed-Witten anomaly in the present type IIA setup, and discuss its consequences for the construction of semi-realistic flux vacua.Comment: 35 pages, 1 figure. One reference adde

Heterotic compactifications and nearly-Kahler manifolds

We propose that under certain conditions heterotic string compactifications on half-flat and nearly-Kahler manifolds are equivalent. Based on this correspondence we argue that the moduli space of the nearly-Kahler manifolds under discussion consists only of the Kahler deformations moduli space and there is no correspondent for the complex structure deformations.Comment: 5 pages, references added, typos correcte

Holographic dual of the Standard Model on the throat

We apply recent techniques to construct geometries, based on local Calabi-Yau manifolds, leading to warped throats with 3-form fluxes in string theory, with interesting structure at their bottom. We provide their holographic dual description in terms of RG flows for gauge theories with almost conformal duality cascades and infrared confinement. We describe a model of a throat with D-branes at its bottom, realizing a 3-family Standard Model like chiral sector. We provide the explicit holographic dual gauge theory RG flow, and describe the appearance of the SM degrees of freedom after confinement. As a second application, we describe throats within throats, namely warped throats with discontinuous warp factor in different regions of the radial coordinate, and discuss possible model building applications.Comment: 46 pages, 21 figures, reference adde

Fossil biogeography: a new model to infer dispersal, extinction and sampling from palaeontological data.

Methods in historical biogeography have revolutionized our ability to infer the evolution of ancestral geographical ranges from phylogenies of extant taxa, the rates of dispersals, and biotic connectivity among areas. However, extant taxa are likely to provide limited and potentially biased information about past biogeographic processes, due to extinction, asymmetrical dispersals and variable connectivity among areas. Fossil data hold considerable information about past distribution of lineages, but suffer from largely incomplete sampling. Here we present a new dispersal-extinction-sampling (DES) model, which estimates biogeographic parameters using fossil occurrences instead of phylogenetic trees. The model estimates dispersal and extinction rates while explicitly accounting for the incompleteness of the fossil record. Rates can vary between areas and through time, thus providing the opportunity to assess complex scenarios of biogeographic evolution. We implement the DES model in a Bayesian framework and demonstrate through simulations that it can accurately infer all the relevant parameters. We demonstrate the use of our model by analysing the Cenozoic fossil record of land plants and inferring dispersal and extinction rates across Eurasia and North America. Our results show that biogeographic range evolution is not a time-homogeneous process, as assumed in most phylogenetic analyses, but varies through time and between areas. In our empirical assessment, this is shown by the striking predominance of plant dispersals from Eurasia into North America during the Eocene climatic cooling, followed by a shift in the opposite direction, and finally, a balance in biotic interchange since the middle Miocene. We conclude by discussing the potential of fossil-based analyses to test biogeographic hypotheses and improve phylogenetic methods in historical biogeography

An Alternative Interpretation for the Moduli Fields of the Cosmology Associated to Type IIB Supergravity with Fluxes

We start with a particular cosmological model derived from type IIB supergravity theory with fluxes, where usually the dilaton is interpreted as a Quintessence field. Instead of that, in this letter we interpret the dilaton as the dark matter of the universe. With this alternative interpretation we find that in this supergravity model gives a similar evolution and structure formation of the universe compared with the $\Lambda$CDM model in the linear regime of fluctuations of the structure formation. Some free parameters of the theory are fixed using the present cosmological observations. In the non-linear regimen there are some differences between the type IIB supergravity theory with the traditional CDM paradigm. The supergravity theory predicts the formation of galaxies earlier than the CDM and there is no density cusp in the center of galaxies. These differences can distinguish both models and can give a distinctive feature to the phenomenology of the cosmology coming from superstring theory with fluxes.Comment: 7 pages, 5 figures, references added, minor modifications, typos corrected. Version accepted for publication in IJMP

Radon-Nikodým Theorems for Multimeasures in Non-Separable Spaces

We prove two Radon-Nikodým theorems for multimeasures using setvalued Pettis integrable derivatives. The first one works for dominated strong multimeasures taking convex compact values in a locally convex space. The second one works for strong multimeasures taking bounded convex closed values in a Banach space with the RNP (and for Bochner integral of the Radon-Nikodým derivative as well). The main advantage of our results is the absence of any separabilityС использованием многозначного интеграла Петтиса доказаны две теоремы типа теоремы Радона-Никодима для многозначных мер. Первая из них касается мажорируемых мер, значения которых - выпуклые компактные под- множества локально выпуклого пространства. Вторая касается мер, принимающих ограниченные выпуклые замкнутые значения в банаховом пространстве со свойством Радона-Никодима (а также интеграла Бохнера соответствующей производной Радона-Никодима). Главное отличие от предыдущих работ - отсутствие условия сепарабельности рассматриваемых пространств

First record of the mangrove palm Nypa from the northeastern Ebro Basin, Spain : with taphonomic criteria to evaluate the drifting duration

Fossil fruits pertaining to the mangrove palm genus Nypa Steck, (Arecaceae, Arecales) were collected from a new plant-bearing assemblage in the Arguis Formation (Fm.), northeastern Ebro Basin (Arguis, Huesca Province, Spain). This formation is Bartonian to early Priabonian in age and comprises pro-delta and carbonate platform deposits. The new assemblage consists of nine specimens of fossil Nypa fruits and one monocotyledon leaf fragment. Over half of these fossil fruits are nearly-complete (i.e. with preserved mesocarps) while the other represent endocarps. From the point of view of morphology and size they resemble other European records of this genus. The type of remain preserved (fruits or endocarps), presence of abrasion, Teredo borings and sedimentary facies provide criteria to infer contrasting lengths of transport (drifting). However, they indicate in all cases that these fossil fruits were afloat in seawater for a considerable time. The discovery of Nypa fruits suggests a tropical-subtropical climate in the area, as well as the presence of a coastal environment and littoral forests during deposition. This interpretation corroborates previous findings from the nearby Eocene outcrops of the Catalan Central Depression (Eastern Pyrenees range)