Two geometric constant for operators acting on a separable Banach space

Sin resume

Isotonies on ordered cones throught the concept of a decreasing scale

Using techniques based on decreasing scales, necessary and sufficient conditions are presented for the existence of a continuous and homogeneous of degree one real-valued function representing a (not necessarily complete) preorder defined on a cone of a real vector space. Applications to measure theory and expected utility are given as consequences

Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity

We investigate the future evolution of the dark energy universe in modified gravities including $F(R)$ gravity, string-inspired scalar-Gauss-Bonnet and modified Gauss-Bonnet ones, and ideal fluid with the inhomogeneous equation of state (EoS). Modified Friedmann-Robertson-Walker (FRW) dynamics for all these theories may be presented in universal form by using the effective ideal fluid with an inhomogeneous EoS without specifying its explicit form. We construct several examples of the modified gravity which produces accelerating cosmologies ending at the finite-time future singularity of all four known types by applying the reconstruction program. Some scenarios to resolve the finite-time future singularity are presented. Among these scenarios, the most natural one is related with additional modification of the gravitational action in the early universe. In addition, late-time cosmology in the non-minimal Maxwell-Einstein theory is considered. We investigate the forms of the non-minimal gravitational coupling which generates the finite-time future singularities and the general conditions for this coupling in order that the finite-time future singularities cannot emerge. Furthermore, it is shown that the non-minimal gravitational coupling can remove the finite-time future singularities or make the singularity stronger (or weaker) in modified gravity.Comment: 25 pages, no figure, title changed, accepted in JCA

Virtual Planetary Space Weather Service offered by the Europlant H2O2O Research Infrastructure

Under Horizon 2020, the Europlanet 2020 Research Infrastructure (EPN2020-RI) will include an entirely new Virtual Access Service, ?Planetary Space Weather Services? (PSWS) that will extend the concepts of space weather and space situational awareness to other planets in our Solar System and in particular to spacecraft that voyage through it. PSWS will make twelve new services accessible to the research community, space agencies, and industrial partners planning for space missions. These services will in particular be dedicated to the following key planetary environments: Mars (in support of the NASA MAVEN and European Space Agency (ESA) Mars Express and ExoMars missions), comets (building on the outstanding success of the ESA Rosetta mission), and outer planets (in preparation for the ESA JUpiter ICy moon Explorer mission), and one of these services will aim at predicting and detecting planetary events like meteor showers and impacts in the Solar System. This will give the European planetary science community new methods, interfaces, functionalities and/or plugins dedicated to planetary space weather as well as to space situational awareness in the tools and models available within the partner institutes. A variety of tools (in the form of web applications, standalone software, or numerical models in various degrees of implementation) are available for tracing propagation of planetary and/or solar events through the Solar System and modelling the response of the planetary environment (surfaces, atmospheres, ionospheres, and magnetospheres) to those events. But these tools were not originally designed for planetary event prediction and space weather applications. PSWS will provide the additional research and tailoring required to apply them for these purposes. PSWS will be to review, test, improve and adapt methods and tools available within the partner institutes in order to make prototype planetary event and space weather services operational in Europe at the end of 2017. To achieve its objectives PSWS will use a few tools and standards developed for the Astronomy Virtual Observatory (VO). This paper gives an overview of the project together with a few illustrations of prototype services based on VO standards and protocolsauthorsversionPeer reviewe

Models and data analysis tools for the Solar Orbiter mission

Context. The Solar Orbiter spacecraft will be equipped with a wide range of remote-sensing (RS) and in situ (IS) instruments to record novel and unprecedented measurements of the solar atmosphere and the inner heliosphere. To take full advantage of these new datasets, tools and techniques must be developed to ease multi-instrument and multi-spacecraft studies. In particular the currently inaccessible low solar corona below two solar radii can only be observed remotely. Furthermore techniques must be used to retrieve coronal plasma properties in time and in three dimensional (3D) space. Solar Orbiter will run complex observation campaigns that provide interesting opportunities to maximise the likelihood of linking IS data to their source region near the Sun. Several RS instruments can be directed to specific targets situated on the solar disk just days before data acquisition. To compare IS and RS, data we must improve our understanding of how heliospheric probes magnetically connect to the solar disk.Aims. The aim of the present paper is to briefly review how the current modelling of the Sun and its atmosphere can support Solar Orbiter science. We describe the results of a community-led effort by European Space Agency's Modelling and Data Analysis Working Group (MADAWG) to develop different models, tools, and techniques deemed necessary to test different theories for the physical processes that may occur in the solar plasma. The focus here is on the large scales and little is described with regards to kinetic processes. To exploit future IS and RS data fully, many techniques have been adapted to model the evolving 3D solar magneto-plasma from the solar interior to the solar wind. A particular focus in the paper is placed on techniques that can estimate how Solar Orbiter will connect magnetically through the complex coronal magnetic fields to various photospheric and coronal features in support of spacecraft operations and future scientific studies.Methods. Recent missions such as STEREO, provided great opportunities for RS, IS, and multi-spacecraft studies. We summarise the achievements and highlight the challenges faced during these investigations, many of which motivated the Solar Orbiter mission. We present the new tools and techniques developed by the MADAWG to support the science operations and the analysis of the data from the many instruments on Solar Orbiter.Results. This article reviews current modelling and tool developments that ease the comparison of model results with RS and IS data made available by current and upcoming missions. It also describes the modelling strategy to support the science operations and subsequent exploitation of Solar Orbiter data in order to maximise the scientific output of the mission.Conclusions. The on-going community effort presented in this paper has provided new models and tools necessary to support mission operations as well as the science exploitation of the Solar Orbiter data. The tools and techniques will no doubt evolve significantly as we refine our procedure and methodology during the first year of operations of this highly promising mission.Peer reviewe

On topological spaces whose topology is induced by a binary relation

We study the problem of characterizing which topologies on a nonemptybset are generated by a binary relation by means of its lower and upper contour sets. In this direction we consider different classical categories of topological spaces whose topology is defined by at least one binary relation. Given a topology defined by some binary relation on a set, we also analyze if the binary relation could belong to some particular category. We furnish some examples of topological spaces whose topology cannot be induced by any binary relation. We analyze some of these items in the context of pointfree topology and extend these questions to the study of bitopological spaces.Keywords: Binary relations, topological and bitopological spaces, ordered structuresQuaestiones Mathematicae 36(2013), 47–65

Further remarks on totally ordered representable subsets of Euclidean space

We introduce the property of ≲ -norm-boundedness on totally ordered subsets of Euclidean spaces. We show that when a closed subset X of the Euclidean space ℝ, endowed with a continuous total order ≲, is ≲ -norm-bounded, the order topology and the induced Euclidean topology must coincide on X. This generalizes a recent result by Beardon, proved on connected totally ordered subsets of Euclidean space, because on totally ordered closed subsets of ℝ connectedness is a particular case of ≲ -norm-boundedness. We also analyze necessary and sufficient conditions for the coincidence of both topologies, and discuss some extension to the infinite-dimensional context

Utility functions on locally connected spaces

We investigate the role of local connectedness in utility theory and prove that any continuous total preorder on a locally connected separable space is continuously representable. This is a new simple criterion for the representability of continuous preferences, and is not a consequence of the standard theorems in utility theory that use conditions such as connectedness and separability, second countability, or path-connectedness. Finally we give applications to problems involving the existence of value functions in population ethics and to the problem of proving the existence of continuous utility functions in general equilibrium models with land as one of the commodities. (C) 2003 Elsevier B.V. All rights reserved