Ranges of operators and Derivatives

[EN] We show a unified method of proving the existence of C(1)-Frechet smooth and Lipschitz mappings which are surjective or whose range of the derivative contains the whole dual unit ball. As an application, under Martin's Maximum axiom, we obtain a complete result for those spaces with density character omega(1). (C) 2009 Elsevier Inc. All rights reserved.Research supported by Project MTM2008-05396 and the Universidad Politecnica de Valencia. Research supported by the grants A100190502, IAA 100190801 and Inst. Research Plan AV0Z10190503. Research supported by Project MTM2008-03211 and the Universidad Politecnica de Valencia.Guirao Sánchez, AJ.; Hájek, P.; Montesinos Santalucia, V. (2010). Ranges of operators and Derivatives. Journal of Mathematical Analysis and Applications. 367(1):29-33. https://doi.org/10.1016/j.jmaa.2009.12.010S2933367

Weakly Compact Generating and Shrinking Markusevic Bases

2000 Mathematics Subject Classification: 46B30, 46B03.It is shown that most of the well known classes of nonseparable Banach spaces related to the weakly compact generating can be characterized by elementary properties of the closure of the coefficient space of Markusevic bases for such spaces. In some cases, such property is then shared by all Markusevic bases in the space

Minimax Estimation of Nonregular Parameters and Discontinuity in Minimax Risk

When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic minimax estimation theory for a parameter that is a nondifferentiable transform of a regular parameter, where the nondifferentiable transform is a composite map of a continuous piecewise linear map with a single kink point and a translation-scale equivariant map. The contribution of this paper is two fold. First, this paper extends the local asymptotic minimax theory to nondifferentiable transforms that are a composite map of a Lipschitz continuous map having a finite set of nondifferentiability points and a translation-scale equivariant map. Second, this paper investigates the discontinuity of the local asymptotic minimax risk in the true probability and shows that the proposed estimator remains to be optimal even when the risk is locally robustified not only over the scores at the true probability, but also over the true probability itself. However, the local robustification does not resolve the issue of discontinuity in the local asymptotic minimax risk

Ozone treatment of stored potato tubers

During storage, potato tubers are susceptible to different pathogen, which can attack the skin and flesh of the tubers. The most serious damage can be caused by rot inducing bacteria and fungi. A possible way to prevent microbial damage may be the use of ozone in the air ventilated through the stored tubers. However, the tubers can undergo qualitative changes, e.g. dehydration and loss of starch content. This article presents the results of a five-month experiment in which ozone concentration of 5 mg m-3 was periodically introduced in some of the stored potato tubers of the cultivar ‘Dali’. All potato tubers were stored in closed storage boxes with a metal frame and wood panels in the floor and walls (ground area 1.6×1.2 m, height 0.95 m) which were continuously aerated using the ambient air in a potato warehouse. There was 900 kg of tubers stored in the box. At the end of the experiment, the ozonated variant was compared with the control (not treated). The ozone-treated tubers had 2.95 times lower incidence of infection by rot and the number of microorganisms on healthy tubers was lower than the control. The ozone-treated tubers were less frequently dehydrated. The water loss was higher in control by 0.86 %. There was no significant difference in silver scurf manifestation or in the starch content between the two variants

Towards a Proof Theory of G\"odel Modal Logics

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish completeness and complexity results for these fragments

Detection and prevention of financial abuse against elders

This article is made available through the Brunel Open Access Publishing Fund. Copyright @ The Authors. This article is published under the Creative Commons Attribution (CC BY 3.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/ by/3.0/legalcode.Purpose – This paper reports on banking and finance professionals' decision making in the context of elder financial abuse. The aim was to identify the case features that influence when abuse is identified and when action is taken. Design/methodology/approach – Banking and finance professionals (n=70) were shown 35 financial abuse case scenarios and were asked to judge how certain they were that the older person was being abused and the likelihood of taking action. Findings – Three case features significantly influenced certainty of financial abuse: the nature of the financial problem presented, the older person's level of mental capacity and who was in charge of the client's money. In cases where the older person was more confused and forgetful, there was increased suspicion that financial abuse was taking place. Finance professionals were less certain that financial abuse was occurring if the older person was in charge of his or her own finances. Originality/value – The research findings have been used to develop freely available online training resources to promote professionals' decision making capacity (www.elderfinancialabuse.co.uk). The resources have been advocated for use by Building Societies Association as well as CIFAS, the UK's Fraud Prevention Service.The research reported here was funded by the UK cross council New Dynamicsof Ageing Programme, ESRC Reference No. RES-352-25-0026, with Mary L.M. Gilhooly asPrincipal Investigator. Web-based training tools, developed from the research findings, weresubsequently funded by the ESRC follow-on fund ES/J001155/1 with Priscilla A. Harries asPrincipal Investigator

Interpretations of Presburger Arithmetic in Itself

Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N,+) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.Comment: Published in proceedings of LFCS 201

Quantum mechanics and elements of reality inferred from joint measurements

The Einstein-Podolsky-Rosen argument on quantum mechanics incompleteness is formulated in terms of elements of reality inferred from joint (as opposed to alternative) measurements, in two examples involving entangled states of three spin-1/2 particles. The same states allow us to obtain proofs of the incompatibility between quantum mechanics and elements of reality.Comment: LaTeX, 12 page