Strongly extreme points and approximation properties

We show that if $x$ is a strongly extreme point of a bounded closed convex subset of a Banach space and the identity has a geometrically and topologically good enough local approximation at $x$, then $x$ is already a denting point. It turns out that such an approximation of the identity exists at any strongly extreme point of the unit ball of a Banach space with the unconditional compact approximation property. We also prove that every Banach space with a Schauder basis can be equivalently renormed to satisfy the sufficient conditions mentioned. In contrast to the above results we also construct a non-symmetric norm on $c_0$ for which all points on the unit sphere are strongly extreme, but none of these points are denting.Comment: 14 page

On the minimal number of matrices which form a locally hypercyclic, non-hypercyclic tuple

In this paper we extend the notion of a locally hypercyclic operator to that of a locally hypercyclic tuple of operators. We then show that the class of hypercyclic tuples of operators forms a proper subclass to that of locally hypercyclic tuples of operators. What is rather remarkable is that in every finite dimensional vector space over $\mathbb{R}$ or $\mathbb{C}$, a pair of commuting matrices exists which forms a locally hypercyclic, non-hypercyclic tuple. This comes in direct contrast to the case of hypercyclic tuples where the minimal number of matrices required for hypercyclicity is related to the dimension of the vector space. In this direction we prove that the minimal number of diagonal matrices required to form a hypercyclic tuple on $\mathbb{R}^n$ is $n+1$, thus complementing a recent result due to Feldman.Comment: 15 pages, title changed, section for infinite dimensional spaces adde

Epuraea imperialis (Reitter, 1877). New invasive species of Nitidulidae (Coleoptera) in Europe, with a checklist of sap beetles introduced to Europe and Mediterranean areas

Australian species Epuraea imperialis (Reitter, 1877), previously introduced to New Zealand, is recorded as a new invasive species from the Canary Islands, Continental Spain, Portugal, France, Belgium, and Italy. It is redescribed and figured, and its taxonomic position in the genus Epuraea Erichson, 1843 is discussed. A tentative checklist of sap beetles introduced to Europe and the Mediterranean areas is finally included

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

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

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

Eco-Physiological Screening of Different Tomato Genotypes in Response to High Temperatures: A Combined Field-to-Laboratory Approach

High temperatures represent a limitation for growth and development of many crop species. Several studies have demonstrated that the yield reduction of tomato under high temperatures and drought is mainly due to a photosynthetic decline. In this paper, a set of 15 tomato genotypes were screened for tolerance to elevated temperatures by cultivating plants under plastic walk-in tunnels. To assess the potential tolerance of tomato genotypes to high temperatures, measurements of chlorophyll fluorescence, pigments content and leaf functional traits have been carried out together with the evaluation of the final yields. Based on the greenhouse trials, a group of eight putative heat-sensitive and heat-tolerant tomato genotypes was selected for laboratory experiments aimed at investigating the effects of short-term high temperatures treatments in controlled conditions. The chlorophyll fluorescence induction kinetics were recorded on detached leaves treated for 60 min at 35 °C or at 45 °C. The last treatment significantly affected the photosystem II (PSII) photochemical efficiency (namely maximum PSII quantum efficiency, Fv/Fm, and quantum yield of PSII electron transport, ΦPSII) and the non-photochemical quenching (NPQ) in the majority of genotypes. The short-term heat shock treatments also led to significant differences in the shape of the slow Kautsky kinetics and its significant time points (chlorophyll fluorescence levels minimum O, peak P, semi-steady state S, maximum M, terminal steady state T) compared to the control, demonstrating heat shock-induced changes in PSII functionality. Genotypes potentially tolerant to high temperatures have been identified. Our findings support the idea that chlorophyll fluorescence parameters (i.e., ΦPSII or NPQ) and some leaf functional traits may be used as a tool to detect high temperatures-tolerant tomato cultivars