Glivenko’s theorem says that classical provability of a propositional formula entails intuitionistic provability of the double negation of that formula. This stood right at the beginning of the success story of negative translations, indeed mainly designed for converting classically derivable formulae into intuitionistically derivable ones. We now generalise this approach: simultaneously from double negation to an arbitrary nucleus; from provability in a calculus to an inductively generated abstract consequence relation; and from propositional logic to any set of objects whatsoever. In particular, we give sharp criteria for the generalisation of classical logic to be a conservative extension of the one of intuitionistic logic with double negation.

Alongside the analogy between maximal ideals and complete theories, the Jacobson radical carries over from ideals of commutative rings to theories of propositional calculi. This prompts a variant of Lindenbaum’s Lemma that relates classical validity and intuitionistic provability, and the syntactical counterpart of which is Glivenko’s Theorem. The Jacobson radical in fact turns out to coincide with the classical deductive closure. As a by-product we obtain a possible interpretation in logic of the axioms-as-rules conservation criterion for a multi-conclusion Scott-style entailment relation over a single-conclusion one.

Fosamine ammonium (Krenite®) is a foliar herbicide that primarily targets woody plant species; however, formal evaluations of its efficacy and potential for non-target impacts are scarce in the literature. The few tests of fosamine ammonium that exist focus primarily on its use in open environments, and the value of fosamine ammonium in controlling invasive understory shrubs is unclear. Here, we test the impact of fosamine ammonium on invasive common buckthorn (Rhamnus cathartica L.) and co-occurring herbaceous plants across six forest sites in Minnesota, USA. Rhamnus cathartica treated with fosamine ammonium had a 95% mortality rate, indicating high efficacy of fosamine ammonium for use against R. cathartica. Non-target impacts varied between forbs and graminoids such that forb cover was reduced by up to 85%, depending on site, whereas graminoid cover was sparse and impacts of fosamine ammonium on graminoids were unclear. These results indicate that while fosamine ammonium can provide effective control of R. cathartica and other understory shrubs, there is potential for significant non-target impacts following its use. We therefore suggest that land managers carefully consider the timing, rate, and application method of fosamine ammonium to achieve desired target and non-target impacts.

Completeness and other forms of Zorn’s Lemma are sometimes invoked for semantic proofs of conservation in relatively elementary mathematical contexts in which the corresponding syntactical conservation would suffice. We now show how a fairly general syntactical conservation theorem that covers plenty of the semantic approaches follows from an utmost versatile criterion for conservation given by Scott in 1974.

To this end we work with multi-conclusion entailment relations as extending single-conclusion entailment relations. In a nutshell, the additional axioms with disjunctions in positive position can be eliminated by reducing them to the corresponding disjunction elimination rules, which in turn prove admissible in all known mathematical instances. In deduction terms this means to fold up branchings of proof trees by way of properties of the relevant mathematical structures.

Applications include the syntactical counterparts of the theorems or lemmas known under the names of Artin–Schreier, Krull–Lindenbaum, and Szpilrajn. Related work has been done before on individual instances, e.g., in locale theory, dynamical algebra, formal topology and proof analysis.

Borderline personality disorder is associated with deficits in personality functioning and mentalisation. In a randomised controlled trial 104 people with borderline personality disorder received either transference-focused psychotherapy (TFP) or treatment by experienced community therapists. Among other outcome variables, mentalisation was assessed by means of the Reflective Functioning Scale (RF Scale). Findings revealed only significant improvements in reflective function in the TFP group within 1 year of treatment. The between-group effect was of medium size (d = 0.45). Improvements in reflective function were significantly correlated with improvements in personality organisation.

We try to recast in modern terms a choice principle conceived by Beppo Levi, who called it the Approximation Principle (AP). Up to now, there was almost no discussion about Levi’s contribution, due to the quite obscure formulation of AP the author has chosen. After briefly reviewing the historical and philosophical surroundings of Levi’s proposal, we undertake our own attempt at interpreting AP. The idea underlying the principle, as well as the supposed faithfulness of our version to Levi’s original intention, are then discussed. Finally, an application of AP to a property of metric spaces is presented, with the aim of showing how AP may work in contexts where other forms of choice are commonly at use.

The aim of the paper is to present the time profile of cosmic radiation exposure obtained by the radiation risks radiometer-dosimeter (R3DR) during the ESA exposition facility for EXPOSE-R mission (EXPOSE-R) in the EXPOSE-R facility outside the Russian Zvezda module of the International Space Station (ISS). Another aim is to make the obtained results available to other EXPOSE-R teams for use in their data analysis. R3DR is a low mass and small dimensions automated device, which measures solar radiation in four channels and in addition cosmic ionizing radiation. The main results of cosmic ionizing radiation measurements are: three different radiation sources were detected and quantified: galactic cosmic rays (GCR), energetic protons from the inner radiation belt (IRB) in the region of the South Atlantic anomaly and energetic electrons from the outer radiation belt (ORB). The highest daily averaged absorbed dose rate of 506 μGy day−1 came from IRB protons; GCR delivered much smaller daily absorbed dose rates of 81.4 μGy day−1 on average, and ORB source delivered on average a dose rate of 89 μGy day−1. The IRB and ORB daily averaged absorbed dose rates were higher than those observed during the ESA exposition facility for EXPOSE-E mission (EXPOSE-E), whereas the GCR rate was smaller than that measured during the EXPOSE-E mission. The reason for this difference is much less surrounding constructions shielding of the R3DR instrument in comparison with the R3DE instrument.

We give a constructive proof showing that every finitely generated polynomial ideal has a Gröbner basis, provided the ring of coefficients is Noetherian in the sense of Richman and Seidenberg. That is, we give a constructive termination proof for a variant of the well-known algorithm for computing the Gröbner basis. In combination with a purely order-theoretic result we have proved in a separate paper, this yields a unified constructive proof of the Hilbert basis theorem for all Noether classes: if a ring belongs to a Noether class, then so does the polynomial ring. Our proof can be seen as a constructive reworking of one of the classical proofs, in the spirit of the partial realisation of Hilbert's programme in algebra put forward by Coquand and Lombardi. The rings under consideration need not be commutative, but are assumed to be coherent and strongly discrete: that is, they admit a membership test for every finitely generated ideal. As a complement to the proof, we provide a prime decomposition for commutative rings possessing the finite-depth property.

Roll-to-roll deposition techniques for the fabrication of chalcopyrite solar cells are of major interest and are a promising alternative to state of the art vacuum processes. However, for roll-to-roll processes the preparation of precursor materials like nanoparticle inks is a crucial point. In this work a study on the preparation technique of copper-indium intermetallic nanoparticles was conducted. The preparation of the nanoparticles is based on the chemical reduction of copper and indium cations with sodium borohydride. Different parameters are discussed regarding their influence on (1) size and shape of the nanoparticles, (2) Cu/In ratio within the synthesised nanoparticles and (3) yield of the synthesis. Results show a strong dependency of the Cu/In ratio of the nanoparticles and the yield of the synthesis on the synthesis parameters. The influence of different parameters like (a) the ratio of metal cations to BH4- anions, (b) the Cu2+/In3+ cation ratio within the precursor solution and (c) the dropping rate of the copper-indium precursor solution are discussed. The Cu/In ratio within the nanoparticles can mainly be controlled by the Cu2+/In3+ cation ratio and the dropping rate of the copper-indium precursor solution. The yield of the synthesis shows saturation behaviour depending on the ratio of metal cations to BH4- anions. Shape and size of the nanoparticles are independent of the varied parameters.

Noether classes of posets arise in a natural way from the constructively meaningful variants of the notion of a Noetherian ring. Using an axiomatic characterisation of a Noether class, we prove that if a poset belongs to a Noether class, then so does the poset of the finite descending chains. When applied to the poset of finitely generated ideals of a ring, this helps towards a unified constructive proof of the Hilbert basis theorem for all Noether classes.

We deal with a restricted form WC-N′ of the weak continuity principle, a version BT′ of Baire's theorem, and a boundedness principle BD-N. We show, in the spirit of constructive reverse mathematics, that WC-N′, BT′ + ¬LPO and BD-N + ¬LPO are equivalent in a constructive system, where LPO is the limited principle of omniscience.

We define what it means for a formal topology to be spatial, and investigate properties related to spatiality both in general and in examples.

The existence and uniqueness of a maximum point for a continuous real–valued function on a metric space are investigated constructively. In particular, it is shown, in the spirit of reverse mathematics, that a natural unique existence theorem is equivalent to the fan theorem.

Nutrigenomics is the study of how constituents of the diet interact with genes, and their products, to alter phenotype and, conversely, how genes and their products metabolise these constituents into nutrients, antinutrients, and bioactive compounds. Results from molecular and genetic epidemiological studies indicate that dietary unbalance can alter gene–nutrient interactions in ways that increase the risk of developing chronic disease. The interplay of human genetic variation and environmental factors will make identifying causative genes and nutrients a formidable, but not intractable, challenge. We provide specific recommendations for how to best meet this challenge and discuss the need for new methodologies and the use of comprehensive analyses of nutrient–genotype interactions involving large and diverse populations. The objective of the present paper is to stimulate discourse and collaboration among nutrigenomic researchers and stakeholders, a process that will lead to an increase in global health and wellness by reducing health disparities in developed and developing countries.