A Splitting Theorem for Scalar Curvature

We show that a Riemannian 3-manifold with nonnegative scalar curvature is flat if it contains an area-minimizing cylinder. This scalar-curvature analogue of the classical splitting theorem of J. Cheeger and D. Gromoll (1971) was conjectured by D. Fischer-Colbrie and R. Schoen (1980) and by M. Cai and G. Galloway (2000). © 2018 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, Inc.     

On the infinite-valued Łukasiewicz logic that preserves degrees of truth

Łukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a “truth-preserving” scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully adequate for it. Another presentation of the same deductive system can be obtained from a substructural Gentzen calculus. In this paper we use the framework of abstract algebraic logic to study a different deductive system which uses the aforementioned algebra under a scheme of “preservation of degrees of truth”. We characterize the resulting deductive system in a natural way by using the lattice filters of Wajsberg algebras, and also by using a structural Gentzen calculus, which is shown to be fully adequate for it. This logic is an interesting example for the general theory: it is selfextensional, non-protoalgebraic, and satisfies a “graded” deduction theorem. Moreover, the Gentzen system is algebraizable. The first deductive system mentioned turns out to be the extension of the second by the rule of Modus Ponens.While writing this paper, the authors were partially supported by grants MTM2004-03101 and TIN2004-07933-C03-02 of the Spanish Ministry of Education and Science, including FEDER funds of the European Union.     

Die kubischen Phasen Na16(ARb6)Sb7, Verbindungen mit den Anionen A = Rb−, Na−, Au−, I−

The Cubic Phases Na₁₆(ARb₆)Sb₇, Compounds with the Anions A = Rb^?, Na^?, Au^?, I^? The novel compounds Na₁₆(ARb₆)Sb₇ have been synthesized from the elements in sealed Nb ampoules at 873 K (A = Rb) and 823 K (A = I, Na, Au). They form brittle cuboctahedra (silver metallic; A = Rb) and irregular polyhedra (silver metallic lustre; A = Na, I; golden metallic lustre; A = Au). They rapidly decompose in moist air to gray products. Their crystal structures have been determined by single crystal X-ray crystallography (A = Rb: a = 1565.8(2) pm; A = I: a = 1563.3(2) pm; A = Na: a = 1562.6(2) pm; A = Au: a = 1560.7(2) pm). They crystallize cubically in the space group Fm3 m (no. 225) with Z = 4 formula units and are isotypic with Sc₁₁Ir₄. The compounds are ZINTL phases and their structures can be described as an eightfold defect variant of the Li₃Bi type of structure (cF128-8; a = 2a′(Li₃Bi)). The Sb atoms form a network of cuboctahedra, centered alternatingly by a SbNa₈ cube or a ARb₆ octahedron. Main structural features are the anions A^? within the Rb₆ octahedron. Supporting the existence of A^? are the isotypical compounds with the more common anion forming elements (A = Au, I), as well as electrostatic potential considerations together with calculations of the volume increments. The semiconducting properties (E_g = 0.33 eV) of Na₁₆(RbRb₆)Sb₇, as well as the diamagnetism χ_mol = ?508 × 10^?6 cm³ mol^?1, are in accordance with those to be expected from the Zintl concept.     

Alteration in the surface structure and properties of norbornene-ethylene copolymer films by direct-current discharge treatment

The effect of dc discharge on norbornene-ethylene copolymer films containing 30 and 60% norbornene was studied. It was found that plasma treatment leads to substantial changes in the surface properties of the copolymer, the enhancement of wettability, and an increase in the work of adhesion and surface energy, including its polar term. The change in the surface structure of the films was investigated by means of Fourier-transform IR spectroscopy. Transparent and colorless triplexes with a light transmission of 86–90% were prepared on the basis of the discharge-modified copolymer films and a cycloaliphatic epoxy resin.     

Cadmium sorption properties of poly(vinyl alcohol)/hydroxyapatite cryogels: I. kinetic and isotherm studies

A new adsorbent for removing heavy metal ions from wastewater, poly(vinyl alcohol)/hydroxyapatite(PVA/HAp) composite cryogel, has been investigated. The PVA/HAp cryogel was prepared through a clean process by using water and freeze-thawing. The PVA/HAp cryogel is provided with interconnected macropores varying from 0.1 um to several um and well dispersed and immobilized HAp in cryogel. Batch experiments of cadmium sorption were carried out to test the sorption ability of PVA/HAp cryogel. The isotherm and kinetics of cadmium sorption were studied by fitting the experimental results to isotherm and kinetics models. The Langmuir isotherm suitable for this system shows the maximum sorption capacity of 53.3 mg/g. For kinetics, the double-exponential model presents best fit compared with pseudo-first-order and pseudo-second-order models. The double-exponential model indicates a diffusion-controlled and a two-step mechanism.     

Four-Wave Mixing in Microwires to All-Optical Signal Processing in Mode-Division Multiplexing Systems

Abstract

Mode-division multiplexing requires all-optical signal processing techniques that are able to deal with a new coding dimension, the spatial mode. In this context, optical microwires emerge as a potential highly non-linear and multi-modal waveguide envisioning the development of all-optical signal processing devices to mode-division multiplexing systems based on the four-wave mixing process. The inter- and intramodal phase-matching conditions for the four-wave mixing process are mapped as a function of the microwire diameter and the wavelength of signals. Moreover, the efficiency of four-wave mixing considering a strong guiding regime is investigated in the multi-modal regime.     

SYNTHESE ET PROPRIETES DE 2-HYDRAZONOPHENYL-SELENOACETAMIDES

Abstract

The two steps synthesis of 2-hydrazonophenylselenoacetamides is described starting from sulfur analogs. Depending on the substitution of hydrazono and selenamide groups they allow the preparation of a 1,2,3-selenadiazolium salt, a 5-imino-Δ³-1,2,3-selenadiazoline, 3,6-dihydro-2H-1,3,4-selenadiazines and a 5-selenoxo-2,3,4,5-tetrahydro-1,2,4-triazin- 3-one.

Les 2-hydrazonophénylsélénoacétamides sont obtenus en deux étapes à partir de leurs analogues soufrés. Selon le degré de substitution de l'atome d'azote du groupement hydrazono et de celui du sélénamide, ils permettent d'accéder à un sel de 1,2,3-sékénadiazolium, à une 5-imino-Δ³-1,2,3-sélénadiazoline, aux 3,6-dihydro-2H- 1,3,4-sélénadiazines ou à une 5-sélénoxo-2,3,4,5-térahydro-1,2,4-triazin-3-one.     

Ripening and Storage Time Effects on the Aromatic Profile of New Table Grape Cultivars in Chile

The aim of this study was to determine the volatile profiles of new seedless table grape cultivars Timco™, Magenta™, Krissy™ and Arra15™ and compare them with the traditional table grape variety Crimson seedless. The volatile profiles were extracted employing solid-phase microextraction and analyzed with gas chromatography coupled with mass spectrometry. Terpenes were present in very different proportions, with the Magenta, Krissy, and Arra15 varieties showing much higher quantities than Crimson and Timco. β-Ionone and octanal, important indicators in the aromatic flavor quality of table grapes, were present in higher levels in Crimson and Arra15, and this might be responsible for driving consumer preference. These compounds significantly increased during ripening, except in Crimson, and gradually decreased from harvest to the end of the storage in all the cultivars. Evolution during ripening was different depending on the variety but the general tendency terpenes was to increase from veraison to harvest. A postharvest study revealed that Crimson could have a better conservation of the volatile components during postharvest storage compared with Timco and Krissy. These results could help in plant breeding programs and to make decisions for new planting according to needs for storing fresh table grapes given distances to consumer markets.     

Stable Pyrrole‐Linked Bioconjugates through Tetrazine‐Triggered Azanorbornadiene Fragmentation

An azanorbornadiene bromovinyl sulfone reagent for cysteine‐selective bioconjugation has been developed. Subsequent reaction with dipyridyl tetrazine leads to bond cleavage and formation of a pyrrole‐linked conjugate. The latter involves ligation of the tetrazine to the azanorbornadiene‐tagged protein through inverse electron demand Diels–Alder cycloaddition with subsequent double retro‐Diels–Alder reactions to form a stable pyrrole linkage. The sequence of site‐selective bioconjugation followed by bioorthogonal bond cleavage was efficiently employed for the labelling of three different proteins. This method benefits from easy preparation of these reagents, selectivity for cysteine, and stability after reaction with a commercial tetrazine, which has potential for the routine preparation of protein conjugates for chemical biology studies.