Real Brauer characters

In this paper, we determine the structure of finite groups with a small number of real-valued irreducible Brauer characters.     

Combined Experimental and Computational Investigations of Rhodium‐Catalysed CH Functionalisation of Pyrazoles with Alkenes

Detailed experimental and computational studies have been carried out on the oxidative coupling of the alkenes C₂H₃Y (Y=CO₂Me ( a ), Ph ( b ), C(O)Me ( c )) with 3‐aryl‐5‐R‐pyrazoles (R=Me ( 1 a ), Ph ( 1 b ), CF₃ ( 1 c )) using a [Rh(MeCN)₃Cp*][PF₆]₂/Cu(OAc)₂ ? H₂O catalyst system. In the reaction of methyl acrylate with 1 a , up to five products ( 2 aa – 6 aa ) were formed, including the trans monovinyl product, either complexed within a novel Cu^I dimer ( 2 aa ) or as the free species ( 3 aa ), and a divinyl species ( 6 aa ); both 3 aa and 6 aa underwent cyclisation by an aza‐Michael reaction to give fused heterocycles 4 aa and 5 aa , respectively. With styrene, only trans mono‐ and divinylation products were observed, whereas with methyl vinyl ketone, a stronger Michael acceptor, only cyclised oxidative coupling products were formed. Density functional theory calculations were performed to characterise the different migratory insertion and β‐H transfer steps implicated in the reactions of 1 a with methyl acrylate and styrene. The calculations showed a clear kinetic preference for 2,1‐insertion and the formation of trans vinyl products, consistent with the experimental results.     

Intramolecular Fluorocyclizations of Unsaturated Carboxylic Acids with a Stable Hypervalent Fluoroiodane Reagent

A new class of fluorinated lactones was prepared by the intramolecular fluorocyclizations of unsaturated carboxylic acids by using the stable fluoroiodane reagent in combination with AgBF₄. This unique reaction incorporates a cyclization, an aryl migration, and a fluorination all in one step. The fluoroiodane reagent, prepared easily from fluoride, can also be used without a metal catalyst to give moderate yields within just 1 hour, thus demonstrating that it is a suitable reagent for developing new ¹⁸F‐labelled radiotracers for PET imaging.     

The valuation of life contingencies: A symmetrical triangular fuzzy approximation

This paper extends the framework for the valuation of life insurance policies and annuities by Andrés-Sánchez and González-Vila (2012, 2014) in two ways. First we allow various uncertain magnitudes to be estimated by means of fuzzy numbers. This applies not only to interest rates but also to the amounts to be paid out by the insurance company. Second, the use of symmetrical triangular fuzzy numbers allows us to obtain expressions for the pricing of life contingencies and their variability that are closely linked to standard financial and actuarial mathematics. Moreover, they are relatively straightforward to compute and understand from a standard actuarial point of view.     

High Entropy Alloys as Filler Metals for Joining

In the search for applications for alloys developed under the philosophy of the High Entropy Alloy (HEA)-type materials, the focus may be placed on applications where current alloys also use multiple components, albeit at lower levels than those found in HEAs. One such area, where alloys with complex compositions are already found, is in filler metals used for joining. In soldering (<450 °C) and brazing (>450 °C), filler metal alloys are taken above their liquidus temperature and used to form a metallic bond between two components, which remain both unmelted and largely unchanged throughout the process. These joining methods are widely used in applications from electronics to aerospace and energy, and filler metals are highly diverse, to allow compatibility with a broad range of base materials (including the capability to join ceramics to metals) and a large range of processing temperatures. Here, we review recent developments in filler metals relevant to High Entropy materials, and argue that such alloys merit further exploration to help overcome a number of current challenges that need to be solved for filler metal-based joining methods.     

Phase transitions in the litharge and antilitharge structures

Abstract

The compounds PbO and LiOD possess the layered, tetragonal B10 structure and the corresponding antistructure respectively at 1 bar. They undergo very different phase transitions at moderate pressure. At 5 kbar, PbO undergoes a slight, reversible distortion to an orthorhombic phase. The structure is probably an expanded NaCl derivative.

The high-P LiOD phase begins to grow slowly above 17 kbar. Infrared and Raman data indicate that hydrogen bonding is present in the new phase. Neutron powder data indexed on a monoclinic cell. The structure is likely to be similar to that of T1I and NaOH, distorted by the H-bonding.     

An electron spin resonance study of dimeric,trimeric, and tetrameric paramagnetic silver atom clusters

The low temperature γ-irradiation of frozen benzene solutions containing AgClO₄ leads directly to the formation of the paramagnetic species Ag₂ ⁺, no Ag⁰ centre being detected. When benzene or toluene solutions containing AgBF₄ were similarly treated and the matrix carefully annealed, well-resolved E.S.R. spectra attributed to paramagnetic clusters containing three and four equivalent silver atoms were detected. The lack of resolved anisotropy in the spectrum of the trimer and tetramer are thought to argue in favour of a triangular and tetrahedral geometry respectively rather than linear chains.     

Identifying Quantum Structures in the Ellsberg Paradox

Empirical evidence has confirmed that quantum effects occur frequently also outside the microscopic domain, while quantum structures satisfactorily model various situations in several areas of science, including biological, cognitive and social processes. In this paper, we elaborate a quantum mechanical model which faithfully describes the Ellsberg paradox in economics, showing that the mathematical formalism of quantum mechanics is capable to represent the ambiguity present in this kind of situations, because of the presence of contextuality. Then, we analyze the data collected in a concrete experiment we performed on the Ellsberg paradox and work out a complete representation of them in complex Hilbert space. We prove that the presence of quantum structure is genuine, that is, interference and superposition in a complex Hilbert space are really necessary to describe the conceptual situation presented by Ellsberg. Moreover, our approach sheds light on ‘ambiguity laden’ decision processes in economics and decision theory, and allows to deal with different Ellsberg-type generalizations, e.g., the Machina paradox.