Kaplansky’s “infinite abelian groups” and its two test problems

Abstract

Kaplansky’s Infinite Abelian Groups, originally published in 1954, has recently been republished. In recognition of its continuing significance after 65?years, the authors illustrate some important ideas and techniques described in the book. In particular, a class of groups is defined for which there are affirmative answers to the author’s two famous “Test Problems.”     

Decacyclene Radical Anions Showing Strong Low‐energy Intramolecular Absorption and Magnetic Coupling of Spins in a Hexagonal Network

Two salts of the aromatic hydrocarbon decacyclene, {cryptand[2.2.2](Cs⁺)} (decacyclene^.?) ( 1 ) and {Bu₃MeP⁺}(decacyclene^.?) ( 2 ), were obtained. In both salts, decacyclene^.? radical anions formed channels occupied by cations. However, corrugated hexagonal decacyclene^.? layers could be outlined in the crystal structure of 1 with several side‐by‐side C???C approaches. The decacyclene^.? radical anions showed strong distortion in both salts, deviating from the C₃ symmetry owing to the repulsion of closely arranged hydrogen atoms and the Jahn‐Teller effect. Radical anions showed intense unusually low energy absorption in the IR‐range, with maxima at 4800 and 6000 cm^?1. According to the carculations, these bands can originate from the SOMO‐LUMO+1 and SOMO‐LUMO+2 transitions, respectively. Radical anions exhibited a S=1/2 spin state, with an effective magnetic moment of 1.72 μ_B at 300 K. The decacyclene^.? spin antiferromagnetically coupled with a Weiss temperature of ?11 K. Spin ordering was not observed down to 1.9 K owing to spin frustration in the hexagonal decacyclene^.? layers.     

Synthesis,Structure, and DFT Analysis of the THF Solvate of 2-Picolyllithium: A 2-Picolyllithium Solvate with Significant Carbanionic Character

Previous studies of different solvates of 2-methylpyridyllithium (2-picolyllithium) have uncovered electronic structures corresponding to aza-allyl and enamido resonance forms of the metallated pyridine-based compounds. Here, we report the synthesis and characterization of [2-CH₂Li(THF)₂C₅H₄N], a new THF solvate. X-ray crystallographic studies reveal a dimeric arrangement featuring a non-planar eight-membered [NCCLi]₂ ring, in which the primary cation-anion interaction is between the central Li atom and the C atom of the deprotonated methyl group [length, 2.285(2) Å], suggesting a new carbanionic resonance structure for this 2-picolyllithium series. The significant carbanionic character of [2-CH₂Li(THF)₂C₅H₄N] was confirmed by gas-phase DFT calculations [B3LYP/6-311+G(d)] with the calculated electron density interrogated by means of quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) analyses. For comparison these computational analyses were also performed on the literature structures of [2-CH₂Li(2-Picoline)C₅H₄N] and [2-CH₂Li(PMDETA)C₅H₄N]. In a reactivity study, [2-CH₂Li(THF)₂C₅H₄N] was found to undergo nucleophilic addition to pyridine to generate dipyridylmethane in a good yield.     

Hybrid Plasmonic–Aerogel Materials as Optical Superheaters with Engineered Resonances

Solar radiation is a versatile source of energy, convertible to different forms of power. A direct path to exploit it is the generation of heat, for applications including passive building heating, but it can also drive secondary energy-conversion steps. We present a novel concept for a hybrid material which is both strongly photo-absorbing and with superior characteristics for the insulation of heat. The combination of that two properties is rather unique, and make this material an optical superheater. To realize such a material, we are combining plasmonic nanoheaters with alumina aerogel. The aerogel has the double function of providing structural support for plasmonic nanocrystals, which serve as nanoheaters, and reducing the diffusion rate of the heat generated by them, resulting in large local temperature increases under a relatively low radiation intensity. This work includes theoretical discussion on the physical mechanisms impacting the system's balanced thermal equilibrium.     

Regarding some thermoelastic models of “coating-substrate” system deformation

In present research, we investigate dynamic coupled thermoelasticity problem for a “coating-substrate” system. We present a number of models of thermoelastic deformation of the “coating-substrate” system with thermomechanical characteristics which may vary both continuously and discontinuously. To solve these problems, we use the variational principle of coupled thermoelasticity in the Laplace transforms space and hypotheses on a distribution of temperature and displacements transforms. The transforms inversion is realized according to the Durbin method. The calculations were carried out based on both proposed simplified models and FEM.     

Synthesis,X-ray and DFT Studies of 6-halo-3-(hydroxymethyl)cinnolin-4(1H)-ones

Chemistry of Heterocyclic Compounds - The Richter cyclization was used for the synthesis of 6-halo-3-(hydroxymethyl)cinnolin-4(1H)-ones. X-ray analysis revealed that these compounds exist as dimers...     

The Impact of Research Culture on Mental Health & Diversity in STEM

The onset of COVID-19, coupled with the finer lens placed on systemic racial disparities within our society, has resulted in increased discussions around mental health. Despite this, mental health struggles in research are still often viewed as individual weaknesses and not the result of a larger dysfunctional research culture. Mental health interventions in the science, technology, engineering, and mathematics (STEM) academic community often focus on what individuals can do to improve their mental health instead of focusing on improving the research environment. In this paper, we present four aspects of research that may heavily impact mental health based on our experiences as research scientists: bullying and harassment; precarity of contracts; diversity, inclusion, and accessibility; and the competitive research landscape. Based on these aspects, we propose systemic changes that institutions must adopt to ensure their research culture is supportive and allows everyone to thrive.