Another refinement of the right-hand side of the Hermite–Hadamard inequality for simplices

We establish a new refinement of the right-hand side of the Hermite–Hadamard inequality for convex functions of several variables defined on simplices.     

Dynamic Lone Pair Expression as Chemical Bonding Origin of Giant Phonon Anharmonicity in Thermoelectric InTe

Loosely bonded (“rattling”) atoms with s² lone pair electrons are usually associated with strong anharmonicity and unexpectedly low thermal conductivity, yet their detailed correlation remains largely unknown. Here we resolve this correlation in thermoelectric InTe by combining chemical bonding analysis, inelastic X-ray and neutron scattering, and first principles phonon calculations. We successfully probe soft low-lying transverse phonons dominated by large In¹⁺ z-axis motions, and their giant anharmonicity. We show that the highly anharmonic phonons arise from the dynamic lone pair expression with unstable occupied antibonding states induced by the covalency between delocalized In¹⁺ 5s² lone pair electrons and Te 5p states. This work pinpoints the microscopic origin of strong anharmonicity driven by rattling atoms with stereochemical lone pair activity, important for designing efficient materials for thermoelectric energy conversion.     

Chiral-at-Molybdenum – A Computational Study on N-Substituted cis-MoO2(nacnac)2

Cis-MoO₂(nacnac)₂ (nacnac=β-diketiminate) can be a viable chiral-at-metal catalyst when its two β-diketiminate (nacnac) ligands are N-substituted to prevent Λ⇌Δ racemization. Even simple methyl groups raise the barriers for racemization significantly for the Bailar, Rây-Dutt, Conte-Hippler, and Dhimba-Muller-Lammertsma (DML) twists to a respectable 28.5, 37.8, 30.5, and 25.1 kcal/mol, respectively, at ωB97X-D/6-311+G(2d,p) (LANL2DZ for Mo) including acetonitrile solvation. The lowest energy DML barrier increases to ΔG^o=27.4 kcal/mol with N-substituted t-butyl groups. The nacnac ligands’ electronic and steric components to the racemization barriers are discussed.     

Glucose,not cellobiose,is the repeating unit of cellulose and why that is important

Despite nomenclature conventions of the International Union of Pure and Applied Chemistry and the International Union of Biochemistry and Molecular Biology, the repeating unit of cellulose is often said to be cellobiose instead of glucose. This review covers arguments regarding the repeating unit in cellulose molecules and crystals based on biosynthesis, shape, crystallographic symmetry, and linkage position. It is concluded that there is no good reason to disagree with the official nomenclature. Statements that cellobiose is the repeating unit add confusion and limit thinking on the range of possible shapes of cellulose. Other frequent flaws in drawings with cellobiose as the repeating unit include incorporation of O-1 as the linkage oxygen atom instead of O-4 (the O-1 hydroxyl is the leaving group in glycoside synthesis). Also, n often erroneously represents the number of cellobiose units when n should denote the degree of polymerization i.e., the number of glucose residues in the polysaccharide.     

Measuring centrality and dispersion in directional datasets: the ellipsoidal cone covering approach

Consider a finite collection \(\{\xi _k\}_{k=1}^p\) of vectors in the space \(\mathbb {R}^n\). The \(\xi _k\)’s are not to be seen as position points but as directions. This work addresses the problem of computing the ellipsoidal cone of minimal volume that contains all the \(\xi _k\)’s. The volume of an ellipsoidal cone is defined as the usual n-dimensional volume of a certain truncation of the cone. The central axis of the ellipsoidal cone of minimal volume serves to define the central direction of the datapoints, whereas its volume can be used as measure of dispersion of the datapoints.     

Flavin Adenine Dinucleotide and N5,N10‐Methenyltetrahydrofolate are the in planta Cofactors of Arabidopsis thaliana Cryptochrome 3

Members of the cryptochrome/photolyase family (CPF) of proteins utilize noncovalently bound light‐absorbing cofactors for their biological function. Usually, the identity of these cofactors is determined after expression in heterologous systems leaving the question unanswered whether these cofactors are identical to the indigenous ones. Here, cryptochrome 3 from Arabidopsis thaliana was expressed as a fusion with the green fluorescent protein in Arabidopsis plants. Besides the confirmation of the earlier report of its localization in chloroplasts, our data indicate that fractions of the fusion protein are present in the stroma and associated with thylakoids, respectively. Furthermore, it is shown that the fusion protein expressed in planta contains the same cofactors as the His₆‐tagged protein expressed in Escherichia coli, that is, flavin adenine dinucleotide and N⁵,N¹⁰‐methenyltetrahydrofolate. This demonstrates that the heterologously expressed cryptochrome 3, characterized in a number of previous studies, is a valid surrogate of the corresponding protein expressed in plants. To our knowledge, this is also a first conclusive analysis of cofactors bound to an Arabidopsis protein belonging to the CPF and purified from plant tissue.     

A refinement of the right-hand side of the Hermite–Hadamard inequality for simplices

Aequationes mathematicae - We establish a new refinement of the right-hand side of the Hermite–Hadamard inequality for simplices, based on the average values of a convex function over the...     

Zum isoperimeterproblem auf vollständigen Flächen mit summierbarer Gau\scher Krümmung

Ohne Zusammenfassung Vorgelegt von R. Finn