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The limiting enthalpy of the solution of liquid indium in liquid tin was measured at 723 K. The calorimetric method was applied to determine the standard enthalpy of the formation of intermetallic phases and alloys from the In-Li system. The measurements were done at 747 K and 756 K. The structures of prepared alloys were confirmed by the X-ray diffraction measurements. Besides that, the ab initio calculations allowed the modeling of the formation energies, the volume thermal expansion, the heat capacity under constant pressure, and the elastic properties of the intermetallic phases. The theoretical formation energies show good agreement with the experimental findings. The analysis of the phonon dispersion indicates an instability of the InLi phase in the Fd-3m space group. A further investigation on the atomic arrangement in the case of the equiatomic ratio is suggested.

The binary In – Li system is a promising Li-ion battery anode material as well as a part of the important ternary Ge – In – Li system. The thermodynamic descriptions of metallic systems are widely used to retrieve information necessary for alloy applications. In this work, a thermodynamic model of a binary indium – lithium system prepared by the Calphad approach is proposed. The liquid phase was described by an associate model, and the solid phases determined by the ab-initio calculation were included in the thermodynamic modeling. The obtained set of self-consistent thermodynamic parameters well reproduces the available experimental data and enables further calculations of multi-component systems. A good agreement between the calculations and the available experimental data was found. The proposed model can be used for further descriptions of ternary systems.

We generalize the Robinson–Schensted–Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to new enumerative results that have representation theoretic interpretations as decompositions of centralizer algebras and the spaces they act on. In addition, restrictions on the multisets lead to further identities and representation theory analogues. For instance, we obtain a bijection between words of length k with entries in [n] and pairs of tableaux of the same shape with one being a standard Young tableau of size n and the other being a standard multiset tableau of content [k]. We also obtain an algorithm from partition diagrams to pairs of a standard tableau and a standard multiset tableau of the same shape, which has the remarkable property that it is well-behaved with respect to restricting a representation to a subalgebra. This insertion algorithm matches recent representation-theoretic results of Halverson and Jacobson [15].

We generalize the Robinson–Schensted–Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to an algorithm from partition diagrams to pairs of a standard tableau and a standard multiset tableau of the same shape, which has the remarkable property that it is well-behaved with respect to restricting a representation to a subalgebra. This insertion algorithm matches recent representation-theoretic results of Halverson and Jacobson.

This book is an exposition of the current state of research of affineSchubert calculus and $k$-Schur functions. This text is based on a series oflectures given at a workshop titled "Affine Schubert Calculus" that took placein July 2010 at the Fields Institute in Toronto, Ontario. The story of thisresearch is told in three parts: 1. Primer on $k$-Schur Functions 2. Stanleysymmetric functions and Peterson algebras 3. Affine Schubert calculus

In a recent work, Jim Haglund, Jennifer Morse, and Mike Zabrocki proved a variety of identities involving Hall–Littlewood symmetric functions indexed by compositions. When they applied ∇ to these symmetric functions, the resulting identities and computer data led them to some truly remarkable refinements of the shuffle conjecture. We prove here the symmetric function side of a recursion which when combined with a recent parking function recursion of Angela Hicks [18] settles some special cases of the Haglund–Morse–Zabrocki conjectures. Our main result of a compositional q,t-Catalan and Schröder theorem yields, as a consequence, surprisingly simple new proofs of the original q,t-Catalan and Schröder results. [ABSTRACT FROM PUBLISHER]

The X-ray diffraction, Scanning Electron Microscopy, Differential Scanning Calorimetry, dilatometric and electrical conductivity measurements were used to study the structural and physicochemical properties of selected silver-rich alloys from Ag–Al system. All the studied alloys, containing from 10 to 37 at. % of Al (Ag 90 Al 10 , Ag 85 Al 15 , Ag 77 Al 23 , Ag 75 Al 25 , Ag 72 Al 28 , Ag 70 Al 30 , Ag 63 Al 37), were prepared from high purity metals by melting in a glove-box filled with a high purity argon atmosphere. The obtained X-ray diffraction patterns and microstructure observation of alloys containing up to 15 at. % of Al suggested that in this range only solid solution of silver exists. The thermal analysis showed heat effects related to phase transitions in Ag–Al system. In addition, the thermal expansion studies revealed an anomalous behavior in expansion for some composition of alloys associated with the phase transition. The electrical conductivity values rapidly changed, which may be associated with the formation of different phase areas in the Ag–Al system. Based on the results obtained in this work and critically reviewed literature data a thermodynamic re-optimization of the binary Ag–Al system using CALPHAD method was proposed. A good agreement between calculation and experiment was found. • The X-Ray Diffraction analysis of investigated Ag–Al alloys. • Microstructure observation of selected Ag–Al alloys. • DSC and dilatometric measurements of Ag-rich alloys from Ag–Al system. • Electrical conductivity of seven alloys from Ag–Al system. • Thermodynamic re-optimization of the binary Ag–Al system based on newest experimental data. [ABSTRACT FROM AUTHOR]

A set of 211 At-astatoarenes were synthesized from corresponding trimethylgermyl arenes with an average radiochemical conversion (RCC) of ca. 50 % for electron-rich and approx. 70 % in case of electron-deficient arenes. Both electron rich and electron poor substrates were successfully radiolabeled at room temperature (RT) using relatively low precursor amounts (0.15 μmol/0.02 mL solvent (7.5 mM)). Ready access to ortho-, para- and meta- astatinated arenes was achievable. Optimized reaction conditions were successfully applied to label a poly (ADP-ribose) polymerase (PARP) inhibitor with a RCC of approx. 50 %. We believe that trimethylgermyl derivatives are a viable addition to the astatination precursor toolbox and facilitate astatination of arenes. The developed labeling method should easily be applicable for productions under good manufacturing practice (GMP)., (© 2024 The Authors. ChemPlusChem published by Wiley-VCH GmbH.)