Tangency and differentiation: Some applications of convergence theory

Summary We present a unified approach based on convergence theory to approximating cones and generalized derivatives.     

Molecular dynamics study of self-diffusion in stoichiometric B2-NiAl crystals

Self-diffusion parameters in stoichiometric B2-NiAl solid state crystals were estimated by molecular statics/dynamics simulations with the study of required simulation time to stabilise diffusivity results. An extrapolation procedure to improve the diffusion simulation results was proposed. Calculations of volume diffusivity for the B2 type NiAl in the 1224–1699?K temperature range were performed using the embedded-atom-model potential. The results obtained here are in much better agreement with the experimental results than the theoretical estimates obtained with other methods.     

Ideals with bases of unbounded Borel complexity

We present several naturally defined σ‐ideals which have Borel bases but, unlike for the classical examples, these ideals are not of bounded Borel complexity. We investigate set‐theoretic properties of such σ‐ideals.     

FeII Spin‐Crossover Phenomenon in the Pentadecanuclear {Fe9[Re(CN)8]6} Spherical Cluster

The self‐assembly of iron(II) ions with rare octacyanidorhenate(V) metalloligands in a methanolic solution results in the formation of a nanometric pentadecanuclear {Fe^II₉[Re^V(CN)₈]₆(MeOH)₂₄}?10 MeOH ( 1 ) molecule with a six‐capped body‐centered cubic topology. The cluster demonstrates a thermally‐induced spin‐crossover phase transition at T_1/2=195 K which occurs selectively for a single Fe^II ion embedded in the center of a cluster core.     

Palladium catalysed regio- and stereoselective synthesis of (E)-4-aryl-1,3-bis(trimethylsilyl)but-3-en-1-ynes

A practical and general synthetic approach to a series of 4-aryl-but-3-en-1-ynes is described. In the presence of palladium complexes a variety of aryl bromides (or iodides) undergo coupling with two equivalents of trimethylsilylacetylene with the formation of (E)-4-aryl-1,3-bis(trimethylsilyl)but-3-en-1-ynes. The protocol is simple, efficient, and affords synthesis of regio- and stereoselectively target products in good to high yields.     

Reversible Humidity-Driven Transformation of a Bimetallic {EuCo} Molecular Material: Structural,Sorption, and Photoluminescence Studies

Functional molecule-based solids built of metal complexes can reveal a great impact of external stimuli upon their optical, magnetic, electric, and mechanical properties. We report a novel molecular material, {[Eu^III(H₂O)₃(pyrone)₄][Co^III(CN)₆]}·nH₂O (1, n = 2; 2, n = 1), which was obtained by the self-assembly of Eu³⁺ and [Co(CN)₆]³⁻ ions in the presence of a small 2-pyrrolidinone (pyrone) ligand in an aqueous medium. The as-synthesized material, 1, consists of dinuclear cyanido-bridged {EuCo} molecules accompanied by two H-bonded water molecules. By lowering the relative humidity (RH) below 30% at room temperature, 1 undergoes a single-crystal-to-single-crystal transformation related to the partial removal of crystallization water molecules which results in the new crystalline phase, 2. Both 1 and 2 solvates exhibit pronounced Eu^III-centered visible photoluminescence. However, they differ in the energy splitting of the main emission band of a ⁵D₀ → ⁷F₂ origin, and the emission lifetime, which is longer in the partially dehydrated 2. As the 1 ↔ 2 structural transformation can be repeatedly reversed by changing the RH value, the reported material shows a room-temperature switching of detailed luminescent features including the ratio between emission components and the emission lifetime values.     

On generalized Szász-Mirakyan operators of functions of two variables

We introduce certain generalized Szász-Mirakyan operators in exponential weight spaces of functions of two variables and we give approximation theorems for them.