Synthesis and Crystal Structure of the Strontium Beryllate Sr3Be2O5

Beryllates show an interesting and diverse structural chemistry, resembling that of well-investigated silicates. The coexistence of tetrahedral and trigonal coordination of Be by O atoms in oxoberyllates allows for an even broader variety of structural motives and implies a plurality of possible atomic ratios Be:O in ternary or higher compounds. We have now synthesized the novel strontium oxoberyllate Sr₃Be₂O₅ via a high-temperature high-pressure reaction and have structurally characterized the ternary oxide by single-crystal and powder X-ray diffraction analysis. Sr₃Be₂O₅, a low condensed oxoberyllate, contains unprecedented [Be₂O₅]^6– double triangles and Sr atoms in both double-capped trigonal-prismatic and octahedral coordination. These motifs show striking resemblance to α-SrBeO₂ and SrO, combining their structural properties. Lattice energy (MAPLE) calculations corroborate found parallels to the known phases SrO and α-SrBeO₂.     

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.     

Study on a Cross Diffusion Parabolic System

This paper considers a kind of strongly coupled cross diffusion parabolic system,which can be usedas the multi-dimensional Lyumkis energy transport model in semiconductor science.The global existence andlarge time behavior are obtained for smooth solution to the initial boundary value problem.When the initialdata are a small perturbation of an isothermal stationary solution,the smooth solution of the problem under theinsulating boundary condition,converges to that stationary solution exponentially fast as time goes to infinity.     

Liouville Theorems for a General Class of Nonlocal Operators

In this paper, we study the equation \(\mathcal {L} u=0\) in \(\mathbb {R}^{N}\), where \(\mathcal {L}\) belongs to a general class of nonlocal linear operators which may be anisotropic and nonsymmetric. We classify distributional solutions of this equation, thereby extending and generalizing recent Liouville type theorems in the case where \(\mathcal {L}= (-{\Delta })^{s}\), s ∈ (0, 1) is the classical fractional Laplacian.     

Colloidal Analysis of Particles Extracted from Microalloyed Steels

Different colloidal particle characterization methods are examined for their suitability to determine the particle size distribution of particles extracted from steels. Microalloyed steels are dissolved to extract niobium and titanium carbonitride particles that are important for the mechanical properties of these steels. Such particles have sizes ranging from several nanometers to hundreds of nanometers depending on the precipitation stage during the thermomechanically controlled rolling process. The size distribution of the particles is analyzed by dynamic light scattering (DLS), analytical ultracentrifugation (AUC), and hollow fiber flow field-flow fractionation (HF5) and compared to data obtained for reference particles as well as data from electron microscopy, the standard sizing technique used in metallurgy today. AUC and HF5 provide high-quality size distributions, average over large particle numbers that enables statistical analysis, and yield useful insights for alloy design; however, DLS fails due to a lack of resolution. Important aspects in the conversion and comparison of size distributions obtained for broadly distributed particle systems with different measurement principles and the role of surfactants used in sample preparation are discussed.     

Disjoint Hamilton cycles in the random geometric graph

We consider the standard random geometric graph process in which n vertices are placed at random on the unit square and edges are sequentially added in increasing order of edge‐length. For fixed k?1, weprove that the first edge in the process that creates a k‐connected graph coincides a.a.s. with the first edge that causes the graph to contain k/2 pairwise edge‐disjoint Hamilton cycles (for even k), or (k?1)/2 Hamilton cycles plus one perfect matching, all of them pairwise edge‐disjoint (for odd k). This proves and extends a conjecture of Krivelevich and M ler. In the special case when k = 2, our result says that the first edge that makes the random geometric graph Hamiltonian is a.a.s. exactly the same one that gives 2‐connectivity, which answers a question of Penrose. (This result appeared in three independent preprints, one of which was a precursor to this article.) We prove our results with lengths measured using the ?_p norm for any p>1, and we also extend our result to higher dimensions. © 2011 Wiley Periodicals, Inc. J Graph Theory 68:299‐322, 2011     

Evolution Galerkin methods for hyperbolic systems in two space dimensions

The subject of the paper is the analysis of three new evolution Galerkin schemes for a system of hyperbolic equations, and particularly for the wave equation system. The aim is to construct methods which take into account all of the infinitely many directions of propagation of bicharacteristics. The main idea of the evolution Galerkin methods is the following: the initial function is evolved using the characteristic cone and then projected onto a finite element space. A numerical comparison is given of the new methods with already existing methods, both those based on the use of bicharacteristics as well as commonly used finite difference and finite volume methods. We discuss the stability properties of the schemes and derive error estimates.

     

Nearest-neighbor configuration in (GaIn)(NAs) probed by x-ray absorption spectroscopy

Ga(1-x)In(x)N(y)As(1-y) is a promising material system for the fabrication of inexpensive "last-mile" optoelectronic components. However, details of its atomic arrangement and the relationship to observed optical properties is not fully known. Particularly, a blueshift of emission wavelength is observed after annealing. In this work, we use x-ray absorption fine structure to study the chemical environment around N atoms in the material before and after annealing. We find that as-grown molecular beam epitaxy material consists of a nearly random distribution of atoms, while postannealed material shows segregation of In toward N. Ab initio simulations show that this short-range ordering creates a more thermodynamically stable alloy and is responsible for blueshifting the emission.     

Collocation discretization for an integral equation in ocean acoustics with depth‐dependent speed of sound

We analyze two collocation schemes for the Helmholtz equation with depth‐dependent sonic wave velocity, modeling time‐harmonic acoustic wave propagation in a three‐dimensional inhomogeneous ocean of finite height. Both discretization schemes are derived from a periodized version of the Lippmann‐Schwinger integral equation that equivalently describes the sound wave. The eigenfunctions of the corresponding periodized integral operator consist of trigonometric polynomials in the horizontal variables and eigenfunctions to some Sturm‐Liouville operator linked to the background profile of the sonic wave velocity in the vertical variable. Applying an interpolation projection onto a space spanned by finitely many of these eigenfunctions to either the unknown periodized wave field or the integral operator yields two different collocation schemes. A convergence estimate of Sloan [J. Approx. Theory, 39:97–117, 1983] on non‐polynomial interpolation allows to show converge of both schemes, together with algebraic convergence rates depending on the smoothness of the inhomogeneity and the source. Copyright © 2016 John Wiley & Sons, Ltd.