A Simple Homoleptic Gallium(I) Olefin Complex: Mimicking Transition‐Metal Chemistry at a Main‐Group Metal?

The earth‐metal olefin complex [Ga ^I (COD)₂]⁺[Al(OR^F)₄]^? (COD=1,5‐cyclooctadiene; R^F=C(CF₃)₃) constitutes the first homoleptic olefin complex of any main‐group metal accessible as a bulk compound. It is straight forward to prepare in good yield and constitutes an olefin complex of a main‐group metal that—similar to many transition‐metals—may adopt the +1 and +3 oxidation states opening potential applications. Crystallographic‐, vibrational‐ and computational investigations give an insight to the atypical bonding between an olefin and a main‐group metal. They are compared to classical transition‐metal relatives.     

Taming Tin(IV) Polyazides

The first charge‐neutral Lewis base adducts of tin(IV) tetraazide, [Sn(N₃)₄(bpy)], [Sn(N₃)₄(phen)] and [Sn(N₃)₄(py)₂], and the salt bis{bis(triphenylphosphine)iminium} hexa(azido)stannate [(PPN)₂Sn(N₃)₆] (bpy = 2,2′‐bipyridine; phen = 1,10‐phenanthroline; py = pyridine; PPN = N(PPh₃)₂) have been prepared using covalent or ionic azide‐transfer reagents and ligand‐exchange reactions. The azides were isolated on the 0.3 to 1 g scale and characterized by IR and NMR spectroscopies, microanalytical and thermal methods and their molecular structures determined by single‐crystal XRD. All complexes have a distorted octahedral Sn[N]₆ coordination geometry and possess greater thermal stability than their Si and Ge homologues. The nitrogen content of the adducts of up to 44 % exceed any Sn^IV compound known hitherto.     

Hydrogen Storage Materials: Room‐Temperature Wet‐Chemistry Approach toward Mixed‐Metal Borohydrides

The poor kinetics of hydrogen evolution and the irreversibility of the hydrogen discharge hamper the use of transition metal borohydrides as hydrogen storage materials, and the drawbacks of current synthetic methods obstruct the exploration of these systems. A wet‐chemistry approach, which is based on solvent‐mediated metathesis reactions of precursors containing bulky organic cations and weakly coordinating anions, leads to mixed‐metal borohydrides that contain only a small amount of “dead mass”. The applicability of this method is exemplified by Li[Zn₂(BH₄)₅] and M[Zn(BH₄)₃] salts (M=Na, K), and its extension to other systems is discussed.     

DAMPING OF VERTICALLY EXCITED SURFACE WAVE IN WEAKLY VISCOUS FLUID

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.     

Weakly R-KKM mappings——intersection theorems and minimax inequalities in topological spaces

In this paper, we introduce the concepts of weakly R-KKM mappings, R-convex and ,R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topological spaces of Fan's matching theorem, namely that Lemma 1.2 in this paper. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. Our results generalize and improve the corresponding results in the literature.     

Aharonov–Bohm effect in non-uniform crater-like quantum dot with double rim

We study electron energies in a double concentric quantum ring with anisotropy in the rims heights in the presence of the external magnetic field applied along the symmetry axis. To this end, we consider a model in which the thickness grows linearly from the axis up to the inner rim with a slope different from one between the inner and the outer rims. The anisotropy in the rims heights originated by the presence in the structure of various valleys we simulate by periodic dependence of the slope on the radial direction. We show that the wave functions of the electron confined in such structure can be found analytically if the slopes in all radial directions are the same, and by using a simple exact diagonalization procedure otherwise. The behavior of the electron energies as functions of the magnetic field, rings radii and rims heights, as well as the number of the valleys and their depths is consistently described with our formalism. The entanglement of the states with different radial and orbital quantum numbers, the period and the amplitude of the Aharonov–Bohm oscillations are very sensible to any variations of the rims heights.     

The depth spectrums of constacyclic codes over finite chain rings

In light of the generator polynomials of constacyclic codes over finite chain rings, the depth spectrum of constacyclic codes can be determined if (n,p)=1$(n,p)=1$.     

Unsteady boundary layers with small cross flows

Despite the intensive development of computer technology and methods of solving the Navier-Stokes and Reynolds equations, the unsteady problems of the three-dimensional boundary layer are of significant interest in aerodynamics. So far these problems have been little studied as a result of objective difficulties related with the large dimensionality of the system of equations and the complexity of its investigation [{xc1}]. Therefore, analytic results in this field are important. In the present study the unsteady three-dimensional boundary layer equations are investigated in the case of small cross flows using the perturbation method. An intermediate system of equations, which includes the basic three-dimensional effects but is significantly simpler than the initial system is derived. The features of the formulation considered are studied in relation to the important practical problems of boundary layer flow past slender wings and weakly asymmetric bodies at small angles of attack.     

流动稳定性弱非线性理论中的问题及其改进

流动稳定性弱非线性理论存在三个主要问题:(1)其摄动参数收敛半径太小且无具体估值;(2)其解有特定结构,一般不能满足很多实际问题的初始条件;(3)当其线性部分不是中性时,Landau系数的确定法不唯一,不知何者应是最好的方法。本文以平面Poiseuille流为例,从理论上解决了问题(1)和(2),并提出了改进办法。又通过将理论和数值模拟结果相比较的方法,澄清了问题(3)。改进了的理论,将可解决许多实际问题。     

Application of X-ray diffraction, micromagnetic and hole drilling methods for residual stress determination in a ball bearing steel ring

A basic understanding of distortion problems requires the analysis of a complete manufacturing process including an almost complete overview of residual stress states in the component during each production step. To reduce the measurement time in the future, three measurements methods (X-ray diffraction, micromagnetic and blind hole drilling methods) have been used to analyze residual stress states in machined AISI 52100 ball bearing rings. X-ray diffraction was used as a state-of-the-art method for machining induced residual stresses with pronounced gradients. The ring exhibited a complex residual stress state with high tensile residual stresses at the surface, a strong gradient in depth, and also showed some variation along the outer circumference due to a superimposition of machining induced residual stresses and effects from the clamping device process. Due to this surface state, micromagnetic signals depend on the analyzing frequency. A calibration of the signals was only possible with the X-ray diffraction data. The results of the three different measurement methods correlate reasonably well.