Theoretical study on structure of boron nitride fullerenes

We propose the parameters of the Stillinger-Weber potential for hexagonal boron nitride (BN) structures. For the reliability of these parameters, the structural property of BN fullerenes is investigated. The stability of BN fullerenes increases with increasing the number of atoms, due to the reduction of the curvature effect of BN fullerenes. The structures of the relative stable fullerenes are B₁₆N₁₆, B₁₈N₁₈, B₂₂N₂₂, B₂₅N₂₅, and B₂₈N₂₈.     

Shifted identical bands: A new phenomenon

The levels in ¹⁶²Gd were identified in spontaneous fission studies. Its transition energies are remarkably similar to those in ¹⁶⁰Gd. From that work, an analysis of yrast bands in even-even proton to neutron-rich Ba to Pb nuclei led to the discovery of a new phenomenon, shifted identical bands (SIB). SIBs are yrast bands in neighboring nuclei (a, b) with moments of inertia which are identical when shifted by a constant amount κ, so J _1a (1+κ)=J _1b , from 2⁺ to 8⁺ and higher to 16⁺. Out of over 700 comparisons, 55 SIBs were found from stable to the most neutron-rich Ce-W nuclei with $\left| {\bar k} \right|$ between 1.5% and 13%, where the spread in κ is less than ±1%, and only four identical bands ( $\bar k \cong 0$ ). As examples, we found for ¹⁵⁸Sm-¹⁶⁰Gd, $\bar k = \left( { - 3.2_{ - 0.2}^{ + 0.1} } \right)\%$ (where the ± is the total spread in κ from ?3.1 to ?3.4); ¹⁵⁶Nd-¹⁶⁰Gd, (?10.6 _?0.2 ^+0.4 )%; ¹⁵⁸Sm-¹⁶⁰Sm, (3.4 _?0.3 ^+0.5 )%. The J ₁ values were fitted to a variable moment of inertia model with parameters J ₀ and C whose values correlate with the SIB J ₁ values. The SIBs are not correlated either with deformation or with the N _p N _n product of the IBA model.     

A recurrence relation for the square root

The behavior of the sequence x_{n + 1} = x_n(3N − x_n²)/2N is studied for N > 0 and varying real x₀. When 0 < x₀ < (3N)^1/2 the sequence converges quadratically to N^1/2. When x₀ > (5N)^1/2 the sequence oscillates infinitely. There is an increasing sequence β_r, with β₋₁ = (3N)^1/2 which converges to (5N)^1/2 and is such that when β_r < x₀ < β_{r + 1} the sequence {x_n} converges to (−1)^rN^1/2. For x₀ = 0, β₋₁, β₀,… the sequence converges to 0. For x₀ = (5N)^1/2 the sequence oscillates: x_n = (−1)ⁿ(5N)^1/2. The behavior for negative x₀ is obtained by symmetry.     

Heat transfer to magnetohydrodynamic flow in a flat duct

Zusammenfassung Die Untersuchung befasst sich mit der Wärmeübertragung von den Wänden eines flachwandigen Kanals auf eine elektrisch leitende Flüssigkeit bei erzwungener Laminarströmung und in Gegenwart eines quergerichteten Magnetfeldes. Betrachtet wird der Fall konstanter Wandtemperatur mit variierender innerer Wärmeentwicklung durch viskose und elektrische Energiedissipation. Die massgebende Differentialgleichung wird durch eine Differenzengleichung ersetzt und mit der elektronischen Rechenmaschine gelöst. Als Resultat wird die Nusseltzahl angegeben, für die Prandtlzahl 1, die Hartmannzahlen 0, 4, 10 und die Graetzzahlen von 10 bis 10 000, wobei die Kennzahlen für Zähigkeit und elektrische Feldstärke als Parameter auftreten.     

关于容许全脐超曲面正交族的Einstein流形

The aim of the present paper is to study globally the Riemannian manifold admitting two or more mutually orthogonal families of totally umbilical hypersurfaccs of which each is Einsteinian. This paper consists of four parts: (i) to establish anew the canonical form of the metric of (M,g) admitting p (p≥2) families of mutually orthogonal totally umbilical hypcrsurf aces from the standpoint of global differential geometry; (ii) to prove in a n-dimensional (n>2) Einsteinian manifold E_n of nonvanishing scalar curvature there doesn't exist one family of compact totally geodesic Einsteinian hypersurfaces (Theorem 1);(iii) to prove in a n-dimensional (n≥5) Einsteinian manifold E_n of nonnegative scalar curvature R there don't exist two orthogonal families of totally umbilical but not geodesic complete Einsteinian hypersurfaces (Theorem Ⅱ);(iv) to show that a n-dimensional (n≥5) Riemannian manifold of negative constant scalar curvature R.     

First-principles computational approach for innovative design of highly functional electrocatalysts in fuel cells

Design of highly active and stable electrocatalyst is a major objective in a fuel cell. The special situation imposed to the electrocatalyst such as one of the most sluggish catalysis of oxygen reduction reaction, inherent structural instability of dispersed nanoparticle, harsh electrochemical conditions of electric potential and nonzero pH aqueous solution requires unique attention in the design. Considering that various attempts have been made for the purpose, high-speed but rigorous formalisms to evaluate the performance of candidates are crucial.This review article briefly introduces recently developed first-principles computational methodologies mainly applied to catalytic activity and electrochemical stability of electrocatalysts in proton exchange membrane fuel cells. Innovative design principles deduced from the outcomes are clearly discussed.     

Molecular Encapsulation of Trimeric Chromium Carboxylate Clusters in Metal–Organic Frameworks and Propylene Sorption

Oxo-bridged trimeric chromium acetate clusters [Cr₃O(OOCCH₃)₆(H₂O)₃]NO₃ have been encapsulated for the first time in the mesoporous cages of the chromium terephthalate MIL-101(Cr). The isolated clusters in MIL-101(Cr) have increased affinity towards propylene compared to propane, due to generation of a new kind of pocket-based propylene-binding site, as supported by DFT calculations.     

Influence of TiO2 nanotube morphology and TiCl4 treatment on the charge transfer in dye-sensitized solar cells

Dye-sensitized solar cells (DSSCs) were fabricated using TiO₂ nanoparticles (NPs), TiO₂ nanotube arrays (NTAs), and surface-modified NTAs with a TiCl₄ treatment. The photovoltaic efficiencies of the DSSCs using TiO₂ NP, NTA, and TiCl₄-treated NTA electrodes are 4.25, 4.74, and 7.47 %, respectively. The highest performance was observed with a TiCl₄-treated TiO₂ NTA photoanode, although in the case of the latter two electrodes, the amounts of N719 dye adsorbed were similar and 68 % of that of the NP electrode. Electrochemical impedance measurements show that the overall resistance, including the charge–transfer resistance, was smaller with NTA morphologies than with NP morphologies. We suggest that a different electron transfer mechanism along the one-dimensional nanostructure of the TiO₂ NTAs contributes to the smaller charge–transfer resistance, resulting in a higher short circuit current (J _sc), even at lower dye adsorption. Furthermore, the TiCl₄-treated NTAs showed even smaller charge–transfer resistance, resulting in the highest J _sc value, because the downward shift in the conduction band edge improves the electron injection efficiency from the excited dye into the TiCl₄-treated TiO₂ electrodes.     

A Note on Shiffman's Theorems

Shiffman proved his famous first theorem, that if A R³ is a compact minimal annulus bounded by two convex Jordan curves in parallel (say horizontal) planes, then A is foliated by strictly convex horizontal Jordan curves. In this article we use Perron's method to construct minimal annuli which have a planar end and are bounded by two convex Jordan curves in horizontal planes, but the horizontal level sets of the surfaces are not all convex Jordan curves or straight lines. These surfaces show that unlike his second and third theorems, Shiffman's first theorem is not generalizable without further qualification.