Structure and dynamics of dense monolayers of no adsorbed on Rh(111) in equilibrium with the gas phase in the Torr pressure range

Using scanning tunneling microscopy, we show the phase transition between new structures of NO on Rh(111) in equilibrium with the gas phase near 300 K, in the Torr pressure range. Two phases with (2 x 2) and (3 x 3) periodicity transform into each other as the pressure and temperature change around the equilibrium P-T line. By measuring P and T at coexistence, we determined the heat of adsorption in the (3 x 3) structure. From the phase boundary dynamics, the activation energy barrier between phases were estimated. The results demonstrate that unique information can be obtained from high-pressure and high-temperature studies.     

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.     

On an estimate for Bloch and Doob norm and covering problem in Doob's class

For any fixed 0 < π ? 2π, let D(π) be the family of all holomorphic functions in the unit disk Δ which satisfy (i)f(0) = 0 and (ii) $\text{lim inf}{}_{\mathrm{z\; \to \; \pi ¦f(z)¦\; ?\; 1}}$, for all π lying on some arc A_f ? ?Δ with arclength $\text{¦A}{}_{\mathrm{f}}\text{¦ ? π}$. We show that for each 0 < ε < 1, there is a π₀ > 0 such that for any f?D(π) with π < π₀, the Bloch and Doob norm respectively satisfy

$\text{6f6}{}_{\mathrm{B}}\text{=}\text{sup}\text{z?Δ}\text{|f′(z)| (1?|z|}{}^2\text{) > 2(1 ? ε)}\text{log}\text{1+}\text{cos}\text{(}\text{p}\text{2}\text{1?}\text{cos}\text{(}\text{p}\text{2}{}^{\mathrm{?1}}$

$\text{6f6}{}_{\mathrm{D}}\text{=}\text{sup}\text{z?Δ}\text{|f′(z)| (1?|z|) > (1 ? ε)}\text{log}\text{1}\text{1?}\text{cos}\text{(}\text{p}\text{2}{}^{\mathrm{?1}}$

These two estimates do not hold with ε = 0.     

Collective bands in 104,106,108Mo

We have used our analysis of γ-γ-γ data (5.7 × 10¹¹ triples and higher folds) taken with Gammasphere from prompt γ rays emitted in the spontaneous fission of ²⁵²Cf to study the collective bands in ^104,106,108Mo. The one-phonon and two-phonon γ-vibrational bands and known two-quasiparticle bands in neutron-rich ^104,106Mo were extended to higher spins. The one-and two-phonon γ-vibrational bands have remarkably close energies for transitions from the same spin states and identical moments of inertia. Several new bands are observed and are proposed as quasiparticle bands in ^104,106Mo, along with the first β-type vibrational band in ¹⁰⁶Mo. The quasiparticle bands have essentially constant moments of inertia near the rigid-body value that indicate blocking of the pairing interaction. Candidates for chiral doublet bands in ¹⁰⁶Mo are strong. These are the first reported chiral vibrational bands in an even-even nucleus. The text was submitted by the authors in English.     

Depth-controlled reconstruction of 3D integral image using synthesized intermediate sub-images

In this paper, we propose a method that controls the depth of the three-dimensional (3D) object existing over the depth-of-focus in integral imaging. The depth control method is performed only in a computer by synthesizing the intermediate sub-images between original sub-images obtained by transforming the captured elemental images. In the reconstruction process, we can obtain reconstructed 3D images with the better image quality within depth-of-focus than that reconstructed over the depth-of-focus. To demonstrate the feasibility of our method, optical and computational experiments are carried out and its results are presented.     

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.