Optimal control approach to stability criteria on Hill’s equations

This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill's equations with nonnegative potential. By optimal control methods developed in 1990s, we obtain several stability criteria including Lyapunov's criterion, Neǐgauz and Lidskiǐ's criterion. Secondly, we present stability criteria on Hill's equations with sign-changing potential in which Brog's criterion and Krein's criterion are included.     

Enantioselective organocatalytic Michael addition reactions between N-heterocycles and nitroolefins

[reaction: see text] A method for Michael addition of N-heterocycles to nitroolefins has been developed. The process is promoted by a cinchona alkaloid derivative to give Michael adducts in moderate to high enantioselectivities.     

Particles’ Tunneling in Spherically Symmetric Spacetimes with Dark Matter

Applying the Hamilton-Jacobi method, we investigate particles’ tunneling behavior in a spherically symmetric spacetime with dark matter. The tunneling rate and Hawking temperature at the event horizon are obtained. The result shows that the dark matter parameter β has an important influence on the Hawking temperature and the tunneling rate.     

Effect of fused silica subsurface defect site density on light intensification

The effect of defect density on the modulation of incident laser waves is investigated. First, based on the actual defect distribution in the subsurface of fused silica, a three-dimensional (3D) grid model of defect sites is constructed. The 3D finite-difference time-domain method is developed to solve the Maxwell equations. Then the electrical field intensity in the vicinity of the defect sites in the subsurface of fused silica is numerically calculated. The relationships between the maximal electrical field intensity in fused silica and the geometry of the defect sites are given. The simulated results reveal that the modulation becomes more remarkable with an increase of the defect density. In addition, the effect of the distribution mode of defects on modulation is discussed. Meanwhile, the underlying physical mechanism is analyzed in detail.     

Role of chelating agent in chemical and fluorescent properties of SnO2 nanoparticles

A modified polyacrylamide gel route is applied to synthesize SnO2 nanoparticles. High-quality SnO2 nanoparticles with a uniform size are prepared using different chelating agents. The average particle size of the samples is found to depend on the choice of the chelating agent. The photoluminescence spectrum detected at λex = 230 nm shows a new peak located at 740 nm due to the surface defect level distributed at the nanoparticle boundaries.     

Coulomb‐enhanced spin–orbit coupling and semiconductor to half‐metal transition under pressure in Sr2CrReO6

Ordered Sr₂CrReO₆ has been synthesized recently. It is measured to be ferrimagnetic semiconductor, in contrary to the previous reports of metallic properties. To solve the discrepancy, we have investigated the compound by using the density functional theory. The semiconducting behavior is reproduced by including the electron correlation and spin–orbit coupling simultaneously. The calculated band gap is 0.22 eV, close to the experimental value of 0.21 eV. A large orbital moment of 0.69µ_B is found for Re, which is caused by the Coulomb‐enhanced spin–orbit coupling. By applying pressure, a semiconductor to half‐metal transition is observed through 5% volume compression.

     

S~(n+1)上具有三个互异常仿Blaschke特征值的超曲面

设x∶M→S⁽ⁿ⁺¹⁾是(n+1)-维单位球面上不含脐点的超曲面.在S(n+1)是(n+1)-维单位球面上不含脐点的超曲面.在S⁽ⁿ⁺¹⁾的Mbius变换群下浸入x的四个基本不变量是:Mbius度量g;Mbius第二基本形式B;Mbius形式φ和Blaschke张量A.对称的(0,2)张量D=A+λB也是Mbius不变量,其中λ是常数.D称为浸入x的仿Blaschke张量,仿Blaschke张量的特征值称为浸入x的仿Blaschke特征值.如果φ=0,对某常数λ,仿Blaschke特征值为常数,那么超曲面x∶M→S(n+1)的Mbius变换群下浸入x的四个基本不变量是:Mbius度量g;Mbius第二基本形式B;Mbius形式φ和Blaschke张量A.对称的(0,2)张量D=A+λB也是Mbius不变量,其中λ是常数.D称为浸入x的仿Blaschke张量,仿Blaschke张量的特征值称为浸入x的仿Blaschke特征值.如果φ=0,对某常数λ,仿Blaschke特征值为常数,那么超曲面x∶M→S⁽ⁿ⁺¹⁾称为仿Blaschke等参超曲面.本文对具有三个互异仿Blaschke特征值(其中有一个重数为1)的仿Blaschke等参超曲面进行了分类.     

A Niobium Oxyiodate Sulfate with a Strong Second‐Harmonic‐Generation Response Built by Rational Multi‐Component Design

A novel niobium oxyiodate sulfate, Nb₂O₃(IO₃)₂ (SO₄), was fabricated by a rational multi‐component design under moderate hydrothermal conditions. This multi‐component design is inspired by an interesting niobium oxysulfate reaction, which opens a new door for synthetic method to effectively introduce refractory metals such as Nb into crystal structures by hydrothermal synthesis. Nb₂O₃(IO₃)₂(SO₄) features a cube‐like topological structure with a large phase‐matching second harmonic generation (SHG) response (6×KDP), a wide transparency window (0.38–8 μm), and a high laser damage threshold (LDT) (20×AgGaS₂). It has the highest thermostability (stable up to 580 °C under air) among reported non‐centrosymmetric (NCS) iodates and sulfates and is stable in water and even concentrated H₂SO₄. Furthermore, Nb₂O₃(IO₃)₂(SO₄) is a unique nonlinear optical (NLO) material among iodates and sulfates, because its SHG effect is mainly caused by the MO₆ units rather than the IO₃ or SO₄ units, which is demonstrated by density functional theory (DFT) calculations.