Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.     

Geometrically distinct solutions for Klein–Gordon–Maxwell systems with super-linear nonlinearities

This paper is concerned with the following Klein–Gordon–Maxwell system $\left\{\begin{array}{c}-△u+V\left(x\right)u-(2\omega +\varphi )\varphi u=f(x,u),x\in {\mathbb{R}}^3,\hfill \\ △\varphi =(\omega +\varphi )u^2,x\in {\mathbb{R}}^3,\hfill \end{array}\right.$where $\omega >0$ is a constant, $V$ and $f$ are periodic with respect to $x$. By combining deformation type arguments, Lusternik–Schnirelmann theory and some new tricks, we prove that the above system admits infinitely many geometrically distinct solutions under weaker superlinear conditions instead of the common super-cubic conditions on $f$. Our result seems new and extends the previous results in the literature.     

Periodic,breather and rogue wave solutions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation in fluid dynamics

Under investigation in this paper is a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the propagation of nonlinear waves in fluid dynamics. Periodic wave solutions are constructed by virtue of the Hirota–Riemann method. Based on the extended homoclinic test approach, breather and rogue wave solutions are obtained. Moreover, through the symbolic computation, the relationship between the one-periodic wave solutions and one-soliton solutions has been analytically discussed, and it is shown that the one-periodic wave solutions approach the one-soliton solutions when the amplitude $\eta \to 0$.     

Refractometer based on a tapered Mach–Zehnder interferometer with Peanut-Shape structure

A novel refractometer based on tapered Mach–Zehnder modal interferometer (MZI) is proposed and experimentally demonstrated. This sensor is composed of a pair of Peanut-Shape structures and an embedded taper – the former excites high-order cladding modes, while the latter enhances the evanescent field. As the effective refractive index (RI) of cladding is based on the changes of surrounding RI, thus extinction ratio will change due to the alteration of the distribution of power in the fiber which is induced by various differences of core and cladding for RI. As a result, the maximum RI sensitivity of 240.78 extinction ratio/RIU (refractive index unit) is achieved within the range from 1.3334 to 1.4081.     

Temps de cohérence d'un condensat de Bose–Einstein dans un gaz isolé harmoniquement piégé

We study the condensate phase dynamics in a low-temperature equilibrium gas of weakly interacting bosons, harmonically trapped and isolated from the environment. We find that at long times, much longer than the collision time between Bogoliubov quasi-particles, the variance of the phase accumulated by the condensate grows with a ballistic term quadratic in time and a diffusive term affine in time. We give the corresponding analytical expressions in the limit of a large system, in the collisionless regime and in the ergodic approximation for the quasi-particle motion. When properly rescaled, they are described by universal functions of the temperature divided by the Thomas–Fermi chemical potential. The same conclusion holds for the mode damping rates. Such universality class differs from the previously studied one of the homogeneous gas.     

Mechanism of Disulfide–Disulfide Interchange in Polysulfide Polymer Melt Blend by Electron Ionization Mass Spectrometry. II

Abstract

The degree of randomization, q, of structural units in melt blends of the polysulfide homopolymers A(PS1) and B(PS2), wherein the disulfide equivalents D _A/D _B = 1, were studied by electron ionization mass spectrometry. Over the temperature range of 207–219°C, the relaxation process, due to the dominant disulfide–disulfide interchange reactions, is postulated to follow an associative reaction mechanism. These intermolecular disulfide–disulfide interactions promote a transient enhancement of the sulfur rank in the activated complex resulting in formation of the randomized co‐polymer AB. The mass spectrometric experimental design enabled measurement of concentrations of reactants A(PS1) and B(PS2), as well as the randomized copolymer AB, by monitoring the abundance of dimer units a₂, b₂, and ab, respectively as a function of time. The degree of randomization, q, was observed in the absence of catalysts or solvents, notwithstanding the solvent/solute and solute/solvent characteristics of the polymer melt blend. The mechanism of this randomization process, was rationalized on the basis of the properties of sulfur, aided by the observation of macrocyclic monomeric and dimeric units during the retro‐polymerization reactions under the EI/MS conditions employed. The model polysulfide polymers A(PS1) and B(P52), used in this study were synthesized from bis(2‐chloroethyl)ether and bis(2‐chloro ethoxy)methane, respectively.     

Effects of laser irradiation on optical properties of a-Se100−x Te x thin films

The effect of laser irradiation on the optical properties of thermally evaporated Se_100?x Te _x (x=8, 12, 16) chalcogenide thin films has been studied. The result shows that the irradiation causes a shift in the optical gap. The results have been analyzed on the basis of laser irradiation-induced defects in the film. The width of the tail of localized state in the band gap has been evaluated using the Urbach edge method. As the irradiation time increases, the values of the optical energy gap for all compositions decrease, while tail energy width increases. It is also observed that the optical energy gap decreases with increasing Te content in the alloy. These changes are a consequence of an increment in disorder produced by laser irradiation in the amorphous structure of thin film.     

Syntheses,structures, and properties of Ni(II) complexes with 5,5′-bis(4-halogenphenyl)diazo-dipyrromethane

Ni(II) complexes with 5,5′-bis(4-halogenphenyl)diazo-dipyrromethane have been synthesized and characterized by X-ray crystallography. All the complexes have similar crystal structures in which Ni(II) is square-planar by coordinating to two pyrrole and two azo nitrogen atoms. The azo-pyrroles of the ligands can be converted to the hydrazone tautomer after complexing nickel. Moreover, the C–H?···?Ni interaction played an important role in directing self-assembly of the complexes. The UV-Vis spectra of the complexes showed great difference with the metal complexes of pyrrol-2-imine.     

Synthesis of Fused Thioxo-Pyran Systems From α-Methylene Carbonyl Compounds and Bismethylene-1,3-dithietane

A number of [2, 1-b] fused phosphono substituted-thioxo-pyrans 7,10,13 and 18 have been regioselectively synthesised from the reaction of the corresponding α-methylene carbonyl compound with phosphenato-substituted 1,3-dithietane 1. Conversely, 2-thiohydantoin 14 reacts with 1 to afford the respective 4-substituted derivative 15.