2个位势的Ablowitz-Ladik等谱方程的Complexiton解

借助双Casoratian技巧和构造双Wronski行列式元素的矩阵方法,求出2个位势的Ablowitz-Ladik等谱方程的Complexiton解和周期解,并通过将矩阵取成不同的组合类型,进而分别得到该方程具有双Casorati行列式形式的新解,即Complexiton解与类有理解的混合解、Complexiton解与Matveev解的混合解.     

Crystalline Boragermenes

Boragermene 3 featuring a double bond between the Ge and dicoordinate B atoms has been synthesized for the first time by reacting the cyclic (alkyl)(boryl)germylene–PMe₃ adduct 1 with Cl₂BN(SiMe₃)₂ followed by reductive dehalogenation with KC₈. Addition of a Lewis base (^MeNHC) to 3 leads to the formation of the corresponding adduct 4 , which shows double bond character between the Ge and tricoordinate B atoms. Compound 3 undergoes hydrogenation with H₂ concomitant with a complete scission of the Ge=B bond.     

α-Mangostin exhibits antidepressant-like effects mediated by the modification of GABAergic,serotonergic and dopaminergic systems

Abstract

The present study explored the antidepressant-like activity of α-mangostin (α-MG) and the possible mechanism in this process in the tail suspension test (TST) in mice. The results revealed that α-MG (5?mg/kg, i.p.) exhibited markedly antidepressant-like activity, which could be reversed by pretreatment with haloperidol (a non-selective D₂ receptor antagonist), bicuculline (a competitive GABA antagonist), p-chlorophenylalanine (an inhibitor of 5-HT synthesis). Meanwhile, α-MG also effectively increased the brain DA, 5-HT and GABA levels in mice exposed to TST, indicating that the antidepressant-like effect of α-MG might be mediated by the GABAergic, serotonergic and dopaminergic systems.

     

若干高维可积和不可积模型的严格解

可积和不可积模型可以描述自然科学中的诸多现象, 寻找高维非线性模型的严格解已成为可积系统的一个重要研究内容. 结合达布变换法和多线性分离变量法, 可以得到多个(2+1)维非线性模型包含任意函数的严格解, 通过选取不同的任意函数, 构造这些非线性模型新的相互激发模式. 进一步推广了形变映射理论, 建立了变系数 场和sine-Gordon以及双sine-Gordon场的形变映射关系, 从而得到高维不可积模型包含任意函数的新严格解. 对任意函数的不同选择, 构造了sine-Gordon和双sine-Gordon可积模型丰富的局域解和周期解, 如多solitoff解及其周期波推广、周期形变的蛇形孤波解以及变模的拟周期解等.     

Similarity of hybrid numbers

The set of hybrid numbers $𝕂$ is a noncommutative number system that unified and generalized the complex, dual, and double (hyperbolic) numbers with the relation ih =− hi =ε+ i. Two hybrid numbers p and q are said to be similar if there exist a nonlightlike hybrid number x satisfying the equality x ⁻¹ qx = p . And, it is denoted by p ∼ q . In this paper, we study the concept of similarity for hybrid numbers by solving the linear equations px = xq and qx − xp = c for $\text{◂,▸}\mathbf{p},\mathbf{q},\mathbf{c}\in 𝕂\mathbf{.}$     

Fano profile in a novel double cavity optomechanical system with harmonically bound mirrors

We investigate a double cavity optomechanical system generating single and double Fano resonance (multi-Fano). By altering a single parameter, the tunnelling rate g of the middle mirror, we are able to switch between single and double Fano line shapes. The first spectral line shape is stronger in the case of multi-Fano than in the case of single Fano. Also the behaviour of the steady state value of the displacement of the middle mirror, with respect to g, heavily influences the behaviour of double Fano lines in our scheme. This tunability along with using a single pump and signal/probe laser has an added advantage in situations where only low power consumption is available.     

Homo‐double helix formation of an optically active conjugated polymer bearing carboxy groups and amplification of the helicity upon complexation with achiral and chiral amines

An optically active, m‐terphenyl‐based π‐conjugated polymer bearing carboxy groups was synthesized by the copolymerization of the diethynyl monomer bearing a carboxy group with (S,S)‐2,5‐bis(2‐methylbutoxy)‐1,4‐dibromobenzene using Sonogashira reaction. The copolymer showed a weak circular dichroism (CD) in the main‐chain chromophore region due to a homo‐double helix formation with an excess helical handedness biased by the chiral alkoxy substituents through self‐association. However, upon complexation with achiral amines, such as piperidine, the CD intensity of the polymer significantly increased resulting in the formation of a greater excess one‐handed homo‐double helix via hydrogen‐bonded inclusion complexation with the achiral amines between each strand, leading to the amplification of the helicity. A preferred‐handed homo‐double helix was also induced in the polymer in the presence of nonracemic amines. The effect of the achiral and chiral amines on the homo‐double helix formation was investigated by comparing the CD spectra of the polymer to those of its model dimer. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 990–999     

Thermoresponsive polymersome from a double hydrophilic block copolymer

The article describes synthesis and thermally triggered self‐assembly of a Poly (ethylene oxide)‐block‐poly (N‐insopropylacrylamide) (PEO‐b‐PNIPAm) in aqueous medium. At rt, the polymer remains as unimer, however, at lower critical solution temperature (LCST) of PNIPAm (32 °C), it forms a rather large undefined aggregate which at slightly elevated temperature (～40 °C) converges to well defined polymersome structure (Critical aggregation concentration = 0.45 mg/mL) with hydrodynamic diameter of 40–50 nm. By lowering the temperature, initial swelling of the compact vesicle followed by reversible disassembly to unimer was noticed. The polymersome exhibits encapsulation ability to a hydrophilic dye Calcein which can be spontaneously released by lowering the temperature below cloud point. Likewise a hydrophobic dye namely 8‐Anilino‐1‐naphthalenesulfonic acid (ANS) can also be encapsulated and released by thermal trigger. Detail photoluminescence studies reveal ANS dye can be used as a generalized probe molecule for detecting LCST of a thermoresponsive polymer by “fluorescence on” above LCST even by cursory observation. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2444–2451     

The double deflating technique for irreducible singular M-matrix algebraic Riccati equations in the critical case

As is known, Alternating-Directional Doubling Algorithm (ADDA) is quadratically convergent for computing the minimal nonnegative solution of an irreducible singular M-matrix algebraic Riccati equation (MARE) in the noncritical case or a nonsingular MARE, but ADDA is only linearly convergent in the critical case. The drawback can be overcome by deflating techniques for an irreducible singular MARE so that the speed of quadratic convergence is still preserved in the critical case and accelerated in the noncritical case. In this paper, we proposed an improved deflating technique to accelerate further the convergence speed – the double deflating technique for an irreducible singular MARE in the critical case. We proved that ADDA is quadratically convergent instead of linearly when it is applied to the deflated algebraic Riccati equation (ARE) obtained by a double deflating technique. We also showed that the double deflating technique is better than the deflating technique from the perspective of dimension of the deflated ARE. Numerical experiments are provided to illustrate that our double deflating technique is effective.