Explicit solutions of Boussinesq--Burgers equation

Darboux transformation with multi-parameters for the Boussinesq--Burgers (B--B) equation is derived. For an application, some important explicit solutions of the B--B equation are obtained, including 2N-soliton solution and periodic solution. Finally, some elegant and interesting figures are plotted.     

蒂巴茵衍生物的合成研究

The reaction of 7α-acetyl-6,14-endoethano-6,7,8,14-tetrahydrothebaine with 2-（thien-2-yl）ethylmagnesium bromide was investigated. The tertiary alcohol derivative 7α-[R-l-hydroxyl-l-methyl-3-（thien-2-yl）propyl]）-6,14- endoethano-6,7,8,14-tetrahydrothebaine （3） and a by-product 4 were isolated. The structure of 4 was elucidated by X-ray analysis. The Grignard reaction shows high degree of stereoselectivity according with Cram rule. The crystal structure of 4 indicates that dihydrofuran ring was opened to form a phenolic hydroxyl group and a three-membered ring structure. It maintains the main rigid structure of morphine and contains a C（6）-C（14） enthano bridge. The 1-hydroxyl-1-methyl-3-（thien-2-yl）propyl group at C（7） position adopted S-configuration.     

Chemo-enzymatic Synthesis of Novel Oligo-N-acetyllactosamine Derivatives having a β(1-4)–β(1-6) Repeating Unit by Using Transition State Analogue Substrate

Chitinase-catalyzed hydrolytic and transglycosylating behavior of 1,2-oxazoline derivative of N-acetyllactosamine (LacNAc-oxa) 1 has been investigated. An extremely rapid hydrolysis (ring-opening of the oxazoline moiety) could be observed, suggesting that 1 behaves as a transition state analogue substrate for chitinase A1 (Bacillus circulans WL-12). This disaccharide monomer 1 was found to polymerize under basic conditions, giving rise to novel oligosaccharides having a β(1-4)–β(1-6) repeating unit in the main chain. The degree of polymerization of the resulting oligosaccharides was up to 5. This is the first example of enzymatic glycosylation reaction forming a β(1-6) bond catalyzed by chitinase.     

A new organic far-red mechanofluorochromic compound derived from cyano-substituted diarylethene

A new cyano-substituted diarylethene derivative (R-NH₂) with reversible far-red mechanofluorochromic property was synthesized and confirmed by standard spectroscopic methods. To the best of our knowledge, the 684 nm red-shifted wavelength of the ground R-NH₂ is the longest wavelength that has appeared in the literature. The mechanofluorochromic mechanism was investigated by small and wide-angle X-ray scattering and was ascribed to the destruction of crystalline structure. More in-depth study by infrared spectra and time-resolved emission-decay behaviors showed that the changes of C–H out-of-plane bending vibrations in aryl group of the compound and the obvious increase of fluorescence lifetime might be the fundamental reasons. The synthetic strategy reported here can be extended to prepare more and more long-wavelength emission mechanofluorochromic materials, which can broaden the scope of application of such materials and for thoroughly understanding the mechanofluorochromic mechanism.     

导数振荡与应变能极小的平面分段三次参数Hermite插值

由于分段三次参数Hermite插值的切矢往往被作为变量,故可对其进行优化以使得构造的插值曲线满足特定的要求.为了构造兼具保形性与光顺性的平面分段三次参数Hermite插值曲线,给出了一种通过同时极小化导数振荡和应变能来确定切矢的方法.首先以导数振荡函数和应变能函数为双目标建立了切矢满足的方程系统;然后证明了方程系统存在唯一解,并给出了解的具体表达式;最后给出了误差分析,并通过数值算例表明方法的有效性.结果表明,相对于导数振荡极小化方法和应变能极小化方法,所提出的导数振荡和应变能极小化方法同时兼顾了平面分段三次参数Hermite插值曲线的保形性和光顺性.     

Fréchet differentiability of the solutions of a semilinear abstract Cauchy problem

Sufficient conditions are found under which the solutions z(t;q) of a semilinear abstract Cauchy problem of the form are Fréchet differentiable with respect to the parameter q. An explicit form is provided for the sensitivity equation satisfied by the Fréchet derivative Dqz(t;q).     

Derivative discontinuities in density functional theory

Fifty years after the original formulation of density functional theory (DFT), subtle consequences of the mathematical mappings underlying its formalism continue to merit new views. In this article, we discuss the origin, the importance, and the challenges associated with finding the derivative discontinuity of the exchange-correlation (XC) energy of DFT at integer–electron numbers. We show how even the energy of a quantum electron gas with finite volume and number of electrons displays such derivative discontinuities, but continuous density functional approximations to the XC functional miss them entirely. We discuss some of the practical problems that arise due to this lack of derivative discontinuities in standard functionals, and explain new ways to recover them.     

Rogue Wave Solutions for Nonlinear Schrödinger Equation with Variable Coefficients in Nonlinear Optical Systems

In this paper, the generalized Darboux transformation is constructed to variable coefficient nonlinear Schrödinger (NLS) equation. The N-th order rogue wave solution of this variable coefficient NLS equation is obtained by determinant expression form. In particular, we present rogue waves from first to third-order through some figures and analyze their dynamics.     

Two-Dimensional Legendre Wavelets for Solving Time-Fractional Telegraph Equation

In this paper, we develop an accurate and efficient Legendre wavelets method for numerical solution of the well known time-fractional telegraph equation. In the proposed method we have employed both of the operational matrices of fractional integration and differentiation to get numerical solution of the time-telegraph equation. The power of this manageable method is confirmed. Moreover, the use of Legendre wavelet is found to be accurate, simple and fast.     

Synthesis and thermal properties of novel calix[4]arene derivatives containing 1,2,3-triazole moiety via K2CO3-catalyzed 1,3-dipolar cycloaddition reaction

Two calix[4]arene derivatives containing 1,2,3-triazole moiety were synthesized via K2CO3-catalyzed1,3-dipolar cycloaddition reaction between calix[4]arene-based azide and active methylene compounds in good yields.The structures of the two compounds synthesized herein were fully confirmed by 1HNMR,,（13）C NMR,and MS（ESI）.The thermal analysis showed that the mass losses of the synthesized compounds 4 and 5 containing 1,2,3-triazole groups are similar to each other.