Solitons and other solutions of the nonlinear fractional Zoomeron equation

In order to investigate the nonlinear fractional Zoomeron equation, we propose three methods, namely the Jacobi elliptic function rational expansion method, the exponential rational function method and the new Jacobi elliptic function expansion method. Many kinds of solutions are obtained and the existence of these solutions is determined. For some parameters, these solutions can degenerate to the envelope shock wave solutions and the envelope solitary wave solutions. A comparison of our new results with the well-known results is made. The methods used here can also be applicable to other nonlinear partial differential equations. The fractional derivatives in this work are described in the modified Riemann–Liouville sense.     

高阶微商系统Dirac猜想的一个反例

由扩展正则作用量导出了高阶微商奇异Lagrange量系统的扩展正则Noether恒等式.从广义约束Hamilton系统相空间中对称性分析，给出高阶微商系统Dirac猜想的一个反例. 用正则Noether定理、 正则Noether恒等式和扩展正则Noether恒等式说明在此反例中Dirac猜想失效, 讨论中没有将约束线性化. 关键词： 高阶微商系统 约束Hamilton系统 正则对称性 Dirac猜想     

Theoretical studies on structure and performance of [1,2,5]‐oxadiazolo‐[3,4‐d]‐pyridazine‐based derivatives

Based on energetic compound [1,2,5]‐oxadiazolo‐[3,4‐d]‐pyridazine, a series of functionalized derivatives were designed and first reported. Afterwards, the relationship between their structure and performance was systematically explored by density functional theory at B3LYP/6‐311 g (d, p) level. Results show that the bond dissociation energies of the weakest bond (N–O bond) vary from 157.530 to 189.411 kJ · mol^?1. The bond dissociation energies of these compounds are superior to that of HMX (N–NO_2, 154.905 kJ · mol^?1). In addition, H1, H2, H4, I2, I3, C1, C2, and D1 possess high density (1.818–1.997 g · cm^?3) and good detonation performance (detonation velocities, 8.29–9.46 km · s^?1; detonation pressures, 30.87–42.12 GPa), which may be potential explosives compared with RDX (8.81 km · s^?1, 34.47 GPa ) and HMX (9.19 km · s^?1, 38.45 GPa). Finally, allowing for the explosive performance and molecular stability, three compounds may be suggested as good potential candidates for high‐energy density materials. Copyright © 2016 John Wiley & Sons, Ltd.     

Morphology and spectral properties of thin films of benzoxazole derivatives of biphenyl

We have studied the spectral properties and morphology of thin films (TVD films) formed by thermal vacuum deposition of 4,4′-bis[(E)-1-(1,3-benzoxazol-2-yl)-2-ethenyl]-1,1′-biphenyl and its substituted derivatives. We have shown that introducing bulky 2,2′-oxyhexyl substituents into the biphenyl units leads to a shift of the fluorescence maximum for the TVD films toward shorter wavelengths, a decrease in their photostability, and aggregation of the films during storage. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 3, pp. 300–303, May–June, 2007.     

吡喃酮型花色苷衍生物的制备、光谱特性及抗氧化活性研究

吡喃酮型花色苷衍生物是一类具有非氧鎓离子结构和内酯型吡喃环结构的新型多酚类化合物。本研究以植物花色苷为原料,通过羧基吡喃花色苷形成及微氧化等两步反应法,结合柱色谱分离纯化技术,制备高纯度的吡喃酮花色苷衍生物A (Oxovitisin A)标准品;高效液相色谱-光电二极管阵列检测器-串联质谱法(HPLC-DAD-ESI-MS/MS)分析鉴定出纯化后反应产物Oxovitisin A的纯度达99%以上。利用荧光光谱仪、紫外可见光谱仪及超微弱化学发光光谱仪研究了Oxovitisin A及其前体物质花色苷(锦葵素-3-葡萄糖苷,Mv-3-gluc)与羧基吡喃花色苷A(Vitisin A))的光谱特性、色泽稳定性及抗氧化活性。结果表明：Oxovitisin A在440 nm激发波长下有最大荧光峰,最大发射波长490 nm,而具有氧鎓离子结构的两种前体物质无荧光特性。紫外光谱结合LAB色泽空间表征参数显示Oxovitisin A在不同pH值条件下具有不同的结构稳定性和色泽稳定性。Mv-3-gluc,VitisinA和Oxovitisin A在不同体系中均表现出良好的抗氧化活性,清除超氧阴离子自由基的IC₅₀值分别为71.4,30.7和19 μg·mL-1(抗坏血酸28 μg·mL-1),清除羟自由基的IC₅₀值分别为1.68,3.524,2.854 μg·mL-1(抗坏血酸8.441 μg·mL-1),对双氧水清除率的IC₅₀值分别为1.311,0.4098和0.288 μg·mL-1(抗坏血酸3.265 μg·mL-1),表明Oxovitisin A清除自由基和抗氧化的能力均高于反应前体物Mv-3-gluc和VitisinA及抗坏血酸。     

C60醛类衍生物非线性光学特性研究

研究了加合不同取代基团的C60醛类衍生物的光学非线性性质。利用简并四波混频（DFMW）方法获得了C60醛类各衍生物的三阶光学非线性超级化率γ^(3)及相应的三阶光学非线性系数χ^(3)值。同时也研究了它们各自的光限幅特性。结果表明：不同的取代基对C60醛类衍生物三阶光学非线性及光限幅特性的影响不同。     

基于遗传算法的非线性映射预测硝基苯化合物的生物毒性

摘要: 非线性映射是一种降维处理技术,通过Sammon算法可以将多维分析问题转化为二维问题分析。应用该法的关键在于寻求二维空间的最佳投影点,这可以转化为一个复杂的非线性优化问题来进行解决。遗传算法是解决各类函数优化和非线性映射问题的一种有效算法。以硝基苯化合物的生物毒性的模式识别为例,编制基于误差函数的目标函数和遗传算法约束参数,应用基于MATLAB的遗传算法工具箱进行优化求解。结果表明:该工具箱在求解此类非线性优化问题上是有效的, 基于遗传算法的非线性映射的预测结果比其它方法要好些。     

Approximate first-order and second-order directional derivatives of a marginal function in convex optimization

Given a convex functionf: ^p × ^q (–, +], the marginal function is defined on ^p by (x)=inf{f(x, y)|y ^q }. Our purpose in this paper is to express the approximate first-order and second-order directional derivatives of atx ₀ in terms of those off at (x ₀,y ₀), wherey ₀ is any element for which (x ₀)=f(x ₀,y ₀).The author is indebted to one referee for pointing out an inaccuracy in an earlier version of Theorem 4.1.     

壳聚糖季铵盐的合成及结构表征

用异相法合成了水溶性壳聚糖季铵盐衍生物，并用红外光谱及核磁共振谱进行结构表征。结果表明：在中性反应条件下，壳聚糖分子的季铵盐衍生化反应主要发生于亲该中心Ｃ２位的氨基上，所合成的壳聚糖季铵盐衍生物可直接溶解于水。其水溶液可以任意比例与乙醇、丙二醇、甘油等混溶。     

Generalized sensitivity analysis of nonlinear programs using a sequence of quadratic programs

ABSTRACT

Local sensitivity information is obtained for KKT points of parametric NLPs that may exhibit active set changes under parametric perturbations; under appropriate regularity conditions, computationally relevant generalized derivatives of primal and dual variable solutions of parametric NLPs are calculated. Ralph and Dempe obtained directional derivatives of solutions of parametric NLPs exhibiting active set changes from the unique solution of an auxiliary quadratic program. This article uses lexicographic directional derivatives, a newly developed tool in nonsmooth analysis, to generalize the classical NLP sensitivity analysis theory of Ralph and Dempe. By viewing said auxiliary quadratic program as a parametric NLP, the results of Ralph and Dempe are applied to furnish a sequence of coupled QPs, whose unique solutions yield generalized derivative information for the NLP. A practically implementable algorithm is provided. The theory developed here is motivated by widespread applications of nonlinear programming sensitivity analysis, such as in dynamic control and optimization problems.