Lagrange equations of nonholonomic systems with fractional derivatives

This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, based on these exchanging relationships, the Hamilton's principle is presented for non-conservative systems with fractional derivatives. Thirdly, Lagrange equations of the systems are obtained. Furthermore, the d'Alembert–Lagrange principle with fractional derivatives is presented,and the Lagrange equations of nonholonomic systems with fractional derivatives are studied. An example is designed to illustrate these results.     

融合插值点优化的多项式结构宽带波束形成器设计方法

多项式结构设计方法是主瓣指向可调宽带波束形成器设计的一类重要方法。多项式结构的阶数是有限的,导致主瓣实际指向与期望指向之间存在偏差,因而影响了波束形成器的指向性指数。针对这一问题,该文提出了一种基于插值点优化的多项式结构宽带波束形成器设计方法。首先,引入多项式结构插值点处阵列响应的空间导数约束,以减小主瓣指向偏差;进而利用粒子群优化算法对多项式结构中的插值点进行优化,以充分利用插值点位置提供的自由度进一步提升多项式结构宽带波束形成器的性能。优化设计结果表明,与现有设计方法相比,该文提出的方法不仅降低了主瓣的指向偏差,同时也提高了指向性指数,有效改善了多项式结构宽带波束形成器的性能。     

ELECTRON-RICH THIAZENES: SOME PRINCIPLES OF SYNTHESIS AND STRUCTURE

Abstract

General methods of preparation and typical bond distances and bond angles (at sulfur and nitrogen) are reviewed for cyclic sulfur–nitrogen compounds. Correlations between sulfur-nitrogen bond distance and unstrained bond angles in SNS and NSN groups can be used to assess angular strain in 4 and 5 atom thiazene rings and the optimum ring geometries of larger thiazene cations such as S₅N⁺ ₅ and S₄N_{2+ 4}. The geometry of S₃N^? ₃ is also discussed.     

Complexation and Transport of Alkali and Alkaline Earth Metal Cations by p-tert-Butyldihomooxacalix[4]arene Tetraketone Derivatives

The binding properties of three p-tert-butyldihomooxacalix[4]arene tetraketone derivatives (tert-butyl 2b, adamantyl 2c and phenyl 2d) in the cone conformation and one derivative (methyl 2a) in a partial cone conformation, towards alkali and alkaline earth metal cations have been established by extraction studies of metal picrates from water into dichloromethane, stability constant measurements in methanol and acetonitrile, and by ¹H NMR spectrometry. Transport experiments of metal picrates through a dichloromethane membrane were also performed. The results are compared to those obtained with closely-related calix[n]arene derivatives (n = 4 and 5) and discussed in terms of the substituents, size and conformational effects. Methylketone 2a is a poor binder for all the cations studied, due to its partial cone conformation. Ketones 2b, 2c and 2d show high extraction and complexation levels for the alkali cations, with similar profiles and preference for K⁺ and Na⁺ (plateau selectivity). Towards alkaline earth cations, these ketones show a strong peak selectivity for Ba²⁺ in extraction, but a plateau selectivity for Ca²⁺, Sr²⁺ and Ba²⁺ in complexation. The nature of the substituent attached to the ketone function has some influence on their binding properties, with phenylketone 2d being a slightly weaker binder than ketones 2b and 2c. ¹H NMR titrations confirm the formation of 1:1 complexes between the ketones and the cations studied, also indicating that they should be located inside the cavity defined by the phenoxy and carbonyl oxygen atoms. Ketones 2b, 2c and 2d show transport rates that do not follow, in general, the same trends observed in extraction and complexation.     

Efficient Friedländer Synthesis of Quinoline Derivatives from 2-Aminoarylketones and Carbonyl Compounds Mediated by Recyclable PEG-Supported Sulfonic Acid

2-Aminoarylketones undergo smooth condensation with α-methylene ketones in the presence of 10 mol% of poly(ethylene glycol) (PEG)–supported sulfonic acid under mild reaction conditions to afford the corresponding poly-substituted quinolines in excellent yields. The catalyst can be recovered by simple filtration and can be recycled in subsequent reactions. The method is simple, cost-effective, and environmentally benign.     

Green Method for the Synthesis of Benzo[f]pyrimido[4,5-b]quinoline Derivatives Catalyzed by Iodine in Aqueous Media

A convenient one-pot synthesis of benzo[f]pyrimido[4,5-b]quinoline derivatives is described via three-component reaction of benzaldehydes, naphthalen-2-amine, and barbituric acid at room temperature in aqueous media catalyzed by iodine. Compared with other methods, this three-component reaction used a green solvent, gave good yields, and was operationally simple.     

三嗪类化合物的合成及其产酸性能研究

合成了一系列的三嗪类光生酸剂1a—1e,确定了它们的结构,并对1e在乙腈溶剂中365和405nm光下的曝光分解产酸性能进行了初步的定量研究.结果表明,在测定浓度范围内分解量子产率和产酸量子产率基本上都不随浓度的变化而变化,在405nm光下比在365nm光下有更高的分解和产酸量子效率.有关这类化合物的光生酸性能与曝光波长的关系正在进一步研究中.     

一种新型三角架罗丹明B荧光探针对Cu～（2＋）识别性能研究

设计、合成了一种新颖的三角架结构罗丹明B衍生物（2）.在乙醇-水（8/1,V/V）介质中,用Tris-HCl控制体系pH为6.8,观察到Cu^2＋对化合物2的荧光及紫外-可见吸收增强性能,同时化合物2对Cu^2＋具有较高的选择性响应.选择最大激发和发射波长为557/577nm,测定了探针2（1.00×10^-5mol·L^-1）对Cu^2＋响应的校准曲线,线性范围为0.10～10.00×10^-5mol·L^-1,相关系数R^2=0.9964（n=15）,检出限为1.129×10^-7mol·L^-1,平行测定5次的相对标准偏差（R.S.D.）为2.2%;以557nm为最大吸收波长测定紫外吸收,Cu^2＋响应的浓度线性范围为0.50～25.00×10^-5mol·L^-1,相关系数R^2=0.9948（n=13）,检出限为3.338×10^-7mol·L^-1.     

Syntheses, Crystal Structures and Fluorescence Properties of Two Triazolyl Derivatives with Biphenyl Links

Two novel triazolyl derivatives with biphenyl links, namely 4,4-bis（1,2,4-triazol-1-ylmethyl）biphenylene 1 and 4,4-bis（3,5-dimethyl-1,2,4-triazol-1-ylmethyl）biphenylene 2, have been synthesized and structurally characterized by single-crystal X-ray diffraction. Compounds 1·H2O·HCl and 2·2H2O·2HCl crystallize in the monoclinic system with space group C2/c and P21/c, respectively. The dihedral angles of the two phenyl rings are 30.26（6）° in 1·H2O·HCl, while co-planar （0.00（7）°） in 2·2H2O·2HCl. In 1·H2O·HCl, the N-H…O hydrogen bonds link 1 to form chain-like structures which are further connected by O-H…Cl, C-H…Cl, C-H…O and π-π supramolecular interactions. The hydrogen bonds of O-H…Cl in 2·2H2O·2HCl provide distinguishing P/M helical chains along the b axis, and these chains are further connected by N-H…O hydrogen bonds to generate a 2D structure. Compounds 1 and 2 in methanol solution show much stronger emission bands at 319 nm than biphenyl at 316 nm under excitation at 260 nm.