Complete solutions of a family of quartic Thue and index form equations

Continuing the recent work of the second author, we prove that the diophantine equation

for has exactly 12 solutions except when , when it has 16 solutions. If denotes one of the zeros of , then for we also find all with .

     

Geometric indices and the Alexander polynomial of a knot

It is well-known that any Laurent polynomial satisfying and is the Alexander polynomial of a knot in . We show that can be realized by a knot which has the following properties simultaneously: (i) tunnel number 1; (ii) bridge index 3; and (iii) unknotting number 1.

     

关于极大子群的指数复合

利用Ｄｅｓｋｉｎｓ在１９５９年所定义的有限群的极大子群的指数复合,给出了有限群为π－可解,可解,超可解,幂零的若干充要条件。     

线阵CCD在折射率测量中的应用

提出利用线阵CCD传感器作为反射光或折射光的光强分布接收装置的折射率测量方法,研究了如何根据光强的空间分布曲线确定布儒斯特角或临界全反射角的定标方案,讨论了测量结果可能达到的精确度。     

两端任意支承的矩形截面钢筋混凝土梁可靠性优化设计

利用雷－莉法把非正态变量转换为当量正态变量,建立了在多个任意分布基本变量情况下的２性结构优化的设计数学模型。最后给出了设计人格最小的矩形截面钢筋混凝土梁的可靠性优化设计实例。     

江汉平原洪涝灾害遥感监测方法

用遥感数据及常规气水文数据获取涝灾信息,用ＤＥＭ（数字高程模型）或微等高距地形图及其导出的高程－面积－容积模型作涝灾淹没损失估算的基本技术手段,用植被指数作主要方法对江汉平原“１９９１．０７”暴雨涝灾作了灾情评价及减产估算。     

以体系可靠度为目标的结构设计

在针对现行结构设计方法不足的同时．论述了以体系可靠度为目标的结构设计是今后结构设计的发展趋势,并提出了"调整截面抗力设计法"以合理分配和调整结构体系各主要失效机构的可靠度。     

Correlations between Van der Waals' volume and retention index general equation applicable to different homologous series

Summary Correlations between retention index (R_I) and Van der Waals' volume (V_W) in homologous series of n-alcohols, n-aldehydes and esters are studied on the stationary phases Carbowax 1540 and squalane. Influence of functional groups is quantified and a method for obtaining one general equation, valid for an indeterminate number of homologous series, is proposed.     

Graphs to chemical structures. 4: Combinatorial enumeration of planted three-dimensional trees as stereochemical models of monosubstituted alkanes

Planted three-dimensional (3D) trees, which are defined as a 3D version of planted trees, are enumerated by means of Fujita’s proligand method formulated in Parts 1–3 of this series [Fujita in Theor Chem Acc 113:73–79, 80–86, 2005; Fujita in Theor Chem Acc 115:37–53, 2006]. By starting from the concepts of proligand and promolecule introduced previously [Fujita in Tetrahedron 47:31–46, 1991], a planted promolecule is defined as a 3D object in which the substitution positions of a given 3D skeleton are occupied by a root and proligands. Then, such planted promolecules are introduced as models of planted 3D-trees. Because each of the proligands in a given planted promolecule is regarded as another intermediate planted promolecule in a nested fashion, the given planted promolecule is recursively constructed by a set of such intermediates planted promolecules. The recursive nature of such intermediate planted promolecules is used to derive generating functions for enumerating planted promolecules or planted 3D-trees. The generating functions are based on cycle indices with chirality fittingness (CI-CFs), which are composed of three kinds of sphericity indices (SIs), i.e., a _d for homospheric cycles, c _d for enantiospheric cycles, and b _d for hemispheric cycles. For the purpose of evaluating c _d recursively, the concept of diploid is proposed, where the nested nature of c _d is demonstrated clearly. The SIs are applied to derive functional equations for recursive calculations, i.e., a(x), c(x ²), and b(x). Thereby, planted 3D-trees or equivalently monosubstituted alkanes as stereoisomers are enumerated recursively by counting planted promolecules. The resulting values are collected up to 20 carbon content in a tabular form. Now, the enumeration problem initiated by mathematician Cayley [Philos Mag 47(4):444–446, 1874] has been solved in such a systematic and integrated manner as satisfying both mathematical and chemical requirements.     

Self aggregation of binary mixtures of sodium dodecyl sulfate and polyoxyethylene alkyl ethers in aqueous solution

The mixed micelles of sodium dodecyl sulphate (SDS) with Brij35 and Brij 97 were studied separately by fluorescence measurement using pyrene as fluorescent probe. In the range of 0–1.0 mole fraction (X) of added SDS to Brij solutions, the cmc value of the mixed micelles varies from 0.085 to 8 mmol with Brij 35 and 0.04 to 8 mmol with Brij 97. The aggregation number also changes. A measure of the stability of mixed micelles is also presented. The interaction parameter ₁₂ and the chain–chain contribution parameter (B₁) are extracted from the analysis of the results. This parameter B₁ is related to the standard free energy change associated with the introduction of one ionic species into a nonionic micelle coupled with the release of one nonionic species from the micelle. The clouding behaviour of Brij 97 in the presence of SDS was investigated and the associated thermodynamic parameters of clouding were generated and discussed.