Directed triangles in directed graphs

We show that each directed graph (with no parallel arcs) on n vertices, each with indegree and outdegree at least n/twhere t=2.888997… contains a directed circuit of length at most 3.     

Vibrational Population of Hydrogen Molecules Excited by an RF Discharge in an Expanding Thermal Arc Plasma as Determined by Emission Spectroscopy

This work is devoted to the determination of the vibrational population of hydrogen molecules in the ground and excited electronic states from the analysis of visible spectra of the H₂ molecules excited by an RF discharge in an expanding thermal arc plasma. Comparison of the experimental results on relative electron-impact excitation cross sections for the transition H₂(X¹Σ, υ⁰ = 0)→ H₂(d³II_u, υ′) with other experiments, and with calculations based on the Franck-Condon principle, shows good agreement. This means, that for plasma under investigation: 1) in the ground electronic state H₂(d³II_u,υ′), only the lowest vibrational level with υ⁰ = 0 is significantly populated, and 2) direct electron exictation of H₂(d³II_u, υ′, υ′) state from the ground state H₂(X¹Σ, υ⁰ = 0) dominates.     

Multivariate calibration of reversed-phase chromatographic systems. Some designs based on three-way data analysis

When retention measurements are available for a set of solutes on different stationary phases, with varying mobile phase compositions, the resulting data set can be represented by a three-way array. Models that describe the systematic variation in this training set sufficiently, can be used to calibrate a new stationary phase. Two models are tested for this purpose: three-way partial least squares and parallel factor analysis.     

The total synthesis of 1-oxygenated eudesmane sesquiterpenes : (±) dihydroreynosin and (±) 1-oxocostic acid

The total synthesis of (±) dihydroreynosin $\text{1}$ and of (±) 1-oxocostic acid $\text{2}$ (R = H) are illustrative examples for a short entry into 1-oxygenated eudesmanes via an easily accessible key intermediate $\text{7}$.     

The synthesis of functionalized cis'-bicyclo ¦3.3.0¦octanes

A number of polyfunctionalized cis-bicycio ¦3.3.0¦octanes have been synthesized starting from the tricyclic key intermediate $\text{5}$ which was obtained by the intramolecular cyclopropanation reaction of the diazo keto ester $\text{4}$. Selected stereocontrolled transformations of $\text{5}$ using nucleophiles and electrophiles have been studied for the preparation of the title compounds.     

高岭石吸附乙烯和苯的Delft分子力学研究

运用Ｄｅｌｆｔ分子力学（ＤＭＭ）程序及其粘土和共轭烯烃力场，计算研究了高岭石对乙烯和苯的吸附作用，探讨了吸附对粘土晶体和有机分子的结构、电荷分布和能量的影响，求得了高岭石吸附乙烯和苯的吸附热等重要物理量．     

Synthesis of new vitamin D3 analogues with a decalin-type CD-ring

Vitamin D analogues, characterized by a decalin CD-ring fragment are described.     

Functionalized enamines—XV: Reactivity patterns of carbene addition to morpholine enamine of 1-β-acetoxy-6-oxo-8a-methyl-Δ-octalin

Carbenes3a-e add to the α-side of the first double bond of dienamine2 (title compound) to give 1 : 1 adducts4a-e, Chlorofluorocarbene3e gives, in addition, ketone7, corresponding to β-addition at the second double bond of2, and a 2 : 1 adduct8. The reaction of2 with dichlorocarbene3a yields, besides4a, novel ring-expansion products5 and6 corresponding to addition of two moles of3a. Ethoxycarbonylcarbene3f reacts with the dienamine (2) to give isomeric esters9 and10a,b. The structure assignments and the mechanism of formation of the reaction products are discussed.