Hamiltonian cycles in 1-tough graphs

For a graphG, let ₃ = min{ _i=1 ³ d(u_i): {u₁, u₂, u₃} is an independent set ofG} and = min{ _i=1 ³ d(u_i) – is an independent set ofG}. In this paper, we shall prove the following result: LetG be a 1-tough graph withn vertices such that ₃ n and – 4. ThenG is hamiltonian. This generalizes a result of Fassbender [2], a result of Flandrin, Jung and Li [3] and a result of Jung [5].Supported in part by das promotionsstipendium nach dem NaFöG and the Post-Doctoral Foundation of China.     

Kinetics issues of CuBr lasers with added hydrogen

A computational kinetics model of the CuBr laser with added hydrogen is presented. The space-time behaviour of the lasers and lasants is described in detail. Besides the discharge field, it is confirmed that the dissociation/recombination of the CuBr molecule plays an important role in the plasma electron temperature. The radial field, which peaks at 30% of the discharge field and has two opposite directions along the radius, results in the skin of electron density and the black centre of the large-bore laser beam.     

An example of applications of the elementary catastrophe theory in Hamiltonian systems

The convection in atmosphere discussed in ref. [1] is rigorously treated by considering the variation of environmental temperature with the height. This represents an example of applications of the elementary catastrophe theory in Hamiltonian systems.     

Electrogenerated Chemiluminescence Based on Tris(2,2′-bipyridyl) Ruthenium(II) with Hydroxyl Carboxylic Acid

Upon the electrochemical oxidation of tris(2,2′-bipyridyl) ruthenium(II) [Ru(bpy)²⁺₃] and hydroxyl carboxylic acids, for instance, citric acid, tartaric acid, malic acid, and -gluconic acid, bright electrochemiluminescences (ECLs) were observed. Different luminescent reactions were presented depending on the applied potential. The light emission was mainly caused by the reaction between alkoxide radical ion and Ru(bpy)³⁺₃below the potential +1.80 V (vs Ag/AgCl). The luminescence intensity obviously increased because of the more complex reaction process. The luminescence wavelength of 608 nm, which could be found either at higher potential than +1.80 V or in the potential range from +1.30 to +1.80 V, confirmed that ECL was caused by Ru(bpy)²⁺₃*. The factors which affect the determination and HPLC separation of the four acids were also investigated.     

Mössbauer Spectroscopic Studies of Ferrocenylaldimines and their TCNQ Complexes

A series of ferrocenylaldimines (Fc-CH=N-R) has been prepared by Schiff base condensation of formylferrocene with polyacenylamines RNH₂ where R = naphthyl, 5,6,7,8-tetrahydronaphthyl, anthracenyl, and pyrenyl groups. This step was followed by oxidation with TCNQ to give [Fc-CH = N-R][TCNQ]² salts. The electronic state of iron in these compounds was investigated by means of⁵⁷Fe Mössbauer spectroscopy.