Delaunay graphs are almost as good as complete graphs

LetS be any set ofN points in the plane and let DT(S) be the graph of the Delaunay triangulation ofS. For all pointsa andb ofS, letd(a, b) be the Euclidean distance froma tob and let DT(a, b) be the length of the shortest path in DT(S) froma tob. We show that there is a constantc (≤((1+√5)/2) π≈5.08) independent ofS andN such that $$\frac{{DT(a,b)}}{{d(a,b)}}< c.$$      

Exponential approximations in the classes of life distributions

In this paper we discuss the approximation of life distributions by exponential ones. The main results are: (1) F NBUE, where its mean is 1, we have , 0, where = 1 - ₂/2, ₂ being the second moment ofF. The inequality is sharp. (2) In the case ofFIFR, the upper bound is . (3) For the HNBUE class, the upper bound is min . Furthermore, the improved upper bound is . In addition, we show 0} |\bar G(t) - e^{ - t} | \leqslant \sqrt {\frac{\rho }{2}} $$ " align="middle" border="0"> , where (4) For the IMRL class, the upper bound is /(1+) ([1]). Here we give a simple proof.Project supported by the National Natural Science Fund of China.     

THE PRESENCE OF PHOTOREACTIVE β-CARBOLINE FLUOROPHORES IN WEATHERED WOOL KERATIN

Abstract Solvent-cleaned Merino wool, which was enzymatically digested with protease K, displayed a fluorescence maximum at 500 nm when excited at 430 nm. The yield of this emission was approximately 15 times greater for a fiber tips digest than for a digest of the mid-length region of the same fibers.
Separation of the components in the wool tip digest by silica gel thin-layer chromatography revealed the presence of several fluorescent species. The chromatographic mobility of these species was similar to the behavior observed in a preparation of authentic 1-methyltetrahydro-P-carboline, 1,3-dicarboxylic acid.
Mass spectroscopy of the fluorescent compounds in the wool tip digest displayed molecular ions, [M + H]⁺ with m/z = 273.0890 and 257.0560, and molecular weights that define the formulae C₁₄H₁₂N₂O₄ and C₁₁H₈O₄N₂, respectively, which correspond to β-carboline 1,3-dicarboxylic acids. Mass spectral evidence also indicates the presence of two other β-carbolines.     

Spectroscopic characterization of effective components anthraquinones in Chinese medicinal herbs binding with serum albumins

The interactions of serum albumins such as human serum albumin (HSA) and bovine serum albumin (BSA) with emodin, rhein, aloe-emodin and aloin were assessed employing fluorescence quenching and absorption spectroscopic techniques. The results obtained revealed that there are relatively strong binding affinity for the four anthraquinones with HSA and BSA and the binding constants for the interactions of anthraquinones with HSA or BSA at 20 degrees C were obtained. Anthraquinone-albumin interactions were studied at different temperatures and in the presence of some metal ions. And the competition binding of anthraquinones with serum albumins was also discussed. The Stern-Volmer curves suggested that the quenching occurring in the reactions was the static quenching process. The binding distances and transfer efficiencies for each binding reactions were calculated according to the F?ster theory of non-radiation energy transfer. Using thermodynamic equations, the main action forces of these reactions were also obtained. The reasons of the different binding affinities for different anthraquinone-albumin reactions were probed from the point of view of molecular structures.     

Poly(ethylene glycol)-supported α,α,α-trifluoroacetophenone in dioxirane mediated alkene epoxidation reactions

Poly(ethylene glycol) (PEG) was used for the immobilization of α,α,α-trifluoroacetophenone and the utility of this supported ketone has been examined in dioxirane mediated epoxidation of alkenes. The PEG-ketone reagent was found to be an effective homogeneous catalyst for the epoxidation of a variety of alkenes in the presence of Oxone^® and was readily recovered from the reaction mixtures and reused.     

Ascorbate-induced oxidation of formate by peroxodisulfate: product yields,kinetics and mechanism

The slow reaction between peroxodisulfate and formate is significantly accelerated by ascorbate at room temperature. The products of this induced oxidation, CO₂ and oxalate (C₂O^2– ₄), were analyzed by several methods and the kinetics of this reaction were measured. The overall mechanism involves free radical species. Ascorbate reacts with peroxodisulfate to initiate production of the sulfate radical ion (SO^– ₄), which reacts with formate to produce carbon dioxide radical ion (CO^– ₂) and sulfate. The carbon dioxide radical reacts with peroxodisulfate to form CO₂ or self-combines to form oxalate. Competition occurring between these two processes determines the overall fate of the carbon dioxide radical species. As pH decreases, protonation of the carbon dioxide radical ion tends to favor production of CO₂.