Mycielski图的BBC染色

基于图G的Mycielski图M（G）,研究xb（G,TG）与xb（M（G）,T’）之间的关系以及xb（G,TG）与xb（M（G）,T＂）之间的关系,其中Tc为G的生成树,T’,T＂分别为M（G）的两类特殊生成树．并给出当G为二部图,完全图以及Halin图时,Xb（M（G）,T＂）的值．     

Picture change error correction in the radial distributions of canonical orbital densities and total electron density of radon atom: the effect of the size of nucleus and the basis set limit

The 2nd order Douglas-Kroll-Hess (DKH2) and the Infinite Order Two Component (IOTC) radial distributions of electron density of canonical Hartree-Fock (HF) orbitals of radon atom are presented. Furthermore, the total electron density is revisited. The picture change error (PCE) correction is investigated by analytical means. The point charge model of nucleus and the Gaussian nucleus model are employed. The basis set is extrapolated by means of including tight s and also p Gaussians within the original triple zeta basis set. It is found that the DKH1 PCE corrected DKH2 total electron and s orbital contact densities are negative for the point charge model of nucleus if tight enough s Gaussians are included in the basis set. It is shown that this failure is caused due to the missing terms of the second order Douglas-Kroll transformation for the DKH2 electron density. PCE is found the most striking in the DKH2/IOTC electron density of s orbitals close to the nucleus. The radial distributions of the 2-component p _1/2 orbital densities are considerably affected by PCE at the nucleus as well. Furthermore, the PCE corrected DKH2/IOTC scalar p orbital densities have a non-zero value of electron density at nucleus and can be considered as an spin-orbit (SO) average of the p _1/2 and p _3/2 orbitals. The d and f orbitals are affected by PCE in the vicinity of the nucleus only little. The PCE corrected DKH2 and IOTC radial distributions of orbital densities are nodeless, which is completely in agreement with the radial distribution of the analytic or numeric DCH orbital densities.     

Synthesis of propylene carbonate from carbon dioxide using trans‐dichlorotetrapyridineru‐ thenium(II) as catalyst

trans‐Dichlorotetrapyridineruthenium(II) [trans‐RuCl₂(py)₄] was synthesized and the structure was determined by single crystal X‐ray crystallography. Highly efficient formation of propylene carbonate (PC) from carbon dioxide and propylene oxide was achieved by using a catalyst system composed of trans‐RuCl₂(py)₄ and hexadecyl trimethyl ammonium bromide under mild conditions (4h, 80 °C, 3.0 MPa). PC was obtained in nearly 100% selectivity without the formation of a polymer. The catalyst could be recycled constantly many times without any significant loss of its catalytic activity. On the basis of the results, a mechanism for the reaction was proposed. Copyright © 2010 European Peptide Society and John Wiley & Sons, Ltd.     

Cosolvent Effect on the Tautomerism of Ethyl Acetoacetate in Supercritical CO_2

There are some unique advantages for chemical reactions in SCFs. For example, reaction rates, yields, and selectivity can be tuned by pressure or small amount of cosolvent. SCFs can be used to replace environmentally undesirable solvents. It is not surprised that in recent years the use of SCFs as solvents for chemical reaction media has received much attention. However, mechanism for the effect of pressure and cosolvents on chemical reactions is not very clear. Tautomeric reactions are id…     

The 2-concavification of a Banach lattice equals the diagonal of the Fremlin tensor square

We investigate the relationship between the diagonal of the Fremlin projective tensor product of a Banach lattice E with itself and the 2-concavification of E.     

Evaluating a four-directional benzene-centered aliphatic polyamine curing agent for epoxy resins

A four-directional benzene-centered aliphatic polyamine, MXBDP, with high functionality and low volatility, is used to cure epoxy resin (DGEBA). Herein we originally report the isothermal cure kinetics and dynamic mechanical properties of DGEBA/MXBDP. Differential scanning calorimetry confirms that MXDBP is more reactive than commercial linear metaxylenediamine and branched Jeffamine T-403 and the isothermal curing reaction is autocatalytic. The Kamal model is found to be able to well describe the curing rate up to the onset of diffusion control, and the excellent match over the whole conversion range is achieved using the extended Kamal model. Interestingly, the isoconversional kinetic analysis indicates that the effective reaction activation energy (E _α ) changes substantially with conversion, and ultimately decreases to a very small value (<10 kJ mol^?1) because of the diffusion-controlled reaction kinetics. Then, dynamic mechanical analysis reveals that DGEBA/MXBDP exhibits the higher α- and β-relaxation temperatures and the much higher crosslink density than DGEBA/metaxylenediamine. Our experiment results support that MXBDP has the high reactivity and improved thermal resistance in combination with the advantages of the high functionality, low volatility and decreased CO₂ absorption. Therefore, MXBDP may be especially suitable for room temperature-cure epoxy coatings and adhesives.