Scaling of a collapsed polymer globule in two dimensions

Extensive Monte Carlo data analysis gives clear evidence that collapsed linear polymers in two dimensions fall in the universality class of athermal, dense self-avoiding walks, as conjectured by Duplantier [Phys. Rev. Lett. 71, 4274 (1993)].10.1103/PhysRevLett.71.4274 However, the boundary of the globule has self-affine roughness and does not determine the anticipated nonzero topological boundary contribution to entropic exponents. Scaling corrections are due to subleading contributions to the partition function corresponding to polymer configurations with one end located on the globule-solvent interface.     

On the spectral radius of unicyclic graphs with prescribed degree sequence

We consider the set of unicyclic graphs with prescribed degree sequence. In this set we determine the (unique) graph with the largest spectral radius (or index) with respect to the adjacency matrix. In addition, we give a conjecture about the (unique) graph with the largest index in the set of connected graphs with prescribed degree sequence.     

fac-[Re(CO)3(dmso-O)3](CF3SO3): a new versatile and efficient Re(I) precursor for the preparation of mono and polynuclear compounds containing fac-[Re(CO)3]+ fragments

We show here that the new complex fac-[Re(CO)3(dmso-O)3](CF3SO3) (1), efficiently prepared in one step from [ReBr(CO)5] and featuring a broad range of solubility, is, in general, a better precursor for the one-step synthesis of mono- and polynuclear inorganic compounds containing fac-[Re(CO)3]+ fragments compared to the commonly used (NEt4)2fac-[ReBr3(CO)3] and fac-[Re(CO)3(CH3CN)3](Y) (Y = PF6, BF4, ClO4) species. Compound 1 is the first example of a Re(I)-dmso complex structurally characterized and confirms the rule that dmso is always O-bonded when trans to CO. The reactivity of 1 was tested in the one-step preparation of several new and known complexes. The O-bonded sulfoxides of 1 are replaced under mild conditions by tri- (L3) and bidentate ligands (L2) to produce fac-[Re(CO)3(L3)]+ and fac-[Re(CO)3(L2)(dmso-O)]+ compounds, respectively. An excess of monodentate ligands (L) and more forcing conditions are needed to prepare fac-[Re(CO)3(L)3]+ compounds. The new compounds include fac-[Re(CO)3(bipy)(dmso-O)](CF3SO3) (4), that turned out to be an excellent precursor for binding the luminescent fac-[Re(CO)3(bipy)]+ fragment to polytopic ligands for the construction of more elaborate assemblies. One example reported here is the two-step preparation of fac-[{Re(CO)3(bipy)}(mu-4,4'-bipy){Ru(TPP)(CO)}](CF3SO3) (8) (TPP = tetraphenylporphyrin). The X-ray structures of the new compounds 1, 4, of the bis-porphyrin complex fac-[Re(CO)3Cl(4'MPyP)2] (13) (4'MPyP = 5-(4'pyridyl)-10,15,20-triphenylporphyrin), and of the rhenium-cyclophane [{(CO)3Re(mu-OH)2Re(CO)3}2(micro-4,4'-bipy)2] (15), among others, are described. Compound 1 might find useful applications in supramolecular chemistry (metal-mediated assembly of large architectures), in the in situ preparation of stable Re compounds to be used in nuclear medicine, and for the labeling of biomolecules.     

On the Vector Process Obtained by Iterated Integration of the Telegraph Signal

We analyse the vector process (X ₀(t), X ₁(t),...,X _n(t), t > 0) where , and X ₀(t) is the o two-valued telegraph process.In particular, the hyperbolic equations governing the joint distributions of the process are derived and analysed.Special care is given to the case of the process (X ₀(t), X ₁(t), X ₂(t), t > 0) representing a randomly accelerated motion where some explicit results on the probability distribution are derived.     

迭代过程及其在高阶微分方程中的应用

通过对布朗运动和电报过程的适当迭代,使之迭代过程的转移函数满足不同形式的高阶抛物型或双曲型微分方程．对迭代过程进行适当的时间变换,还可以使迭代过程的转移函数满足系数依赖于时间的高阶微分方程．本文还讨论了迭代布朗运动最大值的分布及其有关性质．     

Strongly indefinite systems with critical Sobolev exponents

We consider an elliptic system of Hamiltonian type on a bounded domain. In the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms. Our proof is based on an adaptation of the dual variational method as applied before to the scalar case.

     

Use of carbon adsorption traps combined with high resolution gas chromatography – mass spectrometry for the analysis of polar and non-polar C4-C14 hydrocarbons involved in photochemical smog formation

A method has been developed for the collection and analysis of polar and non-polar C₄-C₁₄ hydrocarbons involved in the formation of photochemical smog. Enrichment of hydrocarbons from both polluted and unpolluted areas has been achieved with three-stage traps packed with carbon adsorbents of different surface area; the use of a home-made desorption unit employing cryofocusing then enables the determination of the compounds by HRGC-FID. Two-stage traps filled with graphitic carbon have been used prior to GC-MS identification and quantitation of compounds producing overlapping peaks. The methodology has been tested in the urban area of Rome and in a pine forest, and more than 140 different compounds identified and quantitated. Many of the constituents were found to be oxygenated, either formed by photochemical reactions or of anthropogenic origin.     

Metallation reactions. XXXIV. Synthesis of 2‐(1‐hydroxy‐1‐arylethyl)‐1,3‐benzoxathiol‐3‐oxide derivatives

The reaction of benzoxathiole‐3‐oxide with lithiumdiisopropylamide in tetrahydrofuran gave an anion, which was reacted with various aryl‐methyl‐ketones to give 2‐(1‐hydroxy‐1‐arylethyl)‐1,3‐benzoxathiol‐3‐oxide derivatives. The reaction was carried out in different temperature conditions: at ‐88 °C the trans addition stereoisomers to the sulfoxide oxygen atom were the main products.     

Separation of geometric isomers of metal β-diketonates by supercritical fluid chromatography

The separation of the geometric isomers of chromium and rhodium chelates of trifluoroacetylacetone and thenoyltrifluor-oacetone was investigated using packed column supercritical fluid chromatography. Mobile phases consisting of neat and alcohol-modified carbon dioxide were used, and the most favorable isomeric resolution was obtained with a phenyl stationary phase. The chromatographic performance was better for chelates with trifluoroacetylacetone than for the corresponding chelates with thenoyltrifluoroacetone. Chromatographic peak area analysis of the metal chelates investigated showed appropriate isomeric concentrations in the final diastereomeric products resulting from the synthetic procedures.