Circuit-switching networks with FIFO plus justifying blockout service on infinite graphs

A class of circuit-switching open queueing networks is discussed. The main result of the paper is that if extra message flows are not too intensive and the path distribution is mainly concentrated on the paths of (graph) distance 1 (nearest neighbour connections), then the network has a unique stationary working regime, no matter how large the configuration graph of the network is. Standard properties of this regime are established such as decay of correlation and continuity.     

Thermodynamic Insight into the Origin of a Calix[n]arene-[60]fullerene Interaction and its Application to a Porphyrin-[60]fullerene Energy Transfer System

The calixarene-fullerene interaction,which causes only a slight change in the absorptionspectra, has been substantiated by calorimetricmeasurements: the H° values arecomparable with those obtained from the associationconstants estimated by a spectroscopic method. Furthermore, we determined the association constantbetween homooxacalix[3]arene and [60]fullerenederivatives with a porphyrin moiety by fluorescencespectra.     

Electrochemical synthesis of carbonyl- and phosphoryl-containing methano[60]fullerenes

The combined electrochemical reduction of fullerene C₆₀ in the presence of p-bromo-benzoyldibromomethane or bis(diisopropoxyphosphoryl)dibromomethane at a brass electrode in a mixed solvent o-dichlorobenzene-MeCN (3:1 v/v)/0.05 M Bu₄NBF₄ at room temperature affords 61-(p-bromobenzoyl)methano[60]fullerene or 61,61-bis(diisopropoxyphosphoryl)methano[60]fullerene, respectively, in 50% yields.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2681–2685, December, 2004.     

Spin-adducts of η2-metallocomplexes of fullerene-60 with phosphoryl radicals

Using ESR spectroscopy, the reaction of P(O)(OPrⁱ)₂ phosphoryl radicals with C₆₀ML₂ (M=Pd, Pt) was studied and the spin-adducts formed were shown to be unstable under the reaction conditions. The ⁵-addition of Pt(PPh₃)₄ to the dimer of phosphorylfullerenyl radicals results in metal-containing dimers (RO)₂(O)PL₂MC₆₀-C₆₀ML₂P(O)(OR)₂, which dissociate when exposed to visible light to afford C₆₀ML₂P(O)(OR)₂ radicals; ML₂ in these complexes is located in different positions in relation to the radical center. As a result, the ESR spectra contain the superposition of at least five signals of radicals that differ in HFS constants andg-factors.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 938–940, May, 1994.The present work was supported by the Russian Foundation for Basic Research (Projects 93-03-18725 and 93-03-4101).     

C120异构富勒烯分子的AM1半经验量子化学研究

以哑铃状2C60聚合体、花生壳状2C60聚合体以及C120富勒烯分子为研究对象,采用AM1半经验量子化学方法,计算了3种C120异构富勒烯分子的几何构型、电子结构、分子能量、疏水常数、极化率与偶极矩;然后,根据计算结果,分析对比了3种C120异构体分子的化学稳定性与物理化学特性.研究结果表明,3种C120分子的形成均为吸热反应,它们的稳定性排序为:C120富勒烯>花生壳状2C60>哑铃状2C60分子.     

Asymptotically independent topological indices on random trees

Topological indices are graph invariants used in computational chemistry to encode molecules. A frequent problem when performing structure-activity studies is that topological indices are inter-correlated. We consider a simple topological index and show asymptotic independence for a random tree model. This continues previous work on the correlation among topological indices. These findings suggest that a size-dependence in a certain class of distance-based topological indices can be eliminated.AMS subject classification: 05C80, 60E10, 92E10     

富烯碳原子簇的石墨层间闭合形成机理

本文提出了富烯碳原子簇的石墨层间闭合形成机理，由该机理推出的许多结果与实验事实符合很好。我们认为碳原子簇自由基的快速淬灭及其淬灭速度是富烯碳原子簇形成及其丰度的决定因素。由此得出富烯碳原子簇在给定实验条件下产生的必然性，并预言不同大小的富烯碳原子簇可以通过优化实验条件选择性地合成。     

A greedy algorithm for finding maximum spanning trees in infinite graphs

In finite graphs, greedy algorithms are used to find minimum spanning trees (MinST) and maximum spanning trees (MaxST). In infinite graphs, we illustrate a general class of problems where a greedy approach discovers a MaxST while a MinST may be unreachable. Our algorithm is a natural extension of Prim's to infinite graphs with summable and strictly positive edge weights, producing a sequence of finite trees that converge to a MaxST.     

Large cycles in random generalized Johnson graphs

This paper studies thresholds in random generalized Johnson graphs for containing large cycles, i.e. cycles of variable length growing with the size of the graph. Thresholds are obtained for different growth rates.     

Spectra of graphs and fractal dimensions II

This paper continues the study of exponentsd(x), d (x), d _R (x) andd (x) for graphG; and the nearest neighbor random walk {X _n } _nN onG, if the starting pointX ₀=x is fixed. These exponents are responsible for the geometric, resistance, diffusion and spectral properties of the graph. The main concern of this paper is the relation of these exponents to the spectral density of the transition matrix. A series of new exponentse, e ,e _R ,e are introduced by allowingx to vary along the vertices. The results suggest that the geometric and resistance properties of the graph are responsible for the diffusion speed on the graph.