An algorithm for the enumeration of spanning trees

Enumeration of spanning trees of an undirected graph is one of the graph problems that has received much attention in the literature. In this paper a new enumeration algorithm based on the idea of contractions of the graph is presented. The worst-case time complexity of the algorithm isO(n+m+nt) wheren is the number of vertices,m the number of edges, andt the number of spanning trees in the graph. The worst-case space complexity of the algorithm isO(n ²). Computational analysis indicates that the algorithm requires less computation time than any other of the previously best-known algorithms.     

Theory of free-electron optical absorption in n-GaAs

Free-electron optical absorption of Se-doped GaAs at room temperature is calculated and compared with existing experimental data. In addition to the standard features the theory takes into account a non-parabolic character of the conduction band, a short-range component of the Se donor potential and a plasmon generation in the presence of donors. Deformation potential constants for the conduction and the valence bands are calculated using the empirical pseudopotential method. A value of C = -15.7 eV is obtained for the conduction band and shown to agree with existing hydrostatic and uniaxial stress experiments. Assuming no impurity compensation and using no adjustable parameters we successfully describe the experimental free-electron absorption in GaAs as a function of photon wavelength for samples with various donor densities.     

Synthesis and study of the rate of aminolysis of O-(acylaminoacyl)oximes of formylpyridines and pyridyl methyl ketones

A number of O-(benzyloxycarbonylglycyl) derivatives of alkyl-, phenyl-, and pyridyl-substituted oximes were synthesized, and their chemical properties and reactivities under aminolysis conditions were studied. The principal factor that determines the reactivities of the investigated compounds during the formation of a peptide bond is the presence of a weakly acidic catalyst; the different reactivities of the compounds under the same conditions are due to the influence of the electron-acceptor effects of the substituents attached to the carbon atom of the oxime group.The authors thank the Polish Academy of Sciences for financial support (state subsidy MR 1.12.1.6.1.5).Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1336–1339, October, 1977.     

On the existence of specified cycles in a tournament

For 2 ≦ p ≦n and n ≧ 3, D(n, p) denotes the digraph with n vertices obtained from a directed cycle of length n by changing the orientation of p- 1 consecutives edges. In this paper, we prove that every tournament of order n ≧ 7 contains D(n, p) for p = 2, 3, …, n. Furthermore, we determine the tournaments of order n, 3 ≦ n ≦ 6, which do not contain D(n, p) for some p.     

Dendrites and light open mappings

It is shown that a metric continuum is a dendrite if and only if for every compact space and for every light open mapping such that there is a copy of in for which the restriction is a homeomorphism. Another characterization of dendrites in terms of continuous selections of multivalued functions is also obtained.

     

Modeling diffusion of adsorbed polymer with explicit solvent

Computer simulations of a polymer chain of length N strongly adsorbed at the solid-liquid interface in the presence of explicit solvent are used to delineate the factors affecting the N dependence of the polymer lateral diffusion coefficient, D(||). We find that surface roughness has a large influence, and D(||) scales as D(||) approximately N(-x), with x approximately 3/4 and x approximately 1 for ideal smooth and corrugated surfaces, respectively. The first result is consistent with the hydrodynamics of a "particle" of radius of gyration R(G) approximately N(nu) (nu=0.75) translating parallel to a planar interface, while the second implies that the friction of the adsorbed chains dominates. These results are discussed in the context of recent measurements.     

Controlling the Scholl reaction

Guidelines for the application of the Scholl reaction were developed. Labeling experiments demonstrate that the Scholl reaction fails in small, unsubstituted oligophenylenes (e.g., o-terphenyl) due to oligomerization of the products (e.g., triphenylene). Incorporation of suitably placed blocking groups (e.g., t-butyl) suppresses oligomerization. The well-established directing group effects in electrophilic aromatic substitution predict the outcome of Scholl reactions of substituted substrates. Activating o,p-directing groups (e.g., MeO) direct bond formation o,p, either intramolecularly or intermolecularly. Deactivating o,p-directing groups (e.g., Br) also direct bond formation o,p but yields are lower. Deactivating m-directors (e.g., NO2) suppress reaction. MoCl5 and PhI(OOCCF3)2/BF3.Et2O are general and effective reagents for the Scholl oxidation. Calculations (B3LYP/6-31G(d)) predict the Scholl reaction in alkoxyarenes to proceed via arenium cations, not radical cations. Suzuki-Miyaura couplings were used to generate 12 substituted o-terphenyl derivatives.     

A spectroscopic and computational study of the neutral and radical cation species of conjugated aryl-substituted 2,5-bis(2-thien-2-ylethenyl)thiophene-based oligomers

A spectroscopic and computational study of a series of 2,5-bis(2-thien-2-ylethenyl) thiophene-based oligomers with a para-R-arylethenyl substituent is reported. The primary aim of this investigation is to increase understanding of how charge moves through these molecules by comparing the neutral and oxidized structures for each molecule. To this end, the B3LYP/6-31G(d) computational method was used to calculate the geometry and vibrational spectra for all molecules considered and their oxidation products. For vibrational data, mean absolute deviations for frequencies between experimental and theoretical results ranging from 2 to 18 cm-1 were obtained. Experimental Raman spectroscopy, in conjunction with calculated bond length analyses, was used to gain an insight into the position and delocalization of the charged defect on the oxidized oligomers. The relative frequencies of different ethylene stretching modes served as a particularly useful probe in this regard. It was found that the ethenyl spacers do not impede pi-electron delocalization and, therefore, give rise to a longer conjugation length relative to the corresponding terthiophenes. Furthermore, the para-R-arylethenyl substituent was found to orientate the charged defect toward a specific region of the 2,5-bis(2-thien-2-ylethenyl)thiophene conjugation path.