Undirected simple connected graphs with minimum number of spanning trees

We show that for positive integers n, m with n(n−1)/2≥m≥n−1, the graph L_n,m having n vertices and m edges that consists of an (n−k)-clique and k−1 vertices of degree 1 has the fewest spanning trees among all connected graphs on n vertices and m edges. This proves Boesch’s conjecture [F.T. Boesch, A. Satyanarayana, C.L. Suffel, Least reliable networks and reliability domination, IEEE Trans. Commun. 38 (1990) 2004-2009].     

Coordination modes of 2-mercapto-1,3-benzothiazolate in gallium and indium complexes

2-Mercapto-1,3-benzothiazole (mbztH) may act as a chelating or bridging ligand. In this study, reactions of mbztH with Me₃Ga and Me₃In were examined. The products were characterized by NMR spectroscopy, elemental analyses, melting point, and molecular weight determinations. Formation of mononuclear chelating complexes Me₂M(mbzt) (M = Ga, In) was observed in solutions. Crystallization of Me₂M(mbzt) yielded uncommon non-symmetrical dinuclear complexes Me₄M₂(mbzt)₂, in which one metal is bonded to two sulfurs and the other to two nitrogens.     

The design, synthesis, and application of a chiral coupling reagent derived from strychnine for the enantioselective activation of a carboxylic group

The concept of a chiral coupling reagent for the enantioselective synthesis of peptides with a predictable configuration and enantiomeric purity from racemic substrates is presented. The reagent was prepared by treatment of strychninium tetrafluoroborate with 2-chloro-4,6-dimethoxy-1,3,5-triazine in the presence of sodium bicarbonate yielding N-(4,6-dimethoxy-1,3,5-triazin-2-yl)strychninium tetrafluoroborate in high yield, which is stable at room temperature, and in a broad range of solvents gave enriched Z-Ala-Phe-OMe (dr from 95/5 to 60/40) in high yield with d-configuration on the alanine residue starting from rac-Z-Ala-OH.     

Identification of acrylate copolymers using pyrolysis and gas chromatography

A combination of pyrolysis and gas chromatography were used to investigate thermal degradation products formed from acrylic copolymers containing alkyl acrylate and methacrylate. The method provided an analytical tool for characterizing the chemical composition and structure of the degradation products. Thermal degradation of the synthesized copolymers was analyzed using isothermal (250 °C) pyrolysis–gas chromatography. The degradation process, and the nature and amount of pyrolysis products, provides relevant information about the thermal degradation of acrylic copolymers and the mechanism of pyrolysis. During pyrolysis, the formation of corresponding olefins, alcohols, acrylates and methacrylate was observed.     

Time-resolved spectroscopic measurements of shock-wave induced decomposition in cyclotrimethylene trinitramine (RDX) crystals: anisotropic response

Plate impact experiments on the (210), (100), and (111) planes were performed to examine the role of crystalline anisotropy on the shock-induced decomposition of cyclotrimethylenetrinitramine (RDX) crystals. Time-resolved emission spectroscopy was used to probe the decomposition of single crystals shocked to peak stresses ranging between 7 and 20 GPa. Emission produced by decomposition intermediates was analyzed in terms of induction time to emission, emission intensity, and the emission spectra shapes as a function of stress and time. Utilizing these features, we found that the shock-induced decomposition of RDX crystals exhibits considerable anisotropy. Crystals shocked on the (210) and (100) planes were more sensitive to decomposition than crystals shocked on the (111) plane. The possible sources of the observed anisotropy are discussed with regard to the inelastic deformation mechanisms of shocked RDX. Our results suggest that, despite the anisotropy observed for shock initiation, decomposition pathways for all three orientations are similar.     

Electric dipole moments of acrylonitrile and of propionitrile measured in supersonic expansion

New determinations of the ground-state electric dipole moments of acrylonitrile and propionitrile have been made from Stark effect measurements at conditions of supersonic expansion. The measurements were made on selected Stark lobes of fully resolved hyperfine components of several lowest-J rotational transitions. The results are μ_a = 3.821(3) D, μ_b = 0.687(8) D, μ_tot = 3.882(3) D for acrylonitrile, and μ_a = 3.816(3) D, μ_b = 1.235(1) D, μ_tot = 4.011(3) D for propionitrile. The new value of μ_b for acrylonitrile is appreciably different from those reported previously and it has been substantiated by both ab initio calculations and relative intensity measurements. The new dipole moment implies a considerable revision in the calculated intensities of the strongest THz-region rotational transitions of acrylonitrile, to 59% of previous values.     

Magnetic Properties of Monomer and Dimer Tetrahedral VO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> Entities Dispersed on Amorphous Silica-based Materials: Prediction of EPR Parameters from Relativistic DFT Calculations and Broken Symmetry Approach to Exchange Couplings

Molecular structures of the isolated tetrahedral oxovanadium(IV) and bridged μ-oxo-divanadium(IV) complexes hosted by the clusters mimicking surfaces of amorphous silica-based materials were investigated using density functional theory (DFT) calculations. Principal values of the g and A tensors for the monomer vanadyl species were obtained using the coupled-perturbed DFT level of theory and the spin–orbit mean-field approximation (SOMF). Magnetic exchange interaction for the μ-oxo bridged vanadium(IV) dimer was investigated within the broken symmetry approach. An antiferromagnetic coupling of the individual magnetic moments of the vanadium(IV) centers in the [VO–O–VO]²⁺ bridges was revealed and discussed in detail. The coupling explains pronounced decrease of the electron paramagnetic resonance signal (EPR) intensity, observed for the reduced VO _x /SiO₂ samples with the increasing coverage of vanadia, in terms of transformation of the paramagnetic monomer species into the dimers with S = 0 ground state.     

A Note on Wiener–Hopf Factorization for Markov Additive Processes

We prove the Wiener–Hopf factorization for Markov additive processes. We derive also Spitzer–Rogozin theorem for this class of processes which serves for obtaining Kendall’s formula and Fristedt representation of the cumulant matrix of the ladder epoch process. Finally, we also obtain the so-called ballot theorem.     

Synthesis and Chemical Transformation of 2 -Acetoxyimino-3,4, 6-tri-O-acetyl-2-deoxy-β-D-arabino-hexopyranosyl Azide

Abstract

The title compound 3 has been synthesized from 3,4,6-tri-O-acetyl-2-deoxy-2-nitroso-α-D-glucopyranosyl chloride (1) via compound 2. Azide reduction of 3 is accompanied by O→N-acetyl migration to afford N-acetyl-N-(3,4,6-tri-O-acetyl-2-deoxy-2-hydroxyimino-β-D-arabino-hexopyranosyl) amine (4), also characterized as its Z and E peracetates. On the basis of IR, ¹H NMR and X-ray structural data from compound 4, its β-NHAc configuration, (Z) 2-hydroxyimino, and °S₂ conformation, were established.     

Significance of comproportionation reaction in multi-step electrochemical reduction of fullerene C60

Voltammetry at platinum ultramicroelectrode in 1,2-dichlorobenzene shows that for a high concentration of supporting electrolyte, THAPF₆, reduction waves 1, 2 and 3 of C₆₀ are of identical height. When supporting electrolyte concentration is lowered, the second and the third wave become lower than the first one. This feature does not agree with simple reduction mechanism under diffusion-migration transport, but supports the model, by Amatore and coworkers, that assumes very fast comproportionation reaction. According to this model, higher-charged fullerene anions are present only in the proximity of the electrode surface, because they react with lower-charged intermediates and are eventually converted to single-charged fullerene anions. Only single-charged anions are transported into the bulk of the solution.