Eigenvalues of large even annulenes in terms ofK 3,S 4 andS 5

Squares of the adjacency matrices of bipartite cycles (C_v) can be block-factored into matrices which correspond to vertex-weighted complete graphs forv = 6, vertex-weighted strongly regular graphs forv = 8 and 10, and vertex-weighted metrically regular graphs forv > 10. Using this fact and some properties of strongly and metrically regular graphs, it is shown that eigenvalues of large bipartite C _v graphs (i.e. large even annulenes) can be expressed by the general formula ± (2 ± (2 ± (... ± (2 +r _p)) ...), wherev = 2 ⁿ ×p,n is the number of surd () signs required andp = 3, 4 and 5. Here,r ₃,r ₄, andr ₅, are the eigenvalues of the complete graphK ₃ and the strongly regular graphsS ₄ andS ₅ respectively. The procedure does not require construction of characteristic polynomials for the determination of eigenvalues, and brings out a common topological origin for the two-fold degeneracies observed in the eigenvalue spectra of all even cycles and many odd cycles.     

Processable heat-resistant polymers. XI. Synthesis and characterization of unsaturated polyamideimides

Polycondensation of the diacid chloride of 2-(3-carboxy vinyl)phenyl-1,3-dioxoisoindoline-5-carboxylic acid with m-phenylenediamine and the diacid chloride of 2-(4-carboxy phenyl)-1,3-dioxoisoindoline-5-carboxylic acid with 1,5-bis(3-aminophenyl)1,4-pentadien-3-one was carried out in polar solvents to produce new unsaturated polyamide–imides. The solution and the thermal, electrical, and a few other properties of the polymers were studies. The polymers were soluble in highly polar solvents. The solubility parameter of the polymers was calculated from the Small's group contribution. The polymers were fairly thermostable and underwent crosslinking creaction when heated, preferably in the presence of a suitable catalyst. The crosslinked polymers were in soluble even in highly polar solvents and possessed higher thermal stability. The swelling behavior of the polymers was studied and the molecular weight between two consecutive crosslinks was determined. X-ray diffraction and the dielectric properties of the polymers and their crosslinked products were also studied.     

Synthesis of pyrrolo[3,2-b]benzofurans and pyrrolo[3,2-b]naphthofurans via addition of a silyloxypyrrole to activated quinones

The uncatalyzed reaction of N-(tert-butoxycarbonyl)-2-tert-butyldimethylsilyloxypyrrole 3 with 1,4-quinones bearing an electron withdrawing group at C-2 has been studied. Use of 1,4-quinones 4, 5 bearing an ester group at C-2 provided an efficient synthesis of the respective pyrrolidinobenzofuran adduct 9 or pyrrolidinonaphthofuran adduct 10 whereas use of 1,4-quinones 6, 7 and 8 bearing an acetyl group at C-2 afforded silyloxypyrroles 11, 12 and 13 resulting from direct electrophilic substitution of the silyloxypyrrole by the electrophilic quinone. Addition of Eu(fod)₃ to the reaction of 2-acetyl-1,4-naphthoquinone 7 and 3-acetyl-5-methoxy-1,4-naphthoquinone 8 with N-(tert-butoxycarbonyl)-2-tert-butyldimethylsilyloxypyrrole 3 provided a method for obtaining the pyrrolidinonaphthofuran adducts 14 and 15 together with silyloxypyrroles 12 and 13. Oxidative rearrangement of pyrrolidinonaphthofuran adduct 15 to pyrrolidino pyranonaphthoquinone 16 using ceric ammonium nitrate in acetonitrile provided a novel approach for the synthesis of an aza-analogue of the pyranonaphthoquinone antibiotic kalafungin.     

Oxomolybdenum(VI) and (IV) complexes of pyrazole derived ONO donor ligands – synthesis,crystal structure studies and spectroelectrochemical correlation

Four cis-dioxomolybdenum complexes of general formula [MoO₂(Lⁿ)EtOH] (n = 1–4) and one oxomolybdenum(IV) complex [MoO(L⁴)EtOH], with potentially tridentate Schiff bases derived from 5-methyl pyrazole-3-carbohydrazide and salicylaldehyde/substituted salicylaldehyde/o-hydroxy acetophenone have been prepared. The Mo(IV) complex is derived from the Mo(VI) dioxo complex by oxotransfer reaction with PPh₃. The complexes are characterized by elemental analysis, electronic spectra, IR, ¹H NMR, and by cyclic voltammetry. All the Mo(VI) species are crystallographically characterized. The complexes have a distorted octahedral structure in which the ligand behaves as a binegative donor one, leaving the pyrazole –N uncoordinated towards the metal center. It is also revealed from the crystal structure that the Mo(VI) center enjoys an NO₅ donor environment.     

Molecular and electronic structure of four- and five-coordinate cobalt complexes containing two o-phenylenediamine- or two o-aminophenol-type ligands at various oxidation levels: an experimental, density functional, and correlated ab initio study

The bidentate ligands N-phenyl-o-phenylenediamine, H(2)((2)L(N)IP), or its analogue 2-(2-trifluoromethyl)anilino-4,6-di-tert-butylphenol, ((4)L(N)IP), react with [Co(II)(CH(3)CO(2))(2)]4H(2)O and triethylamine in acetonitrile in the presence of air yielding the square-planar, four-coordinate species [Co((2)L(N))(2)] (1) and [Co((4)L(O))(2)] (4) with an S=1/2 ground state. The corresponding nickel complexes [Ni((4)L(O))(2)] (8) and its cobaltocene reduced form [Co(III)(Cp)(2)][Ni((4)L(O))(2)] (9) have also been synthesized. The five-coordinate species [Co((2)L(N))(2)(tBu-py)] (2) (S=1/2) and its one-electron oxidized forms [Co((2)L(N))(2)(tBu-py)](O(2)CCH(3)) (2 a) or [Co((2)L(N))(2)I] (3) with diamagnetic ground states (S=0) have been prepared, as has the species [Co((4)L(O))(2)(CH(2)CN)] (7). The one-electron reduced form of 4, namely [Co(Cp)(2)][Co((4)L(O))(2)] (5) has been generated through the reduction of 4 with [Co(Cp)(2)]. Complexes 1, 2, 2 a, 3, 4, 5, 7, 8, and 9 have been characterized by X-ray crystallography (100 K). The ligands are non-innocent and may exist as catecholate-like dianions ((2)L(N)IP)(2-), ((4)L(N)IP)(2-) or pi-radical semiquinonate monoanions ((2)L(N)ISQ)(*) (-), ((4)L(N)ISQ)(*) (-) or as neutral benzoquinones ((2) L(N)IBQ)(0), ((4) L(N)IBQ)(0); the spectroscopic oxidation states of the central metal ions vary accordingly. Electronic absorption, magnetic circular dichroism, and EPR spectroscopy, as well as variable temperature magnetic susceptibility measurements have been used to experimentally determine the electronic structures of these complexes. Density functional theoretical (DFT) and correlated ab initio calculation have been performed on the neutral and monoanionic species [Co((1)L(N))(2)](0,-) in order to understand the structural and spectroscopic properties of complexes. It is shown that the corresponding nickel complexes 8 and 9 contain a low-spin nickel(II) ion regardless of the oxidation level of the ligand, whereas for the corresponding cobalt complexes the situation is more complicated. Spectroscopic oxidation states describing a d(6) (Co(III)) or d(7) (Co(II)) electron configuration cannot be unambiguously assigned.     

Characterization of framework and extra-framework aluminum species in non-hydrated zeolites Y by 27Al spin-echo, high-speed MAS, and MQMAS NMR spectroscopy at B0 = 9.4 to 17.6 T

27Al spin-echo, high-speed MAS (nu(rot) = 30 kHz), and MQMAS NMR spectroscopy in magnetic fields of B0 = 9.4, 14.1, and 17.6 T were applied for the study of aluminum species at framework and extra-framework positions in non-hydrated zeolites Y. Non-hydrated gamma-Al2O3 and non-hydrated aluminum-exchanged zeolite Y (Al,Na-Y) and zeolite H,Na-Y were utilized as reference materials. The solid-state 27Al NMR spectra of steamed zeolite deH,Na-Y/81.5 were found to consist of four signals. The broad low-field signal is caused by a superposition of the signals of framework aluminum atoms in the vicinity of bridging hydroxyl protons and framework aluminum atoms compensated in their negative charge by aluminum cations (delta(iso) = 70 +/- 10 ppm, C(QCC) = 15.0 +/- 1.0 MHz). The second signal is due to a superposition of the signals of framework aluminum atoms compensated by sodium cations and tetrahedrally coordinated aluminum atoms in neutral extra-framework aluminum oxide clusters (delta(iso) = 65 +/- 5 ppm, C(QCC) = 8.0 +/- 0.5 MHz). The residual two signals were attributed to aluminum cations (delta(iso) = 35 +/- 5 ppm, C(QCC) = 7.5 +/- 0.5 MHz) and octahedrally coordinated aluminum atoms in neutral extra-framework aluminum oxide clusters (delta(iso) = 10 +/- 5 ppm, C(QCC) = 5.0 +/- 0.5 MHz). By chemical analysis and evaluating the relative solid-state 27Al NMR intensities of the different signals of aluminum species occurring in zeolite deH,Na-Y/81.5 in the non-hydrated state, the aluminum distribution in this material was determined.     

A first principle study of hydrogen storage in titanium-doped small carbon clusters (C2nTin,n = 2–6)

Structural Chemistry - Hydrogen storage in Ti-doped small carbon clusters, C2nTin (n = 2–6), has been studied using density functional theory. Using the principle of maximum hardness (η)...     

CONDENSING HEAT TRANSFER IN VERTICAL CYCLONE

The heat transfer coefficient for condensation of steam has been determined experimentally for a cyclone surface. Ambient air is used as the coolant and the outer surface is maintained in a free-convection condition. A twofold increase in heat transfer coefficient is observed over a cyclone surface in comparison with a vertical tube.     

Toward low‐noise synthetic turbulent inflow conditions for aeroacoustic calculations

The accuracy of boundary conditions for computational aeroacoustics is a well‐known challenge, due in part to the necessity of truncating the flow domain and replacing the analytical boundary conditions at infinity with numerical boundary conditions. In particular, the inflow boundary condition involving turbulent velocity or scalar fields is likely to introduce spurious waves into the domain, therefore degrading the flow behavior and deteriorating the physical acoustic waves. In this work, a method to generate low‐noise, divergence‐free, synthetic turbulence for inflow boundary conditions is proposed. It relies on the classical view of turbulence as a superposition of random eddies convected with the mean flow. Within the proposed model, the vector potential and the requirement that the individual eddies must satisfy the linearized momentum equations about the mean flow are used. The model is tested using isolated eddies convected through the inflow boundary and an experimental benchmark data for spatially decaying isotropic turbulence. Copyright © 2013 John Wiley & Sons, Ltd.