Boundary Problems for Parabolic Equations with Degenerate Boundary Condition of the Third Kind

Doklady Mathematics - The solvability of initial-boundary value problems for linear parabolic equations of the second order with a degenerate boundary value condition of the third kind is studied....     

Degenerate rearrangement of 9-isopropenyl-9,10-dimethyl-phenanthren-9-yl and 9,10-dimethyl-9-(trans-1-methylprop-1-en-1-yl)phenanthren-9-yl cations

¹H NMR study has shown that long-lived 9-R-9,10-dimethylphenanthren-9-yl cations (R = isopropenyl, trans-1-methylprop-1-en-1-yl) generated in the system HSO₃F-SO₂ClF-CD₂Cl₂ at ?130°C undergo degenerate rearrangement via 1,2-vinyl shifts (ΔG’ = 37 and 39 kJ/mol, respectively, at ?88°C). Analysis of the geometric parameters of the initial structures and transition states calculated by the DFT method indicates that unfavorable steric factors are responsible for the sharp deceleration of 1,2-shifts of the isopropenyl and trans-1-methylprop-1-en-1-yl groups as compared to vinyl and cis-1-methylprop-1-en-1-yl groups, respectively.     

Photochemical synthesis of 1,2,3,4,5,6,8,9-octamethyl-C2V-bishomocubane

1,2,3,4,5,6,8,9-Octamethyl-C_2V-bishomocubane was prepared by the photochemical cyclization of 1R,3S,4,5,6R,8S,9,10-octamethyltricyclo[6.2.0.0^3,6]deca-4,9-di-ene in benzene.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 6, pp. 1440–1442, June, 1991.The authors express their gratitude to V. I. Eroshkin for a number of valuable suggestions for carrying out the photochemical experiments.     

Crystal and molecular structure of 6b,7,8,8a-tetramethyl-6b,8a-dihydrocyclobut[a]acenaphthylene and 1,2,2a,10b-tetramethyl-2a,10b-dihydrocyclobuta[l]phenanthrene

The crystal and molecular structure of 6b,7,8,8a-tetramethyl-6b,8a-dihydrocyclobut[a]acenaphthylene (I) and 1,2,2a,10b-tetramethyl-2a,10b-dihydrocyclobuta[l]phenanthrene (II) is established by XRD analysis. The C(6b)-C(8a) bond in I is lengthened to 1.603(3) ∢, and the C(2a)-C(10b) bond in II is prolonged to 1.589(6) ∢. The acenaphthene and dihydrophenanthrene frameworks are planar; the rms deviations of atoms from the plane are 0.011 and 0.032 ∢, respectively. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 6, pp. 1140–1145, November–December, 1997.     

Water concentration profiles in membranes measured by ESEEM of spin-labeled lipids

Electron spin-echo envelope modulation (ESEEM) spectroscopy of phospholipids spin-labeled systematically down the sn-2 chain was used to detect the penetration of water (D2O) into bilayer membranes of dipalmitoyl phosphatidylcholine with and without 50 mol % cholesterol. Three-pulse stimulated echoes allow the resolution of two superimposed 2H-ESEEM spectral components of different widths, for spin labels located in the upper part of the lipid chains. Quantum chemical calculations (DFT) and ESEEM simulations assign the broad spectral component to one or two D2O molecules that are directly hydrogen bonded to the N-O group of the spin label. Classical ESEEM simulations establish that the narrow spectral component arises from nonbonded water (D2O) molecules that are free in the hydrocarbon chain region of the bilayer membrane. The amplitudes of the broad 2H-ESEEM spectral component correlate directly with those of the narrow component for spin labels at different positions down the lipid chain, reflecting the local H-bonding equilibria. The D2O-ESEEM amplitudes decrease with position down the chain toward the bilayer center, displaying a sigmoidal dependence on position that is characteristic of transmembrane polarity profiles established by other less direct spin-labeling methods. The midpoint of the sigmoidal profile is shifted toward the membrane center for membranes without cholesterol, relative to those with cholesterol, and the D2O-ESEEM amplitude in the outer regions of the chain is greater in the presence of cholesterol than in its absence. For both membrane types, the D2O amplitude is almost vanishingly small at the bilayer center. The water-penetration profiles reverse correlate with the lipid-chain packing density, as reflected by 1H-ESEEM intensities from protons of the membrane matrix. An analysis of the H-bonding equilibria provides essential information on the binding of water molecules to H-bond acceptors within the hydrophobic interior of membranes. For membranes containing cholesterol, approximately 40% of the nitroxides in the region adjacent to the lipid headgroups are H bonded to water, of which ca. 15% are doubly H bonded. Corresponding H-bonded populations in membranes without cholesterol are ca. 20%, of which ca. 6% are doubly bonded.     

Lewis Acid Effects in Mesitylene Amination in the System NaN3MHlgnHCl

Russian Journal of Organic Chemistry -