Reciprocity principles associated with the general linear gravity wave problem

Summary Reziprocity principles are presented which hold for the general problem of small amplitude wave motion on the surface of an incompressible liquid. The effects of viscosity, surface tension, irrotationality, free surface sources and solid boundary geometry at liquid-solid intersections are discussed.

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Zusammenfassung Reziprozitätsprinzipien, die für das allgemeine Problem der Wellenbewegung mit kleinen Amplituden auf der Oberfläche einer inkompressiblem Flüssigkeit gelten, werden angegeben. Die Einflüsse von Viskosität, Oberflächenspannung, Wirbelfreiheit, Quellen an der freien Oberfläche un die Geometrie fester Ränder bei flüssig-festen Übergängen werden diskutiert.

     

Rigorous information-theoretic derivation of quantum-statistical thermodynamics. II

Part I of the present work outlined the rigorous application of information theory to a quantum mechanical system in a thermodynamic equilibrium state. The general formula developed there for the best-guess density operator \(\hat \rho\) was indeterminate because it involved in an essential way an unspecified prior probability distribution over the continuumD _H of strong equilibrium density operators. In Part II mathematical evaluation of \(\hat \rho\) is completed after an epistemological analysis which leads first to the discretization ofD _H and then to the adoption of a suitable indifference axiom to delimit the set of admissible prior distributions. Finally, quantal formulas for information-theoretic and thermodynamic entropies are contrasted, and the entire work is summarized.     

Evaporatively cooled M+ (H2O)Ar cluster ions: infrared spectroscopy and internal energy simulations

Rotationally resolved IR spectra of M+ (H2O)Ar cluster ions for M=Na, K, and Cs in the O-H stretch region were measured in a triple-quadrupole mass spectrometer. Analysis of the spectra yields O-H stretch vibrational band origins and relative IR intensities of the symmetric and asymmetric modes. The effect of the alkali-metal ions on these modes results in frequency shifts and intensity changes from the gas phase values of water. The A-rotational constants are also obtained from the rotational structure and are discussed. Experimentally, the temperatures of these species were deduced from the relative populations of the K-rotational states. The internal energies and temperatures of the cluster ions for Na and K were simulated using RRKM calculations and the evaporative ensemble formalism. With binding energies and vibrational frequencies obtained from ab initio calculations, the average predicted temperatures are qualitatively consistent with the experimental values and demonstrate the additional cooling resulting from argon evaporation.     

Unexpected conversion of a polycyclic thiophene to a macrocyclic anhydride

Oxygenation of 2,5,9,12-tetra(tert-butyl)diacenaphtho[1,2-b:1′,2′-d]-thiophene (1, C₄₀H₄₄S) by peracids gave the cyclic sulfonic ester 4 (2,7,10,13-tetra(tert-butyl)diacenaphtho[1,2-c:1′,2′-e]oxathiin 5,5-dioxide, C₄₀H₄₄O₃S) which, when heated in nitrobenzene, is converted into a complex, macrocyclic anhydride 3 (C₈₀H₈₈O₃), which is derived from two molecules of 4. Further investigation found a likely intermediate in this reaction, 4,4′,7,7′-tetra(tert-butyl)-1,1′-biacenaphthylenylidene-2,2′-dione (5, C₄₀H₄₄O₂), apparently formed from 4 by additional oxidation. Anhydride 3 plausibly arises by Diels-Alder reaction of 4 and 5 followed by several ring fragmentations. The structures of 3, 4, and 5 were unambiguously established by X-ray crystallography.     

Pairwise exchanges of oxo and imido groups in rhenium(VII) compounds

The kinetic and thermodynamic parameters for the oxo and imido exchange reactions among MeReO(3), MeReO(2)(NR), MeReO(NR)(2), and MeRe(NR)(3) (R = 1-adamantyl, Ad; or 2,6-diisopropylphenyl, Ar) have been measured. The rate constant for the NAr series decreases from 0.27 to 0.0024 L mol(-1) s(-1) at 25 degrees C in benzene as the total number of participating imido groups increases from 2 to 4, indicating that steric effects play an important role in the kinetics of the ligand exchange reactions. But, with NAd, the values of k/L mol(-1) s(-1) are 0.2 (4 NAd), 100 (3 NAd), and 0.74 (2 NAd). The equilibrium constants, also subject to steric effects, are much larger than those predicted by ligand combination statistics and greatly favor the mixed oxo-imido compounds. The different steric demands by imido and oxo ligands are believed to be the main factor for the larger equilibrium constants because the equilibrium constant shows minimal dependence on temperature. The large negative activation entropies for the ligand exchange reactions are consistent with a metathesis mechanism featuring nearly concurrent interchange of oxo and imido groups.     

Condensation reactions of a comenaldehyde derivative

Condensation reactions of comenaldehyde methyl ether (I) with malonic acid, ethyl cyanoacetate, and cyanoacetamide to give β-(5-methoxy-4H-pyran-4-on-2-yl)acrylic acid (II), ethyl 2-cyano-3-(5-methoxy-4H-pyran-4-on-2-yl)propenoate (III), and 2-cyano-3-(5-methoxy-4H-pyran-4-on-2-yl)propenamide (IV), respectively, are described. Ultraviolet absorption spectra for 2-hydroxymethyl-5-methoxy-4H-pyran-4-one, I and II are presented.     

The polarized electronic spectra and electric field spectra of benzo-diazoles. II. 2,1,3-benzothiadiazole

The S₁ ← S₀ absorption spectra of 2,1,3-benzothiadiazole (BTD) have been measured at 4.2 K in four different host crystals: naphthalene, durene, p-dichlorobenzene (DCB) and p-dibromobenzene. Detailed vibrational analyses are given for BTD imbedded in napthalene and DCB. The polarization measurements show that the S₁ state has B₂ symmetry, like its selenium analogue (BSD). The transition is dominated by a single totally symmetric mode - 484 cm^?1. The Herzberg-Teller coupling contributes only a very small fraction of the total intensity. The Stark measurements of a DCB sample containing both BTD and BSD enabled us to compare the charge distribution of BTD and BSD in the state S₁. The Stark splittings of BTD are 17% greater than the splittings of BSD. Reorganization of the σ-core during the excitation is used to explain the difference. The drastic change in dipole moment upon excitation implies that the S₁←S₀ transitions of BTD and BSD are not localized in the six-membered ring as suggested by previous workers. Weak phosphorescence of BTD in napthalene and DCB and singlet-triplet absorption spectrum of neat BTD have been observed. The heavy atom effect of spin-orbit coupling is to explain the ST absorption intensity of BTD and BSD.     

A universal temperature controlled membrane interface for the analysis of volatile and semi-volatile organic compounds

A universal temperature controlled membrane interface (TCMI) has been constructed for hollow-fibre membranes. The membrane temperature is controllable in the range -70 to 250 degrees C using an electric heater and a flow of cooled nitrogen or helium gas. Volatile and semi-volatile organic compounds may be detected either by continuous diffusion across the membrane or by in-membrane pre-concentration followed by thermal desorption into the detector. The TCMI interface is demonstrated in combination with mass spectrometry and GC-MS, for the determination of VOCs and SVOCs in aqueous and air samples and for the on-line monitoring of a bioreactor.     

Molecular modeling of cytochrome P450 3A4

The three-dimensional structure of human cytochrome P450 3A4 was modeled based on crystallographic coordinates of four bacterial P450s: P450 BM-3, P450cam, P450terp, and P450eryF. The P450 3A4 sequence was aligned to those of the known proteins using a structure-based alignment of P450 BM-3, P450cam, P450terp, and P450eryF. The coordinates of the model were then calculated using a consensus strategy, and the final structure was optimized in the presence of water. The P450 3A4 model resembles P450 BM-3 the most, but the B helix is similar to that of P450eryF, which leads to an enlarged active site when compared with P450 BM-3, P450cam, and P450terp. The 3A4 residues equivalent to known substrate contact residues of the bacterial proteins and key residues of rat P450 2B1 are located in the active site or the substrate access channel. Docking of progesterone into the P450 3A4 model demonstrated that the substrate bound in a 6-orientation can interact with a number of active site residues, such as 114, 119, 301, 304, 305, 309, 370, 373, and 479, through hydrophobic interactions. The active site of the enzyme can also accommodate erythromycin, which, in addition to the residues listed for progesterone, also contacts residues 101, 104, 105, 214, 215, 217, 218, 374, and 478. The majority of 3A4 residues which interact with progesterone and/or erythromycin possess their equivalents in key residues of P450 2B enzymes, except for residues 297, 480 and 482, which do not contact either substrate in P450 3A4. The results from docking of progesterone and erythromycin into the enzyme model make it possible to pinpoint residues which may be important for 3A4 function and to target them for site-directed mutagenesis.