The problem of scalar field theory in curved space-time

It is demonstrated that (1) there exist infiniteG ₁ that satisfy Lichnerowicz's conditions (L conditions) in a globally hyperbolic manifold; and, (2) there is noG ₁ in an expanding universe that would satisfy those conditions and that would behave as the ordinary ₁ of flat space whenx x. The author thinks that these results present a serious problem for finding a semiclassical theory of scalar field in curved space-time.     

Cyclisation of (R)- and (S)-N-allyl-N-(1-phenylethyl) methoxycarbonylacetamide mediated by Mn(III): Preparation and structural assignment of 3-aza-2-oxobicyclo[3.1.0]hexanes

(R)- and (S)-N-allyl-N-(1-phenylethyl)methoxycarbonylacetamide, 5 and 6, underwent oxidative cyclisation mediated by Mn(III), to give easily separable diastereomeric mixtures of 3-aza-2-oxobicyclo[3.1.0]hexanes 8a,b and 9a,b, respectively, whose structures were assigned on the basis of ¹H NMR spectra and then confirmed by X-ray diffraction analysis of the derivatives 11b and 14.     

Synthesis of peptides containing 1,2,3,4-tetrahydroquinoline-2-carboxylic acid. Part 3. Cyclization of dipeptides and amides with acetic anhydride

Treatment of protected dipeptides containing 1,2,3,4-tetrahydroquinoline-2-carboxylic acid with acetic anhydride affords only 1H,3H,5H-oxazolo[3,4-a]quinolin-3-one derivatives. The formation of a-acylaminomethylketones, arising from the competitive Dakin-West reaction, was generally observed when the cyclization procedure was extended to some amides of the cyclic imino acid. The preferential stabilization of one of two probable mesoionic intermediates seems to determine the preferred pathway.     

Interrelation between side chain crystallization and dynamic glass transitions in higher poly(n-alkyl methacrylates)

Calorimetric and dielectric results for crystallizable poly(n-alkyl methacrylates) (PnAMA) with C=12, 16 and 18 alkyl carbons per side chain are presented. Degree of crystallization D_cal and melting peak temperature T_M are estimated from conventional DSC measurements. For poly(n-hexadecyl methacrylate) (C=16) the influence of isothermal crystallization is studied by DSC as well as TMDSC. Changes in dielectric relaxation strength Δε and α peak shape during crystallization are investigated. Effects of side chain crystallization on the complex dynamics of PnAMA are discussed. The results are related to the relaxation behavior of lower nanophase-separated PnAMA with two co-existing glass transitions, the conventional glass transition (a or α) and the polyethylene-like glass transition (α_PE) within alkyl nanodomains formed by aggregated alkyl rests. It is shown that amorphous as well as semicrystalline PnAMA can be understood as nanophase-separated polymers with alkyl nanodomains having a typical dimension of 1-2 nm. The results are compared with the predictions of simple morphological pictures for side chain polymers. X-ray scattering data for the amorphous and semicrystalline PnAMA are included in the discussion. Common aspects of nanophase-separated systems in both states as well as differences caused by crystallization are discussed. Indications for the existence of rigid amorphous regions are compiled. Different approaches to explain a similar increase of T_g(α_PE)—the glass temperature of the amorphous alkyl nanodomains—and T_M—the melting temperature of crystalline alkyl nanodomains—with side chain length are considered. Pros and cons of both approaches, based on increasing order within the alkyl nanodomains and confinement effects in nanophase-separated systems, are discussed. Main trends concerning crystallization and cooperative dynamics are compared with those in other systems with self-assembled nanometer confinements like microphase-separated blockcopolymers or semicrystalline main chain polymers.     

Reaction of ketenes with N,N-disubstituted α-aminomethyleneketones. XII. Synthesis of N,N-disubstituted 4-amino-3-chloro-6-(2-methyl-l-propenyl) (2-phenylethenyl)-2H-pyran-2-ones

Cycloaddition of dichloroketene to N,N-disubstituted (E)-amino-5-methyl-1,4-hexadien-3-ones IV and (E,E)-1-amino-5-phenyl-1,4-pentadien-3-ones V occurred in moderate to good yield only in the case of aromatic N-substitution to give N,N-disubstituted 4-amino-3,3-dichloro-3,4-dihydro-6-(2-methyl-l-propenyl) (2-phenylethenyl)-2H-pyran-2-ones, which were dehydrochlorinated with DBN to afford in good yield N,N-disubstituted 4-amino-3-chloro-6-(2-methyl-propenyl)(2-phenylethenyl)-2H-pyran-2-ones. In the case of aliphatic N,N-disubstitution (dimethylamino group) of enaminones IV and V, the Cycloaddition led directly in low yield to 3-chloro-4-dimethylamino-6-(2-methyl-l-propenyl)(2-phenylethenyl)-2H-pyran-2-ones.     

Thermodynamic Properties of Alanylpeptide Buffer Systems and Their Potential as Standards in Biological Applications

The second dissociation constants pK ₂of the NH₃ ⁺charge center of the alanylpeptides, alanylglutamine (Ala–Gln), alanylleucine (Ala–Leu), alanylglycine (Ala–Gly), and DL-alanyl–DL-methionine (DL-Ala–DL-Met) were determined at ten temperatures in the range, 5–50°C. These pK ₂values were calculated from the emf of cells containing buffer solutions of these dipeptides. A cell of the type described by Harned and Ehlers,⁽¹⁾utilizing hydrogen and silver–silver bromide electrodes was used. The thermodynamic quantities, H^o, S^o, and C_p ^owere derived from the temperature coefficients of the dissociation constants. The pK ₂values at 25°C, 8.2105 ( Ala–Gln), 8.2668 ( Ala–Leu), 8.2940 ( Ala–Gly), and 8.3054 ( DL-Ala–DL-Met). These values show that different substituent groups on the -carbon atom (which include polar and nonpolar groups), have a small effect on the dissociation of the NH₃ ⁺charge center. These compounds were also found to be suitable as buffers in the pH range(7–9). The thermodynamics of the solute–solvent interaction is interpreted in terms of the mixture model.⁽²⁾     

Reaction of ketenes with N,N-disubstituted α-aminomethyleneketones. XVI. Synthesis of N,N-disubstituted 4-amino-5,6-tetramethylene-3-phenyl-2-pyranones

1,4-Cycloaddition of phenylchloroketene (prepared in situ from α-chlorophenylacetyl chloride and triethyl-amine) to a number of N,N-disubstituted (E)-2-aminomethylenecyclohexanones gave the corresponding adducts, namely N,N-disubstituted 4-amino-3-chloro-3,4,5,6,7,8-hexahydro-2H-1-benzopyran-2-ones III in the case of aliphatic N,N-disubstitution or aromatic N-monosubstitution. Purification of III was possible only in the case of IIIh (NR₂ = NMePh), therefore they were dehydrochlorinated in situ with DBN to give the title compounds in moderate overall yields.     

Cyclodextrin derivatives for GC separation of racemic mixtures of volatile compounds. Part VIII: 2,6-di-O-methyl-3-O-pentyl-γ-cyclodextrin and 2,6-di-O-methyl-3-O-(4-oxo-pentyl)- and 2,6-di-O-pentyl-3-O-(4-oxo-pentyl)-β-and -γ-cyclodextrins

In pre vious papers, 2,6-di-O-methyl-3-O-pentyl-β-cyclodextrin (CD) was demonstrated to be successful in separating volatile compounds, while avoiding the drawbacks of 2,3,6-tri-O-methyl-O-methyl-β-CD in terms of column stability and operating temperature. Since a CD chiral selector of universal use has not yet been found, and at least two (or more) columns coated with different CD derivatives are therefore necessary for routine work, the performance of 2,6-di-O-methyl-3-O-pentyl-γ-CD, 2,6-di-O-methyl-3-O-(4-oxopentyl)-γ-CD, 2,6-di-O-pentyl-3-O-(4-oxo-pentyl)-β-CD, and 2,6-di-O-pentyl-3-O-(-4-oxo-pentyl)-γ-CD diluted in polysiloxanes for the separation of volatile compounds in aromas and essential oils will be illustrated; each column coated with each of the newly synthesized CD derivatives was evaluated by analyzing more than 150 different recemates with different structures.     

Thermal decomposition of 2-amino-3-aziridino-1,4-naphthoquinones

The course of the thermal decomposition of various 2-amino-3-substituted aziridino-1,4-naphthoquinones (Ia-g) was investigated. In all the cases, the thermal decomposition gave variable amounts of 2,3-diamino-1,4-naphthoquinone (II) and of substituted 1,2,3,4,5,10-hexahydrobenzo[g]quinoxaline-5,10-diones (IIIa-g) with complete stereospecificity. The decomposition of the aziridines Ib,f also gave significative amounts of 2-amino-3-allylamino-1,4-naphthoquinones (IVb,f). In the case of 2-amino-3-(2′-phenyl-3′-ethylaziridino)-1,4-naphthoquinone (Ig), the formation of trans-1-phenyl-1-butene (V), 2-(1-phenylpropyl)-1H-naphtho-imidazole-4,9-dione (VI), 2-phenyl-3-ethyl-3,4,5,10-tetrahydrobenzo[g]quinoxaline-5,10-dione (VII), 2-phenyl-3-ethyl-5,10-dihydrobenzo[g]quinoxaline-5,10-dione (VIII), and a mixture of cis- and trans-4H-2,3,5,6-tetra-hydro-2-phenyl-3-ethyl-5-iminonaphtho[1,2-b]oxazin-6-one (IX) also occurred. Hypotheses concerning the mechanism and the steric course of this reaction are given. The reaction is a general method for the stereospecific synthesis of 2,3-disubstituted 1,2,3,4,5,10-hexahydrobenzo[g]quinoxalines.     

Optimization of virtual orbitals in the framework of a multiconfiguration spin-coupled wave function

A new method is introduced for the optimization of nonorthogonal virtual orbitals for use in general multiconfiguration spin-coupled wave functions. The use of a number of highly effective approximations greatly reduces the computational effort involved, the most important being the use of a second-order perturbation expression for the energy and an approximate expression for the elements of the Hessian. As a result, the overall scheme scales very favourably with respect to the numbers of active electrons and of basis functions, making it suitable for the accurate study of large systems. Benchmark calculations are presented for the dissociation of LiH(X¹Σ⁺) and Li₂(X¹Σ⁺ _g ) using a highly compact four-configuration wave function. Standard spin-coupled valence bond expansions in the same virtual space are required to be significantly larger before equivalent results are obtained. The results are shown to compare very favourably with full valence complete active space self-consistent field calculations using an identical basis, and binding energies are within 4% of the values obtained from full configuration interaction calculations in the same basis set. Received: 10 June 1997 / Accepted: 7 October 1997