Isogonal Prismatoids

The study of the polyhedra (in Euclidean 3-space) in which faces may be self-intersecting polygons, and distinct faces may intersect in various ways, was quite fashionable about a century ago. The Kepler—Poinsot regular polyhedra, and several of their generalizations, were investigated about that time by Cayley, Wiener, Badoureau, Fedorov, Hess, Pitsch, and others; the accumulated wisdom was presented in Max Brückner's well-known book Vielecke und Vielflache in 1900. Despite the intrinsic interest of the topic, and its relations to various other disciplines, there have been very few additional investigations during the intervening century, except for discussions of uniform polyhedra. In particular, there has been no mention or clarification of the many errors and other shortcomings of Brückner's book. One of our aims is to point out the extent of these inadequacies; they are illustrated by a discussion of isogonal prismatoids, the investigation of which is our main objective. A prismatoid is a polyhedron having all its vertices in two parallel planes. Familiar examples are prisms and antiprisms. A polyhedron P is isogonal if all its vertices form one transitivity class under isometric symmetries of P. Although these restrictions appear very severe, there exist many different kinds of isogonal prismatoids. Some general concepts concerning polyhedra with possible self-intersections are presented, and several classes of isogonal prismatoids are discussed in some detail. Received April 5, 1995.     

Inclusive charmed-baryon decays and lifetimes

We have quantitatively reanalyzed the inclusive charmed-baryon decays. New ingredients are the Voloshin preasymptotic effects in semileptonic decays and the Cabibbo-subleading contributions to both semileptonic and nonleptonic decays. It has been found that the Cabbibo-subleading Voloshin contribution essentially improves the theoretical semileptonic branching ratio of , in agreement with experiment. The semileptonic branching ratios for and are found to be large, i.e., of the order of 20%. The lifetimes hierarchy is in a good qualitative and even quantitative agreement with experiment except for the lifetime, which is somewhat smaller than the experimental value. Future measurements, especially measurements of the semileptonic branching ratios for , and should be decisive for the check of this approach. Received: 29 April 1997 / Revised version: 25 June 1997 / Published online: 20 February 1998     

Some interlacing results for indefinite Hermitian matrices

A classical theorem of Cauchy states that the eigenvalues of a principal submatrix A₀ of a Hermitian matrix A interlace the eigenvalues of A. We consider the case of a matrix A which is Hermitian with respect to an indefinite inner product.     

Precise pion electroproduction in thep(e,e′ π+)n reaction at W=1125 MeV

The reactione+p →> e+π ⁺+n at c.m. energyW=1125MeV and momentum transfer Q²=0.117GeV²/c₂ has been measured. The transverse and longitudinal structure functions have been separated by varying the polarization of the virtual photon (Rosenbluth plot) with a 3 to 4% error. In addition the longitudinal-transverse interference term has been determined measuring the right-left asymmetry with an accuracy of 3%. The experimental data are compared to model calculations, and the sensitivity of the results to the axial and pion formfactors is discussed.     

Remarks on the perturbation of analytic matrix functions

Integral Equations and Operator Theory -     

Investigation of azoxides and olefins [3 + 2] cycloaddition to 1,2,3-oxadiazolidines by a combination of density functional theory and semiempirical methods

Theoretical studies of the aspects of an azoxide addition to olefins is presented. The stability of the 1,2,3-oxadiazolidine ring is discussed in regard to its capability to undergo a retro cycloaddition reaction. The structural features necessary to increase the stability of the heterocycle is proposed and evaluated. The computational results are supported with experimental observations.     

Tautomerism of 4-phenyl-2,4-dioxobutanoic acid. Insights from pH ramping NMR study and quantum chemical calculations

Aryldiketo acids (ADKs) exhibit the variety of biological activities, mainly due to large affinity toward divalent metal ions. Metal complexation ability of ADKs, as well as interactions with proteins, depend on tautomeric form present in solution. The main aim of this study was to fully explore the tautomeric preferences of 4-phenyl-2,4-dioxobutanoic acid (4PDA), as ADKs representative, in aqueous media at different pH values. 1D and 2D NMR spectroscopy in combination with quantum chemical calculations was applied in order to better understand the tautomeric preferences of 4PDA. The data in highly acidic media are especially interesting since there are no such findings in the literature due to low solubility of ADKs in molecular form. At low pH values, where 4PDA is unionized, the most abundant tautomeric form is enol with keto group closer to phenyl ring. At higher pH values, mixture of two 4PDA ionic forms coexists in solution. Their ratio calculated according to NMR data fits the values predicted using two experimentally determined pK _a values. Based on the complexity of ¹H NMR spectrum of monoanionic 4PDA form, coexistence of two stable rotamers was assumed. In an alkaline media, 4PDA is mostly present in dianionic form. As π-electrons of dianion are delocalized over an entire keto-enol moiety, spectral distinction between tautomers was not possible. Quantum chemical calculations were used to predict relative stability of tautomers. The predictions were in good accordance with experimental results only in case when explicit water molecule was included in calculations.     

Thermogravimetric study of the reduction of CuO–WO<Subscript>3</Subscript> oxide mixtures in the entire range of molar ratios

The present study reports the results of investigation on the role of metakaolin in the formation of ettringite in a model relevant to Portland cement. The model consists of ternary system (Trio) metakaolin–lime–gypsum. Five samples of defined ternary system were cured at different temperatures 20, 30, 40, 50 and 60 °C. Conduction calorimeter TAM AIR was mainly used to capture heat evolution at different temperatures. Thermoanalytical (simultaneous TGA/DSC) and X-ray diffraction methods were used to identify different products after curing. It results that ettringite is the main hydration product supplemented by calcium silicate and calcium aluminosilicate hydrates according to sample composition. The mechanism and kinetics of hydration, as displayed by calorimetric curves, depend on composition of samples and curing temperatures. Two main types of processes have been elucidated: reaction of aluminum ions with sulfate ones in the presence of calcium ions in aqueous solution to form ettringite supplemented by pozzolanic activity leading to the formation of calcium silicate and calcium aluminosilicate hydrates. Concomitant condensation of alumina and silica species and carbonation have influenced the course of hydration. Activation energy E _a depends slightly on composition of ternary system.     

Nitrosation of methyl 2-cinnamoylamino-3-dimethylaminopropenoates. Alkyl N-cinnamoyloxalic acid hydroxyimidic amides,intermediates in the synthesis of alkyl 5-styryl-1,2,4-oxadiazole-3-carboxylates

Alkyl 2-(substituted cinnamoylamino)-3-dimethylaminopropenoates 5, prepared either from glycine ( 1 ) and substituted cinnamoyl chlorides 2 via oxazol-5(4H)-ones 4 , or from cinnamoylglycinate with t-butoxy-bisdimethylaminomethane, were transformed by nitrosation into 5-substituted-1,2,4-oxadiazole-3-carboxylates 8 . The formation of alkyl N-cinnamoyloxalic acid hydroxyimidic amides 7, which were isolated as intermediates, represent a novel synthesis of N-acyl substituted hydroxyimidic amides.