A Study of the 13C NMR Shifts in Two Tetradehydrocyclodecabiphenylenes and Related Aryl and Biphenylenylacetylenes

The ¹³C spectra of 5,6,9,10-tetradehydrocyclodeca[1,2,3,4-def]-benzo [7,8]biphenylene, 1, and 5,6,9,10-tetradehydrocyclodeca [1,2,3,4-def]-naphtho [2,3-7,8]biphenylene, 2, are reported as are those of a number of simpler acetylenic hydrocarbons used as spectral references. Most of the shifts can be assigned unambiguously. The acetylenic shift assignments were verified by ortho-proton, sp-carbon (¹H(1)-¹³C_sp(3)) decoupling experiments. A simple additive shift correlation is found for the hydrocarbons containing unstrained acetylenic groups. However, significant discrepencies are found for the ¹³C shifts for the strained hydrocarbons 1, 2, 1,2-bis(phenylethynyl)-benzene, 12, and 2,3-bis(phenylethynyl)-naphthalene, 13. The discrepencies are particularily large for carbons near the triple bonds and are attributed to a combination of strain, rehybridization, and other proximity effects related to the interaction between the ortho-substituted acetylenic carbons.     

Aromatic substitution

It is demonstrated that a previously developed topological expression for the total π-electron energy of aromatic molecules provides a good qualitative account of localization energies. The logarithm of the ratio of the algebraic structure counts for the ground state and the localized reaction intermediate is the principle energy determining factor. This expression fails for hydrocarbons with unusually small HOMO-LUMO separations. An alternative topological expression that includes a correction for this situation provides an excellent non-empirical explanation for the successful empirical use of Dewar reactivity numbers in correlating exact localization energies. The present analysis provides an explanation for the success of the traditional resonance structure counting technique in predicting relative rates of aromatic substitution. The analysis develop applied only to alternant hydrocarbons.     

Biogenesis of betalaine. Biotransformation of dopa and tyrosine in betalaminic acid part of the betanins

During studies on the biogenesis of betalains (I) in cactus fruits (Opuntia sp.). DL -dopa-1-[¹⁴C] and -2-[¹⁴C] were incorporated into betanin (III) which was obtained radiopure after crystallization. The specific activity remained constant after conversion to betanidin (IV) and to a neobetanidin derivative (IX). Reaction of radiobetanin with proline afforded indicaxanthin (V) carrying more than 90% of the radioactivity. Dopa (VI) is thus an efficient precursor for betalamic acid (VIII) but not for cyclodopa (VII). Decarboxylation of radiobetanidin and radioindicaxanthin showed that the carboxyl group of dopa remained a carboxyl group in the biotransformation to betalamic acid. It is concluded that the aromatic ring of dopa is cleaved and that re-cyclization involving the nitrogen generates the dihydropyridine moiety. Under the same conditions mevalonic acid, aspartic acid and phenylalanine showed low incorporations. Studies with beet seedlings and DL -dopa-1-[¹⁴C], -2-[¹⁴C] and DL -tyrosine-1-[¹⁴C] afforded similar results but with low incorporations.     

The number of Kekulé structures and the thermodynamic stability of conjugated systems

The dependence of Hückel π-electron energies, E_π, on the basic graph theoretical parameters N (the number of vertices), ν (the number of edges) and ASC (the algebraic structure count) is explored. The form with the ASC enters E_π is established and an equation for E_π is developed. It is shown how the early and apparent success of the (resonance) theory rested on the fortunate fact that all Kekulé structures for benzenoid hydrocarbons and acyclic polyenes have the same parity. The significance of ASC in determining chemical stability and reactivity is dicussed briefly.     

Sonar echo analysis

Pulse mode sonar operation is analyzed under the assumption that the scattering object Γ lies in the far fields of both the transmitter and the receiver. It is shown that, in this approximation, the sonar signal is a plane wave s(x · θ₀ – t) near Γ, where θ₀ is a unit vector directed from the transmitter toward Γ, and similarly the echo is a plane wave e(x · θ – t) near the receiver, where θ is a unit vector directed from Γ toward the receiver. Moreover, if Γ is stationary with respect to the sonar system then it is shown that where ?(ω) is the Fourier transform of S(τ) and T+(ωθ,ωθ₀) is the scattering amplitude in the direction θ due to the scattering by Γ of a time-harmonic plane wave with frequence ω and propagation direction θ₀. A generalization of this relation is derived for moving scatterers.     

An analysis of cross-correlations in an emerging market

We apply random matrix theory to compare correlation matrix estimators C$C$ obtained from emerging market data. The correlation matrices are constructed from 10 years of daily data for stocks listed on the Johannesburg stock exchange (JSE) from January 1993 to December 2002. We test the spectral properties of C$C$ against random matrix predictions and find some agreement between the distributions of eigenvalues, nearest neighbour spacings, distributions of eigenvector components and the inverse participation ratios for eigenvectors. We show that interpolating both missing data and illiquid trading days with a zero-order hold increases agreement with RMT predictions. For the more realistic estimation of correlations in an emerging market, we suggest a pairwise measured-data correlation matrix. For the data set used, this approach suggests greater temporal stability for the leading eigenvectors. An interpretation of eigenvectors in terms of trading strategies is given, as opposed to classification by economic sectors.     

Application of the bispectrum for detection of small nonlinearities excited sinusoidally

The nonlinear behaviour of damaged systems excited by vibration or ultrasound offers potential as a technique for damage detection in machine condition monitoring and non-destructive testing applications. The bispectrum, a third-order spectrum, has properties that lend themselves to the measurement of nonlinearities in systems. The properties of interest are insensitivity to Gaussian noise and ability to detect quadratic phase coupling. However, thus far analysis of the statistics of bispectrum estimation has been mainly aimed at stochastic systems. Many applications to vibration and ultrasound involve primarily deterministic, periodic excitations in the presence of stochastic noise. This paper considers the properties of a bispectrum estimate when applied to a system with weak quadratic nonlinearity excited by the superposition of two sinusoids in the presence of additive Gaussian noise. This is compared, using signal-to-noise ratios, to the powerspectrum, with the results validated using numerical data. Also addressed is the effect of quadratic phase coupling on such a system (in the absence of noise).     

Scattering of plane guided waves obliquely incident on a straight feature with uniform cross-section

A frequency-domain finite element (FE) method is presented for modeling the scattering of plane guided waves incident on an infinitely-long, straight feature with uniform cross-section in a planar host waveguide. The method utilizes a mesh of 2-dimensional finite elements with harmonic shape functions in the perpendicular direction. The model domain comprises a cross-section through the feature and short lengths of the adjoining host waveguide. A spatial frequency equal to the wavenumber of the desired incident mode multiplied by the sine of the desired incidence angle is prescribed for the element shape functions. An integral representation of the incident mode is used to determine a suitable system of harmonic forces to uniquely excite that mode. These are applied at nodes through the thickness of the host waveguide on one side of the feature. The displacement field is measured at nodes through the thickness of the host waveguide on either side of the feature and decomposed into reflected and transmitted modes. The cases of guided wave transmission in a featureless waveguide and the reflection of guided waves from a free-edge are examined as validation cases. Finally, the results for transmission at an adhesively-bonded stiffener are presented and compared with experimental measurements.