Limit cycles of generalized Liénard equations

The generalized Liénard equations of the form:

where F, g, and h are polynomials, are examined. It has been found that the results given by Blows, Lloyd and Lynch [1–5] for Liénard equations hold also for the generalized systems. A new result is also presented within this article.     

Excited state properties from the equations of motion method. Application of the MCTDHF-MCRPA to the dipole moments and oscillator strengths of the A 1Π, a′3Π, a′3Σ+ and d3Δ low-lying valence states of CO

By examining the exact operator O_λ⁺ which is the solution of the equations of motion-Green's function method, we rederive expressions for non-reference (usually excited) state properties. Hence, additional useful information such as state expectation values, oscillator strengths, and frequency dependent and independent polarizabilities may be easily obtained from an equation of motion-Green's function calculation. With the multiconfigurational random phase approximation (MCRPA), which is equivalent to the multiconfigurational time dependent Hartree-Fock (MCTDHF), excitation energies, oscillator strengths, and excitation operators from the ground states are obtained for the low-lying valence (under 10 eV above the ground state) states of CO at the experimental ground state equilibrium geometry. We apply these techniques to obtain the excited state dipole moments for and oscillator strengths between the A ¹Π, a ³Π, a′ ³Σ⁺, and d ³Δ states of CO and compare our results to other calculations and experiments.     

Error behavior in optimal relaxation methods

Summary Stiefel's theory of optimal relaxation methods is applied to study the behavior of the error, measured by (the square of) an energy-type norm, as the number of iteration steps tends to infinity. It is shown how certain features of the initial residual vector affect the rate of convergence. Of particular interest are cases in which the higher-order components of the initial residual vector, in the coordinate system of principal axes, are more and more attenuated.

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Zusammenfassung Stiefels Theorie der optimalen Relaxationsverfahren wird angewandt, um das Verhalten des Fehlers zu studieren, wenn die Zahl der Iterationsschritte nach Unendlich geht, wobei der Fehler durch das Quadrat einer Energie-Norm gemessen wird. Es wird gezeigt, wie gewisse Eigenschaften des Anfangsresiduumvektors die Konvergenzgeschwindigkeit beeinflussen. Von besonderem Interesse sind Fälle, in welchen die höheren Komponenten des Anfangsresiduumvektors in den Koordinaten der Hauptachsen mehr und mehr abgeschwächt sind.

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The work of the first author was supported, in part, by the National Science Foundation under Grant MCS-7927158. The work of the second author was supported, in part, by the National Science Foundation under Grant MCS-7610225.     

Structure determination of soybean and wheat glucosylceramides by tandem mass spectrometry

Glucosylceramide (GluCer) is a major sphingolipid of plant tissue and, thus, abundant in nature and in dietary food sources. The lipid backbones of mammalian GluCer (sphingosine, d18:1(delta4), and ceramide) induce cell death (apoptosis) and inhibit colon carcinogenesis, it is critical to know the structures of GluCer present in plants as a first step toward understanding this potential link between diet and cancer. This study characterized the molecular species of GluCer from soybean and wheat by low-resolution, high-resolution and tandem mass spectrometry. Soybean GluCer was comprised primarily (>95%) of ceramide with 4,8-sphingadiene (d18:2(delta4,delta8)) and alpha-hydroxypalmitic acid (h16:0); the remainder had the same backbone with h18:0, h20:0, h22:0 and h24:0 fatty acids. Wheat GluCer had three major ceramide, d18:2(delta4,delta8) with h16:0, d18:1(delta8) with h16:0 and d18: 2(delta4,delta8) with h20:0, and smaller amounts of other homologs. These backbones differ from those of mammalian sphingolipids, which often have a delta4-double bond (but rarely a delta8-double bond), and have alpha-hydroxy fatty acids in only some cases. Previously unexplained fragmentations that were diagnostic for the type of sphingoid base backbone (i.e. by homolytic cleavage of the doubly allylic C-6-C-7 bond to yield a stable distonic allylic radical cation and an allylic radical neutral) were also identified. Hence this method should be useful in the identification of double bonds in sphingolipids, and structure-function relationships between sphingolipids and colon carcinogenesis.     

Space-frequency distribution of sound field intensity in the vicinity of the temperature front in shallow water

The sound field produced by a low-frequency (100–1000 Hz) point source in a shallow water region in the presence of the temperature front is considered. It is shown that the latter anisotropic inhomogeinity leads to a substantial horizontal refraction and to a number of related effects: a redistribution of the sound field in the horizontal plane, changes in the spectral and mode contents of a pulse in the course of its propagation, and changes in the arrival times at the receiver. A theoretical analysis and a numerical modeling are carried out for the Polar Front of the Barents Sea.