Locating and counting bifurcation points of satellite components from the main component in the degree-n bifurcation set

The bifurcation point where a satellite component buds from another component is characterized by the existence of the common tangent line between the two osculating components appearing in the degree-n bifurcation set. We investigate the existence, location and number of bifurcation points for satellite components budding from the main component in the degree-n bifurcation set as well as a parametric boundary equation of the main component of the degree-n bifurcation set. Cusp points are also located on the boundary of the main component. Typical degree-n bifurcation sets and their components are illustrated with some computational results.     

Backward extensions of subnormal operators

The concept of backward extension for subnormal weighted shifts is generalized to arbitrary subnormal operators. Several differences and similarities in these contexts are explored, with emphasis on the structure of the underlying measures.

     

Features of polystyrene synthesis in the presence of (diphenylbutadiene)tricarbonylchromium

Features of radical polymerization of styrene in the presence of (diphenylbutadiene)tricarbonylchromium were studied.     

On <Emphasis Type="Italic">W</Emphasis>-geometry of Toda systems

We describe W-geometry of two-dimensional Toda systems associated with the Lie algebra C _n . __________ Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.     

Nusselt number correlations for heat transfer to small spheres in thermal plasma flows

Seven different equations predicting heat transfer rates to small spheres in plasma flows are examined considering argon and nitrogan as plasma gases from 300 to 21,000 K at 1 atm. For argon there is a general consensus up to 9000 K, beyond which wide deviations in behavior occur. For nitrogen, the seven correlations are in good agreement up to 4000 K, but show substantial deviations beyond this value. Comparisons with the sparsely available experimental data are made for argon from 300 to 17,000 K and for nitrogen up to 5500 K. Disagreement between the various correlations and experiment can exceed one order of magnitude.     

A family of maximal surfaces in Lorentz-Minkowski three-space

We prove the existence of an infinite family of complete spacelike maximal surfaces with singularities in Lorentz-Minkowski three-space and study their properties. These surfaces are distinguished by their number of handles and have two elliptic catenoidal ends.

     

O− and OH− chemical ionization of some fatty acid methyl esters and triacylglycerols

O^? and OH^? react with fatty acid methyl esters (FAMES) under chemical ionization conditions both as Bronsted bases to form [M - H]^? and as nucleophiles to form the carboxylate ion RCOO^?. O^? shows a much greater tendency to react as a nucleophile than does OH^?. The [M - H]^? ions fragment by elimination of CH³OH, with unsaturation in certain positions in the fatty acid hydrocarbon chain promoting this elimination for unknown reasons. The reaction of O^? and OH^? with triacylglycerols leads to [M - H]^?, characteristic of the molecular mass, and to carboxylate ions characteristic of the fatty acid(s) present in the lipid. The presence of the three ester functions in the lipids greatly enhances the formation of carboxylate ions compared to the FAMES.     

Wilcoxon signed rank test using ranked-set sample

Ranked-set sampling is useful when measurements are destructive or costly to obtain but ranking of the observations is relatively easy. The Wilcoxon signed rank test statistic based on the ranked-set sample is considered. We compared the asymptotic relative efficiencies of the RSS Wilcoxon signed rank test statistic with respect to the SRS Wilcoxon signed rank test statistic and the RSS sign test statistic. Throughout the ARE’s, the proposed test statistic is superior to the SRS Wilcoxon signed rank test statistic and the RSS sign test statistic.