On the exceptional zeros of cross-products of derivatives of spherical Bessel functions

The lowest zeros of the cross-products of derivatives of spherical Bessel functions are not obtainable from a McMahon-type formula. This paper derives an analytical approximation for these lowest, exceptional, zeros, through to 4th order in a parameter specifying the thinness of the corresponding concentric spherical region.

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Zusammenfassung Die kleinsten Nullstellen der Kreuzprodukte der Ableitungen von spherischen Bessel-funktionen können nicht durch eine Formel von McMahon Typ erhalten werden. Durch eine Entwicklung bis zu vierter Ordnung in einem Parameter proportional zur Dicke des zugeordneten spherischen Gebietes berechnen wir eine analytische Näherung für diese kleinsten, außergewöhnlichen, Nullstellen.

     

Elution of organic solutes from different polarity sorbents using subcritical water

The intermolecular interactions between organic solutes and sorbent matrices under subcritical water conditions have been investigated at a pressure of 50 bar and temperatures ranging from 50 to 250°C. Both polar and nonpolar organics (chlorophenols, amines, n-alkanes, and polycyclic aromatic hydrocarbons) and five different sorbent matrices (glass beads, alumina, Florisil, silica-bonded C₁₈, and polymeric XAD-4 resins) were used. From the same matrix, the polar solutes always eluted at lower temperatures, while the moderately polar and nonpolar solutes only eluted at higher temperatures. Similar to matrix effects previously observed using supercritical carbon dioxide, the sorbent type greatly influenced the elution efficiency under subcritical water conditions. Lower temperatures are sufficient to elute a particular solute from glass beads, alumina, and Florisil, but higher temperatures (less polar water) are needed to elute the same solute from silica-bonded C₁₈. The highest temperatures were required to elute aromatic organics from XAD-4. These matrix effects demonstrate that, while low temperature water can break inert or dipole interactions between solutes and glass beads, alumina, and Florisil, higher temperature water is required to interrupt the van der Waals attractions between solutes and silica-bonded C₁₈, and even higher temperatures needed to overcome the π-electron interactions between aromatic solutes and XAD-4.     

Luminol Oxidation by Hydrogen Peroxide Catalyzed by Tobacco Anionic Peroxidase: Steady-State Luminescent and Transient Kinetic Studies

The properties of a newly isolated anionic tobacco peroxidase from transgenic tobacco plants overexpressing the enzyme have been studied with respect to the chemiluminescent reaction of luminol oxidation. These were compared to the properties of horseradish peroxidase in the cooxidation of luminol and p -iodophenol, the enhanced chemiluminescence reaction. The pH, luminol and hydrogen peroxide concentrations were optimized for maximum sensitivity using the tobacco enzyme. The detection limit for the latter under the optimal conditions (2.5 m M luminol, 2 m M hydrogen peroxide, 100 m M Naborate buffer, pH 9.3) was about 0.1 p M , which is at least five times lower than that for horseradish peroxidase in enhanced chemiluminescence with p -iodophenol. The rate constants for the elementary steps of the enzyme-catalyzed reaction have been determined: k ₁= 4.9 × 10⁶ M ⁻¹ s¹, k ₂= 7.3 × 10⁶ M ⁻¹ s⁻¹, k ³= 2.1 × 10⁶ M ⁻¹ s⁻¹ (pH 9.3). The similarity of these rate constants is unusual for plant peroxidases. The high catalytic activity of tobacco peroxidase in the luminescent reaction is explained by the high reactivity of its Compound II toward luminol and the high stability of the holoenzyme with respect to heme dissociation. This seems to be a unique property of this particular enzyme among other plant peroxidases.     

A hydrogenation product derived from the diterpenoid barbatusin:A revised structure

The structure of the hydrogenation product of barbatusin, a diterpenoid from Coleus barbatus Bentham has been revised on the basis of NMR and X-ray data. A geminal coupling of unusually high magnitude has been observed and analysed.     

Certain bilateral generating relations for generalized hypergeometric functions

Recently, we introduced a class of generalized hypergeometric functionsI n:(b _q)/α:(a _p) (x, w) by using a difference operator Δ _x,w , where . In this paper an attempt has been made to obtain some bilateral generating relations associated withI _n ^ga (x, w). Each result is followed by its applications to the classical orthogonal polynomials.     

Gauge theory of fermions onR × S 3 spacetime

A Lorentz-invariant gauge theory for massive fermions on R × S ³ spacetime is built up. Using the symmetry of S ³,we obtain Dirac-type equation and derive the expression of the fermionic propagator. Finally, starting from the SU(N) gauge-invariant Lagrangian, we obtain the set of Dirac-Yang-Mills equations on R × S ³ spacetime, pointing out major differences from the Minkowskian case.