Moore-Penrose inverse in an indefinite inner product space

The concept of the Moore-Penrose inverse in an indefinite inner product space is introduced. Extensions of some of the formulae in the Euclidean space to an indefinite inner product space are studied. In particular range-hermitianness in completely characterized. Equivalence of a weighted generalized inverse and the Moore-Penrose inverse is proved. Finally, methods of computing the Moore-Penrose inverse are presented.     

Magnetic-Zenith Effect

We develop a theory of the magnetic-zenith effect (MZE) observed upon the ionosphere modification by powerful radio waves. The dependences of MZE on main parameters, such as the magnetic-field inclination angle, pump-wave frequency and power, and angular width of HF beam are obtained. The optimal elevation angle of pump-wave beam is predicted. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 9, pp. 772–787, September 2005.     

Decay of neutron-rich Ga isotopes near N = 50 at PARRNe

The PARRNe facility has been used to produce neutron-rich isotopes ^83,84Gaby the ISOL method. Their decay has been studied, and β-γ coincidence and γ-γ coincidence data were collected as a function of time. The first two excited levels in ⁸³Ge and the first excited level in ⁸⁴Ge have been measured for the first time.     

Synthesis and Crystal Structure of the Hydrogen Polyphosphide Bis(Tetraphenylphosphonium) hydrogenheptaphosphide‐ammonia(1/3) (PPh4)2HP7 · 3NH3

(PPh₄)₂HP₇ · 3NH₃ was prepared by the reaction of K₃P₇ with a proton‐charged ion exchange resin in the presence of (PPh₄)Br in liquid ammonia, and characterized by low temperature X‐ray structure analysis. The thermally very unstable compound contains the hydrogenheptaphosphide anion HPequation/tex2gif-stack-1.gif, the nortricyclane‐like cage of which is slightly distorted by the attachment of the hydrogen atom.     

The single-valued extension property for bilateral operator weighted shifts

In this paper, we give necessary and sufficient conditions for a bilateral operator weighted shift to enjoy the single-valued extension property.

     

Catalysis by ionic liquid: a simple, green and efficient procedure for the Michael addition of thiols and thiophosphate to conjugated alkenes in ionic liquid, [pmIm]Br

A room temperature ionic liquid, 1-pentyl-3-methylimidazolium bromide, [pmIm]Br efficiently catalyzes Michael addition of thiols and diethyl dithiophosphate to a variety of conjugated alkenes such as α,β-unsaturated carbonyl compounds, carboxylic esters, nitriles and chalcones without requiring any other organic solvent and catalyst. The ionic liquid can be recycled for subsequent reactions without any appreciable loss of efficiency.     

Hexaphyrin(1.0.1.0.0.0). A new colorimetric actinide sensor

Hexaphyrin(1.0.1.0.0.0) (isoamethyrin) undergoes a significant color change in the presence of UO₂²⁺, PuO₂²⁺, and NpO₂²⁺. The complexation of the first of these dioxo actinide cations was studied in semi-quantitative fashion in 1:1 MeOH-CH₂Cl₂. Under these conditions, the detection limit for UO₂²⁺ was found to be ca. 5.8 ppm by naked eye monitoring and <28 ppb by UV-vis spectroscopy. Isoamethyrin does not undergo a color change in the presence of most transition metals or when exposed to Gd(III). Isoamethyrin thus constitutes an attractive alternative to 2,2′(1,8-dihydroxy-3,6-disulfonaphthylene-2,7-bisazo)-bisbenzenarsonic acid (AzIII) and 2-(5-bromo-2-pyridylazo)-5-(diethylamino)phenol (BrPADAP), systems currently used as actinide cation sensors.     

Synthesis of highly condensed heterocycles using radical reactions

Using radical chemistry novel highly condensed heterocycles have been synthesized. The mechanism for their formation is discussed.     

Numerical simulations of a filament in a flowing soap film

Experiments concerning the properties of soap films have recently been carried out and these systems have been proposed as experimental versions of theoretical two‐dimensional liquids. A silk filament introduced into a flowing soap film, was seen to demonstrate various stable modes, and these were, namely, a mode in which the filament oscillates and one in which the filament is stationary and aligns with the flow of the liquid. The system could be forced from the oscillatory mode into the non‐ oscillatory mode by varying the length of the filament. In this article we use numerical and computational techniques in order to simulate the strongly coupled behaviour of the filament and the fluid. Preliminary results are presented for the specific case in which the filament is seen to oscillate continuously for the duration of our simulation. We also find that the filament oscillations are strongly suppressed when we reduce the effective length of the filament. We believe that these results are reminiscent of the different oscillatory and non‐oscillatory modes observed in experiment. The numerical solutions show that, in contrast to experiment, vortices are created at the leading edge of the filament and are preferentially grown in the curvature of the filament and are eventually released from the trailing edge of the filament. In a similar manner to oscillating hydrofoils, it seems that the oscillating filaments are in a minimal energy state, extracting sufficient energy from the fluid to oscillate. In comparing numerical and experimental results it is possible that the soap film does have an effect on the fluid flow especially in the boundary layer where surface tension forces are large. Copyright © 2004 John Wiley & Sons, Ltd.