Sympathetic cooling rate of gas-phase ions in a radio-frequency-quadrupole ion trap

We theoretically investigated the mass dependence of the sympathetic cooling rate of gas-phase ions trapped in a linear radio-frequency-quadrupole ion trap. Using an a priori molecular dynamical calculation, tracing numerically with Newtonian equations of motion, we found that ions with a mass greater than 0.54±0.04 times that of the laser-cooled ions are sympathetically cooled; otherwise, they are heated. To understand the mass dependence obtained using the molecular-dynamical calculation, we made a heat-exchange model of sympathetic cooling, which shows that the factor of 0.54±0.04 is a consequence of absence of micro-motion along the axis of the linear ion trap. Received: 10 December 2001 / Revised version: 28 January 2002 / Published online: 14 March 2002     

Conditional Time Before Ruin of an Insurance Company

The statistical characteristics of conditional time before ruin of an insurance company, including the distribution function of conditional time and its moments are examined.     

Influence of the counterion size on swelling and collapse of polyelectrolyte gel

A theory that predicts the effect of the counterion size on the swelling and collapse of a weakly charged polyelectrolyte gel was developed. In addition to excluded-volume interactions between monomer units of the gel, the theory involves the counterion-monomer unit and counterion-counterion interactions in terms of the virial approximation. The character of interactions between different units in the system varies from repulsion to attraction depending on the type of solvent, counterion, and dielectric permittivity of the solvent. For solvents with a low permittivity, the effect of condensation of counterions resulting in the formation of ion pairs is taken into account.     

Synthesis of New Plant Growth Regulators,Isomeric 1-(Dimethyloctyl)- and 1-Alkylpiperidinium and -morpholinium Halides by Telomerization of Isoprene with Secondary Amines

The known plant growth regulator, Al'den [1-(3,7-dimethyloctyl)-1-allylpiperidinium bromide], and also 1-(3,7-dimethyloctyl)-1-methylpiperidinium iodide were synthesized by treatment with allyl bromide and methyl iodide, respectively, of exhaustively hydrogenated 1-nerylpiperidine which was obtained by anionic telomerization of isoprene with piperidine. Various quaternary ammonium salts having a terpene sub- stituent with unnatural dimethyloctane skeleton, which effectively stimulate florification of Aster Chinensis L., were prepared by the action of alkyl halides on telomerization products derived from isoprene and piperidine or morpholine in the presence of palladium complexes.     

Lubin–Tate Formal Groups over the Ring of Integers of a Multidimensional Local Field

Some isomorphism criteria for Lubin–Tate formal groups over the ring of integers of a multidimensional local field are given. Bibliography: 4 titles.     

Embedding of Nonprimary Subgroups in the Symmetric Group S 9

The nonprimary subgroups of the symmetric group S ₉ are investigated. Embedding properties of these subgroups are listed in a table. Properties such as abnormality, pronormality, paranormality, weak normality, etc. were checked with the help of a computer. Algorithms and codes of the first author were used for this purpose. The research leans upon the technique of Burnside marks, as well as upon pertinent information on the table of marks of S ₉ from the computer algebra package GAP. The subgroups were investigated up to conjugacy; the total number of conjugacy classes of nonprimary subgroups of S ₉ is 432. Some subgroups were additionally checked by other programs based on the double coset method. Bibliography: 24 titles.