Transfer and Tate’s theorem

Let H be a subgroup of a finite group G, and assume that p is a prime that does not divide |G : H|. In favorable circumstances, one can use transfer theory to deduce that the largest abelian p-groups that occur as factor groups of G and of H are isomorphic. When this happens, Tate’s theorem guarantees that the largest not-necessarily-abelian p-groups that occur as factor groups of G and H are isomorphic. Known proofs of Tate’s theorem involve cohomology or character theory, but in this paper, a new elementary proof is given. It is also shown that the largest abelian p-factor group of G is always isomorphic to a direct factor of the largest abelian p-factor group of H. Received: 17 June 2008     

Weakly self-injective semilattices

In this note we characterize weakly self-injective semilattices as Brouwerian semilattices which are compact in the residuated interval topology. We also characterize weakly self-injective semigroups which are semilattices of groups with trivial multiplication. Research of first author supported in part by a research grant from the Faculty Research Committee of Bowling Green State University. Research of second author supported in part by a postdoctoral fellowship in the Biomathematics Program at North Carolina State University under PHS Grant #GM-678 from NIGMS.     

Determination of 8[(3S)-3-amino-1-pyrrolidinyl]-1-cyclopropyl-7-fluoro-9-methyl-4-oxo-4H-quinolizine-3-carboxylic acid hydrochloride and related substances by high performance liquid chromatography

Summary The purity of the investigational antibacterial Abbott-086719.1 (I) which is 8[(3S)-3-amino-1-pyrrolidinyl]-1-cyclopropyl-7-fluoro-9-methyl-4-oxo-4H-quinolizine-3-carboxylic acid hydrochloride is determined using gradient elution HPLC. The chromatographic separation was optimized and the chromatographic parameters critical to separation are discussed in detail. Most acceptable separations were achieved using an Alltima C18 column (5 m) measuring 4.6 mm I.D.×15 cm with 0.01M–0.03M citrate eluents which were modified with acetonitrile or with mixtures of acetonitrile and methanol. Related substances in I were determinable to 0.05%. Repeatability (RSD values) for determining related substances at levels of 0.50 to 0.06% ranged from ±1.9 to ±10%. Determinations of I in 5% dextrose in water and in hydroxypropyl methylcellulose were made using the same column and a simple isocratic system. The determination of I was stability indicating with precision (RSD values) of ±0.5% to ±2.0% and good agreement with theory for formulations containing I at 1.0 to 95 mg/mL concentrations. Recoveries of I from the vehicles were quantitative and linearity of the detector response of I was demonstrated to at least 0.10 mg/mL.     

Regions of stability of high-power gyrotron oscillators

The problem of mode competition in a high-power gyrotron oscillator is considered. The regions of parameter space in which a preexisting large-amplitude mode is able to suppress competing satellites are determined for cases in which the coupling coefficients and cavity quality factors for the operating and satellite modes are different. In addition, the effect of beam quality on the regimes of stable single-mode operation is investigated. Generally speaking, the requirement of stable operation favors devices whose interaction length measured by the parameter μ is not too large. It is found that for μ near 10 the operation is relatively stable and μ near 17 is not     

The low-lying electronic states of YCu

The spectroscopic constants for the singlet and tripletstates of YCu below about 15 000 cm⁻¹ are determined using an internally contracted multireference configuration-interaction approach. These calculations are calibrated by studies of fewer states using higher levels of correlation treatment and/or basis sets. The computed T_c values and radiative lifetimes are in reasonable agreement with experiment. The calculations confirm the previous experimental assignment for all but one state, where theory helps resolve between two possible assignments.     

Spin observables in small-angle elastic → d scattering with an L-type deuteron target at 800 MeV

We have measured spin correlation parameters that describe the elastic scattering of 800 MeV polarized protons from an L-type polarized deuteron target at laboratory angles below 20°. The measured parameters include the correlated analyzing powers A_SL, A_LL and A_NLL and the proton spin-transfer coefficients C_0L,S, C_0L,L, C_SL,N, C_NL,S, C_NL,L and C_LL,N. The results are compared with single-scattering predictions based on different phase-shift solutions for the nucleon-nucleon scattering matrix.     

In-beam γ-ray spectroscopy of the neutron deficient 100Ag

Conversion coefficients and conversion ratios of someγ-transitions in²⁰¹Tl and²⁰³Tl were measured by means of simultaneous spectroscopy ofγ-quanta and conversion electrons employing intensity calibrated semiconductor detectors. The experiments aimed at a precision as high as possible within the limits of the experimental methode used. Theγ-transitions were of the typeM 1(+E2). From the measured values the penetration parameters of the internal conversion for theM 1 components (λ) together with the multipol mixing ratios (δ²) were deduced. The necessary theoretical coefficients were taken from the tables of Hager and Seltzer. The results are for the ?-forbidden 331 keV transition in²⁰¹Tl,λ=+4.0±1.0,δ ²=1.78±0.16; for the ?-allowed 361 keV transition in²⁰¹Tl,λ=+0.5±0.5,δ ²=0.02±0.02; for the ?-forbidden 279 keV transition in²⁰³Tl,λ=+ 5.71±0.45,δ ²=1.55±0.08.     

Crystal structure and emission study of [(PPh3)2Cu(dmp)-O-(dmp)Cu(PPh3)2]2+ (dmp = 2,9-dimethyl-1,10-phenanthroline)

The synthesis and crystal structure of a luminescent dinuclear Cu(I) complex as the BF^– ₄ salt from toluene and methanol containing triphenylphosphine and -oxo-bis(2,9-dimethyl-1,10-phenanthroline) is described. The coordination geometry about the Cu(I) center is distorted tetrahedral. An unusual feature of the structure is a pseudo-inversion center located near the oxygen atom at approximately 0.51, 0.26, 0.25, such that all of the atoms except for the oxygen are related by a pseudo-inversion center to another atom in the same molecule, as well as by crystallographic inversion to the other molecule in the unit cell. The complex displays luminescence from an MLCT band in fluid solution and emission from both a metal-centered charge-transfer and intraligand (phenanthroline) state at 77K in a chloroform snow. Crystal data: triclinic, P , a = 15.163(2), b = 16.985(2), c = 18.731(2) Å, = 106.458(9), = 91.416(8), = 102.557(9)°, V = 4496(1) ų, and Z = 2.     

Rutin as an Electrochemical Mediator in the Determination of Captopril using a Graphite Paste Electrode

A simple, rapid and sensitive cyclic voltammetry method is described for the determination of the antihypertensive drug captopril in aqueous solution using a graphite paste electrode with rutin as mediator. The catalytic role of rutin in the oxidation of captopril was confirmed by the increase observed in anodic peak current at+0.44 V vs. SCE in the presence of the mediator. Anodic peak current varied linearly with the concentration of captopril in the dynamic range 0.2 to 1.0 mmol L^?1. The method exhibited a limit of detection of 89.4 μmol L^?1 and a reproducibility of 1 %, values that are comparable with those exhibited by other methodologies employing electrodes without any modification. The recovery rate for the determination of captopril in a pharmaceutical sample was good (91.21 %) suggesting that the described analytical technique would be effective in industrial applications whilst offering a number of advantages over published cyclic voltammetric methods.