Completely Integrable Systems Associated with Classical Root Systems

We study integrals of completely integrable quantum systems associated with classical root systems. We review integrals of the systems invariant under the corresponding Weyl group and as their limits we construct enough integrals of the non-invariant systems, which include systems whose complete integrability will be first established in this paper. We also present a conjecture claiming that the quantum systems with enough integrals given in this note coincide with the systems that have the integrals with constant principal symbols corresponding to the homogeneous generators of the $B_n$-invariants. We review conditions supporting the conjecture and give a new condition assuring it.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Integral transformations of hypergeometric functions with several variables

As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.Comment: 25page

A stable intermediate product of the archaeal zinc-containing 7Fe ferredoxin from Sulfolobus sp. strain 7 by artificial oxidative conversion

AbstractIrreversible conversion of the purified zinc-containing 7Fe ferredoxin from the thermoacidophilic archaeon Sulfolobus sp. strain 7 was found to occur under aerobic conditions at pH 5.0 and at 4°C. This process accompanied a substantial increase of the electron paramagnetic resonance signal attributed to a [3Fe-4S]1+ cluster, and the converted form containing ∼6 Fe/Zn (mol/mol) had a net charge different from that of the native 7Fe ferredoxin. These data provide evidence for the formation of a stable intermediate product of the archaeal ferredoxin having two [3Fe-4S] clusters and a zinc center by artificial oxidative degradation. This further explains the discrepancy that a zinc center and two [3Fe-4S] clusters (but not a zinc center and one [3Fe-4S] cluster plus one [4Fe-4S] cluster) are observed in the crystal structure at pH 5.0

Kinetic-spectrophotometric method for the determination of trace amounts of bromide in seawater

A novel simple, sensitive and rapid kinetic-spectrophotornetric method is proposed for the determination of trace amounts of bromide. The method is based on its catalytic effect on the oxidation of methylene blue (MB) by hydrogen peroxide in strongly acidic solution. The oxidation reaction is activated by large amounts of chloride and can be monitored spectrophotometrically by measuring the decrease in the absorbance of MB at 746 run. The determination of bromide is performed by a fixed-time method at the first 100 s from the initiation of the reaction. Unlike other kinetic-spectrophotornetric methods for the determination of bromide, the proposed method does not require heating the solution. Bromide can be determined in the range from 80 to 960 mu g l(-1) with the detection limit of 35 mu g l(-1). The relative standard deviation of ten replicate determination of 480 mu g l(-1) bromide was 1.4%. The influence of potential interfering ions was studied. The proposed method was satisfactorily applied to the determination of bromide in seawater without interfering effect from chloride ion.</p