A note on the nucleolus and the kernel of the assignment game

There exist coalitional games with transferable utility which have the same core but different nucleoli. We show that this cannot happen in the case of assignment games. Whenever two assignment games have the same core, their nucleoli also coincide. To show this, we prove that the nucleolus of an assignment game coincides with that of its buyer–seller exact representative.I am grateful to C. Rafels and to the referees for their comments. Institutional support from research grants BEC 2002-00642 and SGR2001–0029 is also acknowledged.     

A priori inequalities for solutions of mixed boundary-value problems in unbounded domains

We prove some a priori inequalities for solutions of mixed boundary-value problems for a class of divergence form elliptic equations with discontinuous and unbounded coefficients in unbounded domains. Mathematics Subject Classification (2000) 35J25     

Specific Interaction of Coproporphyrin I with Antibodies in Water and Reverse Micelles: Dimerization of Antibodies Affects Antigen Binding Site

The antigen-antibody interaction between coproporphyrin I and anti-coproporphyrin antibodies was studied by a fluorescence method in water and a reverse micellar system: n-octane/Aerosol OT. Coproporphyrin fluorescence was quenched, and coproporphyrin emission maximum was shifted to the long-wavelength region after binding to the antibodies or Fab-fragments. The mechanism of this quenching is static, most probably, by a tryptophan residue (or maybe lysine or methionine). Apparent dynamic quenching, in this case, arises from protein backbone motion. A special kind of antibody Fab-Fab dimerization was proposed.     

High-performance liquid chromatographic determination of diltiazem in human plasma after solid-phase and liquid–liquid extraction

A selective, sensitive, and accurate high-performance liquid chromatographic method for determination of diltiazem in plasma samples has been developed and validated. The effects of mobile phase composition, buffer concentration, mobile phase pH, and concentration of organic modifiers on retention of diltiazem and internal standard were investigated. Solid-phase and liquid–liquid extraction were examined and proposed for isolation of the drug and elimination of endogenous plasma interferences. A 5 m Lichrocart Lichrospher 60 RP-select B chromatographic column was used; the mobile phase was acetonitrile–0.025 mol L^–1 KH₂PO₄ (pH 5.5), 35:65 ( v / v) at a flow-rate of 1.5 mL min^–1. The detection wavelength was 215 nm. The calibration plots were linear in the concentration range 20.0–500.0 ng mL^–1. The method has been implemented to monitor diltiazem levels in patient samples.     

Crown Inclusion Compounds with 3,4-Diamino-1,2,5-Oxadiazole. X-Ray Structures of Its 1:1 Inclusion Complexes with 15-Crown-5 and Benzo-15-crown-5

The X-ray crystal structures of two closely related molecular complexes of 15-crown-5 and benzo-15-crown-5 with 3,4-diamino-1,2,5-oxadiazole are reported (I and II). Both complexes are of 1:1 stoichiometry with the host–guest alternation in the infinitechains formed due to the unsymmetrical H-bonding patterns between the components. Crystals of I are monoclinic, P2_1/c, a = 7.856(3), b = 12.994(1), c = 16.033(1) , = 94.79(2)°, Z = 4, final R-factor is 0.0488. Crystals of II are orthorhombic, P2₁2₁2₁, a = 8.260(4), b = 15.692(5),c = 13.955(7) , Z = 4, final R-factor is 0.0522.     

Buyer-seller exactness in the assignment game

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the core of the game. These games will be called buyer-seller exact games and satisfy the condition that each mixed-pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyer-seller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer-seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed-pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a “45^o-lattice” by means of the core of an assignment game can now be answered. Received: March 2002/Revised version: January 2003 RID="*" ID="*"  Institutional support from research grants BEC 2002-00642 and SGR2001-0029 is gratefully acknowledged RID="**" ID="**"  The authors thank the referees for their comments     

Bis­(tetra­methyl­ammonium) hexa­molyb­date hydrate, [(CH3)4N]2[Mo6O19]·H2O

The crystal and molecular structure of the title compound, (C₄H₁₂N)₂[Mo₆O₁₉]·H₂O, has been determined from X‐ray diffraction data. The poly­oxo­anion [Mo₆O₁₉]^2? is built up from six distorted MoO₆ octa­hedra sharing common edges and one common vertex at the central O atom, and has crystallographic m3m (O_h) symmetry. The cation has crystallographic 3m symmetry.