The Congruences of Clausen-von Staudt and Kummer for Half-integral Weight Eisenstein Series

We extend sharp forms of the classical uncertainty principle to the context of commutative hypergroups. This hypergroup setting includes Gelfand pairs, Riemannian symmetric spaces, and locally compact abelain groups. For some Gelfand pairs our inequalities will be sharper than those in a recent paper by J. A. WOLF.     

Reactions of excited states of phenoxazin-3-one dyes with amino acids

The interaction with amino acids of the excited states of the N-oxide resazurin and its deoxygenation product resorufin, has been studied in aqueous solution at pH 7.5. Steady-state and time-resolved studies show that the fluorescence is quenched by amino acids. Complexation of the dyes in the ground state with aromatic amino acids was also observed. The singlet quenching is attributed to electron transfer from the amino acids to the excited dye based on the dependence of the bimolecular rate constants with the ionization potential of quenchers. Flash photolysis experiments allowed determination of the quenching rate constants for the triplet deactivation of dyes by several amino acids, as well as the characterization of the transients formed in the process. These data show that the triplet is also deactivated by an electron transfer process. However, the deactivation of the N-oxide dye by tryptophan can be described by a hydrogen atom transfer. The protolytic dissociation constants of the dye radical ions are reported. The irradiation of rezasurin in the presence of amino acids leads to deoxygenation of the dye to give resorufin. This process involves the triplet excited state of resazurin and is efficient only in the presence of amino acids containing the -SH group.     

A spectroscopic and computational study on the effects of methyl and phenyl substituted phenanthroline ligands on the electronic structure of Re(I) tricarbonyl complexes containing 2,6-dimethylphenylisocyanide

[Re(CO)3(CNx)(L)]+, where CNx = 2,6-dimethylphenylisocyanide, forms complexes with L = 1,10-phenanthroline (1), 4-methyl-1,10-phenanthroline (2), 4,7-dimethyl-1,10-phenanthroline (3), 3,4,7,8-tetramethyl-1,10-phenanthroline (4), 2,9-dimethyl-1,10-phenanthroline (5) and 2,9-dimethyl-4,7-diphenyl-1,10-phenanthroline (6). The metal-ligand-to-ligand charge transfer transition (MLLCT) absorption bands follow the series: (27800 cm(-1)) > 1, 2, 4 and 5(27500 cm(-1)) > 6 (26600 cm(-1)). Density functional theory (DFT) geometry optimizations reveal elongated Re-N (L) distances of 2.28 and 2.27 A for 5 and 6, respectively, compared to 2.23 A for 1-4. The reversible reduction potentials (E(1/2(red))) of 1-4 are linearly dependent on the B3LYP calculated LUMO energies. Time-dependent (TD) DFT and conductor-like polarizable continuum model (CPCM) calculated singlet excited states deviate by 700 cm(-1) or less from the experimental absorption maxima and aid in the spectral assignments. The (3)MLLCT emitting state energies are within 900 cm(-1) of the experimental 77 K emission energies for 1-6. The 77 K emission energies, E(1/2(red)), and the room temperature emission quantum yields (phi(LUMO)(em)) decrease in the order 1 >2 >3 >4 whereas E(LUMO) and the room temperature emission energies follow the opposite trend. The emission lifetimes (tau(em)) decrease in the order 3 > 4 >2 >1 >5 with 3 having the highest emission lifetime values of 26.9 micros at room temperature and 384 micros at 77 K and complex 5 having the lowest emission lifetimes of 4.6 micros at room temperature and 61 micros and 77 K.     

Lattice polytopes,Hecke operators,and the Ehrhart polynomial

Let P be a simple lattice polytope. We define an action of the Hecke operators on E(P), the Ehrhart polynomial of P, and describe their effect on the coefficients of E(P). We also describe how the Brion–Vergne formula for E(P) transforms under the Hecke operators for nonsingular lattice polytopes P.