Spaces of Densely Continuous Forms

The set C(X,Y) of continuous functions from a topological space X into a topological space Y is extended to the set D(X,Y) of densely continuous forms from X to Y, such form being a kind of multifunction from X to Y. The topologies of pointwise convergence, uniform convergence, and uniform convergence on compact sets are defined for D(X,Y), for locally compact spaces X and metric spaces Y having a metric satisfying the Heine–Borel property. Under these assumptions, D(X,Y) with the uniform topology is shown to be completely metrizable. In addition, if X is compact, D(X,Y) is completely metrizable under the topology of uniform convergence on compact sets. For this latter topology, an Ascoli theorem is established giving necessary and sufficient conditions for a subset of D(X,Y) to be compact.     

Continued fractions and fermionic representations for characters of M(p,p′) minimal models

We present fermionic sum representations of the characters _{, s} ^{(p, p)} of the minimal M(p,p) models for all relatively prime integers p>p for some allowed values of r and s. Our starting point is biomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin 1/2 chain of anisotropy –=–cos((p/p)). We use the Takahashi-Suzuki method to express the allowed values of r (and s) in terms of the continued fraction decomposition of {p/p} (and p/p), where {x} stands for the fractional part of x. These values are, in fact, the dimensions of the Hermitian irreducible representations of SU _q- (2) (and SU _q+ (2)) with q–=exp(i{p/p}) (and q+=exp(i(p/p))). We also establish the duality relation M(p,p) M(p–p,p) and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Dedicated to Prof. Vladimir Rittenberg on his 60th birthday     

Fundamental excitations of the shared proton in the H3O2- and H5O2+ complexes

We exploit recent advances in argon predissociation spectroscopy to record the spectroscopic signature of the shared proton oscillations in the H3O2- system and compare the resulting spectrum with that of the H5O2+ ion taken under similar conditions. Very intense 1 <-- 0 transitions are observed below 1100 cm(-1) in both cases and are surprisingly sharp, with the 697 cm(-1) transition in H3O2- being among the lowest in energy of any shared proton system measured to date. The assignments of the three fundamental transitions associated with the three-dimensional confinement of the shared proton in H3O2- are carried out with full-dimensional (DMC) calculations to treat this strongly anharmonic vibrational problem.     

Vibrational manifestations of strong non-Condon effects in the H3O(+)·X3 (X = Ar, N2, CH4, H2O) complexes: a possible explanation for the intensity in the "association band" in the vibrational spectrum of water

The harmonic approximation provides a powerful approach for interpreting vibrational spectra. In this treatment, the energy and intensity of the 3N- 6 normal modes are calculated using a quadratic expansion of the potential energy and a linear expansion of the dipole moment surfaces, respectively. In reality, transitions are often observed that are not accounted for by this approach (e.g. combination bands, overtones, etc.), and these transitions arise from inherent anharmonicities present in the system. One interesting example occurs in the vibrational spectrum of H(2)O((l)), where a band is observed near 2000 cm(-1) that is commonly referred to as the "association band". This band lies far from the expected bend and stretching modes of the water molecule, and is not recovered at the harmonic level. In a recent study, we identified a band in this spectral region in gas-phase clusters involving atomic and molecular adducts to the H(3)O(+) ion. In the current study we probe the origins of this band through a systematic analysis of the argon-predissociation spectra of H(3)O(+)·X(3) where X = Ar, CH(4), N(2) or H(2)O, with particular attention to the contributions from the non-linearities in the dipole surfaces, often referred to as non-Condon effects. The spectra of the H(3)O(+) clusters all display strong transitions between 1900-2100 cm(-1), and theoretical modeling indicates that they can be assigned to a combination band involving the HOH bend and frustrated rotation of H(3)O(+) in the solvent cage. This transition derives its oscillator strength entirely from strong non-Condon effects, and we discuss its possible relationship to the association band in the spectrum of liquid water.     

Ebselen and congeners inhibit NADPH oxidase 2-dependent superoxide generation by interrupting the binding of regulatory subunits

NADPH oxidases (Nox) are a primary source of reactive oxygen species (ROS), which function in normal physiology and, when overproduced, in pathophysiology. Recent studies using mice deficient in Nox2 identify this isoform as a novel target against Nox2-implicated inflammatory diseases. Nox2 activation depends on the binding of the proline-rich domain of its heterodimeric partner p22phox to p47phox. A high-throughput screen that monitored this interaction via fluorescence polarization identified ebselen and several of its analogs as inhibitors. Medicinal chemistry was performed to explore structure-activity relationships and to optimize potency. Ebselen and analogs potently inhibited Nox1 and Nox2 activity but were less effective against other isoforms. Ebselen also blocked translocation of p47phox to neutrophil membranes. Thus, ebselen and its analogs represent a class of compounds that inhibit ROS generation by interrupting the assembly of Nox2-activating regulatory subunits.