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     

Kinetics of nonisothermal polymer crystallization

We adopt a cluster size distribution model to investigate the kinetics of nonisothermal polymer crystallization. The time dependencies of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots) are presented for different cooling rates. The incubation period is also investigated at different cooling rates and initial temperatures. The relationship between cooling rates and incubation time is presented graphically and compared with experimental measurements. The initial temperature (relative to melting point) has a significant effect on nonisothermal crystallization. A comparison of moment and numerical solutions of the population balance equations shows the influence of Ostwald ripening. Agreement between modeling results and experimental measurements at different cooling rates supports the application of the distribution kinetics model for nonisothermal crystallization.     

Authentication of black cohosh (Actaea racemosa) dietary supplements based on chemometric evaluation of hydroxycinnamic acid esters and hydroxycinnamic acid amides

Analytical and Bioanalytical Chemistry - Ester and amide derivatives of hydroxycinnamic acids are found in black cohosh (Actaea racemosa) and other Actaea plants. These two compound groups were...     

Multiple scattering calculations of step contrast in REM images of the Si(001) surface

Simulations of reflection electron microscopy (REM) images of both monolayer and bilayer steps on the bulk-terminated Si(001) surface, for the case when the primary electron beam azimuth is directed parallel to the line of the step, are presented. The simulations employ our previously reported theory of REM image formation which uses a 2D Bloch wave formulation of dynamical (multiple scattering) elastic RHEED theory to calculate diffracted amplitudes propagating from the surface. The only step contrast mechanism considered here is phase contrast and this is sufficient to produce the characteristic “black-white” appearance observed experimentally. Defocusing of the simulated images is also discussed.     

Some aspects of single-grain luminescence dating

Single-grain methods of luminescence dating have been developed in order to circumvent problems of variability among aliquots of the sample being dated. Sufficient single grains must be separated in order to make an appropriate interpretation of the variability among such grains. We describe an automated apparatus for sorting grains for routine age determinations by green light stimulation. The sorted grains are then available for study of their collective luminescence physics characteristics. Examples are given of statistical frequency functions of grain brightness obtained with the apparatus and their interpretation. These frequency functions are lognormal or similar, covering up to four orders of magnitude, with consequent implications for luminescence dating application.     

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.