Hyperidentities and solid varieties

Let V be a variety of type τ. A type τ hyperidentity of V is an identity of V which also holds in an additional stronger sense: for every substitution of terms of the variety (of appropriate arity) for the operation symbols in the identity, the resulting equation holds as an identity of the variety. Such identities were first introduced by Walter Taylor in [27] in 1981. A variety is called solid if all its identities also hold as hyperidentities. For example, the semigroup variety of rectangular bands is a solid variety. For any fixed type τ, the collection of all solid varieties of type τ forms a complete lattice which is a sublattice of the lattice L(τ) of all varieties of type τ. In this paper we give an overview of the study of hyperidentities and solid varieties, particularly for varieties of semigroups, culminating in the construction of an infinite collection of solid varieties of arbitrary type. This paper is dedicated to Walter Taylor. Received July 16, 2005; accepted in final form January 3, 2006. This paper is an expanded version of a talk presented at the Conference on Algebras, Lattices and Varieties in Honour of Walter Taylor, in Boulder Colorado, August 2004. The author’s research is supported by NSERC of Canada.     

Intermolecular vibrational coherence in bacteriochlorophyll a with clustered polar solvent molecules

We show that resonant impulsive excitation of the Qy absorption band of bacteriochlorophyll a (BChl) launches a rapidly damped (gamma < 200 fs) ground-state coherent wave-packet motion that arises from intermolecular modes with clustered solvent molecules. Femtosecond pump-probe, dynamic-absorption signals were obtained at room temperature with BChl solutions in pyridine, acetone, and 1-propanol. The vibrational coherence observed in the 0-800-fs regime is modeled in the time domain by two (or three, in the case of 1-propanol) modulation components with asymmetric, inhomogeneously broadened line shapes and frequencies in the 100-200-cm(-1) range. The mean frequency of the vibrational coherence exhibits at least a quadratic dependence on the dipole moment of the solvent molecules and a y-intercept in the 100-cm(-1) regime. This trend is modeled by an expression for the natural frequency of a "6-12" potential composed of attractive terms from van der Waals forces and a repulsive term from the exchange (Pauli exclusion) force. The model suggests that comparable contributions to the potential are provided by the dipole-dipole and London dispersion interactions. These results support the hypothesis that the low-frequency vibrational modes in the 100-cm(-1) regime that are coupled to the light-driven charge-separation reactions in the reaction center from purple bacteria are derived from intermolecular vibrational modes between the chromophores and the surrounding protein medium.     

Homology and derived p-series of groups

We give homological conditions that ensure that a group homomorphisminduces an isomorphism modulo any term of the derived p –series, in analogy to Stallings's 1963 result for the p-lowercentral series. In fact, we prove a stronger theorem that isanalogous to Dwyer's extensions of Stallings’ results.It follows that spaces that are _p-homology equivalent have isomorphicfundamental groups modulo any term of their p-derived series.Various authors have related the ranks of the successive quotientsof the p-lower central series and of the derived p-series ofthe fundamental group of a 3-manifold M to the volume of M,to whether certain subgroups of ₁(M) are free, to whether finiteindex subgroups of ₁(M) map onto non-abelian free groups, andto whether finite covers of M are ‘large’ in variousother senses.     

Vicinal deuterium perturbations on hydrogen NMR chemical shifts in cyclohexanes

The substitution of a deuterium for a hydrogen is known to perturb the NMR chemical shift of a neighboring hydrogen atom. The magnitude of such a perturbation may depend on the specifics of bonding and stereochemical relationships within a molecule. For deuterium-labeled cyclohexanes held in a chair conformation at -80 degrees C or lower, all four possible perturbations of H by D as H-C-C-H is changed to D-C-C-H have been determined experimentally, and the variations seen, ranging from 6.9 to 10.4 ppb, have been calculated from theory and computational methods. The predominant physical origins of the NMR chemical shift perturbations in deuterium-labeled cyclohexanes have been identified and quantified. The trends defined by the Delta delta perturbation values obtained through spectroscopic experiments and by theory agree satisfactorily. They do not match the variations typically observed in vicinal J(H-H) coupling constants as a function of dihedral angles.     

Difference in precedence effect between children and adults signifies development of sound localization abilities in complex listening tasks

The precedence effect refers to the fact that humans are able to localize sound in reverberant environments, because the auditory system assigns greater weight to the direct sound (lead) than the later-arriving sound (lag). In this study, absolute sound localization was studied for single source stimuli and for dual source lead-lag stimuli in 4-5 year old children and adults. Lead-lag delays ranged from 5-100 ms. Testing was conducted in free field, with pink noise bursts emitted from loudspeakers positioned on a horizontal arc in the frontal field. Listeners indicated how many sounds were heard and the perceived location of the first- and second-heard sounds. Results suggest that at short delays (up to 10 ms), the lead dominates sound localization strongly at both ages, and localization errors are similar to those with single-source stimuli. At longer delays errors can be large, stemming from over-integration of the lead and lag, interchanging of perceived locations of the first-heard and second-heard sounds due to temporal order confusion, and dominance of the lead over the lag. The errors are greater for children than adults. Results are discussed in the context of maturation of auditory and non-auditory factors.     

Micellar behavior of aqueous solutions of dodecyldimethylethylammonium bromide, dodecyltrimethylammonium chloride and tetradecyltrimethylammonium chloride in the presence of alpha-, beta-, HPbeta- and gamma-cyclodextrins

Conductivity, static fluorescence and (1)H NMR measurements have been carried out to study the micellar behavior of aqueous solutions of dodecyldimethylethylammonium bromide (DDAB), dodecyltrimethylammonium chloride (DTAC) and tetradecyltrimethylammonium chloride (TDAC) in absence and presence of alpha-cyclodextrin (alpha-CD), beta-cyclodextrin (beta-CD), hydroxypropyl-beta-cyclodextrin (HPbeta-CD) and gamma-cyclodextrin (gamma-CD). The conductivity measurements were carried out at 298.15 K. The influence of cyclodextrins on the micellar parameters, such as cmc* (apparent critical micellar concentration), beta (degree of ionization) have been analyzed. Thermodynamics of the systems was discussed in terms of the change in standard free energy of micellization, DeltaG(m)(0). Micellization was found to be less spontaneous in presence of cyclodextrins. The fluorescence intensity of the surfactant solutions is enhanced by the addition of cyclodextrins. The association constants obtained from conductivity and fluorescence data suggest the binding of gamma-CD with the surfactants to be strongest among all the cyclodextrins used. (1)H NMR chemical shift changes provide powerful means for probing the cyclodextrin-micellar interactions and inclusion of surfactant is shown by the change in the chemical shift of some of the guest and host protons in comparison with the chemical shifts of the same protons in the free compounds.     

Cellular Uptake of the ATSM−Cu(II) Complex under Hypoxic Conditions

The Cu(II)-diacetyl-bis (N4-methylthiosemicarbazone) complex (ATSM−Cu(II)) has been suggested as a promising positron emission tomography (PET) agent for hypoxia imaging. Several in-vivo studies have shown its potential to detect hypoxic tumors. However, its uptake mechanism and its specificity to various cancer cell lines have been less studied. Herein, we tested ATSM−Cu(II) toxicity, uptake, and reduction, using four different cell types: (1) mouse breast cancer cells (DA-3), (2) human embryonic kidney cells (HEK-293), (3) breast cancer cells (MCF-7), and (4) cervical cancer cells (Hela) under normoxic and hypoxic conditions. We showed that ATSM−Cu(II) is toxic to breast cancer cells under normoxic and hypoxic conditions; however, it is not toxic to normal HEK-293 non-cancer cells. We showed that the Cu(I) content in breast cancer cell after treatment with ATSM−Cu(II) under hypoxic conditions is higher than in normal cells, despite that the uptake of ATSM−Cu(II) is a bit higher in normal cells than in breast cancer cells. This study suggests that the redox potential of ATSM−Cu(II) is higher in breast cancer cells than in normal cells; thus, its toxicity to cancer cells is increased.