Z 3-Graded exterior differential calculus and gauge theories of higher order

We present a possible generalization of the exterior differential calculus, based on the operator d such that d³=0, but d²0. The entities dx ⁱ and d² x ^k generate an associative algebra; we shall suppose that the products dx ⁱ dx ^k are independent of dx ^k dx ⁱ , while theternary products will satisfy the relation: dx ⁱ dx ^k dx ^m =jdx ^k dx ^m dx ⁱ =j ²dx ^m dx ^m dx ⁱ dx ^k , complemented by the relation dx ⁱ d² x ^k =jd² x ^k dx ⁱ , withj:=e^2i/3.We shall attribute grade 1 to the differentials dx ⁱ and grade 2 to the second differentials d² x ^k ; under the associative multiplication law the grades add up modulo 3.We show how the notion ofcovariant derivation can be generalized with a 1-formA so thatD:=d+A, and we give the expression in local coordinates of thecurvature 3-form defined as :=d² A+d(A ²)+AdA+A ³.Finally, the introduction of notions of a scalar product and integration of theZ ₃-graded exterior forms enables us to define the variational principle and to derive the differential equations satisfied by the 3-form . The Lagrangian obtained in this way contains the invariants of the ordinary gauge field tensorF _ik and its covariant derivativesD _i F _km .     

On the extremality of the disordered state for the Ising model on the Bethe lattice

We give a simple proof that the limit Ising Gibbs measure with free boundary conditions on the Bethe lattice with the forward branching ratio k2 is extremal if and only if is less or equal to the spin glass transition value, given by tanh( _c ^SG = 1/k.The work was partially supported by the NSF grant DMS 9504513.     

Emerging supramolecular chemistry of gases

Molecular recognition of gases is an emerging area of chemistry. Supramolecular chemistry helps us to understand how gases interact with biological molecules and offers delicate insights into the mechanisms of their physiological activity. Principles of molecular recognition have been used for gas sensing, and have provided fundamental knowledge about the structure and dynamics of receptor-analyte complexes, and novel materials for gas sensing and storage have been developed. Supramolecular chemistry is also enabling us to learn how to transform gases into synthetically useful reagents. The rational design of novel catalysts for gas conversion and, more recently, encapsulation complexes with gases open novel directions in preparative synthetic chemistry.     

A new expression for the direct quantum mechanical evaluation of the thermal rate constant

Based on the formalism of Miller, Schwartz, and Tromp [J. Chem. Phys. 79, 4889(1983)], we derive a new expression for the thermal rate constant for a chemical reaction. The expression involves an unperturbed, i.e., reactant or product channel Boltzmann operator for the imaginary time propagation, making it possible to compute efficiently the rate constant for a range of temperatures. We illustrate numerical aspects with an extensive study of the one-dimensional Eckart barrier problem, as well as a study of the three-dimensional (J = 0) D + H2 problem.     

Supramolecular fixation of NO2 with calix[4]arenes

Reaction of NO2 with simple calix[4]arenes in chloroform in the presence of a Lewis acid rapidly results in intense coloration caused by the encapsulation of nitrosonium cation.     

Interaction between indigo and adsorbed protein as a major factor causing backstaining during cellulase treatment of cotton fabrics

A model microassay system was developed to measure indigo backstaining on cotton fabrics in the presence of enzymes on a small laboratory scale. Backstaining indexes for 11 cellulase samples were measured, and the enzymes were ranked from lower to higher backstaining. Two multienzyme cellulase preparations were separated into fractions using chromatofocusing on a Mono P column. Adsorption ability and backstaining properties of purified enzyme fractions were studied. Evidence was obtained that protein adsorption on cotton fabrics is a crucial parameter causing backstaining (both for crude cellulase samples and purified enzyme components).     

Branched Star-Type Polysilyllithium Compounds: The Effects of beta-Silyl Substitution and of Complexation on Their Molecular Structure

No Abstract     

On linear free energy correlations in liquid-phase catalytic hydrogenation of aromatic compounds

Application of linear free energy relationships (correlation between kinetics and thermodynamics) to catalytic hydrogenation of aromatic compounds in the liquidphase over supported metal catalysts is discussed.     

Reversible storage of molecular hydrogen by sorption into multilayered TiO2 nanotubes

The sorption of hydrogen between the layers of the multilayered wall of nanotubular TiO2 was studied in the temperature range of -195 to 200 degrees C and at pressures of 0 to 6 bar. Hydrogen can intercalate between layers in the walls of TiO2 nanotubes forming host-guest compounds TiO2 x xH2, where x < or = 1.5 and decreases at higher temperatures. The rate of hydrogen incorporation increases with temperature and the characteristic time for hydrogen sorption in TiO2 nanotubes is several hours at 100 degrees C. The rate of intercalate formation is limited by the diffusion of molecular hydrogen inside the multilayered walls of the TiO2 nanotube. 1H NMR-MAS and XRD data confirm the incorporation of hydrogen between the layers in the walls of TiO2 nanotubes. The nature and possible applications of the observed intercalates are considered.     

Off-resonance R(1rho) NMR studies of exchange dynamics in proteins with low spin-lock fields: an application to a Fyn SH3 domain

An (15)N NMR R(1rho) relaxation experiment is presented for the measurement of millisecond time scale exchange processes in proteins. On- and off-resonance R(1rho) relaxation profiles are recorded one residue at a time using a series of one-dimensional experiments in concert with selective Hartmann-Hahn polarization transfers. The experiment can be performed using low spin-lock field strengths (values as low as 25 Hz have been tested), with excellent alignment of magnetization along the effective field achieved. Additionally, suppression of the effects of cross-correlated relaxation between dipolar and chemical shift anisotropy interactions and (1)H-(15)N scalar coupled evolution is straightforward to implement, independent of the strength of the (15)N spin-locking field. The methodology is applied to study the folding of a G48M mutant of the Fyn SH3 domain that has been characterized previously by CPMG dispersion experiments. It is demonstrated through experiment that off-resonance R(1rho) data measured at a single magnetic field and one or more spin-lock field strengths, with amplitudes on the order of the rate of exchange, allow a complete characterization of a two-site exchange process. This is possible even in the case of slow exchange on the NMR time scale, where complementary approaches involving CPMG-based experiments fail. Advantages of this methodology in relation to other approaches are described.