Racemization of sulfinic esters with trichloroacetic anhydride

Both alkane- and arene-sulfinates undergo racemization and oxygen exchange reaction with trich-loroacetic anhydride. The rate of racemization of (?)menthyl (?)p-toluenesulfinate was found to be twice that of oxygen exchange, suggesting the reaction involves a Walden inversion. When reaction was carried out in benzene, the rate of racemization was found to be first order with respect to both sulfinic ester and trichloroacetic anhydride. The substituent effect is large (p = ?1.53) suggesting that the initial acylation is the rate-determining step. The rate of racemization was found to be retarded by the addition of perhaloacetic acid while very small catalytic effect of mercuric chloride was observed.     

On expectation value calculations of one-electron properties using the coupled cluster wave functions

The ability of various approximate coupled cluster (CC) methods to provide accurate first-order one-electron properties calculated as expectation values is theoretically analysed and computationally examined for BH and CO. For actual calculations the infinite number of terms of the expectation value expansion (O=¦exp (T ⁺)O exp (T)¦_c) was truncated so that T ₁ T ₂, T ₃, and (1/2) T ₂T₂ clusters were retained on both sides of O. The role of individual clusters is carefully discussed. Inclusion of T ₁, is unavoidable, but if triples are essential in the energy evaluation, they may play an even more important role in the property expansion, as shown in the case of CO. It is shown that the CC wave function, which is exact to second order, effectively satisfies the Hellmann-Feynman theorem.     

The effect of crosslinking on the reactivity of free radicals in isotactic polypropylene

Isotactic polypropylene of various degrees of crosslinking was prepared using high concentrations of dicumyl peroxide as the crosslinking agent. Free radicals were generated by γ irradiation of crosslinked iso-PP with a dose of 2.4 Mrad. It was found that the rate constant for free-radical decay is independent of crosslinking in the temperature range from ?30 to +20°C. The result is discussed from the point of view of degradation processes taking place simultaneously with crosslinking of iso-PP.     

Stress-biased rearrangements and preyield behavior in glasses

On the basis of a physical picture of a glass as a mosaic of mesoscopic clusters differing in their yield characteristics, we propose a model for the preyield behavior in glassy materials; the model describes the stress-strain relationship at different strain rates in terms of one reduced variable. A test using experimental data for polycarbonate materials at different rates and temperatures appears favorable for the model. The model may be used to interpolate and extrapolate limited experimental data, and also provides a practical means to assess dynamic heterogeneities within polymeric glasses. When applied at different temperatures, the model gives insight into the dependence of the excitation energies on temperature (glassformer fragility) in the glassy state.     

Determination of the interconversion energy barrier of 2,3-pentadienedioic acid enantiomers by HPLC. 2. On-column interconversion

In this paper, an HPLC method is used to determine the enantiomerization barrier of 2,3-pentadienedioic acid enantiomers. The racemate of 2,3-pentadienedioic acid was separated by HPLC on a chiral CHIROBIOTIC T column with a 90:10 (100:0.5:0.5 MeOH/HOAc/TEA)/H2O mobile phase. Peak areas of enantiomers prior to (A(+)0, A(-)0) and after the separation (A(+), A(-)), were used for calculation of the rate constants and the enantiomerization barrier, as determined by computer-assisted peak deconvolution of the peak clusters on the chromatograms. The kinetic equation for irreversible reactions was used to determine the apparent enantiomerization rate constants and the interconversion energy barrier. The dependence of the apparent enantiomerization barrier (deltaG1(app), deltaG-1(app)) on temperature was used to determine the apparent activation enthalpy (deltaH1(app), deltaH(-1)app) and entropy (deltaS1(app), deltaS-1(app)) for the interconversion of 2,3-pentadienedioic acid enantiomers, where the coefficients 1 and -1 designate the interconversions (+) --> (-) and (-) --> (+), respectively.     

Generalized algebraic transformations and exactly solvable classical-quantum models

The rigorous approach aimed at providing exact analytical results for hybrid classical-quantum models is elaborated on the grounds of generalized algebraic mapping transformations. This conceptually simple method allows one to obtain novel interesting exact results for the hybrid classical-quantum models, which may for instance describe interacting many-particle systems composed of the classical Ising spins and quantum Heisenberg spins, the localized Ising spins and delocalized electrons, or many other hybrid systems of a mixed classical-quantum nature.     

Non-orientable Regular Maps of a Given Type over Linear Fractional Groups

It is known that for any given k and m such that 1/k + 1/m < 1/2 there exist infinitely many regular maps M of valence k and face length m on orientable surfaces such that the automorphism group of M is isomorphic to a linear fractional group over a finite field. We examine the pairs (k, m) for which this result can be extended to regular maps on non-orientable surfaces.     

Backbone colorings of graphs with bounded degree

We study backbone colorings, a variation on classical vertex colorings: Given a graph G and a subgraph H of G (the backbone of G), a backbone coloring for G and H is a proper vertex k-coloring of G in which the colors assigned to adjacent vertices in H differ by at least 2. The minimal k∈N for which such a coloring exists is called the backbone chromatic number of G. We show that for a graph G of maximum degree Δ where the backbone graph is a d-degenerated subgraph of G, the backbone chromatic number is at most Δ+d+1 and moreover, in the case when the backbone graph being a matching we prove that the backbone chromatic number is at most Δ+1. We also present examples where these bounds are attained.Finally, the asymptotic behavior of the backbone chromatic number is studied regarding the degrees of G and H. We prove for any sparse graph G that if the maximum degree of a backbone graph is small compared to the maximum degree of G, then the backbone chromatic number is at most .