The NMR spectra of porphyrins—19: 13C and proton NMR spectra of metal-free porphyrins with the Type-IX substituent orientation,and of their zinc(II) complexes

The ¹³C and proton NMR spectra of six porphyrins bearing the substituent orientation characteristic of the natural “Type-IX” arrangement are reported and assigned. Significant concentration effects in the spectra of the free base porphyrins, together with the broadening of the C_α (and occasionally C_β) carbon resonances due to NH tautomerism caused a significant loss of data in these spectra. However, the spectra of the corresponding zinc(II) porphyrins (with addition of excess pyrrolidine) show that both these extraneous effects are completely removed to give well-resolved spectra with accurately reproducible chemical shifts. These spectra are assigned and an analysis of the chemical shifts allows the deduction of substituent chemical shift (SCS) parameters for the peripheral substituents at the beta and meso carbons. There is no global effect of these beta substituents, the beta carbon SCS being confined to the immediate pyrrole ring, and the meso carbon SCS to the two adjacent pyrrole rings. The SCS parameters are analyzed and it is shown how they can be used to predict the peripheral and meso carbon chemical shifts of any porphyrin bearing the substituents discussed.     

Isomorphism of maximum length circuit codes

Designs, Codes and Cryptography - Douglas (J Comb Theory 6(4):323–339, 1969) proved that for odd spread k and dimension $$d={\frac{1}{2}(3k+3)}$$ all maximum length (d, k) circuit...     

Frobenius distributions of elliptic curves in short intervals on average

The Ramanujan Journal - For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E....     

On some global well-posedness and asymptotic results for quasilinear parabolic equations

We prove that the quasilinear parabolic initial-boundary value problem (1.1) below is globally well-posed in a class of high order Sobolev solutions, and that these solutions possess compact, regular attractors ast+.     

Stability of rarefaction waves in viscous media

We study the time-asymptotic behavior of weak rarefaction waves of systems of conservation laws describing one-dimensional viscous media, with strictly hyperbolic flux functions. Our main result is to show that solutions of perturbed rarefaction data converge to an approximate, Burgers rarefaction wave, for initial perturbations w ₀ with small mass and localized as w ₀(x)= The proof proceeds by iteration of a pointwise ansatz for the error, using integral representations of its various components, based on Green's functions. We estimate the Green's functions by careful use of the Hopf-Cole transformation, combined with a refined parametrix method. As a consequence of our method, we also obtain rates of decay and detailed pointwise estimates for the error.This pointwise method has been used successfully in studying stability of shock and constant-state solutions. New features in the rarefaction case are time-varying coefficients in the linearized equations and error waves of unbounded mass (log (t)). These diffusion waves have amplitude (t ^-1/2logt) in linear degenerate transversal fields and (t ^-1/2logt) in genuinely nonlinear transversal fields, a distinction which is critical in the stability proof.     

The determination of aluminium in seawater and freshwater by cathodic stripping voltammetry

Dissolved aluminium in seawater and freshwater is determined by cathodic stripping voltammetry (c.s.v.) preceded by adsorptive collection of complex ions with 1,2-dihydroxyanthraquinone-3-sulphonic acid (DASA) on the hanging mercury drop electrode. Complexation of aluminium by DASA is rapid and no waiting period or heating of the sample is required. Optimal conditions are a DASA concentration of 10^?5 M, a solution pH of 7.1–7.3 and an adsorption potential of ?0.9 V; the c.s.v. scan is done in the differential-pulse mode. The limit of detection is 1 nM aluminium for an adsorption time of 45 s. The total time needed, including 50min deaeration and a standard addition, is 10–15 min per sample. No serious interferences were found; u.v. irradiation is recommended for samples containing high levels of organic materials.     

CHEMISTRY OF SINGLET OXYGEN—XXV. PHOTOOXYGENATION OF METHIONINE*

Abstract— Methionine (Met) photooxidation sensitized by rose bengal has been studied as a function of pH and other variables. At pH ≤ 6, the reaction is a simple one, 2 Met + O₂→ 2 Methionine sulfoxide (MetO). At pH 6–10, another mechanism becomes important, leading to dehydromethionine; the structure of this compound was correctly assigned by Lavine (1945) as the heterocyclic N-S compound 2. One mole of H₂O₂ is also produced in this process. Dehydromethionine hydrolyzes slowly to MetO. Above pH9, a process leading directly to MetO + H₂O₂ becomes important. The stoichiometry of the latter two processes are Met + O₂+ H₂O → MetO + H₂O₂; competition among these three processes accounts for the puzzling variations in O₂ uptake. N-Formylated derivatives of methionine undergo only the first and third processes. Substantial catalytic effects of buffers complicate the picture. All the reactions appear to involve singlet oxygen, since there is the predicted effect of D₂O vs H₂O on the rate of reaction, although the situation is complicated by apparent aggregation of Met above 5 mM.     

Charge transfer in FeO: a combined molecular-dynamics and ab initio study

Molecular-dynamics simulations and ab initio electronic structure calculations were carried out to determine the rate of charge transfer in stoichiometric wustite (FeO). The charge transfer of interest occurs by II/III valence interchange between nearest-neighbor Fe atoms, with the Fe(III) constituting a "hole" electronic defect. There are two possible nearest-neighbor charge transfers in the FeO lattice, which occur between edge-sharing or corner-sharing FeO(6) octahedra. Molecular-dynamics simulations predict charge-transfer rates of 3.7 x 10(11) and 1.9 x 10(9) s(-1) for the edge and corner transfers, respectively, in good agreement with those calculated using an ab initio cluster approach (1.6 x 10(11) and 8.0 x 10(8) s(-1), respectively). The calculated rates are also similar to those along the basal and c-axis directions in hematite (alpha-Fe(2)O(3)) determined previously. Therefore, as is the case for hematite, wustite is predicted to show anisotropic electrical conductivity. Our findings indicate that a rigid-ion model does not give acceptable results, thus showing the need to account for the change in polarizability of the system upon charge transfer. Our model achieves this by using a simple mechanical shell model. By calculating the electronic coupling matrix elements for many transition state configurations obtained from the molecular-dynamics simulations, we found evidence that the position of the bridging oxygen atoms can greatly affect the amount of electronic coupling between the donor and acceptor states. Finally, we address the effect of oxygen vacancies on the charge transfer. It was found that an oxygen vacancy not only creates a driving force for holes to transport away from the vacancy (or equivalently for electrons to diffuse toward the vacancy) but also lowers the free-energy barriers for charge transfer. In addition, the reorganization energy significantly differed from the nondefective case in a small radius around the defect.