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....     

Triazene proton affinities: A comparison between density functional,Hartree–Fock,and post-Hartree–Fock methods

The consistency of three density functional computational implementations (DMol, DGauss, and deMon) are compared with high-level Hartree–Fock and Møller–Plesset (MP) calculations for triazene (HN?NNH₂) and formyl triazene (HN?NNHCOH). Proton affinities on all electronegative sites are investigated as well as the geometries of the neutral and protonated species. Density functional calculations employing the nonlocal gradient corrections show agreement with MP calculations for both proton affinities and geometries of neutral and protonated triazenes. Local spin density approximation DMol calculations using numerical basis sets must employ an extended basis to agree with other density functional codes using analytic Gaussian basis sets. The lowest energy conformation of triazene was found to be nonplanar; however, the degree of nonplanarity, as well as some bond lengths, is dependent on the basis set, electron correlation treatment, and methods used for the calculation. © 1994 by John Wiley & Sons, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain in the United States of America.

     

Cross-channel coupling in positron-atom scattering

Coupled-state calculations including positronium channels are reported for positron scattering by atomic hydrogen, lithium and sodium. Integrated cross sections and total cross sections are presented for all three atoms. For lithium differential cross sections are also given. Throughout, comparison is made between results calculated with and without inclusion of the positronium channels. S-wave cross sections for positron scattering by atomic hydrogen in the Ps(1s, 2s, 2p)+H(1s, 2s, 2p) approximation show the high energy resonance first observed by Higgins and Burke in the coupled-static approximation. This resonance has now moved up to 51.05 eV and narrowed in width to 2.92 eV. Other pronounced structure is seen in the S-wave cross sections between 10 and 20 eV; it is tentatively suggested that this structure may be due to the formation of a temporary pseudo-molecular collision complex. Results calculated in the Ps(1s, 2s, , 2p, ,+H(1s, 2s, , 2p, approximation show convergence towards accurate values in the energy region below and in the Ore gap. Contrary to previous work on lithium using only an atomic basis, it is found that coupling to the 3d state of lithium is not so important when positronium channels are included; this is because a mixed basis of atom and positronium states gives a more rapidly convergent approximation than an expansion based on atom states alone. The threshold behaviour of the elastic cross section and the Ps(1s) formation cross section for lithium is investigated. Results in the Ps(1s, 2s, 2p)+Na(3s, 3p) approximation for sodium show good agreement with the total cross section measurements of Kwan et al.     

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.