Logarithmic Regge pole

This work presents the subtraction procedure and the Regge cut in the logarithmic Regge pole approach. The subtraction mechanism leads to the same asymptotic behavior as previously obtained in the non-subtraction case. The Regge cut, in contrast, introduces a clear role to the non-leading contributions for the asymptotic behavior of the total cross-section. From these results, some simple parameterization is introduced to fit the experimental data for the proton-proton and antiproton-proton total cross-section above some minimum value up to the cosmic-ray. The fit parameters obtained are used to present predictions for the \begin{document}$ \rho(s)$\end{document} -parameter as well as to the elastic slope \begin{document}$ B(s)$\end{document} at high energies.     

On the redox reactions between allyl radicals and NOx

NO_x mitigation is a central focus of combustion technologies with increasingly stringent emission regulations. NO_x can also enhance the autoignition of hydrocarbon fuels and can promote soot oxidation. The reaction between allyl radical (C₃H₅) and NO_x plays an important role in the oxidation kinetics of propene. In this work, we measured the absolute rate coefficients for the redox reaction between C₃H₅ and NO_x over the temperature range of 1000–1252 K and pressure range of 1.5–5.0 bar using a shock tube and UV laser absorption technique. We produced C₃H₅ by shock heating of C₃H₅I behind reflected shock waves. Using a Ti:Sapphire laser system with frequency quadrupling, we monitored the kinetics of C₃H₅ at 220 nm. Unlike low-temperature chemistry, the two target reactions, C₃H₅ + NO → products (R1) and C₃H₅ + NO₂ → products (R2), exhibited a strong positive temperature dependence for this radical-radical type reaction. However, these reactions did not show any pressure dependence over the pressure range of 1.5–5.0 bar, indicating that the measured rate coefficients are close to the high-pressure limit. The measured values of the rate coefficients resulted in the following Arrhenius expressions (in unit of cm³/molecule/s):$k_1\left({\mathrm{C}}_3{\mathrm{H}}_5+\text{NO}\right)=1.49\times {10}^{?10}\exp \left(?6083.6\frac{\mathrm{K}}{T}\right)\left(1017?1252K\right)$$k_2\left({\mathrm{C}}_3{\mathrm{H}}_5+\mathrm{N}{\mathrm{O}}_2\right)=1.71\times {10}^{?10}\exp \left(?3675.7\frac{\mathrm{K}}{T}\right)\left(1062?1250K\right)$To our knowledge, these are the first high-temperature measurements of allyl + NO_x reactions. The reported data will be highly useful in understanding the interaction of NO_x with resonantly stabilized radicals as well as the mutual sensitization effect of NO_x on hydrocarbon fuels.     

Infinitely Many Solutions of Nonlocal Kirchhoff-Type Equations via Perturbation Methods

Mathematical Notes - We study the multiplicity of weak solutions to the boundary-value problem $$\begin{alignedat}{2} - M\biggl(\iint_{\mathbb R^{2N}}|u(x)-u(y)|^2 K(x-y)\,d x\,d y\biggr)\mathscr...     

Broadening and Shift of the D1 and D2 Lines of Rb Atoms by Neon: Resolving Hyperfine Components in a Half-Wave Cell Using Double Differentiation with Respect to Frequency

Optics and Spectroscopy - A cell with a submicron thickness was used to measure the broadening and shift of the D1 and D2 lines of Rb atoms by neon. The resolution of hypefine components...     

Unbounded Solutions to Systems of Differential Equations at Resonance

Journal of Dynamics and Differential Equations - We deal with a weakly coupled system of ODEs of the type $$\begin{aligned} x_j'' + n_j^2 \,x_j + h_j(x_1,\ldots ,x_d) = p_j(t), \qquad...     

A tight Hermite–Hadamard inequality and a generic method for comparison between residuals of inequalities with convex functions

Periodica Mathematica Hungarica - We present a tight parametrical Hermite–Hadamard type inequality with probability measure, which yields a considerably closer upper bound for the mean value...     

On the Distributivity and Modularity Properties of the Lattice of Fitting Classes

Mathematical Notes - It is proved that the lattice of all Fitting classes of finite groups is not distributive, and conditions under which Fitting classes satisfy the distributive and modular laws...