Discrete,nonlinear approximation problems in polyhedral norms

Summary A Levenberg-like algorithm is given for the solution of discrete nonlinear approximation problems in polyhedral norms. Convergence and rate of convergence results are discussed and some numerical results presented.     

Next-nearest neighbor effects in the Mössbauer spectra of (Cr,Al) spinels

Fe²⁺T-site quadrupole splitting observed in the Mössbauer spectra of synthetic chromite-hercynite spinels (Fe(Cr_1?xAl_x)₂O₄, with x = 0 to 1.5) is systematically related to the substitution of octahedrally coordinated cations in the next-nearest neighbor coordination sphere. Conditions of synthesis include dry reagents contained in a stainless-steel crucible and enclosed in an evacuated silica-glass tube, held at 1250°C for up to 4 days. A simple singlet spectrum for FeCr₂O₄ changes with progressive Al substitution into a broadened doublet spectrum, with quadrupole splitting of 1.28 mm/sec and line half-width of 0.82 mm/sec, for FeCrAlO₄. Partial quadrupole splitting theory is used to calculate the quadrupole splittings for individual next-nearest neighbor configurations. Bulk quadrupole splitting is calculated relative to the statistical distribution of possible next-nearest neighbor configurations. Calculated quadrupole splittings are in good agreement with those obtained for unconstrained two-peak fits, at room temperature and at low and high temperature. Also, predicted spectral details are resolved in low temperature spectra. The local site distortion responsible for the quadrupole splitting appears to be associated with spatial accommodation of substituent Al³⁺ cations.     

Dissociative electron-ion recombination of the interstellar species protonated glycolaldehyde, acetic acid, and methyl formate

Recently, methyl formate, glycolaldehyde, and acetic acid have been detected in the Interstellar Medium, ISM. The rate constants, α(e), for dissociative electron-ion recombination of protonated gycolaldehyde, (HOCH(2)CHO)H(+), and protonated methyl formate, (HCOOCH(3))H(+), have been determined at 300 K in a variable temperature flowing afterglow using a Langmuir probe to obtain the electron density. The recombination rate constants at 300 K are 3.2 × 10(-7) cm(3) s(-1) for protonated methyl formate and 7.5 × 10(-7) cm(3) s(-1) for protonated glycolaldehyde. The recombination rate constant of protonated acetic acid could not be directly measured, but it appears to have a rate constant, α(e), on the 10(-7) cm(3) s(-1) scale. Several high- and low-temperature measurements for protonated methyl formate were made. In addition, an α(e) measurement at 220 K for protonated glycolaldehyde was performed. The astrochemical implications of the rates of recombination, α(e), and protonation routes are discussed.     

Propagation of a solitary fission wave

Reaction-diffusion phenomena are encountered in an astonishing array of natural systems. Under the right conditions, self stabilizing reaction waves can arise that will propagate at constant velocity. Numerical studies have shown that fission waves of this type are also possible and that they exhibit soliton like properties. Here, we derive the conditions required for a solitary fission wave to propagate at constant velocity. The results place strict conditions on the shapes of the flux, diffusive, and reactive profiles that would be required for such a phenomenon to persist, and this condition would apply to other reaction diffusion phenomena as well. Numerical simulations are used to confirm the results and show that solitary fission waves fall into a bistable class of reaction diffusion phenomena.     

Charged ρ photoproduction in the energy range 2.8–4.8 GeV

Measurements of the photoproduction processes γρ→ρ⁺ n and γρ→ρ^-Δ⁺⁺ (1236) are reported in the energy range 2.8 to 4.8 GeV. The data show shrinkage of the differential cross section in this energy region for the process γρ→ρ^-Δ⁺⁺ (1236); no shrinkage is observed for the ρ⁺ n process. The energy dependences of the ρ⁺ n and ρ^-Δ⁺⁺ (1236) total cross sections are much steeper than current model prediction. The ρ spin density matrices for each process are also presented.     

Cesium chromate,Cs2CrO4: heat capacity and thermodynamic properties from 5 to 350 K

The heat capacity of a sample of Cs₂CrO₄ was determined in the temperature range 5 to 350 K by aneroid adiabatic calorimetry. The heat capacity at constant pressure C_p^o(298.15 K), the entropy S^o(298.15 K), the enthalpy {H^o(298.15 K) - H^o(0)} and the function $\text{? {G}{}^{\mathrm{o}}\text{(298.15}\text{K}\text{) - H}{}^{\mathrm{o}}\text{(0)}}\text{298.15}\text{K}$ were found to be (146.06 ± 0.15) J K^?1 mol^?1, (228.59 ± 0.23) J K^?1 mol^?1, (30161 ± 30) J mol^?1, and (127.43 ± 0.13) J K^?1 mol^?1, respectively. The heat capacity C_p^o(298.15 K) and entropy S^o(298.15 K) and entropy S^o(298.15 K) of Rb₂CrO₄ are estimated to be (146.0 ± 1.0) J K^?1 mol^?1 and (217.6 ± 3.0) J K^?1 mol^?1, respectively.