Electron Swarm Parameters and Dielectric Properties of the Superconducting Binary Mixtures of He-H2

In this study, the electron energy distribution function EEDF, the electron swarm parameters, the effective ionization coefficients, and the critical field strength (dielectric strength) in binary He-H2 gas mixture which used as cryogenic for high-temperature superconducting power application, are evaluated by using two-term approximation of the Boltzmann equation over the range of E/N ( the electric field to gas density) from 1 to 100 Td ( 1 Td=10-17 Vcm2) at temperature 77 K and pressure 2MPa, taking into account elastic and inelastic cross-section. Using the calculated EEDF, the electron swarm parameters (electron drift velocity, mean electron energy, diffusion coefficient, electron mobility, ionization and attachment coefficient) are calculated. At low reduced electric field E/N, the EEDF close Maxwellian distribution, at high E/N, due to vibrational excitation of H2 the calculated distribution function is non-Maxwellian. Besides, in the He-H2 mixture, it is found that increasing small amount of H2 enhances to shift the tail of EEDF to the lower energy region, the reduced ionization coefficient α/N. reduced effective ionization coefficient (α-η)/N) decreases, while, reduced attachment coefficient η/N, reduced critical electric field strength (E/N)crt. and critical electric field Ecrt. Increases, because of hydrogen’s large ionization cross-sections. The dielectric strength of 5% H2 in mixture is in good agreement with experimental values, it is found that dielectric strength depend on pressure and temperature. The electron swarm parameters in pure gaseous helium (He) and hydrogen (H2), in satisfying agreement with previous available theoretical and experimental values. The validity of the calculated values has been confirmed by two-term approximation of the Boltzmann equation analysis.

A New One-term Approximation to the Standard Normal Distribution

This paper deals with a new, simple one-term approximation to the cumulative distribution function (c.d.f) of the standard normal distribution which does not have closed form representation. The accuracy of the proposed approximation measured using maximum absolute error (M.S.E) and the same criteria is used to compare this approximation with the existing one-term approximation approaches available in the literature. Our approximation has a maximum absolute error of about 0.0016 and this accuracy is sufficient for most practical applications.

Occupations and the recent trends in wage inequality in Europe

We aim to contribute to a better understanding of the role that occupations played in recent trends in wage inequality in some European countries. Using EU-SILC data, we observe that most of the changes in wage inequality between 2005 and 2014 were the result of changes in the distribution of wages within occupations. A longer term approximation using data from the Luxembourg Income Study (LIS) shows similar patterns. We conclude that occupational dynamics did not drive recent trends in wage inequality in Europe.

Perturbation Analysis of Orthogonal Least Squares

The Orthogonal Least Squares (OLS) algorithm is an efficient sparse recovery algorithm that has received much attention in recent years. On one hand, this paper considers that the OLS algorithm recovers the supports of sparse signals in the noisy case. We show that the OLS algorithm exactly recovers the support of $K$-sparse signal $\boldsymbol{x}$ from $\boldsymbol{y}=\boldsymbol{\unicode[STIX]{x1D6F7}}\boldsymbol{x}+\boldsymbol{e}$ in $K$ iterations, provided that the sensing matrix $\boldsymbol{\unicode[STIX]{x1D6F7}}$ satisfies the restricted isometry property (RIP) with restricted isometry constant (RIC) $\unicode[STIX]{x1D6FF}_{K+1}<1/\sqrt{K+1}$, and the minimum magnitude of the nonzero elements of $\boldsymbol{x}$ satisfies some constraint. On the other hand, this paper demonstrates that the OLS algorithm exactly recovers the support of the best $K$-term approximation of an almost sparse signal $\boldsymbol{x}$ in the general perturbations case, which means both $\boldsymbol{y}$ and $\boldsymbol{\unicode[STIX]{x1D6F7}}$ are perturbed. We show that the support of the best $K$-term approximation of $\boldsymbol{x}$ can be recovered under reasonable conditions based on the restricted isometry property (RIP).