Landé factor Happ applied magnetic field (vector) Happ applied magnetic field (magnitude) Hm molecular field J exchange integral J total angular momentum k0 propagation vector l orbital quantum number l orbital momentum L orbital momentum L Langevin function m magnetic quantum number m0 measured magnetic moment at 0 K m magnetic moment ml orbital moment ms spin moment mz projection of m along H...

Information about fractal dimension is collected so that it can be applied to time series interpreting Hurst coefficient. The population size of a species is modelled as a dynamic system. The Hurst coefficient is calculated for these times series. A computer programme has been elaborated to compute the Hurst exponent of time series using the algorithms of range increment, second order moment in...

We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an asymptotically efficient estimator of the moment type functional or of a parameter which has a one-to-one correspondence to such a functional. Next, we clarify a higher...

Spearman’s rank correlation coefficient (denoted here by rs) is a nonparametric (distribution-free) rank statistic proposed by Charles Spearman as a measure of the strength of the associations between two variables. It is a measure of a monotone association that is used when the distribution of the data makes Pearson’s correlation coefficient undesirable or misleading. Spearman’s coefficient is...

In recent years, Sum–Of–Squares (SOS) method has attracted increasing interest as a new approach for stability analysis and controller design of nonlinear dynamic systems. This paper utilizes SOS method to design a robust nonlinear controller for longitudinal dynamics of a hypersonic aircraft model. Specifically, the searching of the nonlinear robust controller is reformulated as a robust SOS/r...

1) The single current dipole moment [strength of the dipole vector in nAm (Q)] 2) The correlation coefficient [the degree of association between the actual measured magnetic field data and the estimated forward solution data (R)] 3) The goodness of fit [the measure of how well the measured magnetic field agrees with the estimated field from an assumed dipole (GoF)] 4) The root mean square (RMS)...

We compute the three-loop QCD corrections to the quark chromomagnetic moment and thus obtain the matching coefficient and the anomalous dimension of the chromomagnetic interaction in HQET. As a byproduct we obtain the three-loop corrections to the quark anomalous magnetic moment.

Pearson product-moment correlation coefficients are a wellpracticed quantification of linear dependence seen across many fields. When calculating a sample-based correlation coefficient, the accuracy of the estimation is dependent on the quality and quantity of the sample. Like all statistical models, these correlation coefficients can suffer from overfitting, which results in the representation...