In China, as a major resource, coal has made great contributions to national energy security and social development. The mining of resources can cause surface subsidence damage, in particular, the thick loose layer mines is most serious. How accurately predict caused by become an urgent problem be solved. To solve this problem, numerical simulations based on measured data were used reveal that ...

We study multiple linear regression model under non-normally distributed random error by considering the family of generalized secant hyperbolic distributions. derive estimators parameters using modified maximum likelihood methodology and explore properties so obtained. show that proposed are more efficient robust than commonly used least square estimators. also develop relevant test hypothesis...

The problem of determining if a bivariate normal correlation changes with respect to time or some other covariate is considered. It is assumed that the means and standard deviations of the normal random variables can be consistently estimated from the entire data run, and do not need to be re-estimated for each covariate value. A new estimator of a bivariate normal correlation is given that has...

Natural exponential families of distributions have probability mass functions of the form [exp(Ox)]#(dx) where # is a given measure, and 0 > 0 is a parameter. When we compute the mean and the variance, and force the variance to be a quadratic function of the mean as 0 is varied, the number of families becomes severely restricted. Morris (1982) showed that there are in fact only six natural expo...

A steady-state solution that describes pulse propagation in inhomogeneously broadening two-level atoms embedded in a dispersive and nonlinear Kerr lossless host medium has been found. The solution is of an unchirped hyperbolic-secant form with a linear spatial phase delay. The features of the solution are (i) the group velocity, the amplitude, and the width of the pulse are uniquely determined ...

By incorporating the hyperbolic secant inversion pulses with the image-selected in vivo spectroscopy localization technique and by applying a gradient-echo imaging method, we have selected only the 31P NMR signals from orthotopic human kidney and liver, using a single concentric 1H/31P surface coil. Corresponding to the experimental results on animal studies, the phosphocreatine signal is drama...

We simulated and analyzed in detail the behavior of ultrashort optical pulses, which are typically used in telecommunications, propagating through graphene-based nanoribbon waveguides. In this work, we showed the changes that occur in the Gaussian and hyperbolic secant input pulses due to the attenuation, high-order dispersive effects and nonlinear effects. We concluded that it is possible to c...

We demonstrate almost chirpand pedestal-free optical pulse compression in a nonlinear fiber Bragg grating with exponentially decreasing dispersion. The exponential dispersion profile can be well-approximated by a few gratings with different constant dispersions. The required number of sections is proportional to the compression ratio, but inversely proportional to the initial chirp value. We pr...