We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations. In this paper we consider a number of exact solutions obtained by the method of separation of variables. Some applications to Cosmology and BH entropy are b...

The influence of the gravity and magnetic field on the propagation of Rayleigh wave in a prestressed inhomogeneous, orthotropic elastic solid medium has been discussed. The method of separation of variable has been used to find the frequency equations for the surface waves. The obtained dispersion equations are in agreement with the classical results when gravity, magnetic field, non-homogeneit...

This study aims to investigate and optimize the effects of the main parameters including the particle size, gravity and magnetic separation combination, high gradient magnetic separation, magnetic field intensity, shaking table slope, washing water flow, and electrostatic separation upon the rare earth element (REE) recoveries from iron mine waste. The electron microprobe showed that high amoun...

The TRINICON (‘Triple-N ICA for convolutive mixtures’) framework is an effective blind signal separation (BSS) method for separating sound sources from convolutive mixtures. It makes full use of the non-whiteness, non-stationarity and nonGaussianity properties of the source signals and can be implemented either in time domain or in frequency domain, avoiding the notorious internal permutation p...

The historic Penouta mine in northwest Spain is the focus of efforts to extract tantalum from tin mining waste. This paper describes the characterisation of the tantalum mineralogy of waste material from the deposit. Characterisation was realised using quantitative mineralogy and geochemistry. This paper further identifies other phases of interest and investigates the potential for extraction u...

2d gravity stress tensor and the problem of the calculation of the multi-loop amplitudes in the string theory Abstract It is shown that the vacuum value of the 2d gravity stress tensor in the free field theory is singular in the fundamental region on the complex plane where the genus-n > 1 Riemann surface are mapped. Because of the above singularity, one can not construct modular invariant mult...

The single-user separation theorem source-channel coding has been D r o v e d D W V ~ O U S ~ V Verdd. Fellow, IEEE, and Yossef Steinberg of joint for wide classes of sources and channels. We find ab informition-stable sourcdchannel pair which does not satisfy the separation theorem. New necessary and sufficient conditions for the transmissibility of a source through a channel are found, and we...