Convolutional Neural Network (CNN) is a deep learning model which has been an active research topic and applied extensively to vibration data for condition monitoring (CM). In CNN, hyper-parameters, such as activation function, have significant effect on the training task and, consequently, overall performance of network. The existing functions some limitations, vanishing gradient problem, dead...

We have analysed the effect of nonlinearity of an activation function on the oscillation of the neural network with asymmetrical cyclic connections by using the averaging method. The oscillation obtained by linear approximation, in which the activation function is approximated by a linear function, is multi-modal although the actual oscillation with numerical simulation is unimodal. When the ac...

Shock waves in gas dynamics can be described by the Euler Nav ie r Stokes, or Boltzmann equations. We prove the existence of shock profile solutions of the Boltzmann equation for shocks which are weak. The shock is written as a truncated expansion in powers of the shock strength, the first two terms of which come exactly from the Taylor tanh (x) profile for the Navie r Stokes solution. The full...

Some preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative, we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of R...

In blind source separation, convergence and separation performance are highly dependent on a relation between a probability density function (pdf) of the output signals y and nonlinear functions f(y) used in updating coefficients of a separation block. This relation was analyzed based on kurtosis κ4 of the output signals. The nonlinear functions, tanh(y) and y have been suggested for super-Gaus...

In writing this last expression, we have used the fact that the integrand is now convergent at large x. The upper limit of the integral βch̄ωc/2 >> 1 in all known cases of superconductivity, so we take the upper limit to infinity. In evaluating the first term note that the limit x → 0 of ln(x)Tanh(x) is convergent even though ln(x) diverges as x→ 0. The integral that remains is a tabulated defin...

Abstract. Inversion formulas have been found, converting between Stirling, tanh and Lah numbers. Tanh and Lah polynomials, analogous to the Stirling polynomials, have been defined and their basic properties established. New identities for Stirling and tangent numbers and polynomials have been derived from the general inverse relations. In the second part of the paper, it has been shown that if ...

We introduce in this paper a new chaotic map with dynamical properties controlled by two free parameters. The map definition is based on the hyperbolic tangent function, so it is called the tanh map. We demonstrate that the Lyapunov exponent of the tanh map is robust, remaining practically unaltered with the variation of its parameters. As the main application, we consider a chaotic communicati...

The nonlocal symmetry of the new (3+1)-dimensional Boussinesq equation is obtained with truncated Painlevé method. can be localized to Lie point for prolonged system by introducing auxiliary dependent variables. finite transformation related integrable studied. Meanwhile, proved consistent tanh expansion method and many interaction solutions among solitons other types nonlinear excitations such...

The aim of this paper is to find the Noether symmetries a generalized Benney-Luke equation. Thereafter, we construct associated conserved vectors. In addition, search for exact solutions equation through extended tanh method. A brief observation on equations arising from Lagrangian density function with high order derivatives field variables, also discussed.