A principal distinction of neural network based methods of approximation from conventional methods is a hidden inside algorithmic function, which is defined by the neural network topology and is enough sophisticated to make appropriate fitting process. There is a new construction named...

We study a symmetric nonlinear eigenvalue problem arising in earthquake initiation and we establish the existence of infinitely many solutions. Under the effect of an arbitrary perturbation, we prove that the number of solutions becomes greater and greater if the perturbation tends to zero with...

Pseudo-monotonicity seems to be a good notion to deal with convergence in nonlinear terms of partial differential equations. J.-L. Lions [16] used two different definitions of pseudo-monotonicity for elliptic and parabolic problems, and derived associated existence results. Nonlinear...

Using the theory of dynamic systems with random structure the representation of nonstationary continuous time, generally non-Gaussian, processes with distinguishable states is considered. Switching of the partial subsystems is intended to be a Poisson point process and so the model has the...

We estimate a small-scale macroeconomic model for Japan by taking into account the nonlinearity stemming from the zero lower bound (ZLB) of the nominal interest rate. To this end, we apply the Sequential Monte Carlo Squared method to the case of Japan, where the ZLB has constrained the country's...

In this paper, by considering the Adomian decomposition method, explicit solutions are calculated for partial differential equations with initial conditions. The method does not need linearization, weak nonlinearly assumptions or perturbation theory. The decomposition series analytic solution of...

In this study by considering the Adomian decomposition scheme, we solve a generalized Boussinesq equation. The method does not need linearization or weak nonlinearly assumptions. By using this scheme, the solutions are calculated in the form of a convergent power series with easily computable...

In this paper, by considering the Adomian decomposition method, explicit solutions are calculated for partial differential equations with initial conditions. The method does not need linearization, weak nonlinearly assumptions or perturbation theory. The decomposition series analytic solution of...

We study the effect of a time-periodic, lateral acceleration on the two-dimensional flow of a fluid with a free surface subject to surface tension, confined between two plane, parallel walls under conditions of zero gravity. We assume that the velocity of each contact line is a prescribed,...

We study complex dynamical synchronization in a nonlinear model of a neural system constituted by local networks of densely interconnected excitatory and inhibitory neurons. Neural dynamics are determined by voltage- and ligand-gated ion channels. Coupling between the local networks is...