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By using a time-dependent operator converting a distribution function (statistical operator) of a total system under consideration into the relevant form, new exact nonlinear generalized master equations (GMEs) are derived. The inhomogeneous nonlinear GME is a generalization of the linear Nakajima-Zwanzig GME and is suitable for obtaining both the linear and nonlinear equations describing the e...

A characterization theorem is derived that motivates a procedure for generating discrete best monotonie approximations to n sequential data values, when a strictly convex objective function is used in the calculation. The procedure is highly useful in the discrete nonlinear optimization calculation that produces the best piecewise monotonie approximations to the data.

in this paper, we present a new computational technique for solving nonlinear fredholm integral equations of the second kind. this proposed method is based on galerkin method and is computationally very attractive. moreover, for reducing the operations in comparing similar works, we design our algorithm based on transformations of orthogonal polynomials in approximation coefficients calculating...

We consider the initial-value problem for the regularized Boussinesq–Ostrovsky equation in the class of periodic functions. Validity of the weakly-nonlinear solution, given in terms of two counter-propagating waves satisfying the uncoupled Ostrovsky equations, is examined. We prove analytically and illustrate numerically that the improved accuracy of the solution can be achieved at the time sca...

The current work introduces three nonlinear control solutions for the regulation of a vibrating plate considering model uncertainty. These are feedback linearization (FBL), virtual velocity error-based (VVEC), and backstepping (BSC). In FBL control, law is designed with linear closed-loop dynamics such that dynamic stability ensured. Whereas, by VVEC (or so-called passivity-based approach in ro...

The neural network with two weights is constructed and its approximation ability to any continuous functions is proved. For this neural network, the activation function is not confined to the odd functions. We prove that it can limitlessly approach any continuous function from limited close subset of R(m) to R(n) and any continuous function, which has limit at infinite place, from limitless clo...

where u : (0, T ) × Ω → < is unknown function, Ω ⊂ < is a polygonal convex domain with the boundary Γ, 0 < T <∞, ν is the outward normal to Γ, f(t, x, s) and ac(t, x) are Lipschitz continuous functions and β : < → < is a nondecreasing Lipschitz continuous function. Finally cg is a real number and cg ≥ 0. There are several linear approximation schemes, deal with the Stefan like problems or with ...