The Volterra delay integral equations have numerous applications in various branches of science, including biology, ecology, physics and modeling of engineering and natural sciences. In many cases, it is difficult to obtain analytical solutions of these equations. So, numerical methods as an efficient approximation method for solving Volterra delay integral equations are of interest to many res...

Abstract The aim of this paper is to determine how a Pyrrhonian (as she/he described by Sextus Empiricus) considers the Law and can respond Aristocles’ objection that unable obey laws. First (1), we analyze function in 10th Mode Aenesidemus, order show laws as dogmatic source value. But (2) shows also Sceptic live human society following customs, according so-called ‘sceptical conformism’. In l...

[1] A fractal mobile/immobile model for solute transport assumes power law waiting times in the immobile zone, leading to a fractional time derivative in the model equations. The equations are equivalent to previous models of mobile/immobile transport with power law memory functions and are the limiting equations that govern continuous time random walks with heavy tailed random waiting times. T...

4 The Lebesgue integral and expectation 14 4.1 The Lebesgue integral and convergence theorems . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Probability measures and modes of convergence . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Uniform integrability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.4 Jensen’s inequality . . . . . ...

This paper is a reflection on the perception of care nursing professionals have and the meaning given to the term, which is a tool for directing the quality of the assistance. It questions the level of depth that this word may have, identifying its presence in all processes of the Universe and throughout mankind's mythological history. It proposes that caring is the law that makes possible the ...

Utilising the Beesack version of the Darst-Pollard inequality, some error bounds for approximating the Riemann-Stieltjes integral are given. Some applications related to the trapezoid and mid-point quadrature rules are provided.

In this comment we demonstrate that the example of a DC conducting wire of finite length as and example for the application of the Biot-Savart Law is flawed due to the non-conservation of electric charge for such an unphysical setting. The implications drawn in [1] on the restrictions of Ampère’s Circuital Law in integral form are unnecessary as long as only physically realizable situations obe...

Abstract: In this paper, the nonlinear Schrödinger equation with power law nonlinearity is studied. The first integral method, the Riccati sub-ODE method are efficient methods to construct the exact solutions of nonlinear partial differential equations.By means of these methods, the periodic and solitary wave solutions of the nonlinear Schrödinger equation with power law nonlinearity are obtained.