abstract scaling methods, which are based on similar media theory, are used to simplify the statistic description of soil spatial variations. to simulate the water flow in heterogeneous soils, simultaneous scaling of soil hydraulic functions, including soil water retention and unsaturated hydraulic conductivity functions, is highly desirable. in the similar media theory, the simultaneous scalin...

Several extensions of Loewner’s theory of monotone operator functions are given. These include a theorem on boundary interpolation for matrix-valued functions in the generalized Nevanlinna class. The theory of monotone operator functions is generalized from scalarto matrix-valued functions of an operator argument. A notion of κ-monotonicity is introduced and characterized in terms of classical ...

in this article using the inverse laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. these transfers have been expressed as the couette flow with the fractional derivative of the caputo sense. also, using the hankel contour for the bromwich's integral, the solutions are given in terms of the generalized airy functions.

in this paper we have solved analytically the schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...

We present a geometric approach to deening an algebra ^ G(M) (the Colombeau algebra) of generalized functions on a smooth manifold M containing the space D 0 (M) of distributions on M. Based on diierential calculus in convenient vector spaces we achieve an intrinsic construction of ^ G(M). ^ G(M) is a diierential algebra, its elements possessing Lie derivatives with respect to arbitrary smooth ...