In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of  rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces...

In previous articles [B. Poirier J. Chem. Phys. 121, 4501 (2004); C. Trahan and B. Poirier, ibid. 124, 034115 (2006); 124, 034116 (2006); B. Poirier and G. Parlant, J. Phys. Chem. A 111, 10400 (2007)] a bipolar counterpropagating wave decomposition, psi = psi(+) + psi(-), was presented for stationary states psi of the one-dimensional Schrodinger equation, such that the components psi(+/-) appro...

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 ...

Cyclic electron flow (CEF) around PSI regulates acceptor-side limitations and has multiple functions in the green alga, Chlamydomonas reinhardtii. Here we draw on recent and historic literature and concentrate on its role in Photosystem I (PSI) photoprotection, outlining causes and consequences of damage to PSI and CEF's role as an avoidance mechanism. We outline two functions of CEF in PSI pho...

For x > 0, let Γ(x) be the Euler's gamma function, and ψ(x) = Γ (x)/Γ(x) the psi function. In this paper, we prove that |ψ (n) (b) − ψ (n) (a)| < (b − L(a, b))|ψ (n+1) (b)| + (L(a, b) − a)|ψ (n+1) (a)| for all b > a > 0 and n = 0, 1, 2, · · ·, where L(a, b) = (b − a)/(log b − log a).