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 ...

The collective behaviour of soliton ensembles (i.e. the solitonic gas) is studied using the methods of the direct numerical simulation. Traditionally this problem was addressed in the context of integrable models such as the celebrated KdV equation. We extend this analysis to non-integrable KdV–BBM type models. Some high resolution numerical results are presented in both integrable and noninteg...

In this article, we address the generalized BBM equation with white noise dispersion which reads du− duxx + ux ◦ dW + uuxdt = 0, in Stratonovich formulation, where W (t) is a standard real valued Brownian motion. It is equivalent to, in Ito’s formulation, du + (1−∆)uxdW − 1 2 (1−∆)uxxdt + (1−∆)uuxdt = 0. The global well posedeness for the initial value problem is shown for any p ≥ 1. Furthermor...

This study investigates exact analytical solutions of some nonlinear partial differential equations arising in mathematical physics. To this reason, the Kudryashov-Sinelshchikov equation, ZK-BBM equation and Gardner have been considered. With implementation trial solution algorithm, solitary wave, bright, dark periodic traveling wave considered attained. The checked graphs given via package pro...

This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...

25 Dietary potassium (K)-deficiency is accompanied by phosphaturia, and decreased renal 26 brush border membrane (BBM) vesicle sodium (Na)-dependent phosphate (Pi) transport 27 activity. We previously showed that K-deficiency in rats leads to increased abundance in 28 the proximal tubule BBM of the apical Na/Pi co-transporter NaPi-IIa, but that the activity, 29 diffusion and clustering of NaPi-...

The present study was undertaken to define the mechanisms governing the regulation of the novel renal brush-border membrane (BBM) Na-phosphate (Pi) cotransporter designated type IIc (Npt2c). To address this issue, the renal expression of Npt2c was compared in two hypophosphatemic mouse models with impaired renal BBM Na-Pi cotransport. In mice homozygous for the disrupted Npt2a gene (Npt2-/-), B...

The molecular mechanisms underlying the initiation and maintenance of the embryonic pathway in plants are largely unknown. To obtain more insight into these processes, we used subtractive hybridization to identify genes that are upregulated during the in vitro induction of embryo development from immature pollen grains of Brassica napus (microspore embryogenesis). One of the genes identified, B...

We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular we consider a KdV-BBM type equation. Explicit and IMEX Runge-Kutta type methods are used for time discretizations. The fully discrete schemes are validated by direct comparisons to analytic solutions. Invariants conservation properties are also studied. M...

Intoxication with gamma-hydroxybutyrate (GHB) is associated with coma, seizure, and death; treatment of overdoses is symptomatic. Previous studies in our laboratory have demonstrated that L-lactate and pyruvate treatment can increase the renal clearance of GHB and increase its elimination in rats, suggesting that GHB may undergo renal reabsorption mediated by monocarboxylic acid transporters (M...