We prove the generalized Hyers--Ulam stability  of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.

Nephrotoxicity in humans and experimental animals due to chronic exposure to cadmium (Cd) is manifested by defects in the reabsorptive and secretory functions of proximal tubules (PT). The main symptoms of Cd nephrotoxicity, including polyuria, phosphaturia, aminoaciduria, glucosuria, and proteinuria, suggest that various brush-border membrane (BBM) transporters are the main targets of Cd. Spec...

Erythrocyte membranes of patients with liver disease are characteristically enriched in cholesterol, a change known to impair several carrier-mediated membrane transport functions. In the present study we have assessed whether experimental liver disease can affect the membrane lipid composition and transport function of kidney epithelial cells. Small (about 5%) but significant (P less than 0.01...

in this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation.this method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation and c...

In the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}A_{l}XB_{l}+overset{v} ‎{underset{s=1}{sum}}C_{s}widetilde{X}D_{s}=F$‎. ‎By this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎When the‎ ‎matrix equation is consistent over...

This paper is devoted to the spatial analyticity of solution BBM equation on real line with an analytic initial data. It shown that radius has a lower bound like $$t^{-\frac{2}{3}}$$ as time t goes infinity, which improvement previous results. The main new ingredient higher order almost conservation law in spaces. proved by introducing equivalent norm smooth symbol and establishing some algebra...

This Letter presents a technique for subdiffraction limit imaging termed Bessel beam microscopy (BBM). By placing a lens in series with an axicon in the optical path of a microscope, the diffraction-limited resolution of the base microscope is improved by one third. This improvement is demonstrated experimentally by resolving individual subdiffraction limit fluorescent beads in a close-pack arr...

Like most coronaviruses, the coronavirus mouse hepatitis virus (MHV) exhibits strong species specificity, causing natural infection only in mice. MHV-A59 virions use as a receptor a 110- to 120-kDa glycoprotein (MHVR) in the carcinoembryonic antigen (CEA) family of glycoproteins (G. S. Dveksler, M. N. Pensiero, C. B. Cardellichio, R. K. Williams, G. S. Jiang, K. V. Holmes, and C. W. Dieffenbach...