Given an ordinary differential field K of characteristic zero, it is known that if y and 1/y satisfy linear differential equations with coefficients in K, then y/y is algebraic over K. We present a new short proof of this fact using Gröbner basis techniques and give a direct method for finding a polynomial over K that y/y satisfies. Moreover, we provide explicit degree bounds and extend the res...

In this paper, we investigate higher-order linear differential equations with entire coefficients of iterated order. We improve and extend a result of Beläıdi and Hamouda by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen and the WinmanValiron theory. We also consider the nonhomogeneous linear differential equations by using the basic...

Abstract. In this paper, we investigate the higher-order linear differential equations with meromorphic coefficients. We improve and extend a result of M.S. Liu and C.L. Yuan, by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen, and the extended Winman-Valiron theory which proved by J. Wang and H.X. Yi. In addition, we also consider th...

One proves here the backward uniqueness of solutions to stochastic semilinear parabolic equations and also for the tamed Navier–Stokes equations driven by linearly multiplicative Gaussian noises. Applications to approximate controllability of nonlinear stochastic parabolic equations with initial controllers are given. The method of proof relies on the logarithmic convexity property known to hol...

abstract spacing between check dams depends on the stream bed slope, effective height of check dams and slope of deposited sediments behind the check dams. the slope of deposited sediments is more important than the other two factors because of complications in the way of its occurrence and its measurement after several years of dam construction. this research presents the effective factors aff...