In this article, we obtain oscillation conditions for second-order differential equation with neutral term. Our results extend, improve, and simplify some known delay equations. Several effective illustrative implementations are provided.

Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these were found. For every type complete list nonequivalent is issued. As exampes equivalence problem for Painleve II equation, III equation with three zero parameters, Emden and some other solved.

A few questions related to white dwarfs' physics is posed. It seems that the modified gravity framework can be a good starting point provide alternative explanations cooling processes, their age determination, and Chandrasekhar mass limits. Moreover, we have also obtained limit coming from Palatini $f(\mathcal{R})$ provided by simple Lane-Emden model.

arises in the study of gas dynamics and fluids mechanics, and in the study of relativistic mechanics, nuclear physics, and chemically reacting system see, e.g., 1 and the references therein for the continuous model. The negative exponent Emden-Fowler equation α < 0 has been used in modeling non-Newtonian fluids such as coal slurries 2 . The physical interest lies in the existence of positive so...

D Since the advent of Horn-clause logic programming in the mid 1970’s, there have been numerous attempts to extend the expressive power of Horn-clause logic while preserving some of its attractive computational properties. This article, the first of a pair, presents a clausal language that extends Hornclause logic by adding negations and embedded implications to the righthand side of a rule, an...

In this paper, a new shifted ultraspherical wavelets operational matrix of derivatives is introduced. The two wavelets operational matrices, namely Legendre and first kind Chebyshev operational matrices can be deduced as two special cases. Two numerical algorithms based on employing the shifted ultraspherical wavelets operational matrix of derivatives for solving linear and nonlinear differenti...

It takes place in a more general work about three-valued (partial) logic and logic programming. We have developped a logical and algebrical theory which seems wellsuited to logic programs with negation. In this theory, we have extended the "consequence" operator of Van Emden and Kowalski associated with a program without negation to a "consequence" operator for programs with negation taking inc...

We propose a numerical method for solving nonlinear initial-value problems of Lane-Emden type. The method is based upon nonclassical Gauss-Radau collocation points, and weighted interpolation. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced on arbitrary intervals. Then they are utilized to reduce the computation of nonlinear initial-value...