‎‎in the category of mordell curves (e_d:y^2=x^3+d) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (e_1), ‎and of the generic rank at least two and at least three as cubic twists of (e_1). ‎previous work‎, ‎in the category of mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with rank at least seven as sextic tw...

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...

The C-metric is a solution to Einstein's vacuum field equation that describes an accelerating black hole. In this paper we discuss the propagation of light rays and resulting lensing features in metric. We first solve lightlike geodesic using elliptic integrals Jacobi functions. Then fix static observer region outer communication introduce orthonormal tetrad parameterise directions ending at po...

Abstract Extending the electromagnetic and gravitational radiations from binary black holes with electric magnetic charges in circular orbits Liu et al. (Phys. Rev. D 102:103520, 2020), we calculate total emission rates of energy angular momentum due to dyonic precessing elliptical orbits. It is shown that have same dependence on conic angle for different Moreover, obtain evolutions find a orbi...