We present a Weierstrass-type representation formula which locally represents every regular two-dimensional lightlike surface in Lorentz-Minkowski 4-Space $\mathbb{M}^4$ by three dual functions $(\rho,f,g)$ and generalizes the for surfaces $\mathbb{M}^3$. give necessary sufficient conditions on $\rho$, $f$, $g$ to be minimal, ruled or $l$-minimal. For surfaces, we itself ruled. Furthermore, res...

To solve the problem of generalized design and batch processing face gear, a method tooth surface side milling ruled line gears is proposed in this paper. First all, discrete points pitch cone gear are calculated, straight-line cluster section curve constructed to analyze deviation gear. Secondly, model constructed, curvature contact trace calculated. Thirdly, tangent analyzed, feed plane equid...