Transversal Intersection Curves of Two Surfaces in Minkowski 3-Space Curvas dadas por la intersección transversal de dos superficies en el espacio tridimesional de Minkowski

In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directrix using quasi frame along a space curve.

We present algorithms for computing the differential geometry properties of Frenet apparatus and higher-order derivatives of intersection curves of implicit and parametric surfaces in 3 for transversal and tangential intersection. This work is considered as a continuation to Ye and Maekawa [1]. We obtain a classification of the singularities on the intersection curve. Some examples are given and plotted.  t, n, b, κ, τ 

Small-angle X-ray scattering (SAXS) patterns from slit cameras (`Kratky cameras') require a subsequent desmearing procedure in order to obtain the pinhole scattering curve that is suitable for subsequent structure analysis. Since the corresponding integral equation contains a singularity, its solutions are usually unstable and fail if large noise is present. It is demonstrated how analytical stability can be achieved by physically reliable conditioning of the experimental data, introduction of the Moore±Penrose pseudoinverse of the equation's discretized integral operator and solving the equation by a FFT algorithm. This ensures the consistency of the solution as well as its stability, and hence its convergence. This solution can account for arbitrarily nonsymmetrical primary-beam pro®les. The algorithm does not require antecedent smoothing of the scattering curve. It allows on the contrary low-pass ®lter smoothing during desmearing but remains stable despite large noise contributions.

In this paper, we have a tendency to investigate a particular Weingarten and linear Weingarten varieties of canal surfaces according to Bishop frame in Euclidean 3-space E 3 satisfying some fascinating and necessary equations in terms of the Gaussian curvature, the mean curvature, and therefore the second Gaussian curvature. On the premise of those equations, some canal surfaces are introduced.