In this paper, we study the special tube surfaces generated by rectifying curves with respect to Darboux frame in terms of geodesic curvature, normal curvature and torsion Galilean 3-space. During establish some definite results geodesics on specific help Clairaut’s theorem detail compute Gaussian mean frame. After that, considering conditions curvatures surface, give theorems for $v$-parameter...

We present a nonparametric Bayesian hierarchical (NBH) model and develop variational approximation (VA) algorithm for the curve fitting of functional radiation response data. The NBH is based on (BH) with Gaussian-Inverse Wishart process (G-IWP) prior, which simultaneously smooths multiple observations estimates mean-covariance functions. use automatic differentiation inference (ADVI) Gaussian ...

The shambles mentioned at the beginning of Part I referred to the confusion in the use of standard deviations and standard errors of means,' with the latter apparently more popular, perhaps because they are so much smaller than their parent standard deviations and thus suggest higher precision. The author defined the standard deviation as representing the variation among the individual measurem...

We provide a new technique to detect the singularities of rational space curves. Given a rational parametrization of a space curve, we first compute a μ-basis for the parametrization. From this μ-basis we generate three planar algebraic curves of different bidegrees whose intersection points correspond to the parameters of the singularities. To find these intersection points, we construct a new...

As a statistical measure of large-scale structure of the universe, the genus number is presented in analytic form for realistic non-Gaussian distributions, i.e., weakly non-Gaussian, lognormal and chi-square distributions. These formulae are compared with the results of N-body simulation. It is shown that the weakly non-Gaussian formula describes the behavior of genus in weakly nonlinear regime...

Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool for generating more general high frequency solutions to PDEs...