In a bivariate data plot, every two points determine an “elementary slope.” For n points with distinct x-values, there are n(n – 1)/2 elementary slopes. These elementary slopes are examined under the two classical regression assumptions: (1) the regressor variable values are fixed and the error is independent and normal, and (2) the data is bivariate normal. For case (1), it is demonstrated tha...

For each prime number p which does not divide N there is a linear operator Tp acting on Sk(N,C), known as the p-th Hecke operator. (In fact, the Tp stabilize Sk(N,Q).) A modular form which is an eigenvector for all of these linear operators simultaneously is called an eigenform; the space Sk(N,C) has a basis made up of eigenforms, and the Fourier coefficients of these eigenforms can be normaliz...

The elastic-plastic behavior of the material is considered to analyze the effect of an external circumferential crack on a pipe with thickness transition and double slopes. Using the extended finite element method (XFEM), the J-integral of 3D cracks were investigated and compared between straight pipes and pipes with thickness transition and different slopes. Considering internal press...

One of the biggest reasons for road accidents is curvy lanes and blind turns. Even one of the biggest hurdles for new autonomous vehicles is to detect curvy lanes, multiple lanes and lanes with a lot of discontinuity and noise. This paper presents very efficient and advanced algorithm for detecting curves having desired slopes (especially for detecting curvy lanes in real time) and detection of...