The Euler–Bernoulli theory of beams is usually presented in two forms: (i) the linear case a small slope using Cartesian coordinates along and normal to straight undeflected position; (ii) non-linear large curvilinear deflected position, namely, arc length angle inclination. present paper starts with exact equation third form, that is, (iii) position like (i), but allowing exactly effects (ii)....

We provide the explicit solutions of linear, left-invariant, (convection)-diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2) = RoT. These diffusion equations are forward Kolmogorov equations for well-known stochastic processes for contour enhancement and contour completion. The solutions are given by groupconvolution with the corresponding Green...

Carnot groups are subRiemannian manifolds. As such they admit geodesic flows, which left-invariant Hamiltonian flows on their cotangent bundles. Some of these integrable. not. The space k-jets for real-valued functions the real line forms a group dimension $k+2$. We show that its flow is integrable and geodesics generalize Euler's elastica, with case $k=2$ corresponding to as shown by Sachkov A...

Recently I quantized an elastica with Bernoulli-Euler functional in two-dimensional space using the modified KdV hierarchy. In this article, I will quantize a Willmore surface, or equivalently a surface with the Polyakov extrinsic curvature action, using the modified Novikov-Veselov (MNV) equation. In other words, I show that the density of state of the partition function for the quantized Will...

The active contour segmentation model of Chan and Vese has been widely used and generalized in different contexts in the literature. One possible modification is to employ Euler’s elastica as the regularization of active contour. In this paper, we study the new effects of this modification and validate them numerically using the augmented Lagrangian method.

This taxonomic study is based on macrofungi collected Babadağ District (Denizli) in the period 2005-2006. As a result of field and laboratory studies, five new records are presented. These species are Leptopodia elastica, Entoloma incarnatofuscescens, Geastrum minimum, Hygrophorus speciosus and Russula sororia.