For the class of quasiperiodic solutions of the vortex filament equation, we study connections between the algebro-geometric data used for their explicit construction, and the geometry of the evolving curves. We give a complete description of genus one solutions, including geometrically interesting special cases such as Euler elastica, constant torsion curves, and self-intersecting filaments. W...

Abstract We consider the following problem: on any given complete Riemannian manifold ( M , g ), among all curves which have fixed length as well endpoints and tangents at endpoints, minimise $$L^\infty $$ L ∞ norm of curvature. show that solutions this problem, a wider...

We consider the following variational problem: among all curves in $\Bbb{R}^n$ of fixed length with prescribed end points and tangents at points, minimise $L^\infty$-norm curvature. show that solutions this problem, a generalised version, are characterised by system differential equations. Furthermore, we have lot information about structure solutions, which allows classification.

We propose a model for finding one-dimensional structure in given measure. Our approach is based on minimizing an objective functional which combines the average-distance to measure quality of approximation and penalizes curvature, similarly elastica functional. Introducing curvature penalization overcomes some shortcomings functional, particular lack regularity minimizers. establish existence,...

Material and Methods: A total of 24 female Wistar rats were divided into two groups. The control group received saline, and the second group was administered medroxyprogesterone acetate in the therapeutic dose of 30 mg/kg bw. The substances were applied daily, intramuscularly for a period of 7 days. Paraffin sections of thymus were dyed with the following methods: hematoxylin eosin and elastica...