In this note, we give an arithmetic criterion for the Lie-irreducibility of linear differential equations based on p-curvatures.

We consider a certain variational problem on Caccioppoli partitions with countably many components, which models immiscible fluids as well as variational image segmentation, and generalizes the well-known problem with prescribed mean curvature. We prove existence and regularity results, and finally show some explicit examples of minimizers. Introduction In this paper we consider a variational p...

For a smooth strictly convex closed hypersurface Σ in R, the Gauss map n : Σ → S is a diffeomorphism. A fundamental question in classical differential geometry concerns how much one can recover through the inverse Gauss map when some information is prescribed on S ([27]). This question has attracted much attention for more than a hundred years. The most notable example is probably the Minkowski...

Clothoids, i.e. curves Z(s) in RI whoem curvatures xes) are linear fitting functions of arclength ., have been nued for some time for curve fitting purposes in engineering applications. The first part of the paper deals with some basic interpolation problems for lothoids and studies the existence and uniqueness of their solutions. The second part discusses curve fitting problems for clothoidal ...

The curvature of the helical trajectory formed by herbaceous stem-twiners has been hypothesized to be constant on uniformly sized cylindrical supports and remains constant on different supports varying in diameter. However, experimental studies on the constant curvature hypothesis have been very limited. Here, we tested the hypothesis in a series of experiments on five herbaceous stem-twiners (...

Abstract Idiopathic scoliosis is a three-dimensional deformity of the vertebral column and one common pediatric spinal diseases, while neuromuscular often associated with cerebral palsy. Especially during periods growth, there high risk progression scoliosis. Thus, frequent clinical monitoring important for proper treatment. X-rays are Gold standard most commonly used method follow-up The curva...

Objective. To identify the mechanism of deformity compensation in patients with post-traumatic kyphosis thoracolumbar junction, based on analysis X-ray results surgical treatment. Material and Methods. The study included data obtained from medical records 69 (47 women, 22 men) operated for painful at levels T12, L1 L2 vertebra. Patients underwent staged interventions a single session. Demograph...