We prove that C∞ curves of constant curvature satisfy, in the sense of Gromov, the relative C-dense h-principle in the space of immersed curves in Euclidean space Rn≥3. In particular, in the isotopy class of any given C knot f there exists a C∞ knot e f of constant curvature which is C-close to f . More importantly, we show that if f is C, then the curvature of e f may be set equal to any const...

The sine-Gordon equation with periodic boundary conditions describes integrable dynamics on the space of closed curves of constant torsion, for which multi-phase solutions provide large classes of canonical knot representatives. In this letter we discuss the use of Bäcklund transformations for studying the topological properties and symmetries of multi-phase solutions and of their homoclinic ma...

Several properties of food webs-the networks of feeding links between species-are known to vary systematically with the species richness of the underlying community. Under the 'latitude-niche breadth hypothesis', which predicts that species in the tropics will tend to evolve narrower niches, one might expect that these scaling relationships could also be affected by latitude. To test this hypot...

We prove the existence of immersed closed curves constant geodesic curvature in an arbitrary Riemannian 2-sphere for almost every prescribed curvature. To achieve this, we develop a min-max scheme weighted length functional.

introduction: raising the knowledge of skeletal and soft tissue changes with aging has been highly essential due to an increasing demand for aesthetic facial surgery following aging. the aim of this study is to evaluate the three dimensional computed tomographic images and process of changes in mandible with aging. materials and methods: in this descriptive study, the facial ct scans were obtai...

The aim of this study is to investigate whether the variation in breadth of the cranial base among modern human populations that inhabit different regions of the world is linked with climatic adaptation. This work provides an examination of two hypotheses. The first hypothesis is that the correlation between basicranial breadth and ambient temperature is stronger than the correlation between te...

We construct unramified central simple algebras representing 2-torsion classes in the Brauer group of a hyperelliptic curve, and show that every 2-torsion class can be constructed this way when the curve has a rational Weierstrass point or when the base field is C1. In general, we show that a large (but in general proper) subgroup of the 2torsion classes are given by the construction. Examples ...