Monolayer spontaneous curvatures for cholesterol, DOPE, POPE, DOPC, DPPC, DSPC, POPC, SOPC, and egg sphingomyelin were obtained using small-angle X-ray scattering (SAXS) on inverted hexagonal phases (HII). Spontaneous curvatures of bilayer forming lipids were estimated by adding controlled amounts to a HII forming template following previously established protocols. Spontaneous curvatures of bo...

We consider the one-dimensional Willmore equation subject to Navier boundary conditions, i.e. the position and the curvature are prescribed on the boundary. In a previous work, explicit symmetric solutions to symmetric data have been constructed. Within a certain range of boundary curvatures one has precisely two symmetric solutions while for boundary curvatures outside the closure of this rang...

It is known that an n-dimensional convex body which is typical in the sense of Baire category, shows a simple, but highly non-intuitive curvature behaviour: at almost all of its boundary points, in the sense of measure, all curvatures are zero, but there is also a dense and uncountable set of boundary points at which all curvatures are infinite. The purpose of this paper is to find a counterpar...

We present a method of obtaining a lower bound estimate of the curvatures of the Bergman metric without using the regularity of the kernel function on the boundary. As an application, we prove the existence of an uniform lower bound of the bisectional curvatures of the Bergman metric of a smooth bounded pseudoconvex domain near the boundary with constant Levi rank.

? Abstract. Image formation is described by means of modern geometry in terms of curvatures. These curvatures are a quantisation of the set of rules for constructing the image. A simpliication of this set of rules is proposed by applying dynamic scale-space theory.

Image formation is described by means of modern geometry in terms of topological and geometric curvatures. These curvatures and derived equivalences are a quantisation of the set of rules for constructing the image in particular along discontinuity, singularity and bifurcation sets. A simpliication of the set of construction rules is proposed by applying a dynamic scale-space theory. Dynamic he...

Muscle fascicles curve during contraction, and this has been seen using B-mode ultrasound. Curvature can vary along a fascicle, and amongst the fascicles within a muscle. The purpose of this study was to develop an automated method for quantifying curvature across the entirety of an imaged muscle, to test the accuracy of the method against synthetic images of known curvature and noise, and to t...

In this paper, we propose a cooperative algorithm between curvatures to escape local minima and choose a optimal possibility to preserve edge. The proposed algorithm between curvatures is relaxation in which weights of center pixel's and neighbor pixel's possibility are determined adaptively using deviation of the other curvature.

We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.

We introduce the epitrochoidal hypersurfaces in four dimensional Euclidean space E^4. serve notations of a geometry Giving definition rotational hypersurface, we define and calculate its differential geometric objects, such as Gauss map curvatures. In end, reveal some relations for curvatures that type hypersurfaces.