(1) He showed that spaces of constant curvature could have several different topological structures.

(2) Among other results, he classified simply connected Riemannian 3-manifolds of constant curvature in this thesis.

(3) In fact the work was of such quality that Weingarten received a prize for work on the lines of curvature of a surface in 1857.

(4) It has a distinct curvature near the middle

(5) It is found that the square of the mean curvature averaged over the entire simulation box is enhanced if the strength of the bonds in the elastic network are modulated in response to local changes in the composition field.

(6) The curvature of the surface determines the concentration of light in this direction, used to create lighter or darker regions on the target surface.

(7) In these cases, hydrolysis is shown to take place at the hole edges where the surface curvature is high, providing an exposed site for hydrolysis.

(8) Although Germain does not offer a physical or geometric derivation of mean curvature , it remains a key concept in the study of minimal surfaces, not to mention the theory of elasticity.

(9) The curvature of the central line is a one-dimension variable characterizing each infinitesimal cross-section.

(10) Spinal curvature

(11) Several such kinks spaced in helical phase will yield a molecule with a more or less planar curvature .

(12) For the unsupponed portion, the mean curvature remains constant.

(13) That is, in this case, the Riemann curvature tensor has 4 x 4 x 4 x 4 = 256 components!

(14) Some of his work on physical topics relates to his non-euclidean geometry for he examined how the gravitational potential as given by Newton would have to be modified in a space of negative curvature .

(15) Surfaces of constant mean curvature or constant Gaussian curvature are now called the Weingarten surfaces.

(16) We have extended previous studies using DOPE / DOPS mixtures, designed to measure the effect of surface charge on monolayer curvature .

(17) We wish to compare the modern formula for curvature with Huygens's expression of ratios.

(18) A formula for the line integral of the geodesic curvature along a closed curve is known as the Gauss Bonnet theorem.

(19) The curvature field along the stem was computed by a numerical analysis of the central line.

(20) As further shown in Fig.4. surface curvature can also be characterized by a simple center/periphery intensity ratio calculation.