i ntroduction: the aim of this study was to compare the shaping ability of two single-file systems and conventional rotary instruments in severely curved root canals of extracted human molars. methods and materials: mesiobuccal canals of 120 mandibular molars with angles of curvature ranging between 25 ° and 35 ° and radii of curvature from 5 to 9 mm, were divided into three groups ( n =40). in...

although, most of the abnormal structures of human brain do not alter the shape of outer envelope of brain (surface), some abnormalities can deform the surface extensively. however, this may be a major problem in a surface-based registration technique, since two nearly identical surfaces are required for surface fitting process. a type of verification known as the circularity check for the shap...

introduction: the objective of this study was to compare the shaping ability of three rotary filing systems; constant taper k3 instruments, constant taper profile instruments and progressive taper protaper rotary instruments in clear resin blocks with simulated curved root canals. materials and methods: forty five resin blocks were divided into three groups. group a preparation was conducted wi...

In this paper we prove two sharp inequalities involving the normalized scalar curvature and the generalized normalized δ-Casorati curvatures for slant submanifolds in quaternionic space forms. We also characterize those submanifolds for which the equality cases hold. These results are a generalization of some recent results concerning the Casorati curvature for a slant submanifold in a quaterni...

We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for these groups. In particular, the Ricci curvature, which is understood as the limit of the Ricci curvature of finite-dimensional groups, is calculated. We show that for some of these groups the Ricci curvatu...

Let f : X −→ S be a smooth projective family and let (L, h) be a singular hermitian line bundle on X with semipositive curvature current. Let Ks := K(Xs, KXs +L | Xs, h | Xs)(s ∈ S) be the Bergman kernel of KXs +L | Xs with respect to h | Xs and let hB the singular hermitian metric on KX + L defined by hB |Xs := 1/Ks. We prove that hB has semipositive curvature. This is a generalization of the ...

Let M be a connected d-manifold without boundary obtained from a (possibly infinite) collection P of polytopes of R by identifying them along isometric facets. Let V (M) be the set of vertices of M . For each v ∈ V (M), define the discrete Gaussian curvature κM (v) as the normal angle-sum with sign, extended over all polytopes having v as a vertex. Our main result is as follows: If the absolute...

The relationship between the n-dimensional surfaces of smooth, strictly convex objects and the m-dimensional surfaces of their orthogonal projections, or shadows, is investigated. Our main results concern the relationships between the local properties of the surface at a point and those of its shadow. Specifically, the curvature Hessian of the projection at a boundary point is shown to be simpl...

The first derivative is about approximation by a linear object. Curvature is a measure of the distance of a smooth nonlinear object from being linear, straight, flat, . . . . Curvature has been studied at least as long ago as the ancient Greeks, and it remains a very tumultuous research area today under the names of differential geometry and its applications. While having been a core subject of...