We compare curvature combs and curvature plots. © 2016 Elsevier Ltd. All rights reserved.

1.1. Connections and derivations. Let S be a scheme, and X smooth and finite type over S throughout. We have the rank-n vector bundle ΩX/S of 1-forms on X over S. We also fix some notation in the case that S is of characteristic p: in this case, we denote by FT the absolute Frobenius map for any scheme T , by X = X×S S the p-twist of X over S, where the map used in the fiber product is FS : S →...

here, a finsler manifold $(m,f)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. certain subspaces of the tangent spaces of $m$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. it is shown that if the dimension of foliation is constant, then the distribution is involutive a...

We prove that the Atiyah-Singer Dirac operator / Dg in L 2 depends Riesz continuously on L∞ perturbations of complete metrics g on a smooth manifold. The Lipschitz bound for the map g → / Dg(1 + / D 2 g) − 12 depends on bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. Our proof uses harmonic analysis techniques related to Calderón’s first commu...

To investigate the effect of coupling edges, we compare cooperative cut (CoopCut) to the standard graph cut (GraphCut), and, for shrinking bias, also to curvature regularization. To ensure equivalent conditions, all methods used the same weights on the terminal edges (i.e., the same unary potentials), the same 8-neighbor graph structure, and the same inter-pixel edge weights. The unary potentia...

in this paper, the lorentzian version of beltrami-euler formula is investigated in 1n . initially,the first fundamental form and the metric coefficients of generalized timelike ruled surface are calculated and by the help of the christoffel symbols, riemann-christoffel curvatures are obtained. thus, the curvatures of spacelike and timelike tangential sections of generalized timelike ruled surf...

A system is described for the examination of phototropism in the epicotyl of a dicot seedling, mung bean (Phaseolus aureus Roxb.), under conditions approximating nature, including the use of intact, nonetiolated plants exposed to elevated, continuous, white, unilateral light. It is found that in this system perception of the phototropic stimulus by the leaves alone cannot account for the curvat...

We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k

In this paper, we study the class of of C3-like Finsler metrics which contains the class of semi-C-reducible Finsler metric. We find a condition on C3-like metrics under which the notions of Landsberg curvature and mean Landsberg curvature are equivalent.

The omentum is a sheet-like tissue attached to the greater curvature of the stomach and contains secondary lymphoid organs called milky spots. The omentum has been used for its healing potential for over 100 years by transposing the omental pedicle to injured organs (omental transposition), but the mechanism by which omentum helps the healing process of damaged tissues is not well understood. O...