We report the first topographical data of the surface of living endothelial cells at sub-light-microscopic resolution, measurements essential for a detailed understanding of force distribution in the endothelium subjected to flow. Atomic force microscopy was used to observe the surface topography of living endothelial cells in confluent monolayers maintained in static culture or subjected to un...

A formulation of the non-commutative geometry for the standard model of particle physics with a Lorentzian signature metric is presented. The elimination of the fermion doubling in the Lorentzian

We show that the normalized Lorentzian state sum is finite on any triangulation. It thus provides a candidate for a perturbatively finite quantum theory of general relativity in four dimensions with Lorentzian signature.

In this note a proof is given for global existence and uniqueness of minimal surfaces of Lorentzian type from a cylinder into certain Lorentzian manifolds for given initial values up to the first derivatives.

We develop a supervised dimensionality reduction method, called Lorentzian discriminant projection (LDP), for feature extraction and classification. Our method represents the structures of sample data by a manifold, which is furnished with a Lorentzian metric tensor. Different from classic discriminant analysis techniques, LDP uses distances from points to their within-class neighbors and globa...

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...