commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order theories of gravity. We can define effective pressure and energy density directly connected to the Ricci scalar of curvature of a generic fourth order theory and then ask for the conditions to get an accelerated expansion. Exact accelerated expanding solutions can be achieved for several fourth ...

Sequence-dependent DNA curvature is known to play an important role in initiation of transcription of many genes. We compared the distribution of predicted intrinsic curvature of Escherichia coli and human promoter sequences with the distribution of curvature of randomly selected coding and non-coding fragments from these organisms. Different methods of curvature calculation were found to yield...

Estimation of a digital curve’s curvature at any given point is needed for many tasks in computer vision, be it differential invariants or curvature scale space. However, curvature estimation is known to be very susceptible to noise on the contour. We shall show how noise on the contour affects the relative accuracy of the curvature computation. One interesting result is that, contrary to intui...

We introduce a curvature function for planar graphs to study the connection of curvature and geometric and spectral properties of the graph. We show that non-positive curvature implies that the graph is infinite, locally similar to a tessellation and admits no cut locus. For negative curvature we prove empty interior of minimal bigons and explicit bounds for the growth of distance balls and Che...

We present a new way to compute the aane curvature of plane curves. We explain how an aane scale-space can be used to gain one order of derivation in the numerical approximation of aane curvature. We outline our implementation and compare our results with previous ones. This paper ends by showing a simple application in pattern recognition using aane curvature.

We obtain divergence theorems on the solution space of an elliptic stochastic differential equation defined on a smooth compact finite-dimensional manifold M . The resulting divergences are expressed in terms of the Ricci curvature of M with respect to a natural metric on M induced by the stochastic differential equation. The proofs of the main theorems are based on the lifting method of Mallia...

Given a Riemannian manifold (M, g), we study the solutions of heat equations associated with second order differential operators in divergence form that are uniformly elliptic with respect to g . Typical examples of such operators are the Laplace operators of Riemannian structures which are quasi-isometric to g . We first prove some Poincare and Sobolev inequalities on geodesic balls. Then we u...

A 4.5-year-old Holstein-Friesian cow underwent surgery because of left abomasal displacement. Intra-operative palpation of the pyloric region revealed a phytobezoar. The abomasum containing the phytobezoar was exteriorized, and an incision was made directly over the mass in the region of the greater curvature of the pyloric part of the abomasum.