differential geometry, the total absolute curvature of a smooth curve is a number defined by integrating the absolute value of the curvature around the curve....

the differential geometry of curves, the total curvature of an immersed plane curve is the integral of curvature along a curve taken with respect to arc...

differential geometry, Fenchel's theorem is an inequality on the total absolute curvature of a closed smooth space curve, stating that it is always at least...

any continuous curve evolution. If the curve is non-convex, its total absolute curvature decreases monotonically, until it becomes convex. Once convex,...

and only if its curvature has a consistent sign, which happens if and only if its total curvature equals its total absolute curvature. Archimedes, in...

the curvature of spacetime. These tidal accelerations are strictly local. It is the cumulative total effect of many local manifestations of curvature that...

In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being...

that is sufficiently smooth to define the curvature κ at each of its points, and if the total absolute curvature is less than or equal to 4π, then K is an...

nanophthalmos. Curvatural: Curvatural hypermetropia occur when curvature of lens or cornea is flatter than normal. About 1 mm increase in radius of curvature results...

Bonn with thesis Totale Absolutkrümmung immersierter Flächen (Total absolute curvature of immersed surfaces). Since 1986 he is professor at TU Berlin...

for utility functions are represented by these measures. The higher the curvature of u ( c ) {\displaystyle u(c)} , the higher the risk aversion. However...

magnetic susceptibility, ...), and general relativity (stress–energy tensor, curvature tensor, ...). In applications, it is common to study situations in which...

or less standard in the United States, has a special shape with more curvature on top than on the bottom; consequently, the air must travel over the...

{{\text{FWHM}}(z)}{\sqrt {2\ln 2}}}.} The wavefronts have zero curvature (radius = ∞) at the waist. Wavefront curvature increases away from the waist, with the maximum...

{1}{R}}{\boldsymbol {e}}_{n},\end{aligned}}} and R {\displaystyle R} is the radius of curvature of the streamline. Therefore, the momentum part of the Euler equations...

parallelism, also referred to as absolute or teleparallelism. In this theory, a spacetime is characterized by a curvature-free linear connection in conjunction...

this is when the universe reaches thermodynamic equilibrium. If the curvature of the universe is hyperbolic or flat, or if dark energy is a positive...

factorization of the curvatures, along with the multiplier needed to go from the previous set to the current one. The absolute values of the curvatures of the "a"...

the mean curvature, as seen in the Young–Laplace equation. For an open soap film, the pressure difference is zero, hence the mean curvature is zero, and...

Bishop−Gromov volume comparison to control the injectivity radius in absolute terms by curvature bounds and volumes of geodesic balls.[CGT82] Their estimate has...

gravity in terms of the curvature of spacetime, caused by the uneven distribution of mass. The most extreme example of this curvature of spacetime is a black...

the curvature of spacetime. These tidal accelerations are strictly local. It is the cumulative total effect of many local manifestations of curvature that...

connection, and the second is also called the curvature. These expressions are differential 2-forms on the total space of a frame bundle. However, they are...

corresponding to a space of positive curvature; or −1, corresponding to a space of positive or negative curvature. The value of R as a function of time...

may have positive, negative, or zero spatial curvature depending on its total energy density. Curvature is negative if its density is less than the critical...

length of a lens is determined by its refractive index n and the radii of curvature R1 and R2 of its surfaces. The power of a thin lens in air is given by...

where the two currents are summed up. This method enhanced further the curvature correction and achieved superior TD performance over a wider temperature...

information is a measure of the curvature of the log likelihood function of α. A low curvature (and therefore high radius of curvature), flatter log likelihood...

only by reference to absolute space. Alternatively, these experiments provide an operational definition of what is meant by "absolute rotation", and do not...

L^{2}} -norm of the curvature, and its Euler–Lagrange equations describe the critical points of this functional, either the absolute minima or local minima...