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The hyperbolic growth of the world population and quadratic-hyperbolic growth of the world GDP observed till the 1970s have been correlated by Andrey Korotayev and his colleagues to a non-linear second order positive feedback between the demographic growth and technological development, described by a chain of causation: technological growth ...
The hyperbolastic rate equation of type II, denoted by H2, is defined as = (() ()),where is the hyperbolic tangent function, is the carrying capacity, and both and > jointly determine the growth rate.
There are two simple derivations of the equation that are commonly used to generate the hyperbolic curve. The first assumes photosynthetic rate increases with increasing light intensity until Pmax is reached and continues to photosynthesize at the maximum rate thereafter. P = P max [I] / (KI + [I]) P = photosynthetic rate at a given light intensity
Hyperbolic functions are used to express the angle of parallelism in hyperbolic geometry. They are used to express Lorentz boosts as hyperbolic rotations in special relativity . They also occur in the solutions of many linear differential equations (such as the equation defining a catenary ), cubic equations , and Laplace's equation in ...
A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone.The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case.
Examples of such properties of finitely generated groups include: the growth rate of a finitely generated group; the isoperimetric function or Dehn function of a finitely presented group; the number of ends of a group; hyperbolicity of a group; the homeomorphism type of the Gromov boundary of a hyperbolic group; [15] asymptotic cones of ...
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
However, a Lévy process that is generalised hyperbolic at one point in time might fail to be generalized hyperbolic at another point in time. In fact, the generalized Laplace distributions and the normal inverse Gaussian distributions are the only subclasses of the generalized hyperbolic distributions that are closed under convolution. [4]