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The logistic equation (sometimes called the Verhulst model or logistic growth curve) is a model of population growth first published by Pierre Verhulst (1845, 1847). The ...

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

The function z=f(x)=ln(x/(1-x)). (1) This function has an inflection point at x=1/2, where f^('')(x)=(2x-1)/(x^2(x-1)^2)=0. (2) Applying the logit transformation to values ...

A generalization of a Heyting algebra which replaces Boolean algebra in "intuitionistic" logic.

The (m,n)-lollipop graph is the graph obtained by joining a complete graph K_m to a path graph P_n with a bridge. Precomputed properties of lollipop graphs are available in ...

The Lommel differential equation is a generalization of the Bessel differential equation given by z^2y^('')+zy^'+(z^2-nu^2)y=kz^(mu+1), (1) or, in the most general form, by ...

There are several functions called "Lommel functions." One type of Lommel function appear in the solution to the Lommel differential equation and are given by ...

The Lommel polynomials R_(m,nu)(z) arise from the equation J_(m+nu)(z)=J_nu(z)R_(m,nu)(z)-J_(nu-1)(z)R_(m-1,nu+1)(z), (1) where J_nu(z) is a Bessel function of the first kind ...

The two integrals involving Bessel functions of the first kind given by (alpha^2-beta^2)intxJ_n(alphax)J_n(betax)dx ...

Intuitively, a d-dimensional discrete percolation model is said to be long-range if direct flow is possible between pairs of graph vertices or graph edges which are "very ...