In algebraic topology there is a more general formula called the Euler-Poincaré formula, which has terms corresponding to the number of components in each dimension and also terms (called Betti numbers) derived from the homology groups that depend only on the topology of the figure.
We developed a more general formula for the population distribution of solid particles in processes involving recirculations, and compared it with the widely used equation in the calculation of several process metrics.
The Campbell-Baker-Hausdorff-Dynkin formula is a special case of a simpler and more general formula for the solution of nonautonomous systems of first order ordinary differential equations in terms of autonomous systems.
We develop a new and more general formula for the construction of two dimensional nodal Riemann solver for a cell-centered Lagrangian scheme developed by Maire and his co-workers which allows us to use general one dimensional Riemann solvers that have intermediate velocity and pressure in the construction.
For the sake of completeness, we also give the more general formula for any value of γ0: p P ( x ) = 2 M P ( 1 − sin γ 0 ) E 1 x M P − E 1 2 x M P ( 1 + sin γ 0 ) (13).
Turning to 2D distributions, this formula can no longer be used, since there now are two properties, A and B. Instead a more general formula is needed.
It is suggested that the more general formula introduced here is reported as δ G, to avoid the implication that items are dichotomously coded.
The model can be fitted by traditional regression techniques with robust standard errors and is derived from a more general formula for assessing tracking, outlined by Twisk [ 23].
To establish a more general formula for defining q under different conditions of X, L, n, we extended the simulations to various initial conditions of n, X both varying from 3 to 20 together with different values of q.
From the viewpoint of the more general PBC formula (Formula 3), Sørensen distances are a special case that is based on a distance matrix that contains information only on identity (zero distances) and non-identity (positive constant k as distances) but no further information on phylogenetic relationships.
Note that Theorem 2.4.1 was used in [10] to obtain considerably more general trace formulae.
