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In mathematics, a closed-form expression is a mathematical expression that uses a finite number of standard operations. It may contain constants, variables, certain well-known operations (e.g., + − × ÷), and functions (e.g., nth root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit, differentiation, or integration.
The Gaddum equation is a further generalisation of the Hill-equation, incorporating the presence of a reversible competitive antagonist. The Gaddum equation is derived similarly to the Hill-equation but with 2 equilibria: both the ligand with the receptor and the antagonist with the receptor.
Basic room purge equation. The basic room purge equation is used in industrial hygiene. It determines the time required to reduce a known vapor concentration existing in a closed space to a lower vapor concentration. The equation can only be applied when the purged volume of vapor or gas is replaced with "clean" air or gas.
The equation of time describes the discrepancy between two kinds of solar time.The word equation is used in the medieval sense of "reconcile a difference". The two times that differ are the apparent solar time, which directly tracks the diurnal motion of the Sun, and mean solar time, which tracks a theoretical mean Sun with uniform motion along the celestial equator.
A) where: v is the fluid flow speed at a point on a streamline, g is the acceleration due to gravity , z is the elevation of the point above a reference plane, with the positive z -direction pointing upward—so in the direction opposite to the gravitational acceleration, p is the pressure at the chosen point, and ρ is the density of the fluid at all points in the fluid. The constant on the ...
This is one form of the Gibbs fundamental equation. In the infinitesimal expression, the term involving the chemical potential accounts for changes in Gibbs free energy resulting from an influx or outflux of particles. In other words, it holds for an open system or for a closed, chemically reacting system where the N i are changing. For a ...
The center of a linear homogeneous differential equation of the second order is an example of a neutrally stable fixed point. Multiple attracting points can be collected in an attracting fixed set. Banach fixed-point theorem. The Banach fixed-point theorem gives a sufficient condition for the existence of attracting fixed points.
where overdots define the scope of the vector derivative. The dotted vector, in this case B, is differentiated, while the (undotted) A is held constant.. For the remainder of this article, Feynman subscript notation will be used where appropriate.