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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.