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Alligation is an old and practical method of solving arithmetic problems related to mixtures of ingredients. There are two types of alligation: alligation medial, used to find the quantity of a mixture given the quantities of its ingredients, and alligation alternate, used to find the amount of each ingredient needed to make a mixture of a given quantity.
The basic room purge equation can be used only for purge scenarios. In a scenario where a liquid continuously evaporates from a container in a ventilated room, a differential equation has to be used:
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In mathematics, an algebraic expression is an expression built up from constants (usually, algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).
In most cases, the mixture consists of two main constituents. For an emulsion, these are immiscible fluids such as water and oil. For a foam, these are a solid and a fluid, or a liquid and a gas. On larger scales both constituents are present in any region of the mixture, and in a well-mixed mixture in the same or only slightly varying ...
One of the basic principles of algebra is that one can multiply both sides of an equation by the same expression without changing the equation's solutions. However, strictly speaking, this is not true, in that multiplication by certain expressions may introduce new solutions that were not present before. For example, consider the following ...
An ideal mixture is any in which the arithmetic mean (with respect to mole fraction) of the two pure substances is the same as that of the final mixture. Among other important thermodynamic simplifications, this means that enthalpy of mixing is zero: Δ H m i x , i d e a l = 0 {\displaystyle \Delta H_{mix,ideal}=0} .
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
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