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In a fluid mixture like a petroleum gas or oil there are lots of molecule types, and within this mixture there are families of molecule types (i.e. groups of fluid components). The simplest group is the n-alkanes which are long chains of CH 2-elements. The more CH 2-elements, or carbon atoms, the longer molecule. Critical viscosity and critical ...
Euler rotations are never expressed in terms of the external frame, or in terms of the co-moving rotated body frame, but in a mixture. They constitute a mixed axes of rotation system, where the first angle moves the line of nodes around the external axis z , the second rotates around the line of nodes and the third one is an intrinsic rotation ...
Multiplication can be thought of as repeated addition. If a single term x appears in a sum n times, then the sum is the product of n and x. If n is not a natural number, the product may still make sense; for example, multiplication by −1 yields the additive inverse of a number. A circular slide rule
This is because the wikitable class in MediaWiki:Common.css contains a number of table.wikitable CSS style rules. These are all applied at once when you mark a table with the class. You can then add additional style rules if desired. These override the class's rules, allowing you to use the class style as a base and build up on it:
The Hadamard transform H m is a 2 m × 2 m matrix, the Hadamard matrix (scaled by a normalization factor), that transforms 2 m real numbers x n into 2 m real numbers X k.The Hadamard transform can be defined in two ways: recursively, or by using the binary (base-2) representation of the indices n and k.
Let F be a free ring (that is, free algebra over the integers) with the set X of symbols, that is, F consists of polynomials with integral coefficients in noncommuting variables that are elements of X. A free ring satisfies the universal property: any function from the set X to a ring R factors through F so that F → R is the unique ring ...
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations.Integration, the process of computing an integral, is one of the two fundamental operations of calculus, [a] the other being differentiation.
In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. [1] Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.