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The Simpson index is in the range [0, 1], where 0 means maximum and 1 means minimum diversity (or heterogeneity). Since diversity indices typically increase with increasing heterogeneity, the Simpson index is often transformed into inverse Simpson, or using the complement 1 − λ {\displaystyle 1-\lambda } , known as the Gini-Simpson Index.
The quadratic formula, which concisely expresses the solutions of all quadratic equations The Rubik's Cube group is a concrete application of group theory. [26] Algebra is the art of manipulating equations and formulas. Diophantus (3rd century) and al-Khwarizmi (9th century) were the two main precursors of algebra.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
If a ≠ 0 and m = b / a , then z = a(1 + mε) is the polar decomposition of the dual number z, and the slope m is its angular part. The concept of a rotation in the dual number plane is equivalent to a vertical shear mapping since (1 + pε)(1 + qε) = 1 + (p + q)ε. In absolute space and time the Galilean transformation
V̇O 2 max (also maximal oxygen consumption, maximal oxygen uptake or maximal aerobic capacity) is the maximum rate of oxygen consumption attainable during physical exertion. [1] [2] The name is derived from three abbreviations: "V̇" for volume (the dot over the V indicates "per unit of time" in Newton's notation), "O 2" for oxygen, and "max" for maximum and usually normalized per kilogram of ...
Tangent line at (x 0, f(x 0)). The derivative f′(x) of a curve at a point is the slope (rise over run) of the line tangent to that curve at that point. Differential calculus is the study of the definition, properties, and applications of the derivative of a function. The process of finding the derivative is called differentiation. Given a ...
For example, with z = 1.5 the third approximation yields 0.4167, which is about 0.011 greater than ln(1.5) = 0.405465, and the ninth approximation yields 0.40553, which is only about 0.0001 greater. The n th partial sum can approximate ln( z ) with arbitrary precision, provided the number of summands n is large enough.
A 1 inch tall uranium fuel pellet is equivalent to about 1 ton of coal, 120 gallons of crude oil, or 17,000 cubic feet of natural gas. [15] In light-water reactors , 1 kg of natural uranium – following a corresponding enrichment and used for power generation– is equivalent to the energy content of nearly 10,000 kg of mineral oil or 14,000 ...