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Data transformation (statistics) A scatterplot in which the areas of the sovereign states and dependent territories in the world are plotted on the vertical axis against their populations on the horizontal axis. The upper plot uses raw data. In the lower plot, both the area and population data have been transformed using the logarithm function.
Definitions. The Lineweaver–Burk plot derives from a transformation of the Michaelis–Menten equation , in which the rate is a function of the substrate concentration and two parameters , the limiting rate, and , the Michaelis constant. Taking reciprocals of both sides of this equation it becomes as follows:
The graph forms a rectangular hyperbola. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/ x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a / b is b / a. For the multiplicative inverse of a real number, divide 1 by the number.
Hyperbola. A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case. Hyperbola (red): features. In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its ...
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves modulated by periodic functions. The theorem is named after the Swiss physicist Felix Bloch, who discovered the theorem in 1929. [1] Mathematically, they are written [2] Bloch function.
Eigenvalues and eigenvectors. In linear algebra, an eigenvector ( / ˈaɪɡən -/ EYE-gən-) or characteristic vector is a vector that has its direction unchanged by a given linear transformation. More precisely, an eigenvector, , of a linear transformation, , is scaled by a constant factor, , when the linear transformation is applied to it: .
Alternately hyperbolic angle is the area of a sector of the hyperbola Some authors call the inverse hyperbolic functions hyperbolic area functions. [ 1] Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. It also occurs in the solutions of many linear differential equations (such as the equation ...
The reciprocal 1/ X of a random variable X, is a member of the same family of distribution as X, in the following cases: Cauchy distribution, F distribution, log logistic distribution . Examples: If X is a Cauchy ( μ, σ) random variable, then 1/ X is a Cauchy ( μ / C, σ / C) random variable where C = μ2 + σ2.