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Any exponential function can be written as the self-composition (()) for infinitely many possible choices of .In particular, for every in the open interval (,) and for every continuous strictly increasing function from [,] onto [,], there is an extension of this function to a continuous strictly increasing function on the real numbers such that (()) = . [4]
Defining equation (physical chemistry) List of equations in classical mechanics; Table of thermodynamic equations; List of equations in wave theory; List of electromagnetism equations; List of relativistic equations; List of equations in fluid mechanics; List of equations in gravitation; List of photonics equations; List of equations in quantum ...
Full width at half maximum. In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the y-axis which are half the maximum ...
It is assumed that the value of a function f defined on [,] is known at + equally spaced points: < < <.There are two classes of Newton–Cotes quadrature: they are called "closed" when = and =, i.e. they use the function values at the interval endpoints, and "open" when > and <, i.e. they do not use the function values at the endpoints.
The values below are standard apparent reduction potentials (E°') for electro-biochemical half-reactions measured at 25 °C, 1 atmosphere and a pH of 7 in aqueous solution. [1] [2] The actual physiological potential depends on the ratio of the reduced (Red) and oxidized (Ox) forms according to the Nernst equation and the thermal voltage.
Geometrically, the construction goes like this: for any point (cos φ, sin φ) on the unit circle, draw the line passing through it and the point (−1, 0). This point crosses the y-axis at some point y = t. One can show using simple geometry that t = tan(φ/2). The equation for the drawn line is y = (1 + x)t.
Here is another geometric point of view. Draw the unit circle, and let P be the point (−1, 0). A line through P (except the vertical line) is determined by its slope. Furthermore, each of the lines (except the vertical line) intersects the unit circle in exactly two points, one of which is P. This determines a function from points on the unit ...
For a semicircle with a diameter of a + b, the length of its radius is the arithmetic mean of a and b (since the radius is half of the diameter). The geometric mean can be found by dividing the diameter into two segments of lengths a and b , and then connecting their common endpoint to the semicircle with a segment perpendicular to the diameter.