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In mathematics, an operator or transform is a function from one space of functions to another. Operators occur commonly in engineering, physics and mathematics. Many are integral operators and differential operators.
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Statement of the theorem. Kaplansky's theorem states that a prime p congruent to 1 modulo 16 is representable by both or none of x2 + 32 y2 and x2 + 64 y2, whereas a prime p congruent to 9 modulo 16 is representable by exactly one of these quadratic forms. This is remarkable since the primes represented by each of these forms individually are ...
The Thiele Modulus was developed to describe the relationship between diffusion and reaction rates in porous catalyst pellets with no mass transfer limitations. This value is generally used to measure the effectiveness factor of pellets. The Thiele modulus is represented by different symbols in different texts, but is defined in Hill [2] as hT.
In the US, paper density is usually measured in "pound per reams " (of 500 sheets). Typical Letter paper has a basis weight of paper of 20 or 24 pounds (9.1 or 10.9 kg) – the weight of 500 sheets (a ream) of 17-by-22-inch (431.8 by 558.8 mm) paper at 70 °F (21 °C) and at 50% humidity. [3] One ream of 20-pound Letter-sized paper weighs 5 ...
There exists a change of variables from the coordinates to a set of variables , in which the equations of motion become , , where the functions are unknown, but depend only on . The variables are the action coordinates, the variables are the angle coordinates. The motion of the system can thus be visualized as rotation on torii.
An archetypal double counting proof is for the well known formula for the number () of k-combinations (i.e., subsets of size k) of an n-element set: = (+) ().Here a direct bijective proof is not possible: because the right-hand side of the identity is a fraction, there is no set obviously counted by it (it even takes some thought to see that the denominator always evenly divides the numerator).
Argument of a function. In mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable. [1] For example, the binary function has two arguments, and , in an ordered pair . The hypergeometric function is an example of a four-argument function.