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Kramers' law is a formula for the spectral distribution of X-rays produced by an electron hitting a solid target. The formula concerns only bremsstrahlung radiation, not the element specific characteristic radiation.
For cancellation of common terms, we have the following rules: If a + k ≡ b + k (mod m), where k is any integer, then a ≡ b (mod m). If k a ≡ k b (mod m) and k is coprime with m, then a ≡ b (mod m). If k a ≡ k b (mod k m) and k ≠ 0, then a ≡ b (mod m). The last rule can be used to move modular arithmetic into division.
If p is a prime number which is not a divisor of b, then ab p−1 mod p = a mod p, due to Fermat's little theorem. Inverse: [(−a mod n) + (a mod n)] mod n = 0. b −1 mod n denotes the modular multiplicative inverse, which is defined if and only if b and n are relatively prime, which is the case when the left hand side is defined: [(b −1 ...
An example of the use of the law of reciprocity is the Sunny 16 rule which gives a rough estimate for the settings needed to estimate the proper exposure in daylight. [ 116 ] A camera's aperture is measured by a unitless number called the f-number or f-stop, f / #, often notated as N {\displaystyle N} , and given by
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
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Gauss published the first and second proofs of the law of quadratic reciprocity on arts 125–146 and 262 of Disquisitiones Arithmeticae in 1801.. In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers.
The "Rule of Four" has been explained by various Justices in judicial opinions throughout the years. [2] For example, Justice Felix Frankfurter described the rule as follows: "The 'rule of four' is not a command of Congress. It is a working rule devised by the Court as a practical mode of determining that a case is deserving of review, the ...