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2. Inverse-variance weighting - Wikipedia

   en.wikipedia.org/wiki/Inverse-variance_weighting

   For normally distributed random variables inverse-variance weighted averages can also be derived as the maximum likelihood estimate for the true value. Furthermore, from a Bayesian perspective the posterior distribution for the true value given normally distributed observations and a flat prior is a normal distribution with the inverse-variance weighted average as a mean and variance ().

3. Lambek–Moser theorem - Wikipedia

   en.wikipedia.org/wiki/Lambek–Moser_theorem

   For this variation, every partition corresponds to a Galois connection of the ordered non-negative integers to themselves. This is a pair of non-decreasing functions ( f , f ∗ ) {\displaystyle (f,f^{*})} with the property that, for all x {\displaystyle x} and y {\displaystyle y} , f ( x ) ≤ y {\displaystyle f(x)\leq y} if and only if x ≤ ...

4. Proportionality (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Proportionality_(mathematics)

   Inverse proportionality with product x y = 1 . Two variables are inversely proportional (also called varying inversely , in inverse variation , in inverse proportion ) [ 2 ] if each of the variables is directly proportional to the multiplicative inverse (reciprocal) of the other, or equivalently if their product is a constant. [ 3 ]

5. Inverse function - Wikipedia

   en.wikipedia.org/wiki/Inverse_function

   Sometimes, this multivalued inverse is called the full inverse of f, and the portions (such as √ x and − √ x) are called branches. The most important branch of a multivalued function (e.g. the positive square root) is called the principal branch , and its value at y is called the principal value of f −1 ( y ) .

6. Involution (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Involution_(mathematics)

   Any involution is a bijection.. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x ↦ −x), reciprocation (x ↦ 1/x), and complex conjugation (z ↦ z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the ...

7. Calculus of variations - Wikipedia

   en.wikipedia.org/wiki/Calculus_of_Variations

   Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [l] is defined as the linear part of the change in the functional, and the second variation [m] is defined as the quadratic part. [22]