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The Problem of Moments. New York: American mathematical society. ISBN 978-1-4704-1228-9. Akhiezer, Naum I. (1965). The classical moment problem and some related questions in analysis. New York: Hafner Publishing Co. (translated from the Russian by N. Kemmer) Kreĭn, M. G.; Nudel′man, A. A. (1977). The Markov Moment Problem and Extremal ...
The Stieltjes moment problems and the Hamburger moment problems, if they are solvable, may have infinitely many solutions (indeterminate moment problem) whereas a Hausdorff moment problem always has a unique solution if it is solvable (determinate moment problem). In the indeterminate moment problem case, there are infinite measures ...
So in this case the solution to the Hamburger moment problem is unique and μ, being the spectral measure of T, has finite support. More generally, the solution is unique if there are constants C and D such that, for all n, | m n | ≤ CD n n! (Reed & Simon 1975, p. 205). This follows from the more general Carleman's condition.
The essential difference between this and other well-known moment problems is that this is on a half-line [0, ∞), whereas in the Hausdorff moment problem one considers a bounded interval [0, 1], and in the Hamburger moment problem one considers the whole line (−∞, ∞).
In statistics, the method of moments is a method of estimation of population parameters.The same principle is used to derive higher moments like skewness and kurtosis. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest.
In statics and structural mechanics, a structure is statically indeterminate when the equilibrium equations – force and moment equilibrium conditions – are insufficient for determining the internal forces and reactions on that structure.
The direction of the moment is given by the right hand rule, where counter clockwise (CCW) is out of the page, and clockwise (CW) is into the page. The moment direction may be accounted for by using a stated sign convention, such as a plus sign (+) for counterclockwise moments and a minus sign (−) for clockwise moments, or vice versa.
The moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2). It should not be confused with the second moment of area, which has units of dimension L 4 ([length] 4) and is used in beam calculations. The mass moment of inertia is often also known as the rotational inertia, and sometimes as the angular mass.