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A classic example is the calculation of the exterior multipole moments of atomic nuclei from their interaction energies with the interior multipoles of the electronic orbitals. The multipole moments of the nuclei report on the distribution of charges within the nucleus and, thus, on the shape of the nucleus.
In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph.If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia.
Moments are usually defined with respect to a fixed reference point and refer to physical quantities located some distance from the reference point. For example, the moment of force, often called torque, is the product of a force on an object and the distance from the reference point to the object. In principle, any physical quantity can be ...
For example, this formula may be used to determine the electrostatic interaction energies of the atomic nucleus with its surrounding electronic orbitals. Conversely, given the interaction energies and the interior multipole moments of the electronic orbitals, one may find the exterior multipole moments (and, hence, shape) of the atomic nucleus.
The first few central moments have intuitive interpretations: The "zeroth" central moment μ 0 is 1. The first central moment μ 1 is 0 (not to be confused with the first raw moment or the expected value μ). The second central moment μ 2 is called the variance, and is usually denoted σ 2, where σ represents the standard deviation.
All 67 people on board the American Airlines regional jet and US Army Black Hawk helicopter that collided midair Wednesday night are presumed dead – a grim tragedy that has left a heartbreaking ...
In probability theory, it is possible to approximate the moments of a function f of a random variable X using Taylor expansions, provided that f is sufficiently differentiable and that the moments of X are finite. A simulation-based alternative to this approximation is the application of Monte Carlo simulations.
For example, Jacobs Hendel said, if we mistake a pair of paper knickers at a spa for a shower cap, we can: 1. Recognize and validate the feeling of embarrassment: "Yikes, I'm so embarrassed!"