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A standing wave. The red dots are the wave nodes. A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the ...
STOs have the following radial part: =where n is a natural number that plays the role of principal quantum number, n = 1,2,...,; N is a normalizing constant,; r is the distance of the electron from the atomic nucleus, and
The function F defined on the unit disk by F(re iθ) = (f ∗ P r)(e iθ) is harmonic, and M f is the radial maximal function of F. When M f belongs to L p (T) and p ≥ 1, the distribution f "is" a function in L p (T), namely the boundary value of F. For p ≥ 1, the real Hardy space H p (T) is a subset of L p (T).
A strange loop is a hierarchy of levels, each of which is linked to at least one other by some type of relationship. A strange loop hierarchy is "tangled" (Hofstadter refers to this as a "heterarchy"), in that there is no well defined highest or lowest level; moving through the levels, one eventually returns to the starting point, i.e., the original level.
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets, satellites, and other spacecraft.
The part of the function that depends on distance r from the nucleus has radial nodes and decays as . The Slater-type orbital (STO) is a form without radial nodes but decays from the nucleus as does a hydrogen-like orbital.
With this operation, the loop space is an A ∞-space. That is, the multiplication is homotopy-coherently associative. The set of path components of ΩX, i.e. the set of based-homotopy equivalence classes of based loops in X, is a group, the fundamental group π 1 (X). The iterated loop spaces of X are formed by applying Ω a number of times.
A radial function is a function : [,).When paired with a norm on a vector space ‖ ‖: [,), a function of the form = (‖ ‖) is said to be a radial kernel centered at .A radial function and the associated radial kernels are said to be radial basis functions if, for any finite set of nodes {} =, all of the following conditions are true: