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Current usage of the term "Mie solution" indicates a series approximation to a solution of Maxwell's equations. There are several known objects that allow such a solution: spheres, concentric spheres, infinite cylinders, clusters of spheres and clusters of cylinders. There are also known series solutions for scattering by ellipsoidal particles.
Contributing structures of the carbonate ion. In chemistry, resonance, also called mesomerism, is a way of describing bonding in certain molecules or polyatomic ions by the combination of several contributing structures (or forms, [1] also variously known as resonance structures or canonical structures) into a resonance hybrid (or hybrid structure) in valence bond theory.
Pushing a person in a swing is a common example of resonance. The loaded swing, a pendulum, has a natural frequency of oscillation, its resonant frequency, and resists being pushed at a faster or slower rate. A familiar example is a playground swing, which acts as a pendulum. Pushing a person in a swing in time with the natural interval of the ...
Hasse–Arf theorem (local class field theory) Hilbert's theorem 90 (number theory) Isomorphism extension theorem (abstract algebra) Joubert's theorem ; Lagrange's theorem (number theory) Mason–Stothers theorem (polynomials) Polynomial remainder theorem (polynomials) Primitive element theorem (field theory) Rational root theorem (algebra ...
Fermat's solution was a landmark in that it unified the then-known laws of geometrical optics under a variational principle or action principle, setting the precedent for the principle of least action in classical mechanics and the corresponding principles in other fields (see History of variational principles in physics). [42]
The theorem statement presented here is due to the proof framework proposed by Krylov-Bogoliubov which is based on an introduction of a near-identity transformation. The advantage of this method is the extension to more general settings such as infinite-dimensional systems - partial differential equation or delay differential equations.
Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency or resonant frequency) closer than it does other frequencies. It may cause violent swaying motions and potentially catastrophic failure in ...
Thus, the lifetime of a particle is the direct inverse of the particle's resonance width. For example, the charged pion has the second-longest lifetime of any meson, at 2.6033 × 10 −8 s. [2] Therefore, its resonance width is very small, about 2.528 × 10 −8 eV or about 6.11 MHz. Pions are generally not considered as "resonances".