DielectricIn electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor, because they have no loosely bound, or free, electrons that may drift through the material, but instead they shift, only slightly, from their average equilibrium positions, causing dielectric polarisation.
Cross section (physics)In physics, the cross section is a measure of the probability that a specific process will take place when some kind of radiant excitation (e.g. a particle beam, sound wave, light, or an X-ray) intersects a localized phenomenon (e.g. a particle or density fluctuation). For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted σ (sigma) and is expressed in units of area, more specifically in barns.
Vieta's formulasIn mathematics, Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. They are named after François Viète (more commonly referred to by the Latinised form of his name, "Franciscus Vieta"). Any general polynomial of degree n (with the coefficients being real or complex numbers and an ≠ 0) has n (not necessarily distinct) complex roots r1, r2, ..., rn by the fundamental theorem of algebra. Vieta's formulas relate the polynomial's coefficients to signed sums of products of the roots r1, r2, .
Impedance of free spaceIn electromagnetism, the impedance of free space, Z0, is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. That is, where is the electric field strength and is the magnetic field strength. Its presently accepted value is Where Ω is the ohm, the SI unit of electrical resistance. The impedance of free space (that is the wave impedance of a plane wave in free space) is equal to the product of the vacuum permeability μ0 and the speed of light in vacuum c0.
Class number formulaIn number theory, the class number formula relates many important invariants of a number field to a special value of its Dedekind zeta function. We start with the following data: K is a number field. [K : Q] = n = r1 + 2r2, where r1 denotes the number of real embeddings of K, and 2r2 is the number of complex embeddings of K. ζK(s) is the Dedekind zeta function of K. hK is the class number, the number of elements in the ideal class group of K. RegK is the regulator of K. wK is the number of roots of unity contained in K.
Path space fibrationIn algebraic topology, the path space fibration over a based space is a fibration of the form where is the path space of X; i.e., equipped with the compact-open topology. is the fiber of over the base point of X; thus it is the loop space of X. The space consists of all maps from I to X that may not preserve the base points; it is called the free path space of X and the fibration given by, say, , is called the free path space fibration. The path space fibration can be understood to be dual to the mapping cone.
