Maxwell–Boltzmann distributionIn physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and used for describing particle speeds in idealized gases, where the particles move freely inside a stationary container without interacting with one another, except for very brief collisions in which they exchange energy and momentum with each other or with their thermal environment.
Kennelly–Heaviside layerThe Heaviside layer, sometimes called the Kennelly–Heaviside layer, named after Arthur E. Kennelly and Oliver Heaviside, is a layer of ionised gas occurring roughly between 90km and 150 km (56 and 93 mi) above the ground — one of several layers in the Earth's ionosphere. It is also known as the E region. It reflects medium-frequency radio waves. Because of this reflective layer, radio waves radiated into the sky can return to Earth beyond the horizon.
Sheffer sequenceIn mathematics, a Sheffer sequence or poweroid is a polynomial sequence, i.e., a sequence (pn(x) : n = 0, 1, 2, 3, ...) of polynomials in which the index of each polynomial equals its degree, satisfying conditions related to the umbral calculus in combinatorics. They are named for Isador M. Sheffer. Fix a polynomial sequence (pn). Define a linear operator Q on polynomials in x by This determines Q on all polynomials. The polynomial sequence pn is a Sheffer sequence if the linear operator Q just defined is shift-equivariant; such a Q is then a delta operator.
Einstein relation (kinetic theory)In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works on Brownian motion. The more general form of the equation in the classical case is where D is the diffusion coefficient; μ is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, μ = vd/F; kB is the Boltzmann constant; T is the absolute temperature.
Orthogonal functionsIn mathematics, orthogonal functions belong to a function space that is a vector space equipped with a bilinear form. When the function space has an interval as the domain, the bilinear form may be the integral of the product of functions over the interval: The functions and are orthogonal when this integral is zero, i.e. whenever . As with a basis of vectors in a finite-dimensional space, orthogonal functions can form an infinite basis for a function space.
