Galerkin methodIn mathematics, in the area of numerical analysis, Galerkin methods are named after the Soviet mathematician Boris Galerkin. They convert a continuous operator problem, such as a differential equation, commonly in a weak formulation, to a discrete problem by applying linear constraints determined by finite sets of basis functions.
Computational complexityIn computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.
Apple Lossless Audio CodecThe Apple Lossless Audio Codec (ALAC), also known as Apple Lossless, or Apple Lossless Encoder (ALE), is an audio coding format, and its reference audio codec implementation, developed by Apple Inc. for lossless data compression of digital music. After initially keeping it proprietary from its inception in 2004, in late 2011 Apple made the codec available open source and royalty-free. Traditionally, Apple has referred to the codec as Apple Lossless, though more recently it has begun to use the abbreviated term ALAC when referring to the codec.
Maxwell's equations in curved spacetimeIn physics, Maxwell's equations in curved spacetime govern the dynamics of the electromagnetic field in curved spacetime (where the metric may not be the Minkowski metric) or where one uses an arbitrary (not necessarily Cartesian) coordinate system. These equations can be viewed as a generalization of the vacuum Maxwell's equations which are normally formulated in the local coordinates of flat spacetime.
Drift velocityIn physics, drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. In general, an electron in a conductor will propagate randomly at the Fermi velocity, resulting in an average velocity of zero. Applying an electric field adds to this random motion a small net flow in one direction; this is the drift. Drift velocity is proportional to current. In a resistive material, it is also proportional to the magnitude of an external electric field.
Plane-wave expansionIn physics, the plane-wave expansion expresses a plane wave as a linear combination of spherical waves: where i is the imaginary unit, k is a wave vector of length k, r is a position vector of length r, jl are spherical Bessel functions, Pl are Legendre polynomials, and the hat ^ denotes the unit vector. In the special case where k is aligned with the z axis, where θ is the spherical polar angle of r. With the spherical-harmonic addition theorem the equation can be rewritten as where Ylm are the spherical harmonics and the superscript * denotes complex conjugation.
