Parseval's theoremIn mathematics, Parseval's theorem usually refers to the result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform. It originates from a 1799 theorem about series by Marc-Antoine Parseval, which was later applied to the Fourier series. It is also known as Rayleigh's energy theorem, or Rayleigh's identity, after John William Strutt, Lord Rayleigh.
Unitary operatorIn functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product. Unitary operators are usually taken as operating on a Hilbert space, but the same notion serves to define the concept of isomorphism between Hilbert spaces. A unitary element is a generalization of a unitary operator. In a unital algebra, an element U of the algebra is called a unitary element if UU = UU = I, where I is the identity element. Definition 1.
Taurus (constellation)Taurus (Latin for "the Bull") is one of the constellations of the zodiac and is located in the northern celestial hemisphere. Taurus is a large and prominent constellation in the Northern Hemisphere's winter sky. It is one of the oldest constellations, dating back to the Early Bronze Age at least, when it marked the location of the Sun during the spring equinox. Its importance to the agricultural calendar influenced various bull figures in the mythologies of Ancient Sumer, Akkad, Assyria, Babylon, Egypt, Greece, and Rome.
Galois cohomologyIn mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups. A Galois group G associated to a field extension L/K acts in a natural way on some abelian groups, for example those constructed directly from L, but also through other Galois representations that may be derived by more abstract means. Galois cohomology accounts for the way in which taking Galois-invariant elements fails to be an exact functor.
Satellite internet constellationA satellite internet constellation is a constellation of artificial satellites providing satellite internet service. In particular, the term has come to refer to a new generation of very large constellations (sometimes referred to as a megaconstellations) orbiting in low Earth orbit (LEO) to provide low-latency, high bandwidth (broadband) internet service.
Earth (classical element)Earth is one of the classical elements, in some systems being one of the four along with air, fire, and water. Earth is one of the four classical elements in ancient Greek philosophy and science. It was commonly associated with qualities of heaviness, matter and the terrestrial world. Due to the hero cults, and chthonic underworld deities, the element of earth is also associated with the sensual aspects of both life and death in later occultism. Empedocles of Acragas (c. 495 – c.
Splitting fieldIn abstract algebra, a splitting field of a polynomial with coefficients in a field is the smallest field extension of that field over which the polynomial splits, i.e., decomposes into linear factors. A splitting field of a polynomial p(X) over a field K is a field extension L of K over which p factors into linear factors where and for each we have with ai not necessarily distinct and such that the roots ai generate L over K. The extension L is then an extension of minimal degree over K in which p splits.
Fire (classical element)Fire is one of the four classical elements along with earth, water and air in ancient Greek philosophy and science. Fire is considered to be both hot and dry and, according to Plato, is associated with the tetrahedron. Fire is one of the four classical elements in ancient Greek philosophy and science. It was commonly associated with the qualities of energy, assertiveness, and passion. In one Greek myth, Prometheus stole fire from the gods to protect the otherwise helpless humans, but was punished for this charity.
