Fractional Fourier transformIn mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the n-th power, where n need not be an integer — thus, it can transform a function to any intermediate domain between time and frequency. Its applications range from filter design and signal analysis to phase retrieval and pattern recognition.
DamA dam is a barrier that stops or restricts the flow of surface water or underground streams. Reservoirs created by dams not only suppress floods but also provide water for activities such as irrigation, human consumption, industrial use, aquaculture, and navigability. Hydropower is often used in conjunction with dams to generate electricity. A dam can also be used to collect or store water which can be evenly distributed between locations.
Jacobian varietyIn mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles. It is the connected component of the identity in the Picard group of C, hence an abelian variety. The Jacobian variety is named after Carl Gustav Jacobi, who proved the complete version of the Abel–Jacobi theorem, making the injectivity statement of Niels Abel into an isomorphism. It is a principally polarized abelian variety, of dimension g, and hence, over the complex numbers, it is a complex torus.
Non-Euclidean geometryIn mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries.
Kodaira embedding theoremIn mathematics, the Kodaira embedding theorem characterises non-singular projective varieties, over the complex numbers, amongst compact Kähler manifolds. In effect it says precisely which complex manifolds are defined by homogeneous polynomials. Kunihiko Kodaira's result is that for a compact Kähler manifold M, with a Hodge metric, meaning that the cohomology class in degree 2 defined by the Kähler form ω is an integral cohomology class, there is a complex-analytic embedding of M into complex projective space of some high enough dimension N.
RS-232In telecommunications, RS-232 or Recommended Standard 232 is a standard originally introduced in 1960 for serial communication transmission of data. It formally defines signals connecting between a DTE (data terminal equipment) such as a computer terminal, and a DCE (data circuit-terminating equipment or data communication equipment), such as a modem. The standard defines the electrical characteristics and timing of signals, the meaning of signals, and the physical size and pinout of connectors.
Canonical bundleIn mathematics, the canonical bundle of a non-singular algebraic variety of dimension over a field is the line bundle , which is the nth exterior power of the cotangent bundle on . Over the complex numbers, it is the determinant bundle of the holomorphic cotangent bundle . Equivalently, it is the line bundle of holomorphic n-forms on . This is the dualising object for Serre duality on . It may equally well be considered as an invertible sheaf.
Euclidean geometryEuclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.
Embankment damAn embankment dam is a large artificial dam. It is typically created by the placement and compaction of a complex semi-plastic mound of various compositions of soil or rock. It has a semi-pervious waterproof natural covering for its surface and a dense, impervious core. This makes the dam impervious to surface or seepage erosion. Such a dam is composed of fragmented independent material particles. The friction and interaction of particles binds the particles together into a stable mass rather than by the use of a cementing substance.
Elliptic geometryElliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Because of this, the elliptic geometry described in this article is sometimes referred to as single elliptic geometry whereas spherical geometry is sometimes referred to as double elliptic geometry.
Differential geometryDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky.
Smooth morphismIn algebraic geometry, a morphism between schemes is said to be smooth if (i) it is locally of finite presentation (ii) it is flat, and (iii) for every geometric point the fiber is regular. (iii) means that each geometric fiber of f is a nonsingular variety (if it is separated). Thus, intuitively speaking, a smooth morphism gives a flat family of nonsingular varieties. If S is the spectrum of an algebraically closed field and f is of finite type, then one recovers the definition of a nonsingular variety.
