Removable singularityIn complex analysis, a removable singularity of a holomorphic function is a point at which the function is undefined, but it is possible to redefine the function at that point in such a way that the resulting function is regular in a neighbourhood of that point. For instance, the (unnormalized) sinc function, as defined by has a singularity at z = 0. This singularity can be removed by defining which is the limit of sinc as z tends to 0. The resulting function is holomorphic.
Diffraction from slitsDiffraction processes affecting waves are amenable to quantitative description and analysis. Such treatments are applied to a wave passing through one or more slits whose width is specified as a proportion of the wavelength. Numerical approximations may be used, including the Fresnel and Fraunhofer approximations. Because diffraction is the result of addition of all waves (of given wavelength) along all unobstructed paths, the usual procedure is to consider the contribution of an infinitesimally small neighborhood around a certain path (this contribution is usually called a wavelet) and then integrate over all paths (= add all wavelets) from the source to the detector (or given point on a screen).
Astronomical objectAn astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists within the observable universe. In astronomy, the terms object and body are often used interchangeably. However, an astronomical body or celestial body is a single, tightly bound, contiguous entity, while an astronomical or celestial object is a complex, less cohesively bound structure, which may consist of multiple bodies or even other objects with substructures.
Linear complex structureIn mathematics, a complex structure on a real vector space V is an automorphism of V that squares to the minus identity, −I. Such a structure on V allows one to define multiplication by complex scalars in a canonical fashion so as to regard V as a complex vector space. Every complex vector space can be equipped with a compatible complex structure, however, there is in general no canonical such structure. Complex structures have applications in representation theory as well as in complex geometry where they play an essential role in the definition of almost complex manifolds, by contrast to complex manifolds.
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.
Scattered discThe scattered disc (or scattered disk) is a distant circumstellar disc in the Solar System that is sparsely populated by icy small Solar System bodies, which are a subset of the broader family of trans-Neptunian objects. The scattered-disc objects (SDOs) have orbital eccentricities ranging as high as 0.8, inclinations as high as 40°, and perihelia greater than . These extreme orbits are thought to be the result of gravitational "scattering" by the gas giants, and the objects continue to be subject to perturbation by the planet Neptune.
Gravitational singularityA gravitational singularity, spacetime singularity or simply singularity is a condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by definition no longer part of the regular spacetime and cannot be determined by "where" or "when". Gravitational singularities exist at a junction between general relativity and quantum mechanics; therefore, the properties of the singularity cannot be described without an established theory of quantum gravity.
Support (mathematics)In mathematics, the support of a real-valued function is the subset of the function domain containing the elements which are not mapped to zero. If the domain of is a topological space, then the support of is instead defined as the smallest closed set containing all points not mapped to zero. This concept is used very widely in mathematical analysis. Suppose that is a real-valued function whose domain is an arbitrary set The of written is the set of points in where is non-zero: The support of is the smallest subset of with the property that is zero on the subset's complement.
Conformal field theoryA conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum statistical mechanics, and string theory. Statistical and condensed matter systems are indeed often conformally invariant at their thermodynamic or quantum critical points.
Topological defectTopological defects or solitons are irregularities or disruptions that occur within continuous fields or ordered states of matter. These defects, which can take various forms such as points, lines, or surfaces, are characterized by their stability and the fact that they cannot be 'smoothed out' or removed through continuous transformations of the field or material. They play a significant role in various areas of physics, including condensed matter physics, cosmology, and quantum field theory, and can have profound effects on the properties and behavior of the systems in which they occur.
