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Degenerate
Degeneracy, degenerate, or degeneration may refer to: Arts and entertainment * ''Degenerate'' (album), a 2010 album by the British band Trigger the Bloodshed * Degenerate art, a term adopted in the 1920s by the Nazi Party in Germany to describe modern art ** Decadent movement, often associated with degeneracy * Dégénération, a single by Mylène Farmer * ''Degeneration'' (Nordau), an 1892 book by Max Nordau * '' Resident Evil: Degeneration'', a 2008 film * "Degenerate", a song by Blink-182 from the album ''Dude Ranch'' * "Degenerates", a song by A Day to Remember from the album '' You're Welcome'' Science, mathematics, and medicine Mathematics * Degeneracy (mathematics), a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class * Degeneracy (graph theory), a measure of the sparseness of a graph * Degeneration (algebraic geometry), the act of taking a limit of a family of varieties * Degenerate form, bilinear f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degenerate Conic
In geometry, a degenerate conic is a conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve. This means that the defining equation is factorable over the complex numbers (or more generally over an algebraically closed field) as the product of two linear polynomials.Some authors consider conics without real points as degenerate, but this is not a commonly accepted convention. Using the alternative definition of the conic as the intersection in three-dimensional space of a plane and a double cone, a conic is degenerate if the plane goes through the vertex of the cones. In the real plane, a degenerate conic can be two lines that may or may not be parallel, a single line (either two coinciding lines or the union of a line and the line at infinity), a single point (in fact, two complex conjugate lines), or the null set (twice the line at infinity or two parallel complex conjugate lines). All these degenerate conics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degenerate Matter
Degenerate matter is a highly dense state of fermionic matter in which the Pauli exclusion principle exerts significant pressure in addition to, or in lieu of, thermal pressure. The description applies to matter composed of electrons, protons, neutrons or other fermions. The term is mainly used in astrophysics to refer to dense stellar objects where gravitational pressure is so extreme that quantum mechanical effects are significant. This type of matter is naturally found in stars in their final evolutionary states, such as white dwarfs and neutron stars, where thermal pressure alone is not enough to avoid gravitational collapse. Degenerate matter is usually modelled as an ideal Fermi gas, an ensemble of non-interacting fermions. In a quantum mechanical description, particles limited to a finite volume may take only a discrete set of energies, called quantum states. The Pauli exclusion principle prevents identical fermions from occupying the same quantum state. At lowest total ener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degeneracy (mathematics)
In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class, and the term degeneracy is the condition of being a degenerate case. The definitions of many classes of composite or structured objects often implicitly include inequalities. For example, the angles and the side lengths of a triangle are supposed to be positive. The limiting cases, where one or several of these inequalities become equalities, are degeneracies. In the case of triangles, one has a ''degenerate triangle'' if at least one side length or angle is zero. Equivalently, it becomes a "line segment". Often, the degenerate cases are the exceptional cases where changes to the usual dimension or the cardinality of the object (or of some part of it) occur. For example, a triangle is an object of dimension two, and a degenerate triangle is contained in a line, which makes its dimension one. This is similar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degenerate Art
Degenerate art (german: Entartete Kunst was a term adopted in the 1920s by the Nazi Party in Germany to describe modern art. During the dictatorship of Adolf Hitler, German modernist art, including many works of internationally renowned artists, was removed from state-owned museums and banned in Nazi Germany on the grounds that such art was an "insult to German feeling", un-German, Freemasonic, Jewish, or Communist in nature. Those identified as degenerate artists were subjected to sanctions that included being dismissed from teaching positions, being forbidden to exhibit or to sell their art, and in some cases being forbidden to produce art. ''Degenerate Art'' also was the title of an exhibition, held by the Nazis in Munich in 1937, consisting of 650 modernist artworks chaotically hung and accompanied by text labels deriding the art. Designed to inflame public opinion against modernism, the exhibition subsequently traveled to several other cities in Germany and Austria. While m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degenerate Form
In mathematics, specifically linear algebra, a degenerate bilinear form on a vector space ''V'' is a bilinear form such that the map from ''V'' to ''V''∗ (the dual space of ''V'' ) given by is not an isomorphism. An equivalent definition when ''V'' is finite-dimensional is that it has a non-trivial kernel: there exist some non-zero ''x'' in ''V'' such that :f(x,y)=0\, for all \,y \in V. Nondegenerate forms A nondegenerate or nonsingular form is a bilinear form that is not degenerate, meaning that v \mapsto (x \mapsto f(x,v)) is an isomorphism, or equivalently in finite dimensions, if and only if :f(x,y)=0 for all y \in V implies that x = 0. The most important examples of nondegenerate forms are inner products and symplectic forms. Symmetric nondegenerate forms are important generalizations of inner products, in that often all that is required is that the map V \to V^* be an isomorphism, not positivity. For example, a manifold with an inner product structure on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degeneracy (graph Theory)
In graph theory, a ''k''-degenerate graph is an undirected graph in which every subgraph has a vertex of degree at most ''k'': that is, some vertex in the subgraph touches ''k'' or fewer of the subgraph's edges. The degeneracy of a graph is the smallest value of ''k'' for which it is ''k''-degenerate. The degeneracy of a graph is a measure of how sparse it is, and is within a constant factor of other sparsity measures such as the arboricity of a graph. Degeneracy is also known as the ''k''-core number, width, and linkage, and is essentially the same as the coloring number or Szekeres–Wilf number (named after ). ''k''-degenerate graphs have also been called ''k''-inductive graphs. The degeneracy of a graph may be computed in linear time by an algorithm that repeatedly removes minimum-degree vertices. The connected components that are left after all vertices of degree less than ''k'' have been (repeatedly) removed are called the ''k''-cores of the graph and the degeneracy of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degenerate Dimension
According to Ralph Kimball, in a data warehouse, a degenerate dimension is a dimension key in the fact table that does not have its own dimension table, because all the interesting attributes have been placed in analytic dimensions. The term "degenerate dimension" was originated by Ralph Kimball. As Bob Becker says: Other uses of the term Although most writers and practitioners use the term degenerate dimension correctly, it is very easy to find misleading definitions in online and printed sources. For example, the Oracle FAQ defines a degenerate dimension as a "data dimension that is stored in the fact table rather than a separate dimension table. This eliminates the need to join to a dimension table. You can use the data in the degenerate dimension to limit or 'slice and dice' your fact table measures." This common interpretation implies that it is good dimensional modeling practice to place dimension attributes in the fact table, as long as you call them a degenerate dimension. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Degeneration
Social degeneration was a widely influential concept at the interface of the social and biological sciences in the 18th and 19th centuries. During the 18th century, scientific thinkers including Georges-Louis Leclerc, Comte de Buffon, Johann Friedrich Blumenbach, and Immanuel Kant argued that humans shared a common origin but had degenerated over time due to differences in climate. This theory provided an explanation of where humans came from and why some people appeared differently from others. In contrast, degenerationists in the 19th century feared that civilization might be in decline and that the causes of decline lay in biological change. These ideas derived from pre-scientific concepts of heredity ("hereditary taint") with Lamarckian emphasis on biological development through purpose and habit. Degeneration concepts were often associated with authoritarian political attitudes, including militarism and scientific racism, and a preoccupation with eugenics. The theory origina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degenerate Distribution
In mathematics, a degenerate distribution is, according to some, a probability distribution in a space with support only on a manifold of lower dimension, and according to others a distribution with support only at a single point. By the latter definition, it is a deterministic distribution and takes only a single value. Examples include a two-headed coin and rolling a die whose sides all show the same number. This distribution satisfies the definition of "random variable" even though it does not appear random in the everyday sense of the word; hence it is considered degenerate. In the case of a real-valued random variable, the degenerate distribution is a one-point distribution, localized at a point ''k''0 on the real line. The probability mass function equals 1 at this point and 0 elsewhere. The degenerate univariate distribution can be viewed as the limiting case of a continuous distribution whose variance goes to 0 causing the probability density function to be a delta f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Codon Degeneracy
Degeneracy or redundancy of codons is the redundancy of the genetic code, exhibited as the multiplicity of three-base pair codon combinations that specify an amino acid. The degeneracy of the genetic code is what accounts for the existence of synonymous mutations. Background Degeneracy of the genetic code was identified by Lagerkvist. For instance, codons GAA and GAG both specify glutamic acid and exhibit redundancy; but, neither specifies any other amino acid and thus are not ambiguous or demonstrate no ambiguity. The codons encoding one amino acid may differ in any of their three positions; however, more often than not, this difference is in the second or third position. For instance, the amino acid glutamic acid is specified by GAA and GAG codons (difference in the third position); the amino acid leucine is specified by UUA, UUG, CUU, CUC, CUA, CUG codons (difference in the first or third position); and the amino acid serine is specified by UCA, UCG, UCC, UCU, AGU, AGC (differen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degenerate Semiconductor
A degenerate semiconductor is a semiconductor with such a high level of doping that the material starts to act more like a metal than as a semiconductor. Unlike non-degenerate semiconductors, these kind of semiconductor do not obey law of mass action, which relates intrinsic carrier concentration with temperature and bandgap. At moderate doping levels the dopant atoms create individual doping levels that can often be considered as localized states that can donate electrons or holes by thermal promotion (or an optical transition) to the conduction or valence bands respectively. At high enough impurity concentrations the individual impurity atoms may become close enough neighbors that their doping levels merge into an impurity band and the behavior of such a system ceases to show the typical traits of a semiconductor, e.g. its increase in conductivity with temperature. On the other hand, a degenerate semiconductor still has far fewer charge carriers than a true metal so that its be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degeneracy (biology)
Within biological systems, degeneracy occurs when structurally dissimilar components/modules/pathways can perform similar functions (i.e. are effectively interchangeable) under certain conditions, but perform distinct functions in other conditions. Degeneracy is thus a relational property that requires comparing the behavior of two or more components. In particular, if degeneracy is present in a pair of components, then there will exist conditions where the pair will appear functionally redundant but other conditions where they will appear functionally distinct. Note that this use of the term has practically no relevance to the questionably meaningful concept of evolutionarily degenerate populations that have lost ancestral functions. Biological examples Examples of degeneracy are found in the genetic code, when many different nucleotide sequences encode the same polypeptide; in protein folding, when different polypeptides fold to be structurally and functionally equivalent; in p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
