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Monogenic (other)
Monogenic may refer to: * Monogenic disorder, disease, inheritance, or trait, a single gene disorder resulting from a single mutated gene ** Monogenic diabetes, or maturity-onset diabetes of the young (MODY), forms of diabetes caused by mutations in an autosomal dominant gene ** Monogenic obesity * Monogenic field, in mathematics, an algebraic number field ''K'' * Monogenic function, a function in an algebra over a field * Monogenic polynomial, an alternate name for monic polynomial * Monogenic semigroup, in mathematics, a semigroup generated by a set containing only a single element * Monogenic signal, in the theory of analytic signals * Monogenic system, in classical mechanics, a physical system See also * Monogenous (other) Monogenous in mathematics may refer to: * A synonym for cyclic in ** ''monogenous group'', a synonym for cyclic group ** ''monogenous module'', a synonym for cyclic module In mathematics, more specifically in ring theory, a cyclic module o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Disorder
A genetic disorder is a health problem caused by one or more abnormalities in the genome. It can be caused by a mutation in a single gene (monogenic) or multiple genes (polygenic) or by a chromosome abnormality. Although polygenic disorders are the most common, the term is mostly used when discussing disorders with a single genetic cause, either in a gene or chromosome. The mutation responsible can occur spontaneously before embryonic development (a ''de novo'' mutation), or it can be inherited from two parents who are carriers of a faulty gene ( autosomal recessive inheritance) or from a parent with the disorder (autosomal dominant inheritance). When the genetic disorder is inherited from one or both parents, it is also classified as a hereditary disease. Some disorders are caused by a mutation on the X chromosome and have X-linked inheritance. Very few disorders are inherited on the Y chromosome or mitochondrial DNA (due to their size). There are well over 6,000 known ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monogenic Obesity
Monogenic obesity is excess weight caused by a mutation in a single gene, as opposed to syndromic obesity not tied to a single gene variation and most obesity, which is caused by multiple genetic and environmental risk factors. Monogenetic obesity mostly affects the hypothalamus and leptin–melanocortin system (see hypothalamic obesity). However, it accounts for less than 5 percent of severe obesity cases. Known mutations leading to monogenetic obesity include: *Leptin deficiency *Leptin receptor deficiency * Melanocortin-4 receptor (MC4R) *Proopiomelanocortin (POMC * Prohormone convertase 1/3 (PC1/3) *SIM1 Single-minded homolog 1, also known as class E basic helix-loop-helix protein 14 (bHLHe14), is a protein that in humans is encoded by the ''SIM1'' gene. Function The ''SIM1'' and ''SIM2'' genes are homologs of ''Drosophila melanogaster'' single-m ... * BDNF * NTRK2 References {{Genetic-disorder-stub Classification of obesity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monogenic Field
In mathematics, a monogenic field is an algebraic number field ''K'' for which there exists an element ''a'' such that the ring of integers ''O''''K'' is the subring Z 'a''of ''K'' generated by ''a''. Then ''O''''K'' is a quotient of the polynomial ring Z 'X''and the powers of ''a'' constitute a power integral basis. In a monogenic field ''K'', the field discriminant of ''K'' is equal to the discriminant of the minimal polynomial of α. Examples Examples of monogenic fields include: * Quadratic fields: : if K = \mathbf(\sqrt d) with d a square-free integer, then O_K = \mathbf /math> where a = (1+\sqrt d)/2 if ''d'' ≡ 1 (mod 4) and a = \sqrt d if ''d'' ≡ 2 or 3 (mod 4). * Cyclotomic fields: : if K = \mathbf(\zeta) with \zeta a root of unity, then O_K = \mathbfzeta Also the maximal real subfield \mathbf(\zeta)^ = \mathbf(\zeta + \zeta^) is monogenic, with ring of integers \mathbf zeta+\zeta^/math>. While all quadratic fields are monogenic, already among cubi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monogenic Function
A monogenic function is a complex function with a single finite derivative. More precisely, a function f(z) defined on A \subseteq \mathbb is called monogenic at \zeta \in A , if f'(\zeta) exists and is finite, with: f'(\zeta) = \lim_\frac Alternatively, it can be defined as the above limit having the same value for all paths. Functions can either have a single derivative (monogenic) or infinitely many derivatives (polygenic), with no intermediate cases. Furthermore, a function f(x) which is monogenic \forall \zeta \in B , is said to be monogenic on B , and if B is a domain of \mathbb, then it is analytic as well (The notion of domains can also be generalized in a manner such that functions which are monogenic over non-connected subsets of \mathbb , can show a weakened form of analyticity) The term monogenic was coined by Cauchy Baron Augustin-Louis Cauchy ( , , ; ; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monic Polynomial
In algebra, a monic polynomial is a non-zero univariate polynomial (that is, a polynomial in a single variable) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1. That is to say, a monic polynomial is one that can be written as :x^n+c_x^+\cdots+c_2x^2+c_1x+c_0, with n \geq 0. Uses Monic polynomials are widely used in algebra and number theory, since they produce many simplifications and they avoid divisions and denominators. Here are some examples. Every polynomial is associated to a unique monic polynomial. In particular, the unique factorization property of polynomials can be stated as: ''Every polynomial can be uniquely factorized as the product of its leading coefficient and a product of monic irreducible polynomials.'' Vieta's formulas are simpler in the case of monic polynomials: ''The th elementary symmetric function of the roots of a monic polynomial of degree equals (-1)^ic_, where c_ is the coefficient of the th po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monogenic Semigroup
In mathematics, a monogenic semigroup is a semigroup generated by a single element. Monogenic semigroups are also called cyclic semigroups. Structure The monogenic semigroup generated by the singleton set is denoted by \langle a \rangle. The set of elements of \langle a \rangle is . There are two possibilities for the monogenic semigroup * ''am'' = ''an'' ⇒ ''m'' = ''n''. * There exist ''m'' ≠ ''n'' such that ''am'' = ''an''. In the former case \langle a \rangle is isomorphic to the semigroup (, +) of natural numbers under addition. In such a case, \langle a \rangle is an ''infinite monogenic semigroup'' and the element ''a'' is said to have ''infinite order''. It is sometimes called the ''free monogenic semigroup'' because it is also a free semigroup with one generator. In the latter case let ''m'' be the smallest positive integer such that ''am'' = ''ax'' for some positive integer ''x'' ≠ ''m'', and let ''r'' be smallest positive integer such that ''am'' = ''a''''m' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Signal
In mathematics and signal processing, an analytic signal is a complex-valued function that has no negative frequency components. The real and imaginary parts of an analytic signal are real-valued functions related to each other by the Hilbert transform. The analytic representation of a real-valued function is an ''analytic signal'', comprising the original function and its Hilbert transform. This representation facilitates many mathematical manipulations. The basic idea is that the negative frequency components of the Fourier transform (or spectrum) of a real-valued function are superfluous, due to the Hermitian symmetry of such a spectrum. These negative frequency components can be discarded with no loss of information, provided one is willing to deal with a complex-valued function instead. That makes certain attributes of the function more accessible and facilitates the derivation of modulation and demodulation techniques, such as single-sideband. As long as the manip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monogenic System
In classical mechanics, a physical system is termed a monogenic system if the force acting on the system can be modelled in a particular, especially convenient mathematical form. The systems that are typically studied in physics are monogenic. The term was introduced by Cornelius Lanczos in his book ''The Variational Principles of Mechanics'' (1970). In Lagrangian mechanics, the property of being monogenic is a necessary condition for certain different formulations to be mathematically equivalent. If a physical system is both a holonomic system and a monogenic system, then it is possible to derive Lagrange's equations from d'Alembert's principle; it is also possible to derive Lagrange's equations from Hamilton's principle. Mathematical definition In a physical system, if all forces, with the exception of the constraint forces, are derivable from the generalized scalar potential, and this generalized scalar potential is a function of generalized coordinates, generalized velo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monogenous (other)
Monogenous in mathematics may refer to: * A synonym for cyclic in ** ''monogenous group'', a synonym for cyclic group ** ''monogenous module'', a synonym for cyclic module In mathematics, more specifically in ring theory, a cyclic module or monogenous module is a module over a ring that is generated by one element. The concept is a generalization of the notion of a cyclic group, that is, an Abelian group (i.e. Z ... See also * Monogenic (other) * Monogenetic (other) {{mathdab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monogenetic (other)
Monogenetic may refer to: * Monogenetic in biology, of or pertaining to monogenesis (Mendelian inheritance) * Monogenetic volcanic field in geology, a cluster of volcanoes that only erupted once * Monogenetic theory of pidgins in linguistics, a theory about the origin of creole languages See also * Monogenous (other) * Monogenic (other) Monogenic may refer to: * Monogenic disorder, disease, inheritance, or trait, a single gene disorder resulting from a single mutated gene ** Monogenic diabetes, or maturity-onset diabetes of the young (MODY), forms of diabetes caused by mutation ... * Monogenism (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
