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Spaces of test functions and distributions Summary Spaces_of_test_functions_and_distributions In mathematical analysis, the spaces of test functions and distributions are topological vector spaces (TVSs) that are used in the definition and application of distributions. Test functions are usually infinitely differentiab... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spaces of test functions and distributions Summary Spaces_of_test_functions_and_distributions There are other possible choices for the space of test functions, which lead to other different spaces of distributions. If U = R n {\displaystyle U=\mathbb {R} ^{n}} then the use of Schwartz functions as test functions gives ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spaces of test functions and distributions Summary Spaces_of_test_functions_and_distributions The set of tempered distributions forms a vector subspace of the space of distributions D ′ ( U ) {\displaystyle {\mathcal {D}}^{\prime }(U)} and is thus one example of a space of distributions; there are many other spaces of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Staircase paradox Summary Staircase_paradox In mathematical analysis, the staircase paradox is a pathological example showing that limits of curves do not necessarily preserve their length. It consists of a sequence of "staircase" polygonal chains in a unit square, formed from horizontal and vertical line segments of d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Staircase paradox Summary Staircase_paradox It shows that, for curves under uniform convergence, the length of a curve is not a continuous function of the curve.For any smooth curve, polygonal chains with segment lengths decreasing to zero, connecting consecutive vertices along the curve, always converge to the arc len... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chebyshev norm Summary Uniform_metric In mathematical analysis, the uniform norm (or sup norm) assigns to real- or complex-valued bounded functions f {\displaystyle f} defined on a set S {\displaystyle S} the non-negative number ‖ f ‖ ∞ = ‖ f ‖ ∞ , S = sup { | f ( s ) |: s ∈ S } . {\displaystyle \|f\|_{\infty }=\|f\|_{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chebyshev norm Summary Uniform_metric The name "uniform norm" derives from the fact that a sequence of functions { f n } {\displaystyle \left\{f_{n}\right\}} converges to f {\displaystyle f} under the metric derived from the uniform norm if and only if f n {\displaystyle f_{n}} converges to f {\displaystyle f} uniforml... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Universal chord theorem Summary Universal_chord_theorem In mathematical analysis, the universal chord theorem states that if a function f is continuous on and satisfies f ( a ) = f ( b ) {\displaystyle f(a)=f(b)} , then for every natural number n {\displaystyle n} , there exists some x ∈ {\displaystyle x\in } such th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multimedia Mathematical and scientific research Multi_Format_Publishing > Usage/application > Mathematical and scientific research In mathematical and scientific research, multimedia is mainly used for modeling and simulation. For example, a scientist can look at a molecular model of a particular substance and manipula... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multimedia Mathematical and scientific research Multi_Format_Publishing > Usage/application > Mathematical and scientific research One well known example of this being applied would be in the movie Interstellar where Executive Director Kip Thorne helped create one of the most realistic depictions of a blackhole in film... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Q-Pochhammer symbol Summary Q-Pochhammer_symbol In mathematical area of combinatorics, the q-Pochhammer symbol, also called the q-shifted factorial, is the product with ( a ; q ) 0 = 1. {\displaystyle (a;q)_{0}=1.} It is a q-analog of the Pochhammer symbol ( x ) n = x ( x + 1 ) … ( x + n − 1 ) {\displaystyle (x)_{n}=x(... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Community matrix Summary Community_matrix In mathematical biology, the community matrix is the linearization of a generalized Lotka–Volterra equation at an equilibrium point. The eigenvalues of the community matrix determine the stability of the equilibrium point. For example, the Lotka–Volterra predator–prey model is ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Community matrix Summary Community_matrix By the Hartman–Grobman theorem the non-linear system is topologically equivalent to a linearization of the system about an equilibrium point (x*, y*), which has the form = A , {\displaystyle {\begin{bmatrix}{\frac {du}{dt}}\\{\frac {dv}{dt}}\end{bmatrix}}=\mathbf {A} {\begin{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pauline van den Driessche Contributions Pauline_van_den_Driessche > Contributions In mathematical biology, van den Driessche's contributions include important work on delay differential equations and on Hopf bifurcations, and the effects of changing population size and immigration on epidemics.She has also done more fu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Transylvania lottery Summary Transylvania_lottery In mathematical combinatorics, the Transylvania lottery is a lottery where players selected three numbers from 1-14 for each ticket, and then three numbers are chosen randomly. A ticket wins if two of the numbers match the random ones. The problem asks how many tickets ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Transylvania lottery Summary Transylvania_lottery Each set of seven uses every line of a Fano plane, labelled with the numbers 1 to 7, and 8 to 14. At least two of the three randomly chosen numbers must be in one Fano plane set, and any two points on a Fano plane are on a line, so there will be a ticket in the collecti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Radó's theorem (Riemann surfaces) Summary Radó's_theorem_(Riemann_surfaces) In mathematical complex analysis, Radó's theorem, proved by Tibor Radó (1925), states that every connected Riemann surface is second-countable (has a countable base for its topology). The Prüfer surface is an example of a surface with no counta... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Schottky theorem Summary Schottky_theorem In mathematical complex analysis, Schottky's theorem, introduced by Schottky (1904) is a quantitative version of Picard's theorem. It states that for a holomorphic function f in the open unit disk that does not take the values 0 or 1, the value of |f(z)| can be bounded in terms... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quasiconformal map Summary Quasi-conformal_mapping In mathematical complex analysis, a quasiconformal mapping, introduced by Grötzsch (1928) and named by Ahlfors (1935), is a homeomorphism between plane domains which to first order takes small circles to small ellipses of bounded eccentricity. Intuitively, let f: D → D... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Geometric function theory Quasiconformal maps Geometric_function_theory > Topics in geometric function theory > Quasiconformal maps In mathematical complex analysis, a quasiconformal mapping, introduced by Grötzsch (1928) and named by Ahlfors (1935), is a homeomorphism between plane domains which to first order takes s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Universal Teichmüller space Summary Universal_Teichmüller_space In mathematical complex analysis, universal Teichmüller space T(1) is a Teichmüller space containing the Teichmüller space T(G) of every Fuchsian group G. It was introduced by Bers (1965) as the set of boundary values of quasiconformal maps of the upper ha... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kleinian integer Summary Kleinian_integer In mathematical cryptography, a Kleinian integer is a complex number of the form m + n 1 + − 7 2 {\displaystyle m+n{\frac {1+{\sqrt {-7}}}{2}}} , with m and n rational integers. They are named after Felix Klein. The Kleinian integers form a ring called the Kleinian ring, which ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Semi colon Mathematics Semi_colon > Mathematics In the calculus of relations, the semicolon is used in infix notation for the composition of relations: A ; B = { ( x , z ): ∃ y x A y ∧ y B z } . {\displaystyle A;B\ =\ \{(x,z):\exists y\ \ xAy\ \land \ yBz\}~.} The ; Humphrey point is sometimes used as the "decimal poin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Continuous-time signal Summary Continuous_time In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Topkis's Theorem Summary Topkis's_Theorem In mathematical economics, Topkis's theorem is a result that is useful for establishing comparative statics. The theorem allows researchers to understand how the optimal value for a choice variable changes when a feature of the environment changes. The result states that if f i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Isoelastic function Summary Isoelastic_function In mathematical economics, an isoelastic function, sometimes constant elasticity function, is a function that exhibits a constant elasticity, i.e. has a constant elasticity coefficient. The elasticity is the ratio of the percentage change in the dependent variable to the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Applied general equilibrium Summary Applied_general_equilibrium In mathematical economics, applied general equilibrium (AGE) models were pioneered by Herbert Scarf at Yale University in 1967, in two papers, and a follow-up book with Terje Hansen in 1973, with the aim of empirically estimating the Arrow–Debreu model of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Applied general equilibrium Summary Applied_general_equilibrium Scarf never built an AGE model, but hinted that “these novel numerical techniques might be useful in assessing consequences for the economy of a change in the economic environment” (Kehoe et al. 2005, citing Scarf 1967b). His students elaborated the Scarf ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Applied general equilibrium Summary Applied_general_equilibrium Earlier analytic work with these models has examined the distortionary effects of taxes, tariffs, and other policies, along with functional incidence questions. More recent applied models, including those discussed here, provide numerical estimates of effi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Applied general equilibrium Summary Applied_general_equilibrium Scarf's fixed-point method was a break-through in the mathematics of computation generally, and specifically in optimization and computational economics. Later researchers continued to develop iterative methods for computing fixed-points, both for topologi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Arrow–Debreu model Summary Arrow–Debreu_model In mathematical economics, the Arrow–Debreu model is a theoretical general equilibrium model. It posits that under certain economic assumptions (convex preferences, perfect competition, and demand independence) there must be a set of prices such that aggregate supplies will... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Arrow–Debreu model Summary Arrow–Debreu_model In general, there may be many equilibria. Arrow (1972) and Debreu (1983) were separately awarded the Nobel Prize in Economics for their development of the model. McKenzie however was not awarded. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Solomon Mikhlin Elasticity theory and boundary value problems Solomon_Mikhlin > Work > Research activity > Elasticity theory and boundary value problems In mathematical elasticity theory, Mikhlin was concerned by three themes: the plane problem (mainly from 1932 to 1935), the theory of shells (from 1954) and the Cosser... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Solomon Mikhlin Elasticity theory and boundary value problems Solomon_Mikhlin > Work > Research activity > Elasticity theory and boundary value problems Mikhlin studied its convergence and gave applications to special applied problems. He proved existence theorems for the fundamental problems of plane elasticity involv... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Solomon Mikhlin Elasticity theory and boundary value problems Solomon_Mikhlin > Work > Research activity > Elasticity theory and boundary value problems He studied the error of the approximate solution for shells, similar to plane plates, and found out that this error is small for the so-called purely rotational state ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Solomon Mikhlin Elasticity theory and boundary value problems Solomon_Mikhlin > Work > Research activity > Elasticity theory and boundary value problems Mikhlin studied also the spectrum of the operator pencil of the classical linear elastostatic operator or Navier–Cauchy operator A ( ω ) u = Δ 2 u + ω ∇ ( ∇ ⋅ u ) {\di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Corner angle Identifying angles Reflex_angle > Identifying angles In mathematical expressions, it is common to use Greek letters (α, β, γ, θ, φ, . . . ) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Corner angle Identifying angles Reflex_angle > Identifying angles as variables denoting the size of some angle (to avoid confusion with its other meaning, the symbol π is typically not used for this purpose). Lower case Roman letters (a, b, c, . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Corner angle Identifying angles Reflex_angle > Identifying angles . ) are also used. In contexts where this is not confusing, an angle may be denoted by the upper case Roman letter denoting its vertex. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Corner angle Identifying angles Reflex_angle > Identifying angles See the figures in this article for examples. The three defining points may also identify angles in geometric figures. For example, the angle with vertex A formed by the rays AB and AC (that is, the half-lines from point A through points B and C) is deno... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Corner angle Identifying angles Reflex_angle > Identifying angles Where there is no risk of confusion, the angle may sometimes be referred to by a single vertex alone (in this case, "angle A"). Potentially, an angle denoted as, say, ∠BAC might refer to any of four angles: the clockwise angle from B to C about A, the an... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Littlewood–Offord problem Summary Littlewood–Offord_problem In mathematical field of combinatorial geometry, the Littlewood–Offord problem is the problem of determining the number of subsums of a set of vectors that fall in a given convex set. More formally, if V is a vector space of dimension d, the problem is to dete... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Littlewood–Offord problem Summary Littlewood–Offord_problem This bound is sharp; equality is attained when all vectors in S are equal. In 1966, Kleitman showed that the same bound held for complex numbers. In 1970, he extended this to the setting when V is a normed space.Suppose S = {v1, …, vn}. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Littlewood–Offord problem Summary Littlewood–Offord_problem By subtracting 1 2 ∑ i = 1 n v i {\displaystyle {\frac {1}{2}}\sum _{i=1}^{n}v_{i}} from each possible subsum (that is, by changing the origin and then scaling by a factor of 2), the Littlewood–Offord problem is equivalent to the problem of determining the num... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pseudoreal representation Summary Pseudoreal_representation In mathematical field of representation theory, a quaternionic representation is a representation on a complex vector space V with an invariant quaternionic structure, i.e., an antilinear equivariant map j: V → V {\displaystyle j\colon V\to V} which satisfies ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pseudoreal representation Summary Pseudoreal_representation From this point of view, quaternionic representation of a group G is a group homomorphism φ: G → GL(V, H), the group of invertible quaternion-linear transformations of V. In particular, a quaternionic matrix representation of g assigns a square matrix of quate... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Symplectic representation Summary Symplectic_representation In mathematical field of representation theory, a symplectic representation is a representation of a group or a Lie algebra on a symplectic vector space (V, ω) which preserves the symplectic form ω. Here ω is a nondegenerate skew symmetric bilinear form ω: V ×... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Smoluchowski equation Particular cases with known solution and inversion Smoluchowski_equation > Particular cases with known solution and inversion In mathematical finance for volatility smile modeling of options via local volatility, one has the problem of deriving a diffusion coefficient σ ( X t , t ) {\displaystyle ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Margrabe's formula Summary Margrabe's_formula In mathematical finance, Margrabe's formula is an option pricing formula applicable to an option to exchange one risky asset for another risky asset at maturity. It was derived by William Margrabe (PhD Chicago) in 1978. Margrabe's paper has been cited by over 2000 subsequen... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Monte Carlo option model Summary Monte_Carlo_methods_for_option_pricing In mathematical finance, a Monte Carlo option model uses Monte Carlo methods to calculate the value of an option with multiple sources of uncertainty or with complicated features. The first application to option pricing was by Phelim Boyle in 1977 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Replicating portfolio Summary Replicating_portfolio In mathematical finance, a replicating portfolio for a given asset or series of cash flows is a portfolio of assets with the same properties (especially cash flows). This is meant in two distinct senses: static replication, where the portfolio has the same cash flows ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Replicating portfolio Summary Replicating_portfolio The notion of a replicating portfolio is fundamental to rational pricing, which assumes that market prices are arbitrage-free – concretely, arbitrage opportunities are exploited by constructing a replicating portfolio. In practice, replicating portfolios are seldom, i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Equivalent Martingale Measure Summary Martingale_measure In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure. This i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Convexity (finance) Summary Convexity_correction In mathematical finance, convexity refers to non-linearities in a financial model. In other words, if the price of an underlying variable changes, the price of an output does not change linearly, but depends on the second derivative (or, loosely speaking, higher-order te... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kelly criterion Application to the stock market Kelly_criterion > Application to the stock market In mathematical finance, if security weights maximize the expected geometric growth rate (which is equivalent to maximizing log wealth), then a portfolio is growth optimal. Computations of growth optimal portfolios can suf... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kelly criterion Application to the stock market Kelly_criterion > Application to the stock market If portfolio weights are largely a function of estimation errors, then Ex-post performance of a growth-optimal portfolio may differ fantastically from the ex-ante prediction. Parameter uncertainty and estimation errors are... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Black-Scholes equation Summary Black–Scholes_equation In mathematical finance, the Black–Scholes equation is a partial differential equation (PDE) governing the price evolution of a European call or European put under the Black–Scholes model. Broadly speaking, the term may refer to a similar PDE that can be derived for... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Constant elasticity of variance model Summary Constant_elasticity_of_variance_model In mathematical finance, the CEV or constant elasticity of variance model is a stochastic volatility model that attempts to capture stochastic volatility and the leverage effect. The model is widely used by practitioners in the financia... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cox–Ingersoll–Ross model Summary CIR_process In mathematical finance, the Cox–Ingersoll–Ross (CIR) model describes the evolution of interest rates. It is a type of "one factor model" (short-rate model) as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Doob decomposition theorem Application Doob_decomposition_theorem > Application In mathematical finance, the Doob decomposition theorem can be used to determine the largest optimal exercise time of an American option. Let X = (X0, X1, . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Doob decomposition theorem Application Doob_decomposition_theorem > Application , XN) denote the non-negative, discounted payoffs of an American option in a N-period financial market model, adapted to a filtration (F0, F1, . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Doob decomposition theorem Application Doob_decomposition_theorem > Application , FN), and let Q {\displaystyle \mathbb {Q} } denote an equivalent martingale measure. Let U = (U0, U1, . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Doob decomposition theorem Application Doob_decomposition_theorem > Application . , UN) denote the Snell envelope of X with respect to Q {\displaystyle \mathbb {Q} } . The Snell envelope is the smallest Q {\displaystyle \mathbb {Q} } -supermartingale dominating X and in a complete financial market it represents the min... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Doob decomposition theorem Application Doob_decomposition_theorem > Application Let U = M + A denote the Doob decomposition with respect to Q {\displaystyle \mathbb {Q} } of the Snell envelope U into a martingale M = (M0, M1, . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Doob decomposition theorem Application Doob_decomposition_theorem > Application , MN) and a decreasing predictable process A = (A0, A1, . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Doob decomposition theorem Application Doob_decomposition_theorem > Application , AN) with A0 = 0. Then the largest stopping time to exercise the American option in an optimal way is τ max := { N if A N = 0 , min { n ∈ { 0 , … , N − 1 } ∣ A n + 1 < 0 } if A N < 0. {\displaystyle \tau _{\text{max}}:={\begin{cases}N&{\te... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Doob decomposition theorem Application Doob_decomposition_theorem > Application . . , N − 1}, hence τmax is indeed a stopping time. It gives the last moment before the discounted value of the American option will drop in expectation; up to time τmax the discounted value process U is a martingale with respect to Q {\dis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Option delta Summary Greeks_(finance) In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
SABR volatility model Summary SABR_volatility_model In mathematical finance, the SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for "stochastic alpha, beta, rho", referring to the parameters of the model. The SABR model is widely used ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Local volatility Formulation Local_volatility > Formulation In mathematical finance, the asset St that underlies a financial derivative is typically assumed to follow a stochastic differential equation of the form d S t = ( r t − d t ) S t d t + σ t S t d W t {\displaystyle dS_{t}=(r_{t}-d_{t})S_{t}\,dt+\sigma _{t}S_{t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Local volatility Formulation Local_volatility > Formulation And when such volatility is merely a function of the current underlying asset level St and of time t, we have a local volatility model. The local volatility model is a useful simplification of the stochastic volatility model. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Local volatility Formulation Local_volatility > Formulation "Local volatility" is thus a term used in quantitative finance to denote the set of diffusion coefficients, σ t = σ ( S t , t ) {\displaystyle \sigma _{t}=\sigma (S_{t},t)} , that are consistent with market prices for all options on a given underlying, yieldin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stochastic volatility jump Summary Stochastic_volatility_jump In mathematical finance, the stochastic volatility jump (SVJ) model is suggested by Bates. This model fits the observed implied volatility surface well. The model is a Heston process for stochastic volatility with an added Merton log-normal jump. It assumes ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
No such thing as a free lunch Finance No_such_thing_as_a_free_lunch > History and usage > Meanings > Finance In mathematical finance, the term is also used as an informal synonym for the principle of no-arbitrage. This principle states that a combination of securities that has the same cash-flows as another security mu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Volatility risk premium Summary Volatility_risk_premium In mathematical finance, the volatility risk premium is a measure of the extra amount investors demand in order to hold a volatile security, above what can be computed based on expected returns. It can be defined as the compensation for inherent volatility risk di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thompson uniqueness theorem Summary Thompson_uniqueness_theorem In mathematical finite group theory, Thompson's original uniqueness theorem (Feit & Thompson 1963, theorems 24.5 and 25.2) states that in a minimal simple finite group of odd order there is a unique maximal subgroup containing a given elementary abelian su... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thompson factorization Summary Thompson_factorization In mathematical finite group theory, a Thompson factorization, introduced by Thompson (1966), is an expression of some finite groups as a product of two subgroups, usually normalizers or centralizers of p-subgroups for some prime p. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Aschbacher block Summary Aschbacher_block In mathematical finite group theory, a block, sometimes called Aschbacher block, is a subgroup giving an obstruction to Thompson factorization and pushing up. Blocks were introduced by Michael Aschbacher. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Groups of GF(2) type Summary Groups_of_GF(2)_type In mathematical finite group theory, a group of GF(2)-type is a group with an involution centralizer whose generalized Fitting subgroup is a group of symplectic type (Gorenstein 1982, definition 1.45). As the name suggests, many of the groups of Lie type over the field ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Groups of GF(2) type Summary Groups_of_GF(2)_type The groups of each of these 8 types were classified by various authors. They consist mainly of groups of Lie type with all roots of the same length over the field with 2 elements, but also include many exceptional cases, including the majority of the sporadic simple gro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Group of symplectic type Summary Group_of_symplectic_type In mathematical finite group theory, a p-group of symplectic type is a p-group such that all characteristic abelian subgroups are cyclic. According to Thompson (1968, p.386), the p-groups of symplectic type were classified by P. Hall in unpublished lecture notes... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quadratic pair Summary Quadratic_pair In mathematical finite group theory, a quadratic pair for the odd prime p, introduced by Thompson (1971), is a finite group G together with a quadratic module, a faithful representation M on a vector space over the finite field with p elements such that G is generated by elements w... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Rank 3 permutation group Summary Rank_3_permutation_group In mathematical finite group theory, a rank 3 permutation group acts transitively on a set such that the stabilizer of a point has 3 orbits. The study of these groups was started by Higman (1964, 1971). Several of the sporadic simple groups were discovered as ra... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
N-group (finite group theory) Summary N-group_(finite_group_theory) In mathematical finite group theory, an N-group is a group all of whose local subgroups (that is, the normalizers of nontrivial p-subgroups) are solvable groups. The non-solvable ones were classified by Thompson during his work on finding all the minim... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Exceptional character Summary Exceptional_character In mathematical finite group theory, an exceptional character of a group is a character related in a certain way to a character of a subgroup. They were introduced by Suzuki (1955, p. 663), based on ideas due to Brauer in (Brauer & Nesbitt 1941). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Baer–Suzuki theorem Summary Baer–Suzuki_theorem In mathematical finite group theory, the Baer–Suzuki theorem, proved by Baer (1957) and Suzuki (1965), states that if any two elements of a conjugacy class C of a finite group generate a nilpotent subgroup, then all elements of the conjugacy class C are contained in a nil... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Brauer–Fowler theorem Summary Brauer–Fowler_theorem In mathematical finite group theory, the Brauer–Fowler theorem, proved by Brauer & Fowler (1955), states that if a group G has even order g > 2 then it has a proper subgroup of order greater than g1/3. The technique of the proof is to count involutions (elements of or... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dade isometry Summary Dade_isometry In mathematical finite group theory, the Dade isometry is an isometry from class function on a subgroup H with support on a subset K of H to class functions on a group G (Collins 1990, 6.1). It was introduced by Dade (1964) as a generalization and simplification of an isometry used b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dempwolff group Summary Dempwolff_group In mathematical finite group theory, the Dempwolff group is a finite group of order 319979520 = 215·32·5·7·31, that is the unique nonsplit extension 2 5 . G L 5 ( F 2 ) {\displaystyle 2^{5\,. }\mathrm {GL} _{5}(\mathbb {F} _{2})} of G L 5 ( F 2 ) {\displaystyle \mathrm {GL} _{5}(... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dempwolff group Summary Dempwolff_group Huppert (1967, p.124) showed that any extension of G L n ( F q ) {\displaystyle \mathrm {GL} _{n}(\mathbb {F} _{q})} by its natural module F q n {\displaystyle \mathbb {F} _{q}^{n}} splits if q > 2 {\displaystyle q>2} , and Dempwolff (1973) showed that it also splits if n {\displ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dempwolff group Summary Dempwolff_group G L 3 ( F 2 ) {\displaystyle 2^{3\,. }\mathrm {GL} _{3}(\mathbb {F} _{2})} is a maximal subgroup of the Chevalley group G 2 ( F 3 ) {\displaystyle G_{2}(\mathbb {F} _{3})} . The nonsplit extension 2 4 . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dempwolff group Summary Dempwolff_group G L 4 ( F 2 ) {\displaystyle 2^{4\,. }\mathrm {GL} _{4}(\mathbb {F} _{2})} is a maximal subgroup of the sporadic Conway group Co3. The nonsplit extension 2 5 . G L 5 ( F 2 ) {\displaystyle 2^{5\,. }\mathrm {GL} _{5}(\mathbb {F} _{2})} is a maximal subgroup of the Thompson sporadi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gorenstein–Harada theorem Summary Gorenstein–Harada_theorem In mathematical finite group theory, the Gorenstein–Harada theorem, proved by Gorenstein and Harada (1973, 1974) in a 464-page paper, classifies the simple finite groups of sectional 2-rank at most 4. It is part of the classification of finite simple groups.Fi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
L-balance theorem Summary L-balance_theorem In mathematical finite group theory, the L-balance theorem was proved by Gorenstein & Walter (1975). The letter L stands for the layer of a group, and "balance" refers to the property discussed below. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Puig subgroup Summary Puig_subgroup In mathematical finite group theory, the Puig subgroup, introduced by Puig (1976), is a characteristic subgroup of a p-group analogous to the Thompson subgroup. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thompson order formula Summary Thompson_order_formula In mathematical finite group theory, the Thompson order formula, introduced by John Griggs Thompson (Held 1969, p.279), gives a formula for the order of a finite group in terms of the centralizers of involutions, extending the results of Brauer & Fowler (1955). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thompson subgroup Summary Thompson_subgroup In mathematical finite group theory, the Thompson subgroup J ( P ) {\displaystyle J(P)} of a finite p-group P refers to one of several characteristic subgroups of P. John G. Thompson (1964) originally defined J ( P ) {\displaystyle J(P)} to be the subgroup generated by the ab... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thompson transitivity theorem Summary Thompson_transitivity_theorem In mathematical finite group theory, the Thompson transitivity theorem gives conditions under which the centralizer of an abelian subgroup A acts transitively on certain subgroups normalized by A. It originated in the proof of the odd order theorem by ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Classical involution theorem Summary Classical_involution_theorem In mathematical finite group theory, the classical involution theorem of Aschbacher (1977a, 1977b, 1980) classifies simple groups with a classical involution and satisfying some other conditions, showing that they are mostly groups of Lie type over a fie... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Regular p-group Summary Regular_p-group In mathematical finite group theory, the concept of regular p-group captures some of the more important properties of abelian p-groups, but is general enough to include most "small" p-groups. Regular p-groups were introduced by Phillip Hall (1934). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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