Wikipedia talk:WikiProject Mathematics/equivlist
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This is a list of all articles returned by this Google search. For each line, please check if the article contains "\equiv" in the meaning of "definition". If so, replace these occurrences with "=" and clarify in text that it is a definition. When done, delete the line from this list and add in the edit summary what you did and if it still contains correctly used instances of "\equiv". (Multiple entries seem to result from redirect pages - just delete all of them.)
In most cases, 
("\equiv") can be replaced with 
("\ \stackrel{\mathrm{def}}{=}\ ") where it is used for a definition.
This page was created 09:21, 22 October 2006. Some instances may have been removed since.
Contents |
[edit] A
- Action-angle coordinates: J_{k} \equiv \oint p_{k} dq_{k}. where the integration is over all possible values of qk, given the energy ... \Delta w_{k} \equiv \oint \frac{\partial w_ ...
- Anonymous recursion: where g (g) (n - 1) \equiv g (g, n . Note that the variation consists of defining \bar g in terms of g(g,n − 1) instead of in terms of g(n − 1,g). ...
- Arrhenius equation: E_a \equiv -R \left( \frac{\partial ~ln. This results in an Ea that is in principle a function of T (since the Arrhenius equation is not exact) but in ...
- Associative algebra: Equality would hold if the product xy were antisymmetric (if the product were the Lie bracket, that is, xy \equiv M(x,y) = [x,y] ), thus turning the ...
- Atkinson resistance: 1 \mbox{ gaul} \equiv 1 \mbox{ atkinson} \times. where g is the standard acceleration of gravity (metres per second squared). ...
- Axial multipole moments: where the axial multipole moments M_{k} \equiv q a^{k} contain everything ... where the interior axial multipole moments I_{k} \equiv \frac{q}{a^{k contain ...
[edit] B
- Behrens-Fisher problem: \tau \equiv {\bar x_1 - \bar x_2 \over \sqrt. where \bar x_1 and \bar x_2 are the two sample means, and s1 and s2 are their standard deviations. ...
- Bertrand's theorem: The next step is to consider the equation for u under small perturbations \eta \equiv u - u_{0} from perfectly circular orbits. On the right-hand side, ...
- BF model: \mathbf{F}\equiv d\mathbf{A}+\mathbf. This action is diffeomorphically invariant and gauge invariant. Its Euler-Lagrange equations are ...
- Black-Scholes: X \equiv \ln(S/S_0) \,. is a normal random variable with mean μT and variance σ2T. It follows that the mean of S is. E(S) = S_0 e^{rT} \, ...
- Branching quantifier: (Q_Lx)(\phi x,\psi x)\equiv Card(. Härtig: "The φs are equinumerous with the ψs". (Q_Ix)(\phi x,\psi x)\equiv (Q_Lx. Chang: "The number of φs is ...
- Brunt-Väisälä frequency: N \equiv \sqrt{\frac{g}{\theta}\ , where θ is potential temperature, g is the local acceleration of gravity, and z is geometric height. ...
[edit] C
- Calculus of constructions: However, this one operator is sufficient to define all the other logical operators:. \begin{matrix} A \Rightarrow B & \equiv & \forall x ...
- Calculus of variations: The preceding reasoning is not valid if σ vanishes identically on C. In such a case, we could allow a trial function \varphi \equiv c , where c is a ...
- Comoving distance: d_p \equiv \chi(z) = {c \over H_0} \. where c is the speed of light and H0 is the Hubble constant. By using sin and sinh functions, proper motion distance ...
- Conditional quantum entropy: By analogy with the classical conditional entropy, one defines the conditional quantum entropy as S(\rho|\sigma) \equiv S(\rho,\ . ...
- Confirmation holism: \sim O \equiv \sim \left( p_1 \wedge p_2 \wedge. which is by De Morgan's law equivalent to ... T \equiv \left( h_1 \wedge h_2 \wedge h_3 \cdots \ ...
- Conformal symmetry: M_{\mu\nu}\equiv-i(x_\mu\ , P_\mu\equiv-i\partial_\mu. D\equiv-x_\mu\partial^\mu , K_\mu\equiv-{i\over2}(x^2\. Where Mμν are the Lorentz generators, ...
- Current (mathematics): \Lambda_c^0(\mathbb{R}^n)\equiv C. so that the following defines a 0-current:. T(f) = f(0).\,. In particular every signed measure μ with finite mass is a ...
- Curry's paradox: X \equiv \left\{ x | ( x \in x ) \. The proof proceeds:. \begin{matrix} \mbox{1.} & ( X \in. Again a particular case of this paradox is when Y is in fact a ...
[edit] D
- Divide-and-conquer eigenvalue algorithm: f(\lambda) \equiv 1 + \sum_{j=1}. The problem has therefore been reduced to finding the roots of a rational function f(λ). This equation is known as the ...
[edit] E
- Epigram (programming language): \mathsf{NatInd}\ P\ mz\ ms\ zero \equiv mz. \mathsf{NatInd}\ P\ mz\ ms\ (\mathsf{ ...And in ASCII: NatInd : all P : Nat -> * => P zero -> (all n : Nat ...
- Event calculus: Clipped(t_1,f,t) \equiv \exists a,t [ ... Happens(a,t) \equiv (a=open \wedge t=. Circumscription can simplify this specification, as only necessary ...
[edit] F
- Frequency mixer: \sin(A) \cdot \sin(B) \equiv \frac. We get:. v_1 \cdot v_2 = \frac{A_1 A_2}{2}\left. So, you can see the sum ( f_1 + f_2\, ) and difference ( f_1 - f_2\, ...
- Used for an identity
- Friedmann equations: H^2 \equiv \left(\frac{\dot{a}. 3\frac{\ddot{a}}{a} = \Lambda ... \Omega \equiv \frac{\rho}{\rho_c} = \. This term originally was used as a means to ...
[edit] I
- Interaction information: I(\mathcal{V})\equiv -\sum_{\mathcal. which is an alternating (inclusion-exclusion) sum over all subsets \mathcal{T}\subseteq \mathcal{V} , where \left\vert ...
[edit] M
- Magnetic resonance imaging: {\vec k}(t) \equiv \int_0^t {\. In other words, as time progresses the signal traces out a trajectory in k-space with the velocity vector of the trajectory ...
- Modal companion: ... of the classical logic (CPC) is Lewis' S5, whereas its largest modal companion is the logic. \mathbf{Triv}=\mathbf K+A\equiv\Box A. More examples: ...
[edit] N
- Numerical aperture: \mathrm{NA} \equiv \sqrt{n_o^2 - n_c^ ,. where no is the refractive index along the central axis of the fiber. Note that when this definition is used, ...
- Nyquist rate: f_N \equiv 2 B\,. where B\, is the highest frequency component contained in the signal. To avoid aliasing, the sampling rate must exceed the Nyquist rate: ...
- Nyquist–Shannon sampling theorem: x[n] \equiv x(nT), \quad n\in (integers). The sampling theorem leads to a ... x[n] \equiv x(nT) = \cos(\pi. are in every case just alternating –1 and +1, ...
[edit] O
- Ordered exponential: ... where t is the "time parameter", the ordered exponential OE[A](t):\equiv \left(e^{ of A can be defined via one of several equivalent approaches: ...
[edit] P
- Poisson random measure: If \mu\equiv 0 then N\equiv 0 satisfies the conditions i)-iii). Otherwise, in the case of finite measure μ given Z - Poisson random variable with rate μ(E) ...
- Pontryagin's minimum principle: When the final time tf is fixed and the Hamiltonian does not depend explicitly on time ( \frac{\partial H}{\partial t} \equiv 0 ), then:. H(x^*(t),u^*(t), ...
[edit] Q
- Quasi-invariant measure: ... measure on E that is quasi-invariant under all translations by elements of E, then either \dim E < + \infty or μ is the trivial measure \mu \equiv 0 . ...
[edit] R
- Relational quantum mechanics: ... corresponding to {intersection, orthogonal sum, orthogonal complement, inclusion, and orthogonality} respectively, where Q_1 \bot Q_2 \equiv Q_1 \supset ...
[edit] S
- Secondary structure: It assigns charges of \pm q_{1} \equiv 0.42e to the carbonyl carbon and oxygen, respectively, and charges of \pm q_{2} \equiv 0.20e to the amide nitrogen ...
- Spinor: In 5 Euclidean dimensions, the relevant isomorphism is Spin(5)\equiv USp(4)\equiv Sp(2) ... In 6 Euclidean dimensions, the isomorphism Spin(6)\equiv SU(4) ...
- Stopped process: Stopping at a deterministic time T > 0: if \tau (\omega) \equiv T , then the stopped Brownian motion Bτ- will evolve as per usual up until time T, ...
[edit] T
- Teleparallelism: D_\mu x^a \equiv (dx^a)_\mu. is defined with respect to the connection form B. Here, d is the exterior ... T^a_{\mu\nu} \equiv (dB^a). is gauge invariant. ...
- Tessarine: They allow for powers, roots, and logarithms of j \equiv \varepsilon , which is a non-real root of 1 (see conic quaternions for examples and references). ...
- Theoretical and experimental justification for the Schrödinger equation \begin{pmatrix} \zeta_x \\ ... |L\rangle \equiv {1 \over \sqrt{2}} . ... \hat{S} \equiv |R\rangle \langle R | - . ...
- Theoretical motivation for general relativity where dτ is c times the proper time interval ... \tau \equiv c t . The acceleration \mathbf{f} is independent of m. ...
- Thermal efficiency: Thermal efficiency is defined as \eta_{th} \equiv \frac{W_{out}}{ or \eta_{th} \equiv 1 - \frac{Q_{out}. where \eta_{th} \, is the thermal efficiency, ...
- Thermodynamic efficiency: e \equiv \frac{T_H - T_C}{T_H}. The equation shows that higher efficiency is achieved with greater temperature differential between hot and cold working ...
- Time-evolving block decimation: G \equiv \sum_{odd \ \ l}(K^{l. Any two-body terms commute: [F[l],F[l']]: = 0, [G[l],G[l']]: = 0 This is done in order to be able to make the Suzuki-Trotter ...
- Treynor ratio: T \equiv Treynor ratio,. r_p \equiv portfolio return,. r_f \equiv risk free rate. \beta \equiv portfolio beta. Like the Sharpe ratio, the Treynor ratio (T) ...
- Triple quad formula proof: \begin{matrix}Q(AC) & \equiv & (C_x -. where use was made of the fact that (-\lambda\ + 1)^2 = (\lambda\ - . Substituting these quadrances into the equation ...
- Two-body problem: By contrast, subtracting equation (2) from equation (1) results in an equation that describes how the vector \mathbf{r} \equiv \mathbf{x}_{1} between the ...
[edit] U-Z
- Vector (spatial): ... can be identified with a corresponding directional derivative. We can therefore define a vector precisely:. \mathbf{a} \equiv a^\alpha \frac{\partial ...
- Vector operator: \operatorname{grad} \equiv \nabla: \operatorname{div} \ \equiv \nabla \cdot: \operatorname{curl} ... \nabla^2 \equiv \operatorname{div}\ \operatorname{grad ...
- Virtual work: Virtual displacements and strains as variations of the real displacements and strains using variational notation such as \delta\ \mathbf {u} \equiv ...
- Voigt profile: G(x;\sigma)\equiv\frac{e^{-. and L(x;γ) is the centered Lorentzian profile:. L(x;\gamma)\equiv\frac{\gamma}{. The defining integral can be evaluated as: ...
- Volume fraction: \phi_i \equiv \frac{N_iv_i}{V}. where the total volume of the system is the sum of the contributions from all the chemical species. V = \sum_j N_jv_j \, ...
- Water activity: a_w \equiv p / p_0. where p is the vapor pressure of water in the ... a_w \equiv l_w x_w. where lw is the activity coefficient of water and xw is the mole ...
- Wavenumber: k \equiv \frac{2\pi}{\lambda} = \. where λ is the wavelength in the medium, ν (Greek letter nu) is the frequency, vp is the phase velocity of wave, ...
- Weinberg-Witten theorem: The current defined as J^\mu(x)\equiv\frac{\delta}{ is not conserved ... T^{MN}(x)\equiv \frac{1}{. The stress-energy operator is defined as a vertex ...
- Widom scaling: t \equiv \frac{T-T_c}{T_c} measures the temperature relative to the critical point. [edit]. Derivation. The scaling hypothesis is that near the critical ...
- Wien's displacement law: x\equiv{hc\over\lambda kT }. then. {x\over 1-e^{-x}}-5=. This equation cannot be solved in terms of elementary functions. It can be solved in terms of ...
- Wigner's classification: The mass m\equiv \sqrt{P^2} is a Casimir invariant of the Poincaré group. So, we can classify the irreps into whether m > 0-, m = 0 but P0 > 0- and m = 0 ...
- Wind turbine: a\equiv\frac{U_1-U_2}{U_1}. a is the axial induction factor. ... \lambda\equiv\frac{R\Omega}{U_1}. One key difference between actual turbines and the ...
- WKB approximation: Note that in this webpage, \mbox{Eq.} (4.x) \equiv (x + : there are two sets of labels for the equations.) ...
- Worm-like chain: \hat t(s) \equiv \frac {\partial \vec r and the end-to-end distance \vec R = \int_{0}^{l}\hat t . It can be shown that the orientation correlation function ...
- Yale shooting problem: In other words, a formula alive(0) \equiv alive(1) must be added to formalize the implicit assumption that loading the gun only changes the value of loaded ...
- Young's modulus: Y \equiv \frac{\mbox {tensile stress}}{\mbox. where Y is the Young's modulus (modulus of elasticity) measured in pascals; F is the force applied to the ...
