Wikipedia talk:WikiProject Mathematics/equivlistrevert

This is a list of all articles that were originally listed on equivlist. First, all math-related articles should be removed. Next, all articles that have had '/equiv' changed to something else should have that specific change reverted, preferably with added prose that clarifies the use of 'equiv' if it is ambiguous.

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_ ...
Alternatives to general relativity: T^{\mu\nu}\equiv{2\over\sqrt. where \omega(\phi)\; is a different dimensionless function ... where h^{\alpha\beta}\equiv g^{\alpha\ , l\; is a length scale, ...
Analytic signal: S_\mathrm{a}(\omega)\,, \equiv \mathcal{F}\left\{s_\mathrm{a ... \omega(t) \equiv \phi '(t) = {d. The amplitude function, and the instantaneous phase and ...
Ankeny-Artin-Chowla congruence
: {u \over t}h \equiv B_{(p-1). where Bn is the nth Bernoulli number. There are some generalisations of these basic results, in the papers of the authors. ...
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). ...
Arithmetical hierarchy: If the relation R(n_1,\ldots,n_l,m_1,\ldots, m_k) is \Sigma^0_n then the relation S(n_1,\ldots, n_l) \equiv \forall m_1\cdots is defined to be \Pi^0_{n+1} ...
Arithmetical set: \theta(Z) \equiv \forall n [n \in Z \ . Not every implicitly arithmetical set is arithmetical, however. In particular, the truth set of first order ...
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). ...
Autocorrelation technique: If we model the power spectrum as a single frequency S(\omega) \equiv \delta(\omega - \omega_0) , this becomes:. R(1) = \frac{1}{2\pi} \: R(1) ...
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 ...

B

Bandlimited
: x[n] \equiv x(nT) = x \left( { for integer n \, and T \equiv { 1 \over f_s }. as long as. f_s > R_N \,. The reconstruction of a signal from its samples can ...
Baryogenesis: s \equiv \frac{\mathrm{entropy}}{\mathrm{. with p and ρ as the pressure and density from the energy density tensor Tμν, and g * as the effective number of ...
Basic introduction to the mathematics of curved spacetime
: (A,A) \equiv -\left ( A^{0} . The term on the left is the notation for the inner ... A_0\equiv -A^0 \quad A_1\equiv A^1 \ . It transforms as a scalar ...
Begriffsschrift: 76: \Vdash aR*b \equiv \forall F [\forall x (aRx . Frege's first result is then that this relation ... 115: \Vdash I(R) \equiv \forall x \forall y \forall ...
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. ...
Belief revision: if \alpha \models \mu then (\psi * \mu) * \alpha \equiv \psi * \ ;; if \alpha \models \neg \mu , then (\psi * \mu) * \alpha \equiv \psi * \ ;; if \psi ...
Bell number: B_{p+n}\equiv B_n+B_{n+1}. Each Bell number is a sum of "Stirling numbers of the second kind". B_n=\sum_{k=1}^n S(n,k). The Stirling number S(n, ...
Benaloh cryptosystem: ... it is computationally infeasible to determine whether z is an rth residue mod n, i.e. if there exists an x such that z \equiv x^r \mod n . ...
Bernoulli distribution: Probability mass function. Cumulative distribution function. Parameters, p>0\, (real) q\equiv 1-p\,. Support, k=\{0,1\}\,. Probability mass function (pmf) ...
Bernstein's inequality: \max(X) \equiv \max_{|z| \leq 1. The inequality is named after Sergei Natanovich Bernstein and finds uses in the field of approximation theory. ...
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} \, ...
Blind signature: s' \equiv (m(r^e))^d\ (. The author of the message can then remove the blinding factor to reveal s, the valid RSA signature of m: ...
Blum-Goldwasser cryptosystem
: Alice generates two large prime numbers p \, and q \, such that p \ne q , randomly and independently of each other, where (p, q) \equiv 3 mod 4. ...
Bose gas: z(\beta,\mu)\equiv e^{\beta \. and β defined as:. \beta \equiv \frac{1}{kT}. where k is Boltzmann's constant and T is the temperature. ...
Bra-ket notation
: \mathbf{p} \psi(\mathbf{x}) \equiv. One occasionally encounters an expression like. - i \hbar \nabla |\psi\rang. This is something of an abuse of notation, ...
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 ...
British and United States military ranks compared
Fleet • Fleet Admiral (FADM), Marshal of the Royal Air Force (MRAF). OF-9, General (Gen), General ...
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. ...

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 ...
Canonical commutation relation: \pi_i \equiv \frac{\partial {\mathcal L}}{. This definition of the canonical momentum ensures that one of the Euler-Lagrange equations has the form ...
Capillary number: Ca \equiv \frac{\mu v}{\sigma}. where:. μ is the viscosity of the liquid; v is a characteristic velocity; σ is the surface or interfacial tension between ...
Cartan connection applications
: Since what we now have here is a SO(p,q) gauge theory, the curvature F defined as \bold{F}\equiv d\bold{A}+\bold is pointwise gauge covariant. ...
Chebyshev rational functions: R_n(x)\equiv T_n\left(\frac{x-1. where Tn(x) is a Chebyshev polynomial of the first ... \omega(x) \equiv \frac{1}{(x+. The orthogonality of the Chebyshev ...
Chemical equilibrium: K_{eq} \equiv \frac{\left[C\right]. [A],[B], etc. represent the chemical activities of the reactants and products, which can sometimes be approximated by ...
Chemical potential: U \equiv U(S,V,N_1,..N_n). By referring to U as the internal energy, it is emphasized ... A \equiv A(T,V,N_1,..N_n). In terms of the Helmholtz free energy, ...
Circle of confusion computation
: N = f-number \equiv \frac{f}{A}. s = distance from lens to point source. s + Δs = distance from lens to external focal plane of sensor ...
Circular polarization: |\psi\rangle \equiv \begin{pmatrix} \psi_x \\. is the Jones vector in the x-y plane. ... \psi_L \equiv \left ( {\cos\theta +i\sin . ...
Circumscription: For example, there are two models of P(a) \equiv P(b) with domain {a,b}, ... For example, in the formula P(a) \equiv P(b) one would consider the value of ...
Coherent information: The coherent information is defined as I(\rho, \mathcal{N}) \equiv S(\ where S(\mathcal{N} \rho) is the von Neumann entropy of the output and S({\mathcal N} ...
Colonel General
: From Wikipedia, the free encyclopedia. Jump to: navigation, search. Colonel General is a senior military rank which is used in some of the world’s ...
Column: f_{cr}\equiv\frac{\pi^2\textit{, (1). where E = modulus of elasticity of the ... f_{cr}\equiv\frac{\pi^{2}E_T, (2) ... f_{cr}\equiv{F_y}-\frac{F^{, (3) ...
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 ...
Completing the square: z \equiv \sqrt{a} x + i \sqrt{b} ,. we then have. \begin{matrix} |z|^2 &=& z z^*. so. ax2 + by2 + c = | z | 2 + c. [edit]. External link ...
Complex projective plane: (z_1,z_2,z_3) \equiv (\lambda z_1,\lambda. That is, these are homogeneous coordinates in the traditional sense of projective geometry. ...
Composite number: (Fundamental theorem of arithmetic); Also, (n-1)! \,\,\, \equiv \, for all composite numbers n > 5. (Wilson's theorem) ...
Conditional entropy: H(Y|X) \equiv H(X,Y) - H . Intuitively, the combined system contains H(X,Y) bits of information. If we learn the value of X, we have gained H(X) bits of ...
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, ...
Conjugate transpose: A^* \equiv {\overline A}^{T}. where A^T \,\! denotes the transpose and \overline A \,\! denotes the matrix with ... a + ib \equiv \Big(\begin{matrix} a & - ...
Consistency (Mathematical Logic)
: Define a binary relation on the set of S-terms t0˜t1 iff \; t_0 \equiv t_1 \in \Phi and let TΦ := \{ \; \overline t \; |\; t \ where TS is the set of terms ...
Continuous Fourier transform
: \mathcal{F}\{f\}(w) \equiv \. Where \omega\in \mathbb{R}^n and \omega ... \Delta^2 A\equiv\langle A^2-\langle A. and similarly for the variance of B(ω), ...
Coupling constant: \alpha_s(k^2) \equiv \frac{g_s^2(. where β0 is a constant computed by Wilczek, Gross and Politzer. Conversely, the coupling increases with decreasing energy ...
Covariant derivative: \nabla_{e_j} {\mathbf v} \equiv v^s {. Once again this shows that the covariant derivative of a vector field is not just simply obtained by differentiating ...
Covariant transformation: {\mathbf v}[f] \equiv \frac{df}{. The parallel between the tangent ... \sigma [{\mathbf u}] \equiv <\sigma, {. where <\sigma, {\mathbf u}> is a real number. ...
Creation and annihilation operators: a^\dagger \equiv \frac{1}{\sqrt{2 as the "creation operator" or the "raising operator" and: a \equiv \frac{1}{\sqrt{2}} \ as the "annihilation operator" or ...
Critical exponent: \tau \equiv (T-T_{c})/T_c,\. where T is the temperature and Tc its critical value, at which a second-order phase transition is observed. ...
Cross covariance
: (f\star g)(x) \equiv \int f^*. where the integral is over the appropriate values of t. The cross-covariance is similar in nature to the convolution of two ...
Cross-correlation: (f\star g)(x) \equiv \int f^*. where the integral is over the appropriate values of t. The cross-correlation is similar in nature to the convolution of two ...
C-symmetry: Now reformulate things so that \psi\equiv {\phi + i \chi\over \sqrt{ . ... But let's redefine \psi\equiv {\chi + i\phi\over\sqrt{ . ...
Cubic reciprocity: \alpha^{(P-1)/3} \equiv \left. We further define a primary prime to be one which is congruent to -1 modulo 3. Then for distinct primary primes π and θ the ...
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 ...
Cyanic acid
: Two tautomers exist for cyanic acid, N \equiv C-O-H and H-N=C=O . It forms in a reaction between potassium cyanate and formic acid. ...
Cyclol: ... can be joined correctly if and only if the dihedral angle between the planes was roughly the tetrahedral bond angle \delta \equiv \cos^{-1}(-1/3 . ...
Cylindrical coordinate system: ... if one knows θ, r and z in terms of Cartesian coordinates, but the general equation is given below:. \nabla \equiv \mathbf{\hat r}\frac{\partial . ...
Cylindrical coordinate system: ... if one knows theta, r and z in terms of Cartesian coordinates, but the general equation is given below. \nabla \equiv \mathbf{\hat r}\frac{\partial . ...
Cylindrical multipole moments: where the interior multipole moments are defined Q \equiv \lambda , I_{k} ... U \equiv \int d\theta \int \rho d\rho \. If the cylindrical multipoles are ...

D

De Morgan's laws: \exists x \, P(x) \equiv P(a) \ . But, using De Morgan's laws, ... \Box p \equiv \neg \Diamond \neg p ,: \Diamond p \equiv \neg \Box \neg p . ...
Dead-end elimination: U_{kl}^{AB} \equiv E_{k}(r_. A given pair of rotamers A and B at positions k and l, respectively, cannot both be in the final solution (although one or the ...
Debye model: T_D\equiv {hc_sR\over2Lk} = {hc_s\over2Lk}\sqrt. We then have the specific internal energy: ... T_E \equiv {\epsilon\over k}. then one can say. T_E \ne T_D ...
Deceleration parameter: q \equiv -\frac{\ddot{a} a }{\. where a is the scale factor of the universe and the dots indicate derivatives by proper time. Recent measurements of dark ...
Deductive reasoning: Transposition, (p → q) ⊢ (¬q → ¬p), If p then q is equiv. to if not q then ... Tautology, p ⊢ (p ∨ ¬p), p is true is equiv. to p is true or p is false ...
Definable set: \varphi=\exists y(y\cdot y\equiv x). Then for a\in\R , a is nonnegative if and only if \mathcal{R}\models\varphi[a] . In conjunction with a formula that ...
Density functional theory: Obviously, n_s(\vec r)\equiv n(\vec r) if \,\!V_s is chosen to be. V_s = V + U + \left(T - T_s\right). Thus, one can solve the so-called Kohn-Sham equations ...
DeWitt notation: ... over the infinite dimensional "functional manifold". The Einstein summation convention is used. In other words,. A^i B_i\equiv \int_M d^dx \sum_\alpha A ...
Diffraction: where the (unnormalized) sinc function is defined by \operatorname{sinc}(x) \equiv \frac{\operatorname{ . Now, substituting in \frac{2\pi}{\lambda} = k ...
Digital Signature Algorithm: \begin{matrix} k & \equiv & \mbox{SHA-1. Since g has order q we have. \begin{matrix} g^k & \equiv & g^{{. Finally, the correctness of DSA follows from ...
Dimensionless quantity: \mathrm{Q} \equiv n \mathrm{U} \. But, ultimately, people always work with dimensionless numbers in reading measuring instruments and manipulating (changing ...
Dirac comb: \Delta_T(t) \equiv \sum_{k=-\infty}. for some given period T. Some authors, notably Bracewell, refer to it as the Shah function (probably because its graph ...
Dirac equation: \epsilon \equiv |E| - mc^2. The first spanning eigenstate in each eigenspace ... \bar\psi \equiv \psi^\dagger \gamma_0. is called the Dirac adjoint of ψ. ...
Dirac equation: p_j \psi(\mathbf{x},t) \equiv - i. To describe a relativistic system, ... \bar\psi \equiv \psi^\dagger \gamma_0. is called the Dirac adjoint of ψ. ...
Dirichlet character: Given an integer k, one defines the residue class of an integer n as the set of all integers congruent to n modulo k: \hat{n}=\{m | m \equiv n \mod That is, ...
Discrete logarithm: The familiar base change formula for ordinary logarithms remains valid: If c is another generator of G, then we have. \log_c (g) \equiv \log_c (b) \cdot \ ...
Discretization: \mathbf x[k] \equiv \mathbf x(kT): \mathbf x[k] = e^{\mathbf AkT}\mathbf: \mathbf x[k+1] = e^{\mathbf A(: \mathbf x[k+1] = e^{\mathbf AT} ...
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 ...
Divisor function: When x is 1, the function is called the sigma function or sum-of-divisors function, and the subscript is often omitted. \sigma_{0}(n) \equiv \tau(n) ...
Dixon's factorization method: x^2\equiv y^2\quad(\hbox{mod }. where n is the integer to be factorized. ... \prod_{k}x_k^2\equiv\prod_{k}p. where the products are taken over all k for ...
Dot product: \mathbf{c} \equiv \mathbf{a} - \mathbf{. creating a triangle with sides a, b, and c. According to the law of cosines, we have. c^2 = a^2 + b^2 - 2 ab \cos ...

E

E=mc²
: m_{\mathrm{rel}} \equiv \gamma m_0 \equiv \. Using this form of the mass, we can again simply write E = mrelc2, even for moving objects. ...
Eddington-Finkelstein coordinates
: d\Omega^2\equiv d\theta^2+\sin^. Define the tortoise coordinate r * by. r^* = r + 2GM\ln\left|\frac{r. The tortoise coordinate approaches −∞ as r ...
Edge-graceful labeling: q(q+1) \equiv \frac{p(p-1. This is referred to as Lo's condition in the literature. This follows from the fact that the sum of the lables of the vertices is ...
Elastic modulus: \lambda \equiv \frac {stress} {strain}. where λ is the elastic modulus; stress is the force causing the deformation divided by the area to which the force ...
Electric field screening
: k_0 \equiv \sqrt{\frac{\rho e^2}{. The associated length λD ≡ 1/k0 is ... k_0 \equiv \sqrt{\frac{3e^2\rho}{. is called the Fermi-Thomas screening wave ...
Electromagnetic tensor: F_{ a b } \equiv \frac{ \partial A_b }{ \partial. where A^a = ( \frac{\phi}{c} , \ and A_a \, = \eta_{ a b } A^b = ( -\ where \, \eta is the Minkowski ...
Electromagnetic tensor: More formally, the electromagnetic tensor may be written in terms of the 4-vector potential Aa:. F_{ a b } \equiv \frac{ \partial A_b }{ \partial ...
Electronvolt: 1eV = 1V \times q_e which indicates why the eV is fundamentally a unit of energy since V \equiv {W\over q_0} or equivalently V \equiv {\triangle E\over q_0} ...
Ellipsoidal coordinates: S(\sigma) \equiv \left( a^{2} +. where σ can represent any of the three variables (λ,μ,ν). Using this function, the scale factors can be written ...
Elliptical polarization: |\psi\rangle \equiv \begin{pmatrix} \psi_x \\. is the Jones vector in the x-y plane. Here θ is an angle that determines the tilt of the ellipse and αx − αy ...
Enzyme kinetics: [\mbox{E}]_{tot} \equiv [\mbox. which is approximately equal to the ... K_{m} \equiv \frac{k_{2} + k_{. ([E] is the concentration of free enzyme). ...
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 ...
Equilibrium constant: K \equiv \frac{\left[C\right]^c \. The law of chemical equilibrium says that this ... K \equiv \frac{k_{f}}{k_{b}. Since the rate constants are constant by ...
Equilibrium unfolding: The dimensionless equilibrium constant K_{eq} \equiv \frac{k_{u}}{k_ can be used to determine the conformational stability ΔG by the equation ...
Euler pseudoprime: a^{(n-1)/2} \equiv \pm 1. (where mod refers to the modulo operation). The motivation for this definition is the fact that all prime numbers p satisfy the ...
Euler's criterion: a(p − 1)/2 ≡ −1 (mod p). Euler's criterion can be concisely reformulated using the Legendre symbol:. \left(\frac{a}{p}\right) \equiv. [edit] ...
Euler's equations
: \frac{d\mathbf{L}}{dt} \equiv \. where \mathbf{I} is the moment of ... Substituting L_{k} \equiv I_{k}\omega_{k} , taking the cross product and using the ...
Euler's formula: f(x) \equiv e^{ix} .\. Considering that i is constant, the first and second derivatives of f(x) are. f'(x) = i e^{ix} \: f(x) = i^2 e^{ix} = ...
Euler's totient function: a^{\phi(n)} \equiv 1\mod n. This follows from Lagrange's theorem and the fact that a belongs to the multiplicative group of \mathbb{Z}/n\mathbb{Z} iff a is ...
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 ...
Ewald summation: As in normal Ewald summation, a generic interaction potential is separated into two terms \phi(\mathbf{r}) \equiv \phi_{sr} - a short-ranged part ...
Exact renormalization group equation
: \Gamma_k[\phi]\equiv \left(-W\left[. So,. \frac{d}{dk}\Gamma_k[\phi]=-. \frac{d}{dk}\Gamma_k=\frac{1}. is the ERGE. As there are infinitely many choices of ...

F

Fabry-Pérot interferometer
: where F\equiv \frac{4R}{{(1-R)^ is the coefficient of finesse. ... and \gamma\equiv\ln(1/R) . The order of integration and summation may be interchanged ...
Factorial: \equiv\ 0 \ ({\rm . A stronger result is Wilson's theorem, which states that ... n\$\equiv \begin{matrix} \underbrace{ n!^ ,. or as,. n\$=n!^{(4)}n! \, ...
Fermat number: a^{(N-1)/2} \equiv -1 \. then N is prime. Conversely, if the above congruence does not hold, and in addition. \left(\frac{a}{N}\right)=- (See Jacobi symbol) ...
Fermionic field: where "psi-bar" is defined as \bar{\psi} \equiv \psi^{\dagger} \ . Given the expression for ψ(x) we can construct the Feynman propagator for the fermion ...
Fermi-Walker transport
: The velocity in spacetime is defined as. v^{\mu} \equiv {dx^{\mu} \ ... \gamma \equiv { 1 \over {\sqrt {1 - {{ . The magnitude of the 4-velocity is one, ...
Feynman slash notation: If A is a covariant vector, i.e. 1-form,. A\!\!\!/\equiv \gamma^\mu A_. using the Einstein summation notation where γ are the gamma matrices. ...
Fine structure: Fermions, such as electrons and protons, compose the "stuff" of matter and have half-integer spin (the unit being \hbar\equiv\frac{h}{2\pi} where h is ...
Fine-structure constant: \Delta \alpha/\alpha \equiv (\alpha _{then}. In the seven years since their results were first announced, extensive analysis has yet to identity any ...
Flow (mathematics): In fact, notationally, one has strict equivalence: x(t)\equiv\phi(x,t) . Similarly. x0 = x(0). is written for x = φ(x,0), and so on. ...
Formulation of Maxwell's equations in special relativity
: where ρ is the charge density and \vec{J} is the current density. The 4-current satisfies the continuity equation. J^{\alpha}_{,\alpha} \, \equiv. [edit] ...
Four-gradient: \partial_\alpha \equiv \left(\frac{1}{c. and is sometimes also represented as D. The square of D is the four-Laplacian, which is called the d'Alembertian ...
Fourier transform: \mathcal{F}\{f\}(w) \equiv \. Where \omega\in \mathbb{R}^n and \omega ... \Delta^2 A\equiv\langle (A-\langle A\. and similarly for the variance of B(ω), ...
Fourier transform: unitary, X_1(\omega) \equiv \frac{1}{\sqrt{. x(t) = \frac{1}{\sqrt{2 \ ... \Delta^2 A\equiv\langle (A-\langle A\. and similarly for the variance of B(ω), ...
Frame problem: In this case, occlude_open(1) is true, making the antecedent of the fourth formula above false for t = 1; therefore, the constraint that open(t-1) \equiv ...
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\, ...
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 ...
Frobenius endomorphism: s_\Phi(x) \equiv x^q \mod \Phi . ... s_\Phi(x) \equiv x^q \mod \Phi ,. where q is the order of the residue field OK mod φ. ...
Frobenius theorem (differential topology) f_i^1 (1). One seeks conditions on the existence of a collection of solutions u1, ..., un-r such that the gradients ...
Fujikawa method: equiv \partial\! and the fermionic action is given by. \int d^dx \overline{\psi}iD\!\! In Euclidean space, the partition function is ...
Fundamental theorem of Riemannian geometry e. To specify the connection it is enough to specify the Christoffel symbols Γkij. Since {\mathbf e}_i are coordinate ...

G

Gauge theory: DX\equiv dX+\bold{A}X. Also, \delta_\varepsilon \bold{F}=\varepsilon \bold{F , which means F transforms covariantly. One thing to note is that not all gauge ...
Gauss' principle of least constraint
: T \equiv \frac{1}{2} \sum_{k=. Since the line element ds2 in the ... K \equiv \sum_{k=1}^{N} \left. Since \sqrt{K} is the local curvature of the trajectory ...
Gaussian beam: E0 and I0 are, respectively, the electric field amplitude and intensity at the center of the beam at its waist, i.e. E_0 \equiv |E(0,0)| and I_0 \equiv I(0 ...
Gaussian integer: In particular, he was looking for relationships between p and q such that q should be a cubic residue of p (i.e. x^3\equiv q ({\rm mod}\ p) ) or such that q ...
Generalization (logic)
: \vdash P(x) \ \equiv \ \vdash \forall x \. which does not mean the same as. P(x) \leftrightarrow \forall x \, P(x) \. which is wrong because here P(x) could ...
Ghost condensate
: X\equiv \frac{1}{2}\eta^{\. in the +--- sign convention. The theories of ghost condensate predict specific non-gaussianities of the cosmic microwave ...
Gibbs free energy: The Gibbs free energy is a thermodynamic potential and is therefore a state function of a thermodynamic system. It is defined as:. G \equiv H-TS \, ...
Grand potential: \Phi_{G} \equiv E - T S - \mu N. Where E is the energy, T is the temperature of the system, S is the entropy, μ is the chemical potential, ...
Green-Kubo relations
: The strain rate γ is the rate of change streaming velocity in the x-direction, with respect to the y-coordinate, \gamma \equiv \partial u_x /\partial y . ...
Green's relations: Green used the lowercase blackletter \mathfrak{l} , \mathfrak{r} and \mathfrak{f} for these relations, and wrote a \equiv b (\mathfrak{l}) for a L b (and ...
Group velocity: v_g \equiv \frac{\partial \omega}{\partial k}. where:. vg is the group velocity: ω is the wave's angular frequency: k is the wave number ...
Gyration tensor: S_{mn} \equiv \frac{1}{N+1}. where r_{m}^{(i)} is the mth Cartesian ... b \equiv \lambda_{z}^{2} - \frac{. which is always non-negative and zero only for a ...

H

Hamiltonian (quantum mechanics): \langle H(t) \rangle \equiv \langle\psi(t. where the last step was obtained by expanding \left| \psi\left(t\right) \right\rangle in terms of the basis ...
Goldwasser-Micali cryptosystem
: Compute xp = x mod p, xq = x mod q. If x_p^{(p-1)/2} \equiv 1 mod p and. x_q^{(q-1)/2} \equiv 1 mod q, then x is a quadratic residue mod N. ...
Hamiltonian fluid mechanics: where \vec{v}\equiv -\nabla \phi is the velocity and is vorticity-free. The second equation leads to the Euler equations. \frac{\partial \vec{v}}{\partial t ...
Hamilton-Jacobi equations
: \mathbf{q} \equiv (q_{1}, q_{2. that need not transform like a vector under rotation. ... \mathbf{p} \cdot \mathbf{q} \equiv \sum_ ...
Hamilton's principle: Maupertuis' principle uses an integral over the generalized coordinates known as the abbreviated action \mathcal{S}_{0} \equiv \int \mathbf{ where ...
Helmholtz equation: where k is the wave vector and \omega \equiv kc is the angular frequency. We now have Helmholtz's equation for the spatial variable \mathbf{r} and a ...
Higher residuosity problem: x^{(p-1)/d} \equiv 1 \mod. When d=2, this is called the quadratic residuosity problem. [edit]. Applications. The semantic security of the Benaloh ...
Homogeneous coordinates: (x:y:z) \equiv (u:v:w). Remark: In some European countries (x:y:z) is customarily represented ... (x:y:z) \equiv a (x:y:z. even though. (x:y:z) \ne a (x:y:z ...
H-theorem: H \equiv \int { P ({\ln P}) d^. where P(v) is the probability. ... S \equiv - N k H. so, according to the H-theorem, S can only increase. ...
Hydrodynamic radius: \frac{1}{R_{hyd}} \equiv \frac{. where rij is the distance between particles i and i, and where the angular brackets \langle \ldots \rangle represent an ...
Hyperbolic function
: \operatorname{sech}(x) = \frac{1}{\. Hyperbolic cosecant, pronounced "cosheck" or "cosech". \operatorname{csch}(x) = \frac{1}{\. where. i \equiv \sqrt{-1} ...
Hyperbolic function
: i \equiv \sqrt{-1}. is the imaginary unit. The complex forms in the definitions above derive from Euler's formula. [edit]. Useful relations ...

I

Identical particles
: \Psi^{(S)}_{n_1 n_2 \cdots n_N}, \equiv \lang x_1 x_2 \cdots x_N; ... \psi_n(x) \equiv \lang x | n \rang. The most important property of these wavefunctions ...
Implementation of mathematics in set theory be reasonably easy to collect ordered pairs into sets. [edit]. Relations. Relations are sets whose members are all ...
Incidence (geometry): L_1 \times L_2 \equiv L_2 \times L_3 \equiv L_3 \times L_1 ... P_3 \equiv P_3.P_1,. but if the points are expressed in homogeneous coordinates then these ...
Indefinite inner product space: The operator J \equiv P_+ - P_- is called the (real phase) metric operator or fundamental symmetry, and may be used to define the Hilbert inner product ...
Inductance/derivation of self inductance
that the inductance is a purely geometrical quantity independent of the current in the circuits. ...
Inertial frame of reference: \gamma \equiv \frac{1}{\sqrt{1 - v. The Lorentz transformation is equivalent to the Galilean transformation in the limit c \rightarrow \infty or, ...
Information flow (information theory): H(h|l) - H(h|l')\equiv. where H(h | l) is the conditional entropy (equivocation) of variable h (before the process started) given the variable l (before the ...
Inhomogeneous electromagnetic wave equation \partial_{\beta} \left( SI \right): \Box A^{\mu} \equiv \partial_{\beta} \left( cgs ... \partial \over { \partial x^a } } \equiv \ ...
Instantaneous frequency
: \omega(t) \equiv \phi^\prime(t) \. and the instantaneous frequency (Hz) is. f(t) = \frac{1}{2 \pi} \ . [edit]. Phase unwrapping ...
Instantaneous frequency
: That is, the instantaneous angular frequency is defined to be. \omega(t) \equiv \phi^\prime(t) \. and the instantaneous frequency (Hz) is ...
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 ...
Intrabeam Scattering
: \frac{1}{T_{p}} \equiv \frac{ ,: \frac{1}{T_{h}} \equiv \frac{ ,: \frac{1}{T_{v}} \equiv \frac{ . The following is general to all bunched beams, ...
Intrinsic viscosity: K \equiv \frac{M}{2}. J \equiv K \frac{J_{\alpha}^{\prime. L \equiv \frac{2}{a b^{2} \left. N \equiv \frac{6}{a b^{2}} \. The J coefficients are the Jeffery ...
Intuitionistic type theory: Of special importance is the conversion rule, which says that given \Gamma\vdash t : \sigma and \Gamma\vdash \sigma\equiv\tau then \Gamma\vdash t : \tau . ...
Inverse temperature
: The inverse temperature is given by \beta\equiv \frac{1}{kT} where k is the Boltzmann constant and T is the temperature. The inverse temperature is actually ...
Inversive congruential generator: x_{i} \equiv (ax_{i-1}^{-. where. 0 \le x_{i} < m. Retrieved from "http://en.wikipedia.org/wiki/Inversive_congruential_generator%22 ...
IP (complexity): a \vee b, a*b \equiv 1 - (1 - a)(1 - b. \neg a, 1 − a. As an example, \phi = a \wedge b \vee \neg c would be converted into a polynomial as follows: ...
Isaac Newton: Defining the acceleration to be \vec a \equiv d\vec v/dt results in the famous equation \vec F = m \, \vec a \,, which states that the acceleration of an ...
ISO 31-11: a ≠ b, a is not equal to b, a \not\equiv b may be used to emphasise that a is not identically equal to b. ≝, a ≝ b, a is by definition equal to b ...

J

Jet bundle: V \equiv \rho^{i}(x,u)\frac. A vector field is called horizontal, meaning all the ... The jet bundle J^{r}\pi\, is co-ordinated by (x,u,w) \equiv (x^{i}, . ...
Joint quantum entropy: S(\rho^A|\rho^B) \equiv S(. and the quantum mutual information:. S(\rho^A:\rho^B) \equiv S(. These definitions parallel the use of the classical joint ...
Josephson phase: then the Josephson phase is \phi\equiv\theta_2-\theta_1 . Retrieved from "http://en.wikipedia.org/wiki/Josephson_phase%22
...

K

Kalman filter: \textbf{Y}_{k|k} \equiv \textbf{: \hat{\textbf{y}}_{k|k} \ ... \textbf{I}_{k} \equiv \textbf{H}: \textbf{i}_{k} \equiv \textbf{H} ...
Kepler's laws of planetary motion: \mathbf{L} \equiv \mathbf{r} \times \mathbf . where \mathbf{r} is the position vector of the particle and \mathbf{p} = m \mathbf{v} is the momentum of the ...
Kerr-Newman metric
: ds^{2}=-\frac{\Delta}{\rho: \Delta\equiv r^{2}-2Mr+a^{2: \rho^{2}\equiv r^{2}+a^: a\equiv\frac{J}{M}. where. M is the mass of the black hole: J is the ...
K-function: \zeta^\prime(a,z)\equiv\left[\. The K-function is closely related to the Gamma function and the Barnes G-function; for natural numbers n, we have ...
KMS state: \alpha_\tau(A)\equiv e^{iH\tau} . A combination of time translation with an ... \alpha^{\mu}_{\tau}\equiv e^. A bit of algebraic manipulation shows that the ...
Knights and knaves
: \equiv {\rm false} \vee (\neg J \wedge \ (because J \wedge \neg J \equiv {\rm ... \equiv (\neg J \wedge J) \vee (\neg J (by the law of distributivity) ...
Kripke semantics: For example, the schema \Box(A\equiv\Box A)\to\Box A generates an incomplete logic, because it corresponds to the same class of frames as GL (viz. ...
Kruskal-Szekeres coordinates
: d\Omega^2\equiv d\theta^2+\sin^. Kruskal-Szekeres coordinates are defined by replacing t and r by new time and radial coordinates: ...

L

Lab color space
: define f_y\equiv (L^*+16)/116; define f_x\equiv f_y+a^*/500; define f_z\equiv f_y-b^*/200; if f_y > \delta\, then Y=Y_nf_y^3\, ...
Lanczos tensor: H_{bd}\equiv H^{~e}_{b\. Thus, the Lanczos potential tensor is a gravitational field analog of the vector potential A for the electromagnetic field. ...
Laplace transform: z \equiv e^{s T} \. where T = 1/f_s \ is the sampling period (in units of time e.g. seconds) ... x[n] \equiv x(nT) \ are the discrete samples of x(t) \ . ...
Laplace-Runge-Lenz vector
: The angular momentum \mathbf{L} \equiv \mathbf{r} \times \mathbf is conserved ... where the momentum \mathbf{p} \equiv m \frac{d\mathbf{r as usual and where ...
Larmor formula: \beta^2 \equiv {v_0^2 \over c^2 }. and the terms on the right are evaluated at the retarded time. t' = t - {R \over c} . The second term, proportional to ...
Lauricella hypergeometric series: (a)_{i} \equiv a (a+1) \ . Lauricella also indicated the existence of ten other hypergeometric functions ... F_A\equiv F_2,F_B\equiv F_3,F_C\equiv F_4,F_D . ...
Leech lattice: a_1+a_2+\cdots+a_{24}\equiv 4a_1\equiv 4a_2. and the set of coordinates i such that ai belongs to any fixed residue class (mod 4) is a word in the binary ...
Legendre polynomials: where we have taken \eta \equiv a/r < 1 and x \equiv \cos \theta . This expansion is used to develop the normal multipole expansion. ...
Legendre rational functions: R_n(x)\equiv \frac{\sqrt{2}}{. where Ln(x) is a Legendre polynomial. These functions are eigenfunctions of the singular Sturm-Liouville problem: ...
Legendre symbol: \left(\frac{a}{p}\right) \equiv. Additionally, the Legendre symbol is a Dirichlet character. [edit]. Related functions ...
Length contraction: L0 is the proper length (the length of the object in its rest frame),: L1 is the length observed by an observer,: \gamma \equiv \frac{1}{\sqrt{1 - \ is the ...
Lévy distribution: m_n\equiv\sqrt{\frac{c}{2\pi}. which diverges for all n > 0 so that the ... M(t;c)\equiv \sqrt{\frac{c}. which diverges for t > 0 and is therefore not ...
Linear dynamical system: If the initial vector \mathbf{x}_{0} \equiv \mathbf{x} is aligned with a right eigenvector \mathbf{r}_{k} of the matrix \mathbf{A} , the dynamics are simple ...
Linear polarization: |\psi\rangle \equiv \begin{pmatrix} \psi_x \\ ... \alpha_x = \alpha_y \equiv \alpha . This represents a wave polarized at an angle θ with respect to the x ...
Linearised Einstein field equations
: where h_{bc,}{}^a \equiv \eta^{ar , and this is used to calculate the Riemann tensor:. 2R^a{}_{bcd} = h^a_{d,. Using Rbd = δcaRabcd gives ...
Logical NOR: "not p" is equivalent to "p NOR p", \overline{p} \equiv \overline{p + p} ... "p or q" is equivalent to "(p NOR q) NOR (p NOR q)", p + q \equiv ...
Loop entropy: \mathbf{W} \equiv \begin{bmatrix} 58 && 26 \. whose determinant is 2340. Taking the logarithm and multiplying by the constants αkB gives the entropy. ...
Lorentz factor: \gamma \equiv \frac{dt}{d\tau} = \. where. \beta = \frac{u}{c} is the velocity in terms of the speed of light,: u is the velocity as observed in the ...
Lorentz force: \gamma \equiv \frac{1}{\sqrt{1 - v. is called the Lorentz factor and c is the speed of light in a vacuum. This expression differs from the expression ...
Lorentz scalar: \gamma \equiv { 1 \over {\sqrt {1 - {{ . The magnitude of the 4-velocity is a ... a^{\mu} \equiv {dv^{\mu} \ . The 4-acceleration is always perpendicular to ...
Lorentz transformation: where now \gamma \equiv \frac{1}{\sqrt{1 - \ . The second of these can be written as:. \vec{r'} = \vec{r} + \left(. These equations can be expressed in ...
Lorentz-Heaviside units
: The charge and fields in Lorentz-Heaviside units are related to the quantities in cgs units by. q_{LH} \equiv \sqrt{4\pi} q_{cgs. \mathbf{E}_{LH} \equiv ...

M

Mach principle
: Mach8: \Omega \equiv 4 \pi \rho G T^2 is a definite number, of order unity, where ρ is the mean density of matter in the universe, and T is the Hubble time. ...
Magic gopher: Since 10^m \equiv 1 \mod 9, n = n_m + n_{ . Hence n - c \equiv 0 \mod 9 so the resulting number z = n - c\, is a multiple of 9. ...
Magnetic flux: \Phi_m \equiv \int \!\!\! \int \mathbf. where \Phi_m \ is the magnetic flux and B is the magnetic field density. We know from Gauss's law for magnetism that ...
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 ...
Mason-Weaver equation
: t_{0} \equiv \frac{D}{s^{2. Defining the dimensionless variables \zeta \equiv z/z_{0} and \tau \equiv t/t_{0} , the Mason-Weaver equation becomes ...
Massey product: It extends the range of the cup product. On differential forms the triple product is formally defined as. MP(\omega_1,\omega_2,\omega_3) \equiv \omega_1\ ...
Matrix representation of conic sections: Q \equiv Ax^2+By^2+Cx+Dy+Exy. That can be written as: ... a_{1,2} \equiv \frac{x-x_0}{. Because a 2x2 matrix has 2 eigenvectors, we obtain 2 axes. ...
Maupertuis' principle
: A few months later, well before Maupertuis' work appeared in print, Euler independently defined action in its modern abbreviated form \mathcal{S}_{0} \equiv ...
Maxwell's equations in curved spacetime: {F_{ab}}_{;a} \equiv D_a F_{ . The second equality in the source-free Maxwell equation is the ... {R^{ a }}_{ b } \equiv {R^. is the Ricci curvature tensor. ...
Maxwell's equations: \partial \over { \partial x^a } } \equiv \. is the 4-gradient. Repeated indices are summed over according to Einstein summation convention. ...
Mean field theory
: where we define \mathbf{\Delta(s) \equiv s - \langle s\ ; this is the fluctuation term of the spin. If we multiply out the RHS, we obtain one term that's ...
Mean free path: \frac{dI}{dx} = -I n \sigma \equiv -. whose solution is I = I_{0} e^{-x/\ell} , where x is the distance traveled by ... \ell \equiv \frac{1}{n\sigma} = \ ...
Minimum phase: H(j \omega) \equiv H(s) \Big|_. be the complex frequency response of system H (s). ... \mathcal{H} \lbrace x(t) \rbrace \equiv \ . ...
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: ...
Mole fraction: x_i \equiv \frac{n_i}{n} = \frac{N_i. where. n = \sum_j n_j \, ... \sum_i x_i \equiv 1 \,. Mole fractions are one way of representing the concentrations of ...
Moment of inertia: I \equiv m r^2\,. where. m is its mass,: and r is its perpendicular distance ... where M is the total mass of the rigid body, R^{2} \equiv \mathbf{R} \cdot ...
Monopsony: \epsilon_{SR}^{-1}\equiv\frac{\ . Now, assume these elasticities to be constant over time. ... e_t\equiv\frac{MRP_t-w_t}{w_t}=\epsilon_ . ...
Multivariate normal distribution: \mu _{1,\dots,N}(X)\equiv. where r_{1}+r_{2}+\cdots+r_{N. The central k-order moments are given as follows. (a) If k is odd, \mu _{1,\dots,N}(X-\mu . ...

N

Naccache-Stern cryptosystem
: c_i \equiv c^{\phi(n)/p_i} \mod . Thus. \begin{matrix} c^{\phi(n)/p_i}. where m_i \equiv m \mod p_i . Since pi is chosen to be small, mi can be recovered be ...
Naccache-Stern knapsack cryptosystem
: c \equiv \prod_{i=0}^n v_i^{x_i. The idea here is that when the vi are relatively prime and much smaller than the modulus p this problem can be solved ...
Narrow class group: p = 2 \quad \mbox{and} \quad d_K \equiv 1. or. p > 2 \quad \mbox{and} \quad \left(\ ... p = 3 \quad \mbox{or} \quad p \equiv 1 (cf. Eisenstein prime) ...
Natural units: \alpha \equiv \frac{e^2}{\hbar c (. cannot take on a different numerical value no matter what system of units are used. Judiciously choosing units can only ...
Navier-Stokes equations
: \frac{D}{Dt}(\star ) \equiv \frac. where \mathbf{v} is the velocity of the fluid. The first term on the right-hand side of the equation is the ordinary ...
N-connected
: \pi_i(X) \equiv 0~, \quad 1\leq i. where the left-hand side denotes the i-th homotopy group. The requirement of being path-connected can also be expressed ...
N-Electron Valence state Perturbation Theory
The full dimensionality of these spaces can be exploited to obtain the definition of the perturbers, by diagonalizing ...
Nernst equation: S \equiv k \ln \Omega,. where Ω is the number of states available to the molecule. ... Q \equiv \frac{[Y]^y [Z]^z. In an electrochemical cell, ...
Neutrino oscillation: where \Delta m_{ij}^{2} \equiv m_{i} . The phase that is responsible for oscillation is often written as (with c and \hbar restored) [2]. \frac{\Delta m^2\, ...
Newman-Penrose formalism
: {}^{(l)}G(t) \equiv \left. The components Ilm and Slm are the mass and current multipoles, respectively. − 2Ylm is the spin-weight -2 spherical harmonic. ...
Newtonian motivations for general relativity The geodesic equation becomes ... {D \over Ds} \equiv {d \over ds} + \. and Γ is a Christoffel symbol. ...
Newton's law of universal gravitation: ... of objects 1 and 2: r21 = | r2 − r1 | is the distance between objects 2 and 1: \mathbf{\hat{r}}_{21} \equiv \ is the unit vector from object 1 to 2 ...
Noether's theorem: \mathcal{S}[\varphi]\equiv\int_M \mathrm{ ... J^\mu\equiv\frac{\partial\mathcal{L}. which is called the Noether current associated with the symmetry. ...
Noether's theorem: S[\varphi]\equiv\int_M d^nx \mathcal{L ... J^\mu\equiv\frac{\partial\mathcal{L}. which is called the Noether current associated with the symmetry. ...
Noncentral chi distribution: Probability density function (pdf), \frac{e^{-(x^2+\lambda^2. Cumulative distribution function (cdf). Mean, \mu\equiv\sqrt{\frac{\pi}{2} ...
Nondimensionalization: 2 \zeta \equiv \frac{b}{\sqrt{ac}. The factor 2 is present so that the solutions can be parameterized in terms of ζ. In the context of mechanical or ...
Norm (mathematics): If we define 0^0 \equiv 0 then we can write the zero norm as \sum_{i=1}^n x_i^0 . It follows that the zero norm of x is simply the number of non-zero ...
Numbering (computability theory): If \nu_1 \le \nu_2 and \nu_1 \ge \nu_2 then we say ν1 is equivalent to ν2 and write \nu_1 \equiv \nu_2 . [edit]. See also ...
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, ...

O

Okamoto-Uchiyama cryptosystem
: H = \{ x : x \equiv 1 \mod p \} . For any element x in (\mathbb{Z}/p^2\mathbb{Z}) , we have xp-1 mod p2 is in H, since p divides xp
Optimal stopping: X_i\equiv Binomial\left(1,\frac{1}{2. are independent, identially distributed for each i, and if. y_i = E((\sum_{k=1}^{i}. then the sequences (X_i)_{i\geq ...
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: ...
Original proof of Gödel's completeness theorem then, considering \Psi \equiv \Phi' \equiv \Phi \wedge \Phi \ , we see that φ is satisfiable as well. ...
Orthogonal coordinates: where D is the dimension and the scaling functions h_{k}(\mathbf{q})\equiv \sqrt{ equal the square roots of the diagonal components of the metric tensor. ...
Oversampling: \beta \equiv \frac{f_s}{2 f_H} \. or. f_s = 2 \beta f_H \ . where. fs is the sampling frequency; fH is the bandwidth or highest frequency of the signal ...

P

Paley's theorem
: m \equiv 0 \mathrm{\,mod\,} 4. If m is of the above form, ... However, Hadamard matrices have been shown to exist for all m \equiv 0 \mathrm{\,mod\,} 4 for ...
Parameterized post-Newtonian formalism: Work in units where the gravitational "constant" measured today far from gravitating matter is unity so set G_{\mbox{today}}\equiv\alpha/c_0 c_1= . ...
Parametric oscillator: \alpha \equiv \alpha_{\mathrm{max}} \cos 2 . In other words, the parametric oscillator phase-locks to the pumping signal f(t). Taking θ(t) = θeq (i.e., ...
Partial molar volume
: \overline V_i \equiv \frac{\partial V}{\partial n_i. and ni is the number of moles of component i. As noted, T and P are held constant when taking these ...
Particle in a spherically symmetric potential equation for the variable u(r)\equiv rR(r) , with a centrifugal term \hbar^2l(l+1)/2m_0r^2 added to V, ...
Particle number operator: with creation and annihilation operators a^{\dagger}(\phi_i) and a(φi) we define the number operator \hat{n_i} \equiv a^{\dagger}(\phi_i and we have: ...
Partition function (statistical mechanics) kB denoting Boltzmann's constant. ... \langle \delta E^2 \rangle \equiv \langle (E -. The heat capacity is ...
Pauli group: ... the group consisting of all the Pauli matrices X = σ1,Y = σ2,Z = σ3, together with multiplicative factors \pm1,\pm i :. G_1 \equiv \{\pm I,\pm iI,\pm X ...
Perrin friction factors: S \equiv 2 \frac{\mathrm{atanh} \ \xi}. where the parameter ξ is defined ... f_{P} \equiv \frac{p^{2/3}. The frictional coefficient is related to the ...
Phase (waves): A(t)\cdot \cos[2\pi ft + \varphi, \equiv I(t)\cdot \cos(2\pi ft). = I(t)\cdot \cos(2\pi ft) +. where f\, represents a carrier frequency, and ...
Phase correlation: i_b(x,y) \equiv i_a(x - \Delta x,. then, the discrete Fourier transform of the images will be shifted relatively in phase:. \mathbf{I}_b(u,v) = \mathbf{I ...
Phonon: Q_k \equiv Q_{k+K} \quad;\quad \Pi_k. for any integer n. A phonon with wave number k is thus equivalent to an infinite "family" of phonons with wave numbers ...
Photon dynamics in the double-slit experiment E_y . and. \mid \mathbf{E} \mid^2 \equiv \left ( . ... |\psi\rangle \equiv \begin{pmatrix} \psi_x \\ ...
Photon polarization: \alpha_x = \alpha_y \equiv \alpha . This represents a wave polarized at an ... |L\rangle \equiv {1 \over \sqrt{2}}. then a circular polarization state can ...
Photon: (known as Dirac's constant or Planck's reduced constant); \mathbf{k} is the wave vector (with the wave number k \equiv 2\pi/\lambda \! as its magnitude) and ...
Pi-calculus
: P \equiv Q if Q can be obtained from P by renaming one or more bound names in P. ... (\nu x)(P | Q) \equiv (\nu x if x is not a free name of Q. ...
Picard–Lindelöf theorem: An application of Grönwall's lemma to |\varphi(t)-\psi(t)| , where \varphi and ψ are two solutions, shows that \varphi(t)\equiv\psi(t) , thus proving the ...
Piezoelectricity: ... 444 (1973) Basic method for the measurement of resonance freq & equiv series resistance of quartz crystal units by zero-phase technique in a pi-network ...
Planck charge
: c \ is the speed of light in the vacuum,: h \ is Planck's constant,: \hbar \equiv \frac{h}{2 \pi} \ is the reduced Planck's constant or Dirac's constant, ...
Planck's constant
: \hbar\equiv\frac{h}{2\pi} = \. The figures cited here are the 2002 CODATA-recommended values for the constants and their uncertainties. ...
Planck's law of black body radiation
: \beta\equiv 1/\left(kT\right) . The denominator Z\left(\beta\right) , is the partition function of a single mode ... \varepsilon\equiv\frac{hc}{2L}\sqrt{n_ ...
Plasma oscillation: v \sim v_{ph} \equiv \frac{\omega}{. so the plasma waves can accelerate electrons that are moving with speed nearly equal to the phase velocity of the wave. ...
Plus-minus sign
: \cos(x \pm y) \equiv \cos(x) \. are most neatly written using the "∓" sign. In ISO-8859-1,7,8,9,13,15 and 16, the plus-minus symbol is given by the code ...
Poisson distribution: The parameter λ is not only the mean number of occurrences \langle k \rangle , but also its variance \sigma_{k}^{2} \equiv \langle k^{ (see Table). ...
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) ...
Poisson summation formula: \omega_0 \equiv \frac{2\pi}{T} . An alternative definition of the continuous Fourier ... Making a change of variables to \tau \equiv t + nT results in ...
Polylogarithm: \operatorname{Li}_{s+1}(z) \equiv. This converges for Re(s) > 0 and all z except ... H_n\equiv \sum_{k=1}^n{1\over. The problem terms now contain −ln(−μ) ...
Polytomous Rasch model: \Omega' \equiv \{1,...1,0,. in which x ones are followed by m-x zeros. For example, in the case of two thresholds, the permissible patterns in this response ...
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), ...
Prenex normal form: \forall x ( P(x) \rightarrow Q ) \equiv \exists. and. \forall x ( P \rightarrow Q(x) ) \equiv P \ ,. The duals of these schemata, involving existential ...
Price equation: \Delta z \equiv z'-z = 1/3 \,\. which indicates that the trait of sightedness is increasing in the ... \operatorname{var}(z_i) \equiv \operatorname{E}( ...
Primordial fluctuations: \delta(\vec{x}) \equiv \frac{\rho. where \bar{\rho} is the average mass ... P(k) \equiv |\delta_k|^2 . For scalar fluctuations, n + 1 is referred to as the ...
Probable prime: a^d\equiv 1\mod n: a^{d\cdot 2^r}\equiv -1\mod. A strong probable prime to base a is called a strong pseudoprime to base a. Every strong probable prime to ...
Probit model: Y \equiv 1(y^* >0). Then it is easy to show that. \Pr(Y=1 | X=x) = \Phi(x. Retrieved from "http://en.wikipedia.org/wiki/Probit_model%22 ...
Projective transformation
: n \leftrightarrow c \equiv \{ (\alpha + m \beta ). All of these exchange symmetries amount to exchanging pairs of rows in the coefficient matrix. ...
Propensity score
: p(x) \equiv Pr(T=1 | X=x). The propensity score was introduced by Rosenbaum and Rubin (1983) to provide an alternative method for estimating treatment ...
Proper time: So for our purposes \tau\ \equiv s. Taking the square root of each side of the line element gives the above definition of d\tau\ . After that, take the path ...
Proth's theorem: a^{(p-1)/2}\equiv -1 \. then p is prime. This is a practical test because if p is prime, any chosen a has about a 50% chance of working. ...
Pythagorean trigonometric identity: All that remains is to prove it for − π < x < 0, this can be done by squaring the symmetry identities to get \sin^2x\equiv\sin^2(-x) and ...

Q

QCD vacuum: \langle (gG)^2\rangle\equiv\langle g^2. \langle \overline\psi\psi\rangle \simeq (-0.23). \langle (gG)^4\rangle\simeq 5:10\langle ...
Quadratic integral: u \equiv x + \frac{b}{2c} ,. define. -A^2 \equiv \frac{a}{c} - \. where. q \equiv 4ac-b^2. is the negative of the discriminant. When q < 0, then ...
Quadratic residue: {q}\equiv{x^2}\mbox{ (mod }. Otherwise, q is called a quadratic non-residue. For prime moduli, roughly half of the residue classes are of each type. ...
Quantum entanglement: \rho_A \equiv \sum_j \langle j|_B \left( |\ . ρA is sometimes called the reduced density matrix of ρ on subsystem A. Colloquially, we "trace out" system B ...
Quantum field theory: \phi(\mathbf{r}) \equiv \sum_{i}. The bosonic field operators obey the commutation relation. \left[\phi(\mathbf{r}) , \phi( ...
Quantum harmonic oscillator: \left[A , B \right] \equiv AB - BA . Using the above, we can prove the identities. H = \hbar \omega \left(a^{\dagger}a: \left[a , a^{\dagger} \right] = 1 . ...
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 . ...
Quasispecies model: x_i\equiv\frac{n_i}{\sum_j n_j} . x'_i\equiv\frac{n'_i}{\sum_j n . The above equations for the quasispecies then become for the discrete version: ...

R

Rabi problem: \kappa \equiv \frac{e}{m \omega x_0}. These equations can be solved as follows:. u(t;\delta) = [u_0 \cos \delta t -: v(t;\delta) = [u_0 \cos \delta t + ...
Radial basis function: K_t( \mathbf{w} ) \equiv \big [ y(t . We have explicitly included the dependence on the weights. ... x(t+1)\equiv f\left [ x(t). where t is a time index. ...
Radiative transfer: I_\nu(s)=I_\nu(s_0)e^{. where τ(s1,s2) is the optical depth of the atmosphere between s1 and s2:. \tau(s_1,s_2) \equiv \int_{s_1}^{ ...
Radius of gyration: \mathbf{r}_{mean} \equiv \frac{1}. The radius of gyration is also proportional to the ... R_{g}^{2} \equiv \frac{1}{. similar to the hydrodynamic radius, ...
Ramanujan graph: Lubotzky, Phillips and Sarnak show how to construct an infinite family of p + 1-regular Ramanujan graphs, whenever p \equiv 1\mod 4 is a prime. ...
Randall-Sundrum model
: The distance between both branes is only −ln(W)/k, though. In another coordinate system,. \varphi\equiv -{\pi \ln(ky)\over \. so that. 0\le \varphi \le \pi ...
RANDU: V_{j+1} \equiv (65539 V_j) \mod 2^. with V0 odd. It is widely considered to be one of the most ill-conceived random number generators designed. ...
Rational sieve: \prod_{p_i\in P} p_i^{a_i} \equiv \. (where the ai and bi are nonnegative integers.) When we have generated enough of these relations (it's generally ...
Rational trigonometry
: s(\ell_1, \ell_2) \equiv {Q(B,C. See also spread polynomials. ... For any triangle \bar{A_{1}}\bar{A_{2}} define the cross c_{3}\equiv 1 - s_{3} . Then: ...
Ray tracing: Let \mathbf{V}\equiv\mathbf{S}-\mathbf{ for simplicity, then. |\mathbf{V}+t\mathbf{d}|^{. \mathbf{V}^2+t^2\mathbf{d}. d^2t^2+2\mathbf{V}\cdot t\ ...
Ray transfer matrix analysis: g \equiv { \operatorname{tr}(\mathbf{M}). is the stability parameter. The eigenvalues are the solutions of the characteristic equation. ...
Receptor-ligand kinetics
: K_{d} \equiv \frac{k_{-1}}{. where k1 and k-1 are the forward and backward ... where the two equilibrium concentrations R_{\pm} \equiv E \pm D are given by ...
Reciprocal polynomial: A polynomial is called reciprocal if p(z) \equiv p^{*}(z) . If the coefficients ai are real then this reduces to ai = an−i. ...
Reduced mass: m_{red} \equiv {1 \over {{1 \over m_1. with the force the actual one. Applying the gravitational formula we get that the position of the first body with ...
Refactorable number: Zelinsky wondered if there exists a refactorable number n_0 \equiv a \mod m , does there necessarily exist n > n0- such that n is refactorable and n \equiv ...
Relational quantum mechanics: ... corresponding to {intersection, orthogonal sum, orthogonal complement, inclusion, and orthogonality} respectively, where Q_1 \bot Q_2 \equiv Q_1 \supset ...
Reproducing kernel Hilbert space: K(x,y) \equiv K_x(y). is called a reproducing kernel for the Hilbert space. In fact, K is uniquely determined by the above condition (*). ...
Reynolds stresses
: R_{ij} \equiv \rho \overline{ u'_i u'. The divergence of this stress is the force density on the fluid due to the turbulent fluctuations. ...
Riemann zeta function: Li_s(z) \equiv \sum_{k=1}^\infty. which coincides with Riemann's zeta-function when z = 1. The Lerch transcendent is given by. \Phi(z, s, q) = \sum_{k=0 ...
Rotating reference frame: \mathbf{v} \equiv \frac{d\mathbf{r}. The time derivative of position in a rotating ... where \mathbf{a}_{\mathrm{rotating}} \equiv \ is the apparent ...
Rushbrooke inequality: M(T,H) \equiv \lim_{N \rightarrow \infty ... t \equiv \frac{T-T_c}{T_c} measures the temperature relative to the critical point. ...

S

Saha ionization equation: \Lambda \equiv \sqrt{\frac{h^2}{2. m_e\, is the mass of an electron; T\, is the temperature of the gas; k_B\, is the Boltzmann constant ...
Schwartz-Zippel lemma and testing polynomial identities
: p_1(x) \equiv p_2(x) ? This problem can be solved by reducing it to the problem of polynomial ... [p_1(x) - p_2(x)] \equiv 0. Hence if we can determine that ...
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 ...
Sedimentation: Hence, it is generally possible to define a sedimentation coefficient s \equiv q/f that depends only on the properties of the particle and the surrounding ...
Shanks-Tonelli algorithm
: When p \equiv 3 \mod 4 , it is much more efficient to use the following identity: x \equiv ... Outputs: R, an integer satisfying R^2 \equiv n \mod p . ...
Shannon expansion
: F \equiv x * F_x + x' * F_x' ,. where F is any function and Fxand Fx' are positive and negative Shannon cofactors of F, respectively. ...
Shear modulus: G \equiv \frac{F/A}{\Delta x/h. where F/A is shear stress and Δx/h is shear strain. Shear modulus is usually measured in ksi (thousands of pounds per square ...
Sheffer stroke: "p or q" is equivalent to "(p NAND p) NAND (q NAND q)", p + q \equiv \overline{\overline{(p \cdot p. "p implies q" is equivalent to "(p NAND q) NAND p" ...
Shor's algorithm: a^r \equiv 1\ \mbox{mod}\ N.\. Therefore, N | (a r − 1). Suppose we are able to obtain r, and it is even. Then. a^r - 1 = (a^{r/2} - 1: \Rightarrow N\ ...
Shot noise: \Delta I^2 \equiv \langle\left(I-\langle. The only exception being if a squeezed coherent state can be formed through correlated photon generation. ...
SIGSALY: 3 - 5 \equiv -2 \equiv -2 + 6 \equiv 4. — giving a value of 4. The sampled value was then transmitted, ... 4 + 5 \equiv 9 \equiv 9 - 6 \equiv 3\mod ...
Sinusoidal plane-wave solutions of the electromagnetic wave equation: \langle \psi | \equiv \begin{pmatrix} \psi_x^* . ... \alpha_x = \alpha_y \equiv \alpha . This represents a wave polarized at an angle θ with respect to the ...
Sinusoidal plane-wave solutions of the electromagnetic wave equation: \alpha_x = \alpha_y \equiv \alpha . This represents a wave polarized at an angle θ with ... |L\rangle \equiv {1 \over \sqrt{2}}. Elliptical polarization. ...
Skellam distribution: \mu\equiv (\mu_1+\mu_2)/2.\,. Then the raw moments mk are. m_1=\left.\Delta\right.\, ... K(t;\mu_1,\mu_2)\equiv \ln(M. which yields the cumulants: ...
Solovay-Strassen primality test
: \left(\frac{a}{p}\right) \equiv. where. \left(\frac{a}{p}\right). is the Legendre symbol. The Jacobi symbol is a generalisation of the Legendre symbol where ...
Source function: S_{\lambda} \equiv \frac{j_{\lambda}}. where jλ is the emission coeffisient, κλ is the absorption coeffisient (also known as the opacity (optics)). ...
Spherical multipole moments: where R \equiv \left|\mathbf{r} - \mathbf{r is the distance between the charge ... Q_{lm} \equiv q \left( r^{\prime} . As with axial multipole moments, ...
Spin tensor: S^{\alpha\beta\mu}(x)\equiv M. Because of the continuity equation. \partial_\mu M^{\alpha\beta\mu}_0= ,. we get. \partial_\mu S^{\alpha\beta\mu}=T ...
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) ...
Spin-weighted spherical harmonics: \bar\eth\eta \equiv - (\sin{\theta}. The spin-weighted spherical harmonics are then defined in terms of the usual spherical harmonics as: ...
Standardized Kt/V: std \frac{K \cdot t}{V} \equiv const \. If one takes the inverse of Equation 8 it can be observed that the inverse of std Kt/V is proportional to the ...
Stokes parameters: \begin{matrix} I & \equiv & |E_x|^{2 ... \begin{matrix} L & \equiv & |L|e^{. Under a rotation \theta \rightarrow \theta+\theta' of the polarization ellipse, ...
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, ...
Strong pseudoprime: a^{d\cdot 2^r}\equiv -1\mod. It should be noted, however, that Guy uses a definition with only the first condition. Because not all primes pass that ...
Strong RSA assumption: More specifically, given a modulus N of unknown factorization, and a ciphertext C, it is infeasible to find any pair (M,e) such that C \equiv M^e~mod~N . ...
Subfactorial
: Subfactorials can also be calculated in the following ways: !n \equiv \frac{\Gamma (n+1, -1. where Γ denotes the incomplete gamma function, ...
Supercritical flow: Fr \equiv \frac{U}{\sqrt{gh}} ,. where. U = velocity of the flow; g = acceleration due to gravity (9.81 m/s² or 32.2 ft/s²); h = depth of flow relative to ...
Superspace: \overline{\theta}\equiv i\theta^\dagger\gamma. where C is the charge conjugation matrix, which is defined by the property that when it conjugates a gamma ...

T

Tarski's axioms: xy \equiv yx\,. The distance from x to y is the same as that from y to x. ... This can be done as xy \le zu \leftrightarrow \forall v ( zv \equiv uv ...
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. ...
Teleparallelism: D_\mu x^a \equiv (dx^a)_\mu. is defined with respect to the connection form B. Here, d is the exterior derivative of the ath component of x, ...
Ternary logic
: Of the four functions defined above, OR, AND, and EQUIV are commutative, while IF/THEN is not. For comparison, there are 8 commutative two-argument binary ...
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. ...
There is no infinite-dimensional Lebesgue measure
\mu \left( B_{r_{0}} (0) \ by local finiteness. This is a contradiction, and completes the proof. ...
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 ...
Thermodynamic equations: F \equiv U-TS = \mu n - PV ~. [edit]. Gibbs free energy. ~ G \equiv U-TS+PV = \mu n ~. [edit]. Enthalpy. ~ H \equiv U+PV = \mu n + TS~ ...
Thomson scattering: \sigma \equiv \left(\frac{q^2}{mc. where q is the charge per particle, and m is the mass per particle. Note that this is the square of the classical radius ...
Time dilation: ... Δ t is that same time interval as measured in the "stationary" system of reference,: \gamma \equiv \frac{1}{\sqrt{1 - \ is the Lorentz factor, ...
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 ...
Tree automaton: Definitions necessary for this theorem: A congruence on tree languages is a relation such that u_i \equiv v_i 1 \leq i \leq n \Rightarrow f(u_1 It is of ...
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) ...
Trigonometric substitution: \sec^2\theta-1\;\equiv\;\tan. to simplify certain integrals containing the radical expressions. \sqrt{a^2-x^2}. \sqrt{a^2+x^2}. \sqrt{x^2-a^2} ...
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 ...
Truth table: The negation of conjunction \neg (p \and q) \equiv p \bar{\and , and the ... The negation of disjunction \neg (p \or q) \equiv p \bar{\or and the ...
Turing jump: K_\varphi \equiv \varnothing' , the Turing jump of the empty set, is Turing equivalent to the halting problem. For each n, the set \varnothing^{(n)} is ...
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 ...

U-Z

Upward Löwenheim–Skolem theorem
: Then let C be an infinite set of constants not in L of size κ and S \equiv \{c_i \neq c_j| i \neq j; i . Then T \cup S is a collection of L(C)-sentences. ...
V sign: From Wikipedia, the free encyclopedia. Jump to: navigation, search. Polish Prime Minister Tadeusz Mazowiecki making the V sign. ...
Variational message passing: L(Q) \equiv \sum_{H} Q(H) \ ,. then the likelihood is simply this bound plus the ... Q(H) \equiv \prod_i Q_i(H_i) ,. where Hi is a disjoint part of the ...
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 ...
Vertex function: \Gamma^\mu\equiv -{1\over e}{\. It is unfortunate that the effective action Γeff and the vertex function Γμ happen to be described by the same letter. ...
Vertex model: where \tau \equiv \operatorname{trace}_{V}(T) is the row-transfer matrix. Two rows of vertices in the square lattice vertex model ...
Vigenère cipher: If the letters A–Z are taken to be the numbers 0–25, and addition is performed modulo 26, then Vigenère encryption can be written,. C_i \equiv (P_i + K_i) ...
Virial theorem: T \equiv \frac{1}{2} \sum_{k=. The average of this derivative over a time τ is ... which is clearly equal and opposite to \mathbf{F}_{kj} \equiv -\nabla_{\ ...
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, ...
Weierstrass factorization theorem: If the sequence, {zi} is finite then p_i \equiv 0 suffices for convergence in condition 2, and we obtain: \, P(z) = \prod_n (z-z_n) . ...
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 ...
Well-quasi-ordering: For example, if we order \mathbb{Z} by divisibility, we end up with n\equiv m if and only if n=\pm m , so that (\mathbb{Z},\mid)\;\;\approx . ...
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 ...
Wilson's theorem: 1\cdot 2\cdots (p-1)\ \equiv\ -. 1\cdot(p-1)\cdot 2\cdot (p- ... \prod_{j=1}^m\ j^2\ \equiv. And so primality is determined by the quadratic residues of p. ...
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 ...
Zero-product property: has solutions {0, 1} in Z, Q, or R, but in Z6 the solution set is {0, 1, 3, 4} since 32 − 3 = 6 \equiv 0 (mod 6) and 42 − 4 = 12 \equiv 0 (mod 6). ...
Zeta distribution: m_n \equiv E(k^n) = \frac{1}{. The series on the right is just a series representation ... M(t;s) \equiv E(e^{tk}). The series is just the definition of the ...