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 		&#8722; 1) instead of in terms of g(n &#8722; 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 &gt; R_N 		\,. The reconstruction of a signal from its samples can ...
 * Baryogenesis: s \equiv 		\frac{\mathrm{entropy}}{\mathrm{. with p and &#961; as the pressure and 		density from the energy density tensor T&#956;&#957;, 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 &quot;Stirling numbers of the second kind&quot;. 		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&gt;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 &#956;T and variance &#963;2T. 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 		&#946; 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: &quot;The &#966;s are equinumerous with the &#968;s&quot;. (Q_Ix)(\phi x,\psi x)\equiv 		(Q_Lx. Chang: &quot;The number of &#966;s 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 &#952; 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 &amp; \equiv &amp; \forall x ...
 * Calculus of variations: The preceding reasoning is not valid if &#963; 		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:. &#956; is the viscosity of the liquid; v is a characteristic 		velocity; &#963; 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 + &#916;s = 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 &amp;=&amp; 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 &gt; 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 M&#956;&#957; 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 &amp; - ...
 * 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 T&#934; := \{ \; 		\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(&#969;), ...
 * Coupling constant: \alpha_s(k^2) \equiv \frac{g_s^2(. 		where &#946;0 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 		&lt;\sigma, {. where &lt;\sigma, {\mathbf u}&gt; is a real number. ...
 * Creation and annihilation operators: a^\dagger \equiv \frac{1}{\sqrt{2 		as the &quot;creation operator&quot; or the &quot;raising operator&quot; and: a \equiv 		\frac{1}{\sqrt{2}} \ as the &quot;annihilation operator&quot; 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 &#960; and &#952; 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 &#956; with finite mass is a ...
 * Curry's paradox: X \equiv \left\{ x | ( x \in x ) \. 		The proof proceeds:. \begin{matrix} \mbox{1.} &amp; ( 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 &#952;, 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 &#8594; q) &#8866; (¬q &#8594; ¬p), If p 		then q is equiv. to if not q then ... Tautology, p &#8866; (p &#8744; 		¬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 		&quot;functional manifold&quot;. 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 &amp; \equiv &amp; 		\mbox{SHA-1. Since g has order q we have. \begin{matrix} g^k &amp; \equiv 		&amp; 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 &#968;. ...
 * 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 &#968;. ...
 * 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(&#955;). 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 &#8722;&#8734; 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 &#955; 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 &#955;D &#8801; 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 &#963; can represent any of the three variables (&#955;,&#956;,&#957;). 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 &#952; is an angle that 		determines the tilt of the ellipse and &#945;x &#8722; &#945;y ...
 * 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 -&gt; * =&gt; P zero -&gt; (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 &#916;G 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 &#8722; 1)/2 &#8801; &#8722;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 &quot;psi-bar&quot; is defined as \bar{\psi} \equiv 		\psi^{\dagger} \ . Given the expression for &#968;(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 &#947; are the gamma matrices. ...
 * Fine structure: Fermions, such as electrons and protons, 		compose the &quot;stuff&quot; 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 = &#966;(x,0), and so on. ...
 * Formulation of Maxwell's equations in special relativity: where &#961; 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(&#969;), ...
 * 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(&#969;), ...
 * 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 &#966;. ...
 * 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 &#915;kij. 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, &#956; is the chemical potential, ...
 * Green-Kubo relations: The strain rate &#947; 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: &#969; 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 &quot;cosheck&quot; or &quot;cosech&quot;. 		\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} &lt; m. Retrieved from 		&quot;http://en.wikipedia.org/wiki/Inversive_congruential_generator&quot; ...
 * IP (complexity): a \vee b, a*b \equiv 1 - (1 - a)(1 		- b. \neg a, 1 &#8722; 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 &#8800; b, a is not equal to b, a \not\equiv 		b may be used to emphasise that a is not identically equal to b. &#8797;, a &#8797; 		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 &quot;http://en.wikipedia.org/wiki/Josephson_phase&quot; ...

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 &gt; \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 		&lt; 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 &gt; 0 so that the ... M(t;c)\equiv 		\sqrt{\frac{c}. which diverges for t &gt; 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 &#952; 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 = &#948;caRabcd gives ...
 * Logical NOR: &quot;not p&quot; is equivalent to &quot;p NOR p&quot;, 		\overline{p} \equiv \overline{p + p} ... &quot;p or q&quot; is 		equivalent to &quot;(p NOR q) NOR (p NOR q)&quot;, p + q \equiv ...
 * Loop entropy: \mathbf{W} \equiv \begin{bmatrix} 		58 &amp;&amp; 26 \. whose determinant is 2340. Taking the logarithm and 		multiplying by the constants &#945;kB 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 &#961; 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 &gt; 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 &#937; 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. &#8722; 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 &#915; is a Christoffel symbol. ...
 * Newton's law of universal gravitation: ... of objects 1 and 2: r21 = | r2 		&#8722; 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 &#950;. 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 &#957;1 is equivalent to &#957;2 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 &quot;time 		parameter&quot;, 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 &#966; 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 		&quot;constant&quot; 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 &#952;(t) = &#952;eq (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(&#966;i) 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 = &#963;1,Y = &#963;2,Z = &#963;3, 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 &#958; 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 &quot;family&quot; 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 &#968; are two solutions, shows that 		\varphi(t)\equiv\psi(t) , thus proving the ...
 * Piezoelectricity: ... 444 (1973) Basic method for the 		measurement of resonance freq &amp; 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 &quot;&#8723;&quot; 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 &#955; 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 &#956; given Z - Poisson random variable with rate &#956;(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) &gt; 0 and all z except ... H_n\equiv 		\sum_{k=1}^n{1\over. The problem terms now contain &#8722;ln(&#8722;&#956;) ...
 * 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^* &gt;0). Then it is easy 		to show that. \Pr(Y=1 | X=x) = \Phi(x. Retrieved from 		&quot;http://en.wikipedia.org/wiki/Probit_model&quot; ...
 * 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 &#8722; &#960; &lt; 		x &lt; 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 &lt; 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( |\ . &#961;A is sometimes called the reduced density matrix of &#961; on 		subsystem A. Colloquially, we &quot;trace out&quot; 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 &lt; + \infty or &#956; 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 &#964;(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 		&#8722;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&#8722;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 &gt; 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 &#916;x/h is shear strain. Shear modulus is 		usually measured in ksi (thousands of pounds per square ...
 * Sheffer stroke: &quot;p or q&quot; is equivalent to &quot;(p NAND p) NAND 		(q NAND q)&quot;, p + q \equiv \overline{\overline{(p \cdot p. &quot;p 		implies q&quot; is equivalent to &quot;(p NAND q) NAND p&quot; ...
 * Shor's algorithm: a^r \equiv 1\ \mbox{mod}\ N.\. 		Therefore, N | (a r &#8722; 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 &#952; 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 &#952; 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 j&#955; is the emission coeffisient, &#954;&#955; 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 &amp; \equiv &amp; 		|E_x|^{2 ... \begin{matrix} L &amp; \equiv &amp; |L|e^{. Under a 		rotation \theta \rightarrow \theta+\theta' of the polarization ellipse,		...
 * Stopped process: Stopping at a deterministic time T &gt; 0: if 		\tau (\omega) \equiv T, then the stopped Brownian motion B&#964;- 		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 &#915; 		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 d&#964; 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: ... &#916; t is that same time interval 		as measured in the &quot;stationary&quot; 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) &amp; \equiv &amp; (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 &#954; 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 &#915;eff and the vertex function &#915;&#956; 		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 &#964; 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;&#947;) 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 &#955; is the wavelength in the medium, &#957; (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 &gt; 0-, m = 0 but P0 &gt; 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 &#8722; 3 = 6 \equiv 0 		(mod 6) and 42 &#8722; 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 ...