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searching for Right! Right! Right! 182 found (190 total)

Limit of a sequence (4,510 words) [view diff] no match in snippet view article find links to article

\left(\forall n\in \mathbb {N} \left(n\geq N\implies |x_{n}-x|<\varepsilon \right)\right)\right)} . If a sequence ( x n ) {\displaystyle (x_{n})} converges to some

LEA (cipher) (2,704 words) [view diff] no match in snippet view article

\left(i+1\right)\right)\right)\lll 3} T[2]←(T[2]⊞(δ[imod4]⋘(i+2)))⋘6{\displaystyle T[2]\leftarrow \left(T[2]\boxplus \left(\delta [i\mod 4]\lll \left(i+2\right)\right)\right)\lll

Paper bag problem (442 words) [view diff] no match in snippet view article find links to article

{\displaystyle V=w^{3}\left(h/\left(\pi w\right)-0.142\left(1-10^{\left(-h/w\right)}\right)\right),} where w is the width of the bag (the shorter dimension), h is

Vincenty's formulae (2,359 words) [view diff] no match in snippet view article find links to article

right)\right]\right)\\B&={\frac {u^{2}}{1024}}\left(256+u^{2}\left[-128+u^{2}\left(74-47u^{2}\right)\right]\right)\\\Delta \sigma &=B\sin

Generalized Maxwell model (1,547 words) [view diff] no match in snippet view article find links to article

_{k\in \left\{{i_{1},...,i_{n}}\right\}}{\tau _{k}}}\right)}\right)}}\right)...}}\right)...}}\right){\frac {\partial ^{n}{\epsilon }}{\partial {t}^{n}}}}}

Differential calculus over commutative algebras (730 words) [view diff] no match in snippet view article find links to article

\left[f_{k}\left[f_{k-1}\left[\cdots \left[f_{0},\Delta \right]\cdots \right]\right]\right]=0} where the bracket [ f , Δ ] : Γ ( E ) → Γ ( F ) {\displaystyle

Pentagonal rotunda (329 words) [view diff] no match in snippet view article find links to article

{30\left(65+29{\sqrt {5}}\right)}}\right)}}\right)a^{2}\\&=\left({\frac {1}{2}}\left(5{\sqrt {3}}+{\sqrt {10\left(65+29{\sqrt {5}}\right)}}\right)\right)a^{2}\approx

Pulse wave (725 words) [view diff] no match in snippet view article find links to article

}\left(\operatorname {sinc} \left(n{\frac {\tau }{T}}\right)\cos \left(2\pi nft\right)\right)\right)} or with d = τ T {\displaystyle d={\frac {\tau }{T}}} as x ( t )

Continuous stochastic process (827 words) [view diff] no match in snippet view article find links to article

\left|\lim _{s\to t}{\big |}X_{s}(\omega )-X_{t}(\omega ){\big |}=0\right.\right\}\right)=1.} Given a time t ∈ T, X is said to be continuous in mean-square

Discontinuous Galerkin method (3,654 words) [view diff] no match in snippet view article find links to article

0)|||{\displaystyle \left|\left|\left|U(\cdot ,T)\right|\right|\right|\leq \left|\left|\left|U(\cdot ,0)\right|\right|\right|},|||u(⋅,T)|||≤|||U(⋅,0)|||{\displaystyle

Classical capacity (4,629 words) [view diff] no match in snippet view article find links to article

_{X^{n}}\left\{{\frac {1}{M}}\sum _{m}{\text{Tr}}\left\{\rho _{X^{n}\left(m\right)}\right\}\right\}} = E X n { 1 M ∑ m Tr { Π ρ , δ n ρ X n ( m ) } + Tr { Π ^ ρ

Index of dispersion (1,274 words) [view diff] no match in snippet view article find links to article

}\left(\operatorname {var} \left[\log \left({\frac {t_{a}}{t_{b}}}\right)\right]\right)}}\right)}} where tj is the mean absolute deviation of the jth sample

Atari joystick port (4,692 words) [view diff] no match in snippet view article find links to article

Left 1Y (-, Left) unused Button 1 Up Left 4 Right Right Right Right Right Right Right Right Right Right 2Y (-, Right) Button 1 Button 2 Button 1 Down

Position of the Sun (3,336 words) [view diff] no match in snippet view article find links to article

}}\cdot 0.0167\sin \left({\frac {360^{\circ }}{365.24}}\left(N-2\right)\right)\right)\right]} which can be simplified by evaluating constants to: δ ⊙ = −

Web Mercator projection (1,702 words) [view diff] no match in snippet view article find links to article

-\ln \left[\tan \left({\frac {\pi }{4}}+{\frac {\varphi }{2}}\right)\right]\right)\right\rfloor {\text{ pixels}}\end{aligned}}} where λ {\displaystyle

Communicating sequential processes (5,247 words) [view diff] no match in snippet view article find links to article

{VendingMachine} \left\vert \left[\left\{\mathrm {coin} ,\mathrm {card} \right\}\right]\right\vert \mathrm {Person} \equiv \mathrm {coin} \rightarrow \mathrm {choc}

Elongated pentagonal rotunda (280 words) [view diff] no match in snippet view article find links to article

{5\left(145+58{\sqrt {5}}+2{\sqrt {30\left(65+29{\sqrt {5}}\right)}}\right)}}\right)a^{2}\approx 32.3472...a^{2}} The dual of the elongated pentagonal

Engel expansion (2,085 words) [view diff] no match in snippet view article find links to article

\left(1+{\frac {1}{a_{2}}}\!\left(1+{\frac {1}{a_{3}}}\left(1+\cdots \right)\right)\right)} For instance, Euler's number e has the Engel expansion 1, 1, 2

Tippu (singer) (145 words) [view diff] no match in snippet view article

Anthem" B. Ajaneesh Loknath Naa... Nuvve "Hey Hey I Love You"(Male) Sharreth "Right Right Right" 2019 1st Rank Raju "Chalo Re Chalo" Kiran Ravindranath

Bremsstrahlung (9,295 words) [view diff] no match in snippet view article find links to article

_{i}}}\right)\right]\right)\\&\left[\left(E_{f}-p_{f}c\right)\left(4p_{i}^{2}p_{f}^{2}\sin ^{2}\Theta _{i}\left[-E_{f}-p_{f}c\right]\right.\right.\\&{}+\left

Elongated pentagonal cupola (282 words) [view diff] no match in snippet view article find links to article

{1}{4}}\left(60+{\sqrt {10\left(80+31{\sqrt {5}}+{\sqrt {2175+930{\sqrt {5}}}}\right)}}\right)\right)a^{2}\approx 26.5797...a^{2}} The dual of the elongated pentagonal

Pentagonal cupola (429 words) [view diff] no match in snippet view article find links to article

A=\left({\frac {1}{4}}\left(20+5{\sqrt {3}}+{\sqrt {5\left(145+62{\sqrt {5}}\right)}}\right)\right)a^{2}\approx 16.57975a^{2},} R = ( 1 2 11 + 4 5 ) a ≈ 2.23295 a

Density matrix (4,927 words) [view diff] no match in snippet view article find links to article

_{m}\left(\sum _{j}p_{j}\left|\psi _{j}\right\rangle \left\langle \psi _{j}\right|\right)\right],} which makes the density operator, defined as ρ=∑jpj|ψj⟩⟨ψj|,{\displaystyle

Linear polarization (666 words) [view diff] no match in snippet view article find links to article

|\mathrm {Re} \left\{|\psi \rangle \exp \left[i\left(kz-\omega t\right)\right]\right\}} B ( r , t ) = z ^ × E ( r , t ) / c {\displaystyle \mathbf {B}

Runge–Kutta methods (6,682 words) [view diff] no match in snippet view article find links to article

{d}{dt}}\left[f(y_{t},\ t)+\left.{\frac {h}{2}}{\frac {d}{dt}}f(y_{t},\ t)\right]\right]\right]\right\rbrace +{\mathcal {O}}(h^{5})\\={}&y_{t}+a\cdot hf_{t}+b\cdot

Player efficiency rating (2,256 words) [view diff] no match in snippet view article find links to article

\left({\frac {lgFT}{lgPF}}-0.44\times {\frac {lgFTA}{lgPF}}\times VOP\right)\right]\right)} When multiplied out and refactored, the equation above becomes:

Madhava series (4,618 words) [view diff] no match in snippet view article find links to article

{s^{2}}{(4^{2}+4)r^{2}}}\cdot {\frac {s^{2}}{(6^{2}+6)r^{2}}}-\cdots \right]\right]\right]} Let θ be the angle subtended by the arc s at the centre of the

Holtsmark distribution (1,297 words) [view diff] no match in snippet view article find links to article

{2x^{3}}{27}}\right)-J_{1/3}\left({\frac {2x^{3}}{27}}\right)\right]\right\}\\&-{\frac {x^{2}}{6\pi }}\left[~_{2}F_{2}\left(1,{\frac {3}{2}};{\frac

Gaussian integer (4,795 words) [view diff] no match in snippet view article find links to article

{\text{and}}\\H_{t}&=\left\{\left.z_{0}\left(x+i\left(t-{\tfrac {1}{2}}\right)\right)\right\vert x\in \mathbf {R} \right\},\end{aligned}}} with s and t integers

Arithmetic–geometric mean (2,596 words) [view diff] no match in snippet view article find links to article

{1-x^{2}}}\right)}}\right)\right)=\left(\sum _{n\in \mathbb {Z} }\exp \left(-n^{2}\pi {\frac {M(1,x)}{M\left(1,{\sqrt {1-x^{2}}}\right)}}\right)\right)^{-2}

Cepstrum (2,261 words) [view diff] no match in snippet view article find links to article

{F}}^{-1}\left\{\log \left(\left|{\mathcal {F}}\{f(t)\}\right|^{2}\right)\right\}\right|^{2}} The power cepstrum has main applications in analysis of sound

Advanced z-transform (526 words) [view diff] no match in snippet view article find links to article

{\begin{aligned}F(z,m)&={\mathcal {Z}}\left\{\cos \left(\omega \left(kT+m\right)\right)\right\}\\&={\mathcal {Z}}\left\{\cos(\omega kT)\cos(\omega m)-\sin(\omega

Darcy–Weisbach equation (4,441 words) [view diff] no match in snippet view article find links to article

{D} }}}}}\left\{1+0.305R_{*}\;\left(1-\exp {\frac {-R_{*}}{26}}\right)\right\}\right),} and : 1fD=−1.93log10⁡(1.91RefD{1+0.34R∗(1−exp⁡−R∗26)}),{\displaystyle

Transmission coefficient (1,229 words) [view diff] no match in snippet view article find links to article

_{x_{1}}^{x_{2}}dx{\sqrt {{\frac {2m}{\hbar ^{2}}}\left(V(x)-E\right)}}\,\right)\right)^{2}}}\ ,} where x 1 , x 2 {\displaystyle x_{1},\,x_{2}} are the

Free fall (2,507 words) [view diff] no match in snippet view article find links to article

{7}{2}}(\arcsin({\sqrt {r}})-{\sqrt {r-r^{2}}})\right)^{-{\frac {2}{3}}n}\right]\right)\right].} Evaluating this yields: y ( t ) = y 0 ( x − 1 5 x 2 − 3 175 x

Green's function (5,050 words) [view diff] no match in snippet view article find links to article

u}{c}}\right)+{\frac {\gamma t}{u}}I_{1}\left({\frac {\gamma u}{c}}\right)\right)\right]} with u = c 2 t 2 − x 2 {\displaystyle u={\sqrt {c^{2}t^{2}-x^{2}}}}

Darcy friction factor formulae (3,950 words) [view diff] no match in snippet view article find links to article

\left({\frac {\varepsilon /D}{3.7}}+{\frac {13}{\mathrm {Re} }}\right)\right)\right]} or 1f=−2log⁡[ε/D3.7−5.02Relog⁡(ε/D3.7+13Re)]{\displaystyle {\frac

Bühlmann model (1,536 words) [view diff] no match in snippet view article find links to article

\right)\left[\mathbb {E} _{X}\left[(m(\vartheta )-\Pi )|X_{i1},\ldots ,X_{im}\right]\right]\right]\\&=0\end{aligned}}} We are using here the law of total expectation

Hans B. Pacejka (825 words) [view diff] no match in snippet view article find links to article

\sin \left\{C\cdot \arctan \left[Bx-E\cdot (Bx-\arctan \left(Bx)\right)\right]\right\}\,} where B, C, D and E represent fitting constants and y is a force

Probability (5,123 words) [view diff] no match in snippet view article find links to article

C\right)+P\left(B\cap C\right)-P\left(\left(A\cap C\right)\cap \left(B\cap C\right)\right)\right)\\P\left(A\cup B\cup C\right)=&P\left(A\right)+P\left(B\right)+P

Indifference price (1,029 words) [view diff] no match in snippet view article find links to article

\left(-{\frac {1.10x}{10}}\right)+\exp \left(-{\frac {1.10x+20\beta }{10}}\right)\right]\right]} . Which is maximized when β = 0 {\displaystyle \beta =0} , therefore

Leibniz integral rule (11,110 words) [view diff] no match in snippet view article find links to article

\left({\frac {1+\alpha }{1-\alpha }}\tan \left({\frac {x}{2}}\right)\right)\right\}\right|_{0}^{\pi }.\end{aligned}}} As x {\displaystyle x} varies from

Symmetric difference (2,399 words) [view diff] no match in snippet view article find links to article

Y\right)\right)-\left(\mu \left(X\cap Y\right)+\mu \left(Y\setminus X\right)\right)\right|\\&=\left|\mu \left(X\setminus Y\right)-\mu \left(Y\setminus X\right)\right|\\&\leq

Elliptical polarization (1,128 words) [view diff] no match in snippet view article find links to article

\right|\mathrm {Re} \left\{|\psi \rangle \exp \left[i\left(kz-\omega t\right)\right]\right\}} B ( r , t ) = z ^ × E ( r , t ) {\displaystyle \mathbf {B} (\mathbf

Relation between Schrödinger's equation and the path integral formulation of quantum mechanics (2,137 words) [view diff] no match in snippet view article find links to article

2}m\left({q_{j+1}-q_{j} \over \delta t}\right)^{2}-V\left(q_{j}\right)\right)\right]} The transition amplitude for the entire time period is ⟨ F | exp

Grouser (816 words) [view diff] no match in snippet view article find links to article

64\left[\left({\frac {h}{b}}\right)\cot ^{-1}\left({\frac {h}{b}}\right)\right]\right)} where: H={\displaystyle H=} soil thrust b={\displaystyle b=} track

Quantum field theory (14,868 words) [view diff] no match in snippet view article find links to article

_{-T}^{T}dt\,H_{I}(t)\right]\right\}\right|0\right\rangle }{\left\langle 0\left|T\left\{\exp \left[-i\int _{-T}^{T}dt\,H_{I}(t)\right]\right\}\right|0\right\rangle

Integer partition (3,294 words) [view diff] no match in snippet view article find links to article

\left[{{\frac {\pi }{k}}{\sqrt {{\frac {2}{3}}\left(n-{\frac {1}{24}}\right)}}}\,\,\,\right]}\right)} where Ak(n)=∑0≤m<k,(m,k)=1eπi(s(m,k)−2nm/k).{\displaystyle

Test functions for optimization (867 words) [view diff] no match in snippet view article find links to article

x\sin y\exp \left(\left|100-{\frac {\sqrt {x^{2}+y^{2}}}{\pi }}\right|\right)\right|+1\right]^{0.1}} Min={f(1.34941,−1.34941)=−2.06261f(1.34941,1.34941)=−2

Biharmonic equation (822 words) [view diff] no match in snippet view article find links to article

{\partial }{\partial r}}\left(r{\frac {\partial \varphi }{\partial r}}\right)\right)\right)+{\frac {2}{r^{2}}}{\frac {\partial ^{4}\varphi }{\partial \theta

Radial trajectory (1,439 words) [view diff] no match in snippet view article find links to article

\left[{\sqrt {r}}\right]-{\sqrt {r-r^{2}}}\right)\right]^{-{\frac {2}{3}}n}\right)\right]\right)} Evaluating this yields: x ( t ) = p − 1 5 w p 2 − 3 175 w 2 p 3

Folded normal distribution (2,954 words) [view diff] no match in snippet view article find links to article

^{2}t^{2}}{2}}-\mu t}\left[1-\Phi \left({\frac {\mu }{\sigma }}-\sigma t\right)\right]\right\rbrace }}. The Laplace transformation is given by

Benford's law (7,277 words) [view diff] no match in snippet view article find links to article

\left(X{\text{ has FSD}}=k\right)-\log _{10}\left(1+{\frac {1}{k}}\right)\right|\right\}.} The leading factor N {\displaystyle {\sqrt {N}}} does not appear

Temperature dependence of viscosity (2,191 words) [view diff] no match in snippet view article find links to article

\left({\ln \left({\nu +0.7+e^{-\nu }K_{0}\left({\nu +1.244067}\right)}\right)}\right)=A-B\ln T} where T {\displaystyle T} is absolute temperature in

Approximations of π (12,344 words) [view diff] no match in snippet view article find links to article

{1}{3}}\left(1+{\frac {2}{5}}\left(1+{\frac {3}{7}}\left(1+\cdots \right)\right)\right)\end{aligned}}} where m!! is the double factorial, the product of

Minimum deviation (1,316 words) [view diff] no match in snippet view article find links to article

^{-1}\left(n\cdot \sin \left(A-\sin ^{-1}\left({\frac {\sin i}{n}}\right)\right)\right)=f(i)(say)} Finding the minima of this equation will also give the

Exact differential equation (4,892 words) [view diff] no match in snippet view article find links to article

\partial y}{dy \over dx}-{d \over dx}\left(I\left(x,y\right)-h\left(x\right)\right)\right)dx} Thus, the second order differential equation f(x,y)+g(x,y,dydx)dydx+d2ydx2(J(x

Forcing (mathematics) (9,287 words) [view diff] no match in snippet view article

p)\land \left(q\Vdash ~u\left({\check {a}}\right)={\check {b}}\right)\right]\right\}.\right.} By the definability of forcing, this definition makes sense

Ordered pair (3,774 words) [view diff] no match in snippet view article find links to article

b\right):=\left\{\left\{\left\{a\right\},\,\emptyset \right\},\,\left\{\left\{b\right\}\right\}\right\}.} He observed that this definition made it possible to define

Inception score (975 words) [view diff] no match in snippet view article find links to article

p_{gen}}\left[D_{KL}\left(p_{dis}(\cdot |x)\|\int p_{dis}(\cdot |x)p_{gen}(x)dx\right)\right]\right)} Equivalent rewrites include ln⁡IS(pgen,pdis):=Ex∼pgen[DKL(pdis

Covariance (4,706 words) [view diff] no match in snippet view article find links to article

{E} \left[X\right]\right)\left(Y-\operatorname {E} \left[Y\right]\right)\right]\\&=\operatorname {E} \left[XY-X\operatorname {E} \left[Y\right]-\operatorname

Ionization (6,098 words) [view diff] no match in snippet view article find links to article

\mathrm {d} \Omega \left|FT\left(I_{KAR}\Psi \left(\mathbf {r} \right)\right)\right|^{2}J_{n}^{2}\left(n_{f},{\frac {n_{\mathrm {osc} }}{2}}\right)}

Viscosity (11,377 words) [view diff] no match in snippet view article find links to article

{\left[(2+\lambda )\alpha _{T}T_{g}\left(1-{\frac {T}{T_{g}}}\right)\right]}\right\}}} where C G {\displaystyle C_{G}} denotes the high-frequency shear

Divisor function (3,734 words) [view diff] no match in snippet view article find links to article

{1}{2}}\left(3i^{2}-i\right)\right)+\sigma _{1}\left(n-{\frac {1}{2}}\left(3i^{2}+i\right)\right)\right),\end{aligned}}} where σ 1 ( 0 ) = n {\displaystyle \sigma _{1}(0)=n}

Postnikov system (3,655 words) [view diff] no match in snippet view article find links to article

{Z} ,n),H_{q}\left(K\left(\pi _{n+1}\left(S^{n}\right),n+1\right)\right)\right)} . And the first non-trivial map to π n + 1 ( S n ) {\displaystyle

Mercator projection (5,968 words) [view diff] no match in snippet view article find links to article

{y_{1}}{R}}\right)\right]-\tan ^{-1}\left[\sinh \left({\frac {y_{2}}{R}}\right)\right]\right|,} where R may be calculated from the width W of the map by R = W/2π

Partition function (number theory) (4,136 words) [view diff] no match in snippet view article

\left[{{\frac {\pi }{k}}{\sqrt {{\frac {2}{3}}\left(n-{\frac {1}{24}}\right)}}}\,\,\,\right]}\right),} where Ak(n)=∑0≤m<k,(m,k)=1eπi(s(m,k)−2nm/k).{\displaystyle

Single-sideband modulation (4,797 words) [view diff] no match in snippet view article find links to article

\left[\cos \left(2\pi f_{0}t\right)+j\cdot \sin \left(2\pi f_{0}t\right)\right]\,\right\}\\&=s(t)\cdot \cos \left(2\pi f_{0}t\right)-{\widehat {s}}(t)\cdot

Helmholtz free energy (4,158 words) [view diff] no match in snippet view article find links to article

\left(P_{r}\right)=\log \left[\left\langle \exp \left(-\beta H-\log \left(Z\right)\right)\right\rangle _{r}\right]\geq \left\langle -\beta H-\log \left(Z\right)\right\rangle

Bretagnolle–Huber inequality (1,627 words) [view diff] no match in snippet view article find links to article

{P}{Q}}}\right)^{-1}\,\right]\right)\right)\\&\geq \exp \left(\operatorname {E} _{P}\left[-\log \left({\frac {P}{Q}}\right)\right]\right)=\exp(-D_{KL}(P,Q))\end{aligned}}}

Real gas (2,587 words) [view diff] no match in snippet view article find links to article

{1}{T^{2}}}\left[C-cd\left(1+\gamma d^{2}\right)\exp \left(-\gamma d^{2}\right)\right]\right)} where d is the molar density and where a, b, c, A, B, C, α, and

Modified discrete cosine transform (3,255 words) [view diff] no match in snippet view article find links to article

{\pi }{2}}\sin ^{2}\left[{\frac {\pi }{2N}}\left(n+{\frac {1}{2}}\right)\right]\right)} for Vorbis. AC-3 uses a Kaiser-Bessel derived (KBD) window, and

Naa Nuvve (451 words) [view diff] no match in snippet view article find links to article

"Nijama Manasa" Anantha Sriram Yazin Nizar, M. M. Manasi 3:27 3. "Right Right Right" Ramajogayya Sastry Tippu 2:34 4. "Chiniki Chiniki" Anantha Sriram

Generative adversarial network (14,076 words) [view diff] no match in snippet view article find links to article

\left(0,-1+D\left(x\right)\right)\right]-\mathbb {E} _{x\sim \mu _{G}}\left[\min \left(0,-1-D\left(x\right)\right)\right]} L G = − E x ∼ μ G [ D (

Wishart distribution (4,094 words) [view diff] no match in snippet view article find links to article

i\operatorname {tr} \left(\,\mathbf {X} {\mathbf {\Theta } }\,\right)\,\right)\,\right]=\left|\,1-2i\,{\mathbf {\Theta } }\,{\mathbf {V} }\,\right|^{-n/2}}

Antiunitary operator (845 words) [view diff] no match in snippet view article find links to article

{\displaystyle W_{\theta }\left(W_{\theta }\left(\left(z_{1},z_{2}\right)\right)\right)=\left(e^{i\theta }z_{1},e^{-i\theta }z_{2}\right),} so such Wθ{\displaystyle

Prime omega function (3,570 words) [view diff] no match in snippet view article find links to article

{sinc} \left(\prod _{y=1}^{\lceil Re(z)\rceil +1}\left(x^{2}+x-yz\right)\right)\right)} An average order of both ω(n){\displaystyle \omega (n)} and Ω(n){\displaystyle

Levenberg–Marquardt algorithm (3,211 words) [view diff] no match in snippet view article find links to article

{T} }\left[\mathbf {y} -\mathbf {f} \left({\boldsymbol {\beta }}\right)\right]\right)^{\mathrm {T} }} . Therefore, for large values of λ {\displaystyle

Decision tree learning (6,385 words) [view diff] no match in snippet view article find links to article

{4}{5}}\right)\right|+\left|\left({\frac {2}{3}}-{\frac {1}{5}}\right)\right|\right)=0.44} To build the tree, the "goodness" of all candidate splits

Common base (1,643 words) [view diff] no match in snippet view article find links to article

r_{o}\\R_{C}&\parallel \left(r_{o}\left[1+g_{m}\left(r_{\pi }\parallel R_{S}\right)\right]\right)\end{aligned}}} RS≪rERS≫rE{\displaystyle {\begin{aligned}R_{S}&\ll

Raised-cosine filter (1,165 words) [view diff] no match in snippet view article find links to article

{1}{2}}\left[1+\cos \left({\frac {\pi T}{\beta }}\left[|f|-{\frac {1-\beta }{2T}}\right]\right)\right],&{\frac {1-\beta }{2T}}<|f|\leq {\frac {1+\beta }{2T}}\\0

List of Hilbert systems (3,863 words) [view diff] no match in snippet view article find links to article

\left(\neg \left(B\wedge C\right)\wedge \neg \neg \left(C\wedge A\right)\right)\right)} Also, modus ponens becomes: A,¬(A∧¬B)B{\displaystyle {\frac {A

Characteristic function (probability theory) (4,877 words) [view diff] no match in snippet view article

{E} \left[\exp \left(i\operatorname {Re} \left({\overline {t}}X\right)\right)\right],} where t¯{\textstyle {\overline {t}}} is the complex conjugate

Phased array (5,023 words) [view diff] no match in snippet view article find links to article

\left(\theta _{el}\right),\sin \left(\theta _{az}\cos \left(\theta _{el}\right)\right)\right)} This represents a coordinate frame whose x {\displaystyle \mathbf

Continuity equation (4,737 words) [view diff] no match in snippet view article find links to article

}{2mi}}\left(\Psi ^{*}\left(\nabla \Psi \right)-\Psi \left(\nabla \Psi ^{*}\right)\right)\right]\\&={\frac {\hbar }{2mi}}\left[\Psi ^{*}\left(\nabla ^{2}\Psi \right)-\Psi

Reversible-jump Markov chain Monte Carlo (767 words) [view diff] no match in snippet view article find links to article

u)p_{m}f_{m}(m)}}\left|\det \left({\frac {\partial g_{mm'}(m,u)}{\partial (m,u)}}\right)\right|\right),} where | ⋅ | {\displaystyle |\cdot |} denotes the absolute value

Projectile motion (5,351 words) [view diff] no match in snippet view article find links to article

{\mu }{g}}v_{y0}\right)e^{-\left(1+{\frac {\mu }{g}}v_{y0}\right)}\right)\right)} . The most typical case of air resistance, for the case of Reynolds

Hoeffding's inequality (2,220 words) [view diff] no match in snippet view article find links to article

{\displaystyle \mathrm {E} \left[e^{s\left(X-\mathrm {E} \left[X\right]\right)}\right]\leq \exp \left({\tfrac {1}{8}}s^{2}(b-a)^{2}\right).} Using this

Kepler's equation (3,263 words) [view diff] no match in snippet view article find links to article

^{-1}({\sqrt {r}})-{\sqrt {r-r^{2}}}{\Big )}\right)^{\!-{\frac {2}{3}}n}\right)\right)\right]} Evaluating this yields: x(t)=p−15p2−3175p3−237875p4−1894303187

Lagrange multiplier (7,741 words) [view diff] no match in snippet view article find links to article

_{j=1}^{n}p_{j}\log _{2}p_{j}\right)+\lambda \left(\sum _{j=1}^{n}p_{j}-1\right)\right\}\right|_{p_{k}=p_{\star k}}=0~.} Carrying out the differentiation of these

Spin (physics) (10,558 words) [view diff] no match in snippet view article

}}\right)(i\theta )^{3}\left[S_{z},\left[S_{z},\left[S_{z},S_{x}\right]\right]\right]+\cdots \end{aligned}}} Using the spin operator commutation relations

Entropic value at risk (2,016 words) [view diff] no match in snippet view article find links to article

_{t>0,\mu \in \mathbb {R} }\left\lbrace t\left[\mu +{\text{E}}_{P}\left(g^{*}\left({\frac {X}{t}}-\mu +\beta \right)\right)\right]\right\rbrace } (16)

Hamiltonian mechanics (9,275 words) [view diff] no match in snippet view article find links to article

\mathbf {r} _{k}({\boldsymbol {q}})}{\partial q_{j}}}{\dot {q}}_{j}\right)\right)\right)\\&=\sum _{k=1}^{N}\sum _{i=1}^{n}\sum _{j=1}^{n}\left({\frac {1}{2}}m_{k}{\frac

Dynamic programming (9,215 words) [view diff] no match in snippet view article find links to article

}\left({\hat {\mathbf {g} }}\left(\mathbf {x} _{n-k},\mathbf {u} _{n-k}\right)\right)\right\}} at the k {\displaystyle k} -th stage of n {\displaystyle n} equally

Bernstein polynomial (3,797 words) [view diff] no match in snippet view article find links to article

{\mathcal {E}} \left(\left|f\left({\frac {K}{n}}\right)-f\left(x\right)\right|\right)}=0} uniformly in x. To this end one splits the sum for the expectation

Intrabeam scattering (1,335 words) [view diff] no match in snippet view article find links to article

I}}\right)-3\operatorname {Tr} \left[L^{i}\left({\frac {1}{L+\lambda I}}\right)\right]\right\}\right\rangle }, where Tp{\displaystyle T_{p}}, Th{\displaystyle T_{h}}

Kalman filter (20,296 words) [view diff] no match in snippet view article find links to article

_{k}\left(\mathbf {z} _{k}-\mathbf {H} _{k}{\hat {\mathbf {x} }}_{k\mid k-1}\right)\right]\right)} and z k {\displaystyle \mathbf {z} _{k}} P k ∣ k = cov ⁡ ( x k

Circular polarization (4,929 words) [view diff] no match in snippet view article find links to article

\left\{\mathbf {Q} \left|\psi \right\rangle \exp \left[i\left(kz-\omega t\right)\right]\right\}\\\mathbf {B} (\mathbf {r} ,t)&={\dfrac {1}{c}}{\hat {\mathbf {z}

Vapnik–Chervonenkis dimension (2,769 words) [view diff] no match in snippet view article find links to article

\left({\tfrac {2N}{D}}\right)+1\right)-\log \left({\tfrac {\eta }{4}}\right)\right]}}\,\right)=1-\eta ,} where D {\displaystyle D} is the VC dimension of the

KMS state (970 words) [view diff] no match in snippet view article find links to article

}(A)\right\rangle =i\left\langle B\alpha _{z}^{\mu }\left(\left[H-\mu N,A\right]\right)\right\rangle } exist. However, we can still define a KMS state as any state

Tensor derivative (continuum mechanics) (8,028 words) [view diff] no match in snippet view article

{1}{\alpha }}+I_{3}\left({\boldsymbol {A}}^{-1}\cdot {\boldsymbol {T}}\right)\right)\right]\right|_{\alpha =0}\\&=\left.\det({\boldsymbol {A}})~{\cfrac {d}{d\alpha

Gompertz function (3,017 words) [view diff] no match in snippet view article find links to article

f^{-1}(t)={\frac {1}{c}}\left[b-\ln \left(\ln \left({\frac {a}{t-d}}\right)\right)\right]} The inverse function only produces numerical values in the set

Horner's method (5,279 words) [view diff] no match in snippet view article find links to article

{d_{1}}{d_{0}}}\left(m+2{\frac {d_{2}}{d_{1}}}\left(m+2{\frac {d_{3}}{d_{2}}}(m)\right)\right)\right).} The denominators all equal one (or the term is absent), so this

Z-buffering (2,650 words) [view diff] no match in snippet view article find links to article

{far}}\cdot {\textit {near}}}{{\textit {far}}-{\textit {near}}}}\right)\right)\right\rfloor } This formula can be inverted and derived in order to calculate

Kubo formula (1,072 words) [view diff] no match in snippet view article find links to article

_{t_{0}}^{t}dt'\left\langle \left[{\hat {A}}(t),{\hat {V}}{\mathord {\left(t'\right)}}\right]\right\rangle _{0}} The brackets ⟨ ⟩ 0 {\displaystyle \langle \rangle _{0}}

Binary option (6,722 words) [view diff] no match in snippet view article find links to article

{sgn} (a)\operatorname {erf} \left({\frac {bT+a}{\sqrt {2T}}}\right)\right]\right\}\,} where erf {\displaystyle \operatorname {erf} } denotes the error

List of Johnson solids (1,286 words) [view diff] no match in snippet view article find links to article

{1}{4}}\left(20+5{\sqrt {3}}+{\sqrt {5\left(145+62{\sqrt {5}}\right)}}\right)\right)a^{2}\\&\approx 16.5798a^{2}\\V&=\left({\frac {1}{6}}\left(5+4{\sqrt

The Living End (7,560 words) [view diff] no match in snippet view article find links to article

backing vocals to "Crossfire". On Australian band Jet's live DVD, Right Right Right, Chris Cheney appears at the end of the recorded concert to feature

Binary logarithm (4,788 words) [view diff] no match in snippet view article find links to article

_{2}x&=n+2^{-m_{1}}\left(1+2^{-m_{2}}\left(1+2^{-m_{3}}\left(1+\cdots \right)\right)\right)\\&=n+2^{-m_{1}}+2^{-m_{1}-m_{2}}+2^{-m_{1}-m_{2}-m_{3}}+\cdots \end{aligned}}}

Absolute convergence (5,141 words) [view diff] no match in snippet view article find links to article

}&=\max \left\{\sigma ^{-1}\left(\left\{1,\ldots ,N_{\varepsilon }\right\}\right)\right\}\end{aligned}}} where σ − 1 ( { 1 , … , N ε } ) = { σ − 1 ( 1 )

Parseval–Gutzmer formula (625 words) [view diff] no match in snippet view article find links to article

2\pi \left|\max _{\theta \in [0,2\pi )}\left(f\left(re^{i\theta }\right)\right)\right|^{2}=2\pi \left|\max _{|z|=r}(f(z))\right|^{2}=2\pi M_{r}^{2}} Ahlfors

Chern class (6,874 words) [view diff] no match in snippet view article find links to article

(V)=\left[\operatorname {tr} \left(\exp \left({\frac {i\Omega }{2\pi }}\right)\right)\right]} where Ω is the curvature of the connection. The Chern character

Standing wave ratio (4,435 words) [view diff] no match in snippet view article find links to article

\operatorname {\mathcal {R_{e}}} \left(\Gamma e^{i2k\left(x-x_{\mathsf {o}}\right)}\right)\ \right]|A|^{2}\end{aligned}}} Depending on the phase of the third term

Paschen's law (2,785 words) [view diff] no match in snippet view article find links to article

U_{\text{breakdown}}={\frac {L\cdot p\cdot d\cdot E_{I}}{e\left(\ln(L\cdot p\cdot d)-\ln \left(\ln \left(1+\gamma ^{-1}\right)\right)\right)}}\qquad \qquad (15)} (15)

Fresnel integral (2,577 words) [view diff] no match in snippet view article find links to article

\left(t^{2}\right)+i\left(\cos \left(t^{2}\right)-\sin \left(t^{2}\right)\right)\right]\,dt\\[6px]&\quad ={\frac {\sqrt {\pi }}{2}}+0i,\end{aligned}}} where

Hadamard's gamma function (396 words) [view diff] no match in snippet view article find links to article

}}\left\{\psi \left({\dfrac {x}{2}}\right)-\psi \left({\dfrac {x+1}{2}}\right)\right\}\right],} where ψ(x) denotes the digamma function. Gamma function Pseudogamma

Taylor expansions for the moments of functions of random variables (1,512 words) [view diff] no match in snippet view article find links to article

\left[f(X)\right]&{}=\operatorname {E} \left[f\left(\mu _{X}+\left(X-\mu _{X}\right)\right)\right]\\&{}\approx \operatorname {E} \left[f(\mu _{X})+f'(\mu _{X})\left(X-\mu

Hydrogen-like atom (4,811 words) [view diff] no match in snippet view article find links to article

{Z^{2}\alpha ^{2}}{n}}\left({\dfrac {1}{|k|}}-{\dfrac {3}{4n}}\right)\right]\right\}\end{array}}} (The energy of course depends on the zero-point used

Stable distribution (8,439 words) [view diff] no match in snippet view article find links to article

{1}{4|x|}}\right)\left[{\frac {1}{2}}-C\left({\tfrac {1}{\sqrt {2\pi |x|}}}\right)\right]\right)} Let K v ( x ) {\displaystyle K_{v}(x)} be the modified Bessel function

List of fractals by Hausdorff dimension (1,139 words) [view diff] no match in snippet view article find links to article

z_{n+1}=a+bz_{n}\exp \left[i\left[k-p/\left(1+\lfloor z_{n}\rfloor ^{2}\right)\right]\right]} . It derives from a model of the plane-wave interactivity field

Tobit model (2,721 words) [view diff] no match in snippet view article find links to article

\gamma +\log \left[\varphi \left(\gamma y_{j}-X_{j}\delta \right)\right]\right\}+\sum _{y_{j}=y_{L}}\log \left[\Phi \left(\gamma y_{L}-X_{j}\delta

Z function (1,384 words) [view diff] no match in snippet view article find links to article

in^{2}\right)-{\frac {\pi ^{s/2}e^{\pi is/4}}{s\Gamma \left({\frac {s}{2}}\right)}}\right)\right)} From the critical line theorem, it follows that the density of

Flux limiter (2,521 words) [view diff] no match in snippet view article find links to article

_{kn}(r)=\max \left[0,\min \left(2r,\min \left({\dfrac {(1+2r)}{3}},2\right)\right)\right];\quad \lim _{r\to \infty }\phi _{kn}(r)=2.} minmod – symmetric ϕ

AIXI (2,223 words) [view diff] no match in snippet view article find links to article

a_{1}\ldots a_{m})=o_{1}r_{1}\ldots o_{m}r_{m}}2^{-{\textrm {length}}(q)}\right)\right)\right)} Intuitively, in the definition above, AIXI considers the sum of

Uniform convergence in probability (2,984 words) [view diff] no match in snippet view article find links to article

{1}{m}}\left(\sum _{i}\left(w_{\sigma _{i}}^{j}-w_{\sigma _{m+i}}^{j}\right)\right)\right|\geq {\frac {\varepsilon }{2}}\right]=\Pr \left[\left|{\frac {1}{m}}\left(\sum

Mean line segment length (1,641 words) [view diff] no match in snippet view article find links to article

\left({\frac {l+d}{w}}\right)+{\frac {l^{2}}{w}}\ln \left({\frac {w+d}{l}}\right)\right)\right]} where d=l2+w2{\displaystyle d={\sqrt {l^{2}+w^{2}}}} is the length

Lambert W function (11,590 words) [view diff] no match in snippet view article find links to article

\left(1-{\frac {\ln \ln x}{\ln x}}\right)}{1+\ln \left({\frac {x}{\ln x}}\right)}}\right)\right).} A few identities follow from the definition: W 0 ( x e x ) =

Distribution (mathematics) (21,601 words) [view diff] no match in snippet view article

\mathbb {R} ^{n}}\left\{(1+|x|)^{k}\left|(\partial ^{\alpha }f)(x)\right|\right\}\right),\qquad k,m\in \mathbb {N} .} Otherwise, one can define a norm on

Pearson's chi-squared test (5,762 words) [view diff] no match in snippet view article find links to article

\left(1-{\frac {\sum _{i=1}^{m-1}{x_{i}}}{{\sqrt {n}}p_{m}}}\right)\right]\right\}\end{aligned}}} By expanding the logarithm and taking the leading

List of recurring characters in The Suite Life of Zack & Cody (6,189 words) [view diff] case mismatch in snippet view article find links to article

of humor, as she says, "Left! Left! Left my husband with 28 kids! Right! Right! Right in the middle of the living room floor!" Some parts of her personality

Stress intensity factor (1,888 words) [view diff] no match in snippet view article find links to article

{\alpha _{A}-\alpha _{B}}{\alpha _{A}+\alpha _{B}}}\right)^{0.9}\right]\right\}}}\right]\end{aligned}}} with β := sin ⁡ ( π α B α A + α B ) , α A

Cylindrical multipole moments (1,804 words) [view diff] no match in snippet view article find links to article

{\rho ^{\prime }}{\rho }}e^{-i\left(\theta -\theta ^{\prime }\right)}\right)\right\}} and expand the logarithms in powers of ( ρ ′ / ρ ) < 1 {\displaystyle

Ideal chain (3,634 words) [view diff] no match in snippet view article find links to article

\over k_{\text{B}}T}\right)-\exp \left(-{\frac {fl}{k_{\text{B}}T}}\right)\right)\right]^{N}\\&=\left[{4\pi \sinh(fl/(k_{\text{B}}T)) \over

Financial models with long-tailed distributions and volatility clustering (1,817 words) [view diff] no match in snippet view article find links to article

}\left(1-i\beta \operatorname {sgn} (u)\tan \left({\frac {\pi \alpha }{2}}\right)\right)\right)&{\text{if }}\alpha \in (0,1)\cup (1,2)\\\exp \left(i\mu u-\sigma

Meissel–Lehmer algorithm (1,131 words) [view diff] no match in snippet view article find links to article

~n=p_{b}p_{c},~{\text{with}}~b\leq c\leq \pi \left({\frac {x}{p_{b}}}\right)\right\}\right|\\&=\sum _{b=a+1}^{\pi (x^{1/2})}\left(\pi \left({\frac

Pulsatile flow (2,440 words) [view diff] no match in snippet view article find links to article

\omega }}\left[{\frac {1-J_{0}(\Lambda _{n})}{J_{0}(\Lambda _{n})}}\right]\right)\right\}\,.} Cardiovascular system Hemodynamics Womersley number Fluid hammer

Method of steepest descent (5,057 words) [view diff] no match in snippet view article find links to article

_{k=1}^{K}e^{\lambda S\left(x^{(k)}\right)}\left(\det \left(-S_{xx}''\left(x^{(k)}\right)\right)\right)^{-{\frac {1}{2}}}f\left(x^{(k)}\right),} where equation (13) was

3D rotation group (11,400 words) [view diff] no match in snippet view article find links to article

{1}{2}}\left[i{\hat {u}}\cdot {\vec {\sigma }},i{\hat {v}}\cdot {\vec {\sigma }}\right]\right)\right),} where cos ⁡ c ′ = cos ⁡ a ′ cos ⁡ b ′ − u ^ ⋅ v ^ sin ⁡ a ′ sin

List of set identities and relations (28,311 words) [view diff] no match in snippet view article find links to article

L_{2}\right)\times R\right)\;\cup \;\left(L\times \left(R\cap R_{2}\right)\right)\right]\\[0.7ex]&=~&&&&\,\left[\left(L\,\setminus \,L_{2}\right)\times \left(R_{2}\

Estimation of covariance matrices (3,691 words) [view diff] no match in snippet view article find links to article

{x}}\right)^{\mathrm {T} }\Sigma ^{-1}\left(x_{i}-{\overline {x}}\right)\right)\right)\\&=\det(\Sigma )^{-{\frac {n}{2}}}\exp \left(-{1 \over 2}\sum

Surface states (4,112 words) [view diff] no match in snippet view article find links to article

\right)\right]\pm \exp \left[-i\left({\frac {\pi }{a}}z\pm \delta \right)\right]\right]e^{\mp i\delta }\end{aligned}}} The energy eigenvalues are given

Vibration of plates (3,062 words) [view diff] no match in snippet view article find links to article

{\partial }{\partial r}}\left(r{\frac {\partial w}{\partial r}}\right)\right\}\right]=-{\frac {2\rho h}{D}}{\frac {\partial ^{2}w}{\partial t^{2}}}\,

Superellipsoid (2,148 words) [view diff] no match in snippet view article find links to article

{\epsilon _{1}}{2}}}\left(g^{-1}\circ (x_{i},y_{i},z_{i})\right)\right|\right)^{2}}, where ri=‖(xi,yi,zi)‖2{\displaystyle r_{i}=\|(x_{i},y_{i}

Models of neural computation (3,349 words) [view diff] no match in snippet view article find links to article

r_{p}=\left|\left[e_{p}-\sum _{j=1,j\neq p}^{n}k_{pj}\left|r_{j}-r_{pj}^{o}\right|\right]\right|} . Here, e p {\displaystyle e_{p}} is the excitation of the target

Riesz function (1,726 words) [view diff] no match in snippet view article find links to article

}{\frac {\mu (n)}{n^{4}}}\left(1-\exp \left(-{\frac {x}{n^{2}}}\right)\right)\right).} Marek Wolf in assuming the Riemann Hypothesis has shown that for

Co-construction (linguistics) (1,768 words) [view diff] no match in snippet view article

kangaekata. soo soo soo way.of.thinking so so so 'Way of thinking. Right, right, right.' Speaker 1: 中国人 Chuugokujin Chinese の no LK か ka- ? 中国人のか Chuugokujin

Mathematics of three-phase electric power (2,238 words) [view diff] no match in snippet view article find links to article

-\varphi \right)+\cos \left(2\theta -{\frac {8}{3}}\pi -\varphi \right)\right]\right\}} Since the three terms enclosed in square brackets are a three-phase

Plate theory (6,047 words) [view diff] no match in snippet view article find links to article

{d}{dr}}\left\{{\frac {1}{r}}{\cfrac {d}{dr}}\left(r{\cfrac {dw}{dr}}\right)\right\}\right]=-{\frac {q}{D}}\,.} For an orthotropic plate [ C 11 C 12 C 13 C

Tape correction (surveying) (2,189 words) [view diff] no match in snippet view article

{1+\left({\frac {d}{dx}}\left(a\cosh \left({\frac {x}{a}}\right)\right)\right)^{2}}}={\sqrt {1+\sinh ^{2}\left({\frac {x}{a}}\right)}}=\cosh \left({\frac

Gurney equations (2,472 words) [view diff] no match in snippet view article find links to article

+1\right)}}\right)-{\frac {3\beta ^{2}+4\beta +3}{10\left(\beta ^{2}+\beta +1\right)}}\right\}\right]^{-1/2}} The spherical Gurney equation has applications in early

Common integrals in quantum field theory (5,991 words) [view diff] no match in snippet view article find links to article

}(f(q))\right]d^{n}q\approx \exp \left[-{1 \over \hbar }\left(f\left(q_{0}\right)\right)\right]{\sqrt {(2\pi \hbar )^{n} \over \det f^{\prime \prime }}}.} A common

Normal distributions transform (808 words) [view diff] no match in snippet view article find links to article

{NDT} \left(f_{\mathbf {R} ,\mathbf {t} }\left(\mathbf {x_{i}} \right)\right)\right\}} where the loss function represents the negated likelihood, obtained

Modular lambda function (3,138 words) [view diff] no match in snippet view article find links to article

\left[{\frac {1}{16}}\left(6-{\sqrt {13}}-3{\sqrt {6{\sqrt {13}}-21}}\right)\right]\right\}} λ∗(55)=sin⁡{12arcsin⁡[1512(35−3−65−2)3]}{\displaystyle \lambda

Phase-comparison monopulse (2,354 words) [view diff] no match in snippet view article find links to article

_{S}-{\frac {4}{N}}arctan\left({\frac {\Delta _{\psi }}{\Sigma _{\psi }}}\right)\right)\right)=arccos\left(cos\theta _{S}-{\frac {2\lambda }{N\pi d}}arctan\left({\frac

Viscoplasticity (6,850 words) [view diff] no match in snippet view article find links to article

\left(-\beta -{\cfrac {\theta \varepsilon _{\rm {p}}}{\alpha \varphi }}\right)\right]\right]\mu (p,T)&{\text{thermal regime}}\\2\tau _{s}\mu (p,T)&{\text{shock

Romanovski polynomials (2,000 words) [view diff] no match in snippet view article find links to article

ght)\right)^{2}\right)^{-\left(-\beta _{n}-n+1\right)}\exp \left(-\alpha _{n}\operatorname {arccot} \left(x+y\left(1+x^{2}\right)\right)\right.} (20)

Bending of plates (6,862 words) [view diff] no match in snippet view article find links to article

{d}{dr}}\left\{{\frac {1}{r}}{\cfrac {d}{dr}}\left(r{\cfrac {dw}{dr}}\right)\right\}\right]=-{\frac {q}{D}}\,.} If q{\displaystyle q} and D{\displaystyle D}

Dominance-based rough set approach (3,765 words) [view diff] no match in snippet view article find links to article

T}Bn_{P}(Cl_{t}^{\geq })\right)\cup \left(\bigcup _{t\in T}Bn_{P}(Cl_{t}^{\leq })\right)\right)\right|}{|U|}}} defines the quality of approximation of the partition Cl{\displaystyle

Complex random variable (2,276 words) [view diff] no match in snippet view article find links to article

{W}}\right]\right|^{2}\leq \left|\operatorname {E} \left[\left|Z{\overline {W}}\right|\right]\right|^{2}\leq \operatorname {E} \left[|Z|^{2}\right]\operatorname {E}

Airborne particulate radioactivity monitoring (6,279 words) [view diff] no match in snippet view article find links to article

^{2}L}}\left[{1\,\,\,-\,\,\,\exp \left({-\lambda {L \over v}}\right)}\right]\,}\right\}} C ˙ R W ( t ) = ε k F m ϕ Q 0 L 2 v {\displaystyle {\dot {C}}_{RW}(t)\

Bayesian programming (6,891 words) [view diff] no match in snippet view article find links to article

_{\text{Free}}\left[\prod _{k=1}^{K}\left[P\left(L_{i}\mid K_{i}\wedge \pi \right)\right]\right]\end{aligned}}} which is usually a much simpler expression to compute

BKL singularity (20,980 words) [view diff] no match in snippet view article find links to article

_{s=0}^{\infty }\left[\left(\pi ^{2}/6\right)\exp \left(\left|-\alpha ^{(0)}\right|\right)\right]^{s}\approx \exp \left(\left|-\alpha ^{(0)}\right|\right).} If the

Jaynes–Cummings model (9,269 words) [view diff] no match in snippet view article find links to article

n\rangle \exp \left({\frac {i\Omega t}{2{\sqrt {\langle n\rangle }}}}\right)\right]\right)} For "small" times such that Ω t 2 ≪ ⟨ n ⟩ {\displaystyle {\frac

Nernst–Planck equation (665 words) [view diff] no match in snippet view article find links to article

{k_{\text{B}}T}}c\left(\nabla \phi +{\partial {\bf {A}} \over {\partial t}}\right)\right]\right\}=0} Rather than a general electric field, if we assume that only

Lévy's stochastic area (648 words) [view diff] no match in snippet view article find links to article

{b}{\sinh(b)}}\exp \left({\frac {\|x\|_{2}}{2t}}\left(1-b\coth \left(b\right)\right)\right),} where ‖x‖2{\displaystyle \|x\|_{2}} is the Euclidean norm.: 172–173

Fraunhofer diffraction equation (5,996 words) [view diff] no match in snippet view article find links to article

{x-S/2}{W}}\right)+\operatorname {rect} \left({\frac {x+S/2}{W}}\right)\right]\right]\\&=2W\left[e^{-i\pi Sx/\lambda z}+e^{i\pi Sx/\lambda z}\right]{\frac

Ratio of uniforms (2,458 words) [view diff] no match in snippet view article find links to article

\mathbb {R} ^{2}:0\leq u\leq g^{-1}\left[f\left({\frac {v}{g'(u)}}\right)\right]\right\}} If ( U , V ) {\displaystyle (U,V)} is a random variable uniformly

Heat transfer physics (8,878 words) [view diff] no match in snippet view article find links to article

}T}}\right)-\ln \left[2\sinh \left({\frac {\hbar \omega }{2k_{\mathrm {B} }T}}\right)\right]\right\}D_{p}(\omega )d\omega ,} where Dp(ω) is the phonon density-of-states

Zemor's decoding algorithm (3,067 words) [view diff] no match in snippet view article find links to article

-\left({\dfrac {\lambda }{d}}\right)}{1-\left({\dfrac {\lambda }{d}}\right)}}\right)\right)^{2}}. Let B{\displaystyle B} be derived from the d{\displaystyle

Music for Animals (286 words) [view diff] no match in snippet view article find links to article

Disc Three No. Title Length 1. "Right Right Right" 7:29 2. "World of Squares" 15:02 3. "Lemon Day" 18:31 4. "Do Dream" 22:36

Reinsurance Actuarial Premium (732 words) [view diff] no match in snippet view article find links to article

\left({\frac {\ln(f-x_{\mathrm {m} })-(\mu +\sigma ^{2})}{\sigma }}\right)\right]\right)\\&+\lambda (x_{\mathrm {m} }-l)\left(1-\Phi \left({\frac {\ln(f-x_{\mathrm

Implementation of mathematics in set theory (10,740 words) [view diff] no match in snippet view article find links to article

\left\{y:\exists x\,\left(x\in A\wedge y=F\!\left(x\right)\right)\right\}} for any set A{\displaystyle A}, but this is more conveniently

Cubic equations of state (8,348 words) [view diff] no match in snippet view article find links to article

\left({\frac {1}{3}}\operatorname {arsinh} \left({\frac {13}{7{\sqrt {7}}}}\right)\right)\right)\approx 0.307401} b ′ = b V m , c = 1 3 ( 8 sinh ⁡ ( 1 3 arsinh ⁡

Random permutation statistics (11,987 words) [view diff] no match in snippet view article find links to article

\left(\sum _{d\mid k}\left(u^{d}{\frac {z^{d}}{d}}-{\frac {z^{d}}{d}}\right)\right)\right|_{u=1}={\frac {\sum _{d\mid k}z^{d}}{1-z}}.} We have shown that the

Datar–Mathews method for real option valuation (9,295 words) [view diff] no match in snippet view article find links to article

\left\{{\frac {\left(b-X_{0}\right)^{2}}{\left[\left(b-a\right)\left(b-m\right)\right]}}\right\}.} Note: μ = 0.5 ∗ ln ⁡ ( a + b ) , σ = 0.25 ∗ ln ⁡ ( b / a )

HRDetect (1,809 words) [view diff] no match in snippet view article find links to article

_{0}+x_{i}^{T}\beta \right)-\log \left(1+e^{\left(\beta _{0}+x_{i}^{T}\beta \right)}\right)\right]+\lambda \|\beta \|_{1}\right)}} where: y i {\displaystyle y_{i}}

Incoherent broad-band cavity-enhanced absorption spectroscopy (3,670 words) [view diff] no match in snippet view article find links to article

{4R^{2}+\left({\frac {I_{0}}{I}}(R^{2}-1)\right)^{2}}}+{\frac {I_{0}}{I}}(R^{2}-1)\right)\right)\right\vert } In case of small losses per pass, L → 0, and high reflectivities

Kirchhoff–Love plate theory (4,012 words) [view diff] no match in snippet view article find links to article

{d}{dr}}\left\{{\frac {1}{r}}{\cfrac {d}{dr}}\left(r{\cfrac {dw}{dr}}\right)\right\}\right]={\frac {q}{D}}\,.} Solutions of this equation for various geometries

Neural tangent kernel (4,873 words) [view diff] no match in snippet view article find links to article

C(f(⋅;θ(t))){\displaystyle {\mathcal {C}}\left(f\left(\cdot ;\theta \left(t\right)\right)\right)} converges to that minimum as t→∞{\displaystyle t\to \infty }. This

Frobenius solution to the hypergeometric equation (13,065 words) [view diff] no match in snippet view article find links to article

{1}{c+\alpha +k}}+{\frac {1}{c+\beta +k}}-{\frac {2}{c+1+k}}\right)\right\}\right)x^{r}\\&=a_{0}x^{c}\sum _{r=0}^{\infty }{\frac {(c+\alpha )_{r}(c+\beta

Spaces of test functions and distributions (18,993 words) [view diff] no match in snippet view article find links to article

\mathbb {R} ^{n}}\left\{(1+|x|)^{k}\left|(\partial ^{\alpha }f)(x)\right|\right\}\right),\qquad k,m\in \mathbb {N} .} Otherwise, one can define a norm on

University War (5,485 words) [view diff] no match in snippet view article find links to article

Paper Lose -2 3 5, Right-Up-Left-Left-Left Red Rock Lose 1 4, Down-Right-Right-Right Draw -2 4 2, Right-Right-Up-Up Win 2 5, Left-Left-Down-Right-Right