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Find link is a tool written by Edward Betts.searching for NoLimits 92 found (101 total)

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Uniform boundedness principle
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F ‖ T ‖ B ( X , Y ) < ∞ . {\displaystyle \sup \nolimits _{T\in F,\|x\|=1}\|T(x)\|_{Y}=\sup \nolimits _{T\in F}\|T\|_{B(X,Y)}<\infty .} The completenessArthur–Merlin protocol (1,826 words) [view diff] case mismatch in snippet view article find links to article

z ) = 1 ) ≥ 2 / 3 , {\displaystyle \exists z\in \{0,1\}^{q(n)}\,\Pr \nolimits _{y\in \{0,1\}^{p(n)}}(M(x,y,z)=1)\geq 2/3,} if x is not in L, then ∀ zMax-flow min-cut theorem (3,349 words) [view diff] case mismatch in snippet view article find links to article

w : ( v , w ) ∈ E } f v w . {\displaystyle \sum \nolimits _{\{u:(u,v)\in E\}}f_{uv}=\sum \nolimits _{\{w:(v,w)\in E\}}f_{vw}.} A flow can be visualizedIP (complexity) (5,514 words) [view diff] case mismatch in snippet view article

{\displaystyle {\text{wt-avg}}_{m_{j+1}}N_{M_{j+1}}:=\sum \nolimits _{m_{j+1}}\Pr \nolimits _{r}[V(w,r,M_{j})=m_{j+1}]N_{M_{j+1}}} where Prr is the probabilityBanach space (9,648 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle \|x\|_{\infty }=\sup \nolimits _{i}|x_{i}|} c ℓ1 No No ‖ x ‖ ∞ = sup i | x i | {\displaystyle \|x\|_{\infty }=\sup \nolimits _{i}|x_{i}|} c0 ℓ1 No NoLieb–Liniger model (1,961 words) [view diff] case mismatch in snippet view article find links to article

x i − x j ) , {\displaystyle H=-\sum \nolimits _{j=1}^{N}\partial ^{2}/\partial x_{j}^{2}+2c\sum \nolimits _{1\leq i<j\leq N}\delta (x_{i}-x_{j})\Diffeomorphism (3,431 words) [view diff] case mismatch in snippet view article find links to article

) ‖ {\displaystyle d_{K}(f,g)=\sup \nolimits _{x\in K}d(f(x),g(x))+\sum \nolimits _{1\leq p\leq r}\sup \nolimits _{x\in K}\left\|D^{p}f(x)-D^{p}g(x)\right\|}Necklace (combinatorics) (725 words) [view diff] case mismatch in snippet view article

N k ( n ) = ∑ d | n M k ( d ) , {\displaystyle N_{k}(n)\ =\ \sum \nolimits _{d|n}M_{k}(d),} where the sum is over all divisors of n, which is equivalentKarp–Lipton theorem (2,266 words) [view diff] case mismatch in snippet view article find links to article

Pr x [ ∃ y . ϕ ( x , y , z ) ] ≥ 2 3 {\displaystyle z\in L\implies \Pr \nolimits _{x}[\exists y.\phi (x,y,z)]\geq {\tfrac {2}{3}}} z ∉ L ⟹ Pr x [ ∃ y .Olivia Schneider (1,448 words) [view diff] exact match in snippet view article find links to article

loan her the cash, she steals the money from Oliver and what he made at NoLimits that night and takes off with the money. She then goes for her auditionTristan von Lahnstein (1,347 words) [view diff] exact match in snippet view article find links to article

very soon in Düsseldorf. He then shows up first at the local coffee bar NoLimits as a mysterious guy, who flirts with no other than the married Tanja vonCosine similarity (2,359 words) [view diff] case mismatch in snippet view article find links to article

_{1}(a,b)={\frac {\sum \nolimits _{i,j}^{N}s_{ij}a_{i}b_{j}}{{\sqrt {\sum \nolimits _{i,j}^{N}s_{ij}a_{i}a_{j}}}{\sqrt {\sum \nolimits _{i,j}^{N}s_{ij}b_{i}b_{j}}}}}Maximum score estimator (2,001 words) [view diff] case mismatch in snippet view article find links to article

i}W(\sum \nolimits _{j\in C,j\neq i}1(x_{t,i}b>x_{t,j}b))} Here, ∑ j ∈ C , j ≠ i 1 ( x t , i b > x t , j b ) {\displaystyle \textstyle \sum \nolimits _{j\inIndependence (probability theory) (4,221 words) [view diff] case mismatch in snippet view article

\left(A_{i}\right)_{i\in I}\in \prod \nolimits _{i\in I}\tau _{i}\ :\ \mathrm {P} \left(\bigcap \nolimits _{i\in I}A_{i}\right)=\prod \nolimits _{i\in I}\mathrm {P} \left(A_{i}\right)}Functional analysis (2,225 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle \sup \nolimits _{T\in F}\|T(x)\|_{Y}<\infty ,} then sup T ∈ F ‖ T ‖ B ( X , Y ) < ∞ . {\displaystyle \sup \nolimits _{T\in F}\|T\|_{B(XAbel–Jacobi map (1,441 words) [view diff] case mismatch in snippet view article find links to article

was proved by Abel: Suppose that D = ∑ i n i p i {\displaystyle D=\sum \nolimits _{i}n_{i}p_{i}} is a divisor (meaning a formal integer-linear combinationVapnik–Chervonenkis theory (3,760 words) [view diff] case mismatch in snippet view article find links to article

assumption ∀ x , sup f ∈ F | f ( x ) − P f | < ∞ {\displaystyle \forall x,\sup \nolimits _{f\in {\mathcal {F}}}\vert f(x)-Pf\vert <\infty } ) the class F {\displaystyleFatou's theorem (1,004 words) [view diff] case mismatch in snippet view article find links to article

continuous path such that lim t → 1 γ ( t ) = e i θ ∈ S 1 {\displaystyle \lim \nolimits _{t\to 1}\gamma (t)=e^{i\theta }\in S^{1}} . Define Γ α = { z : arg zStella Mann (Verbotene Liebe) (547 words) [view diff] exact match in snippet view article

challenge. Stella first stalked Christian and Gregor when she entered NoLimits, she even followed them to the old helicopter hangar. When they saw StellaHolomorphic functional calculus (5,480 words) [view diff] case mismatch in snippet view article find links to article

π i ∫ Γ f ( ζ ) ζ − z d ζ {\displaystyle f(z)={\frac {1}{2\pi i}}\int \nolimits _{\Gamma }{\frac {f(\zeta )}{\zeta -z}}\,d\zeta } for any z in U. The ideaHITS algorithm (1,699 words) [view diff] case mismatch in snippet view article find links to article

t o h u b ( q ) {\displaystyle \mathrm {auth} (p)=\displaystyle \sum \nolimits _{q\in P_{to}}\mathrm {hub} (q)} where P t o {\displaystyle P_{to}} isHomological conjectures in commutative algebra (1,048 words) [view diff] case mismatch in snippet view article find links to article

of free R-modules such that ⨁ i H i ( G ∙ ) {\displaystyle \bigoplus \nolimits _{i}H_{i}(G_{\bullet })} has finite length but is not 0. Then the (KrullJohn Wardley (510 words) [view diff] exact match in snippet view article find links to article

Wicker Man at Alton Towers in 2017. RollerCoaster Tycoon 3 - consultation NoLimits Coaster 2 - technical adviser Creating My Own Nemesis - print edition (AprilTutte polynomial (5,295 words) [view diff] case mismatch in snippet view article find links to article

) ( y − 1 ) k ( A ) + | A | − | V | , {\displaystyle T_{G}(x,y)=\sum \nolimits _{A\subseteq E}(x-1)^{k(A)-k(E)}(y-1)^{k(A)+|A|-|V|},} where k ( A ) {\displaystyleDisjoint union (868 words) [view diff] case mismatch in snippet view article find links to article

the notation ⋃ ∗ A ∈ C A {\displaystyle {\underset {A\in C}{\,\,\bigcup \nolimits ^{*}\!}}A} is sometimes used. In category theory the disjoint union isNojazz (160 words) [view diff] exact match in snippet view article find links to article

Trumpet Pascal Reva : Percussion Jeffrey Mpondo : lead Vocal Nojazz (2002) NoLimits (2004) Have Fun (2005) ZooLand (2009) Live au Sunset (2013) Soul stimulationWu–Sprung potential (1,334 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle f^{-1}(x)={\frac {2}{\sqrt {4x+1}}}+{\frac {1}{4\pi }}\int \nolimits _{-{\sqrt {x}}}^{\sqrt {x}}{\frac {dr}{\sqrt {x-r^{2}}}}\left({\frac {\GammaWeak operator topology (1,619 words) [view diff] case mismatch in snippet view article find links to article

λ i {\displaystyle \sum \nolimits _{i}\lambda _{i}} converges. Suppose sup α ‖ T α ‖ = k < ∞ , {\displaystyle \sup \nolimits _{\alpha }\|T_{\alpha }\|=k<\inftyNewton's identities (7,486 words) [view diff] case mismatch in snippet view article find links to article

= x 1 k + ⋯ + x n k , {\displaystyle p_{k}(x_{1},\ldots ,x_{n})=\sum \nolimits _{i=1}^{n}x_{i}^{k}=x_{1}^{k}+\cdots +x_{n}^{k},} and for k ≥ 0 denotePetersen's theorem (1,444 words) [view diff] case mismatch in snippet view article find links to article

that ∑ v ∈ V i deg G ( v ) = 2 | E i | + m i , {\displaystyle \sum \nolimits _{v\in V_{i}}\deg _{G}(v)=2|E_{i}|+m_{i},} where Ei is the set of edgesQuantum Byzantine agreement (2,107 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle |\mathrm {Leader} _{i}\rangle ={\tfrac {1}{n^{3/2}}}\sum \nolimits _{a=1}^{n^{3}}|a,a,\ldots ,a\rangle } on n {\displaystyle n} qubits, anConvex function (4,053 words) [view diff] case mismatch in snippet view article find links to article

convex in x then g ( x ) = sup y ∈ C f ( x , y ) {\displaystyle g(x)=\sup \nolimits _{y\in C}f(x,y)} is convex in x even if C is not a convex set. Composition:Solution concept (1,755 words) [view diff] case mismatch in snippet view article find links to article

function F : Γ → ⋃ G ∈ Γ 2 S G {\displaystyle F:\Gamma \rightarrow \bigcup \nolimits _{G\in \Gamma }2^{S_{G}}} such that F ( G ) ⊆ S G {\displaystyle F(G)\subseteqNormal matrix (1,406 words) [view diff] case mismatch in snippet view article find links to article

| λ j | 2 {\displaystyle \operatorname {tr} \left(A^{*}A\right)=\sum \nolimits _{j}\left|\lambda _{j}\right|^{2}} . The Hermitian part 1/2(A + A*) andLydia Brandner (1,136 words) [view diff] exact match in snippet view article find links to article

encounter with Sebastian von Lahnstein. They meet at the coffee lounge "NoLimits" and Sebastian immediately begins to fall for the young beautiful blondGamma distribution (5,717 words) [view diff] case mismatch in snippet view article find links to article

= s + n , {\displaystyle {\begin{aligned}p'&=p\prod \nolimits _{i}x_{i},\\q'&=q+\sum \nolimits _{i}x_{i},\\r'&=r+n,\\s'&=s+n,\end{aligned}}} where nDiscrete-time Markov chain (3,985 words) [view diff] case mismatch in snippet view article find links to article

\lim \nolimits _{n\rightarrow \infty }p_{ii}^{(n)}} does not exist, although the limit lim n → ∞ p i i ( k n + r ) {\displaystyle \lim \nolimits _{n\rightarrowSimplex (6,326 words) [view diff] case mismatch in snippet view article find links to article

= ∑ i a i f ( σ i ) {\displaystyle f\left(\sum \nolimits _{i}a_{i}\sigma _{i}\right)=\sum \nolimits _{i}a_{i}f(\sigma _{i})} where the a i {\displaystyleHarmonic Maass form (1,419 words) [view diff] case mismatch in snippet view article find links to article

k , − 4 π n y ) q n , {\displaystyle f(z)=\sum \nolimits _{n\geq n^{+}}c^{+}(n)q^{n}+\sum \nolimits _{n\leq n^{-}}c^{-}(n)\Gamma (1-k,-4\pi ny)q^{n}Roller Derby Brasil (759 words) [view diff] case mismatch in snippet view article find links to article

Kozmic Killa Ladies of HellTown 7 Lobster Capital City Derby Dolls 100 Lola Nolimits Sugar Loathe Derby Girls 5 Mariah Bearings Ladies of HellTown 777 MatadoraWeil cohomology theory (894 words) [view diff] case mismatch in snippet view article find links to article

K-algebra H ∗ ( X ) = ⨁ i H i ( X ) {\displaystyle H^{*}(X)=\bigoplus \nolimits _{i}H^{i}(X)} is subject to the following: H i ( X ) {\displaystyle H^{i}(X)}Étale cohomology (5,049 words) [view diff] case mismatch in snippet view article find links to article

\bigoplus \nolimits _{x\in |X|}H^{0}(i_{x*}\mathbf {Z} )\to \\&\to H^{1}(\mathbf {G} _{m})\to H^{1}(j_{*}\mathbf {G} _{m,K})\to \bigoplus \nolimits _{x\inGorenstein ring (1,596 words) [view diff] case mismatch in snippet view article find links to article

Hilbert series f ( t ) = ∑ j dim k ( R j ) t j . {\displaystyle f(t)=\sum \nolimits _{j}\dim _{k}(R_{j})t^{j}.} Namely, a graded domain R is Gorenstein ifLindemann–Weierstrass theorem (3,804 words) [view diff] case mismatch in snippet view article find links to article

j = c ( i ) . {\displaystyle {\begin{aligned}&n_{0}=0,&&\\&n_{i}=\sum \nolimits _{k=1}^{i}m(k),&&i=1,\ldots ,r\\&n=n_{r},&&\\&\alpha _{n_{i-1}+j}=\gammaLinear complementarity problem (1,944 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle z^{T}w=0} or equivalently ∑ i w i z i = 0. {\displaystyle \sum \nolimits _{i}w_{i}z_{i}=0.} This is the complementarity condition, since it impliesRebecca Jarvis (1,324 words) [view diff] case mismatch in snippet view article find links to article

-real-biz-rebecca-jarvis-42951308 http://abcnewspr.tumblr.com/post/155677527286/abc-radio-announces-new-podcast-no-limits-with http://abcn.ws/nolimitsDefinite symmetric matrix (6,928 words) [view diff] case mismatch in snippet view article find links to article

det ( N ) ∏ i m i i . {\displaystyle \det(M\circ N)\geq \det(N)\prod \nolimits _{i}m_{ii}.} det ( M ∘ N ) ≥ det ( M ) det ( N ) {\displaystyle \det(M\circGraded ring (2,666 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle T^{n}V} . The exterior algebra ⋀ ∙ V {\displaystyle \bigwedge \nolimits ^{\bullet }V} and the symmetric algebra S ∙ V {\displaystyle S^{\bulletBlue Fire (1,021 words) [view diff] exact match in snippet view article find links to article

"2019 Top Steel". Golden Ticket Awards. Amusement Today. September 2019. Retrieved September 12, 2016. NoLimits simulation of Blue Fire (Google Video)Artin–Verdier duality (775 words) [view diff] case mismatch in snippet view article find links to article

⋯ {\displaystyle \cdots \to H_{c}^{r}(U,F)\to H^{r}(U,F)\to \bigoplus \nolimits _{v\notin U}H^{r}(K_{v},F)\to H_{c}^{r+1}(U,F)\to \cdots } The sum is takenFractional Fourier transform (3,539 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle {\mathcal {F}}_{\alpha }\left[\sum \nolimits _{k}b_{k}f_{k}(u)\right]=\sum \nolimits _{k}b_{k}{\mathcal {F}}_{\alpha }\left[f_{k}(u)\right]}Supersymmetric theory of stochastic dynamics (8,454 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle {\mathcal {W}}=\left\langle \int \dots \int J\left(\prod \nolimits _{\tau }\delta ({\dot {x}}(\tau )-{\mathcal {F}}(x(\tau )))\right)Dx\right\rangleMotive (algebraic geometry) (4,731 words) [view diff] case mismatch in snippet view article

components: X = ∐ i X i , d i := dim X i . {\displaystyle X=\coprod \nolimits _{i}X_{i},\qquad d_{i}:=\dim X_{i}.} If r ∈ Z {\displaystyle r\in \mathbbHodge structure (4,807 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle H:=H_{\mathbb {Z} }\otimes _{\mathbb {Z} }\mathbb {C} =\bigoplus \nolimits _{p+q=n}H^{p,q},} H p , q ¯ = H q , p . {\displaystyle {\overline {H^{pAnn Lewis (1,096 words) [view diff] exact match in snippet view article find links to article

the conclusion of Clinton's 2008 presidential campaign, Lewis founded NoLimits.org, an issue-based educational organization enabling individuals to stayOliver Sabel (2,103 words) [view diff] exact match in snippet view article find links to article

that he's right about Rob. But Oliver refuses to believe it, even when NoLimits gets raided by the police when being tipped off by any anonymous call thatDependent type (2,068 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle \prod _{x:A}B(x)} or ∏ x : A B ( x ) . {\displaystyle \prod \nolimits _{x:A}B(x).} If B : A → U {\displaystyle B:A\to {\mathcal {U}}} is a constantBPP (complexity) (2,291 words) [view diff] case mismatch in snippet view article

i.o.-DTIME ( 2 n ε ) . {\displaystyle {\textsf {i.o.-SUBEXP}}=\bigcap \nolimits _{\varepsilon >0}{\textsf {i.o.-DTIME}}\left(2^{n^{\varepsilon }}\right)Banach fixed-point theorem (2,180 words) [view diff] case mismatch in snippet view article find links to article

cnd(x, y) for all x and y, and that ∑ n c n < ∞ . {\displaystyle \sum \nolimits _{n}c_{n}<\infty .} Then T has a unique fixed point. In applications, theRunning Start: Bringing Young Women to Politics (761 words) [view diff] case mismatch in snippet view article find links to article

/WomenCount-Radio-Talks-to-Susannah-Shakow-of-Running-Start http://www.nolimits.org/blog/main/2009/4/14/a-running-start-in-political-leadership http://wwwHodge conjecture (3,006 words) [view diff] case mismatch in snippet view article find links to article

k Hdg k ( X ) {\displaystyle \operatorname {Hdg} ^{*}(X)=\bigoplus \nolimits _{k}\operatorname {Hdg} ^{k}(X)} is generated by Hdg 1 ( X ) {\displaystyleGerm (mathematics) (2,686 words) [view diff] case mismatch in snippet view article

C k ( X , Y ) ⊆ Hom ( X , Y ) {\displaystyle C^{\infty }(X,Y)=\bigcap \nolimits _{k}C^{k}(X,Y)\subseteq {\mbox{Hom}}(X,Y)} of smooth functions and theSpectral radius (2,510 words) [view diff] case mismatch in snippet view article find links to article

. {\displaystyle \ell ^{2}(G)=\left\{f:V(G)\to \mathbf {R} \ :\ \sum \nolimits _{v\in V(G)}\left\|f(v)^{2}\right\|<\infty \right\}.} Let γ be the adjacencyMark Ormrod (Royal Marine) (846 words) [view diff] exact match in snippet view article

Plymouth Marjon University in 2018. A documentary about his life entitled NoLimits was released in 2017. Ormrod is married to Becky, and they live in PlymouthLifting theory (1,601 words) [view diff] case mismatch in snippet view article find links to article

p p ( μ ) : ( T 0 U n ) ( p ) < U n ( p ) } {\displaystyle N:=\bigcup \nolimits _{n}\left\{p\in \mathrm {Supp} (\mu ):(T_{0}U_{n})(p)<U_{n}(p)\right\}}Chow's lemma (1,213 words) [view diff] case mismatch in snippet view article find links to article

≠ j X j ) . {\displaystyle U:=\bigsqcup \left(U_{i}\setminus \bigcup \nolimits _{i\neq j}X_{j}\right).} It is not hard to see that each of the disjointGauss–Markov theorem (4,244 words) [view diff] case mismatch in snippet view article find links to article

{\displaystyle X_{ij}} . Now, let ∑ j = 1 K λ j β j {\displaystyle \sum \nolimits _{j=1}^{K}\lambda _{j}\beta _{j}} be some linear combination of the coefficientsHolm–Bonferroni method (2,307 words) [view diff] case mismatch in snippet view article find links to article

intersection of all null hypotheses ⋂ i = 1 m H i {\displaystyle \bigcap \nolimits _{i=1}^{m}H_{i}} is not rejected too, such that there exist at least oneDyadic cubes (1,263 words) [view diff] case mismatch in snippet view article find links to article

( X ∖ ⋃ Q ∈ Δ k Q ) = 0. {\displaystyle \mu \left(X\backslash \bigcup \nolimits _{Q\in \Delta _{k}}Q\right)=0.} All sets Q in Δk have roughly the sameFrequent subtree mining (1,833 words) [view diff] case mismatch in snippet view article find links to article

\forall P\in {\mathcal {P}}:\quad \mathrm {freq} (P,{\mathcal {D}})=\sum \nolimits _{T\in {\mathcal {D}}}d(P,T)\geq \mathrm {minfreq} ,} where d is an anti-monotoneChristian Mann (3,437 words) [view diff] exact match in snippet view article find links to article

Oliver's surprise party, Oliver has a one-night stand with a patron at NoLimits. Jessica tries to convince Oliver not to tell Christian as Christian hasClifford analysis (3,311 words) [view diff] case mismatch in snippet view article find links to article

< j ≤ n + 1 e i e j ( x i ∂ ∂ x j − x j ∂ ∂ x i ) {\displaystyle \sum \nolimits _{1\leq i<j\leq n+1}e_{i}e_{j}\left(x_{i}{\frac {\partial }{\partial x_{j}}}-x_{j}{\fracMultiple scattering theory (3,379 words) [view diff] case mismatch in snippet view article find links to article

l m i {\displaystyle \phi _{i}^{in}\left({{\bf {r}}_{i}}\right)=\sum \nolimits _{l,m}{{Y_{lm}}\left({{\bf {r}}_{i}}\right){j_{l}}\left({\alphaStone–Čech compactification (2,777 words) [view diff] case mismatch in snippet view article find links to article

take the closure of the image of X in ∏ f : X → K K {\displaystyle \prod \nolimits _{f:X\to K}K} where the product is over all maps from X to compact HausdorffAlexandre Arrechea (1,166 words) [view diff] case mismatch in snippet view article find links to article

buildings. His work will be showcased in the upcoming Venice Bienale. 2013 NOLIMITS, Park Avenue Project, New York, NY 2012 Skyline Adrift: Cuban Art and ArchitectureMultivariate normal distribution (8,740 words) [view diff] case mismatch in snippet view article find links to article

2 ( x − μ ) T Σ + ( x − μ ) {\displaystyle f(\mathbf {x} )=\left(\det \nolimits ^{*}(2\pi {\boldsymbol {\Sigma }})\right)^{-{\frac {1}{2}}}\,e^{-{\fracTensor product of modules (8,283 words) [view diff] case mismatch in snippet view article find links to article

) , {\displaystyle M\otimes _{R}\left(\bigoplus \nolimits _{i\in I}N_{i}\right)=\bigoplus \nolimits _{i\in I}\left(M\otimes _{R}N_{i}\right),} for anFlat module (3,896 words) [view diff] case mismatch in snippet view article find links to article

module is projective. The direct sum ⨁ i ∈ I M i {\displaystyle \bigoplus \nolimits _{i\in I}M_{i}} is flat if and only if each M i {\displaystyle M_{i}} isLocal linearization method (12,544 words) [view diff] case mismatch in snippet view article find links to article

expression ∑ i = 1 l ϕ i ( A , h ) a i = L e h H r , {\displaystyle \sum \nolimits _{i=1}^{l}\phi _{i}(\mathbf {A} ,h)\mathbf {a} _{i}=\mathbf {L} e^{h\mathbfHierarchical equations of motion (2,068 words) [view diff] case mismatch in snippet view article find links to article

density J ( ω ) = ∑ j c j 2 δ ( ω − ω j ) {\displaystyle J(\omega )=\sum \nolimits _{j}c_{j}^{2}\delta (\omega -\omega _{j})} By writing the density matrixConstruction of t-norms (3,677 words) [view diff] case mismatch in snippet view article find links to article

denoted by T = ⨁ i ∈ I ( T i , a i , b i ) , {\displaystyle T=\bigoplus \nolimits _{i\in I}(T_{i},a_{i},b_{i}),} or ( T 1 , a 1 , b 1 ) ⊕ ⋯ ⊕ ( T n , a nBaker–Campbell–Hausdorff formula (5,424 words) [view diff] case mismatch in snippet view article find links to article

we may interpret lim s → 0 s / ( 1 − e − s ) = 1 {\displaystyle \lim \nolimits _{s\to 0}s/(1-e^{-s})=1} .) We also obtain a simple "braiding identity":Ring of symmetric functions (3,690 words) [view diff] case mismatch in snippet view article find links to article

sequence α and set m α = ∑ β ∼ α X β . {\displaystyle m_{\alpha }=\sum \nolimits _{\beta \sim \alpha }X^{\beta }.} This symmetric function corresponds toValuation ring (3,875 words) [view diff] case mismatch in snippet view article find links to article

}a_{i}X^{i}\right\}} has the valuation v ( f ) = inf a n ≠ 0 n {\displaystyle v(f)=\inf \nolimits _{a_{n}\neq 0}n} . The subring F [ [ X ] ] {\displaystyle \mathbb {F} [[X]]}Enriques–Kodaira classification (4,147 words) [view diff] case mismatch in snippet view article find links to article

− e = ∑ i , j ( − 1 ) j h i , j . {\displaystyle \tau =4\chi -e=\sum \nolimits _{i,j}(-1)^{j}h^{i,j}.} b ± {\displaystyle b^{\pm }} are the dimensionsIntegral element (5,222 words) [view diff] case mismatch in snippet view article find links to article

\sigma } . G fixes the element y = ∏ σ σ ( x ) {\displaystyle y=\prod \nolimits _{\sigma }\sigma (x)} and thus y is purely inseparable over K. Then someCartan connection (6,746 words) [view diff] case mismatch in snippet view article find links to article

\varphi \colon \Omega ^{k}(P,V)\cong \Omega ^{0}(P,V\otimes \bigwedge \nolimits ^{k}{\mathfrak {g}}^{*})} given by φ ( β ) ( ξ 1 , ξ 2 , … , ξ k ) = βBRST quantization (7,784 words) [view diff] case mismatch in snippet view article find links to article

− j = n K i , j {\displaystyle \operatorname {Tot} (K)^{n}=\bigoplus \nolimits _{i-j=n}K^{i,j}} with a differential D = d + δ. The cohomology groups ofPolymer field theory (3,494 words) [view diff] case mismatch in snippet view article find links to article

r ) = ∑ G w ( G ) exp [ i G r ] {\displaystyle w(\mathbf {r} )=\sum \nolimits _{\mathbf {G} }w(\mathbf {G} )\exp \left[i\mathbf {G} \mathbf {r} \right]}Tanja von Lahnstein (8,133 words) [view diff] exact match in snippet view article find links to article

plan goes wrong from the beginning when she is expecting someone in the NoLimits and mistakes Ansgar's cousin Tristan von Lahnstein for the assistance.Mean field particle methods (8,363 words) [view diff] case mismatch in snippet view article find links to article

) = 1. {\displaystyle 0\leqslant \eta _{n}(x)\leqslant 1,\qquad \sum \nolimits _{x\in S}\eta _{n}(x)=1.} Therefore, Φ {\displaystyle \Phi } is a mappingAdele ring (17,547 words) [view diff] case mismatch in snippet view article find links to article

\cdots \oplus K_{v}\omega _{n}\cong K_{v}\otimes _{K}L\cong L_{v}=\prod \nolimits _{w|v}L_{w}} For the second we used the map: { K v ⊗ K L → L v α v ⊗ a