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Find link is a tool written by Edward Betts.searching for NoLimits 94 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 completenessBanach space (8,997 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 NoArthur–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 (3,333 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}} holds. 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 probabilityDistribution (mathematics) (8,089 words) [view diff] case mismatch in snippet view article

\left\langle \sum \nolimits _{|\alpha |\leq k}p_{\alpha }\partial ^{\alpha }T,\varphi \right\rangle =\left\langle T,\sum \nolimits _{|\alpha |\leq k}(-1)^{|\alphaLieb–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 (3,446 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\|}Karp–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 .Holomorphic 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 ideaOlivia Schneider (1,436 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 auditionNecklace (combinatorics) (726 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 equivalentVapnik–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 {\displaystyleMaximum score estimator (1,996 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\inTristan 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 vonWeak 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<\inftyCosine similarity (2,423 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}}}}}Independence (probability theory) (4,223 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)}Abel–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 combinationFatou'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 zFunctional analysis (2,241 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(XTutte polynomial (5,310 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 ) {\displaystyleStella 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 StellaHomological 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 (KrullDisjoint 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 isHITS 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}} isWu–Sprung potential (1,339 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 {\GammaPetersen'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 edgesNormal matrix (1,242 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*) andConvex function (3,929 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:John Wardley (500 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 (AprilNojazz (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 stimulationGamma distribution (5,640 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 nSolution concept (1,758 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)\subseteqMarkov chain (15,534 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\rightarrowQuantum 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, anLydia 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 blondNewton'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 denoteSimplex (6,334 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 (1,427 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}Definiteness of a matrix (6,645 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\circWeil 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 (5,100 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\inLindemann–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}=\gammaSupersymmetric theory of stochastic dynamics (8,452 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\rangleArtin–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 takenRoller 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 MatadoraArtin–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 takenSpectral radius (2,375 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 adjacencyBlue Fire (998 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)List of Verbotene Liebe minor characters (6,373 words) [view diff] exact match in snippet view article find links to article

contact for Oliver Sabel to influence the party scene in Düsseldorf with the NoLimits. Oliver is impressed by Robert's ideas, which soon leads to tension withAnn 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 stayRebecca Jarvis (1,304 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/nolimitsLinear complementarity problem (1,901 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 impliesBPP (complexity) (2,275 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 (2,137 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, theOscillator representation (21,581 words) [view diff] case mismatch in snippet view article find links to article

^ ( 2 π n a ) , {\displaystyle \sum \nolimits _{n\in \mathbf {Z} }f(na)={\frac {\sqrt {2\pi }}{a}}\sum \nolimits _{n\in \mathbf {Z} }{\widehat {f}}\left({\tfracGorenstein ring (1,612 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 ifHodge structure (4,646 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^{pDependent type (2,079 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 constantOliver Sabel (2,100 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 thatGauss–Markov theorem (3,460 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 coefficientsMotive (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 \mathbbChow's lemma (1,210 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 disjointRunning Start: Bringing Young Women to Politics (755 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://wwwGerm (mathematics) (2,660 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 theHodge conjecture (3,009 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 ) {\displaystyleList of Astragon games (1,277 words) [view diff] exact match in snippet view article find links to article

Friends (2009) Windows Nikita (2009) Windows Nipplegate (2006) Windows NoLimits Fairground (2005) Windows Operation Air Assault 1+2 (2006) Windows P.JDyadic 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 sameStone–Čech compactification (2,615 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 HausdorffMultiple 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({\alphaMultivariate normal distribution (8,621 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^{-{\fracFrequent subtree mining (1,836 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-monotoneHolm–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 oneChristian Mann (3,431 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 hasTensor product of modules (8,253 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 (3,891 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}} isConstruction 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 nLifting theory (1,555 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\}}Valuation ring (3,910 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]]}Integral element (4,588 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 someHierarchical equations of motion (2,064 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 matrixAlexandre 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 ArchitectureRing 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 toClifford analysis (3,294 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}{\fracEnriques–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 dimensionsBaker–Campbell–Hausdorff formula (5,446 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":Local linearization method (12,541 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\mathbfCartan connection (6,755 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 (7,774 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 (8,134 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.Adele ring (19,566 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 ⊗ aMean 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 mapping