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In mathematics, a pullback is either of two related processes: precomposition and fiber-product; precomposition is a special case of the general fiber-product...

A pullback motor (also pull back, pull back and go or pull-back) is a simple clockwork motor used in toy cars. A patent for them was granted to Bertrand...

In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...

In mathematics, a pullback bundle or induced bundle is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle π : E → B {\displaystyle...

space of 1-forms on M {\displaystyle M} . This linear map is known as the pullback (by ϕ {\displaystyle \phi } ), and is frequently denoted by ϕ ∗ {\displaystyle...

given a continuous map f: X → Y of topological spaces and a ring R, the pullback along f on cohomology theory is a grade-preserving R-algebra homomorphism:...

{\displaystyle f\colon X\to Y} . We will call the result the inverse image or pullback sheaf f − 1 G {\displaystyle f^{-1}{\mathcal {G}}} . If we try to imitate...

non-autonomous. This requires one to consider the notion of a pullback attractor or attractor in the pullback sense. Consider a random dynamical system φ {\displaystyle...

In shogi, Iijima Bishop Pullback or Iijima's Back Bishop (飯島流引き角 Iijima-ryuu hiki kaku) is a less common defensive Static Rook opening used against a Ranging...

forms along with the exterior derivative defined on it is preserved by the pullback under smooth functions between two manifolds. This feature allows geometrically...

Bust-a-Move DS, known as Hippatte!! Puzzle Bobble (Japanese: ひっぱって!!パズルボブル, Hepburn: Hippatte!! Pazuru Boburu; "Pull Back!! Puzzle Bobble") in Japan, is...

Choro-Q is a line of Japanese 3–4 cm pullback car toys produced by Takara Tomy (formerly Takara). Known in North America as Penny Racers, they were introduced...

and for all arrows f:c″→c′, S(f) is the restriction of Hom(f, c), the pullback by f (in the sense of precomposition, not of fiber products), to S(c′);...

{\displaystyle P=X+_{Z}Y} . The pushout is the categorical dual of the pullback. Explicitly, the pushout of the morphisms f and g consists of an object...

Radon–Nikodym derivatives of both the pullback and pushforward measures of m {\displaystyle m} under T {\displaystyle T} . The pullback measure in terms of a transformation...

step, shuffle, leap, toe. The Maxie Ford is famous for its use of the pullback (or graboff) after the shuffle and best known as the Maxie Ford Break:...

In mathematics, an algebraic cycle on an algebraic variety V is a formal linear combination of subvarieties of V. These are the part of the algebraic topology...

(category theory), a generalization of mathematical products Fibre product or pullback Coproduct or pushout Wick product of random variables Graph product Product...

December 23, 2013. Retrieved June 13, 2023. Jennings, Katie. "Defying Pullback In Investments, General Catalyst Launches $670 Million Healthcare Fund"...

A homotopy pullback (or homotopy fiber-product) is the dual concept of a homotopy pushout.It satisfies the universal property of a pullback up to homotopy...

c_{X,Y,Z}(g,f)=g\circ f.} For a morphism p:X → Y, suppose the following pullback square exists, which defines the subobject of XY corresponding to maps...

pullback square, and the morphism which goes from the domain of f × g {\displaystyle f\times g} to the domain of f is opposite to g in the pullback square...

international law prohibition on refoulement. Pushback is contrasted with "pullback", a form of extraterritorial migration control the country seeking to repel...

categories. A morphism is a monomorphism if it is idempotent with respect to pullbacks. The categorical dual of a monomorphism is an epimorphism, that is, a...

the essential properties of universal constructions such as products, pullbacks and inverse limits. The dual notion of a colimit generalizes constructions...

feel a sense of urgency in making a fourth Deadpool film amidst a wider "pullback" of the superhero genre. In January 2026, Kim Masters of Puck reported...

a kernel along arbitrary morphisms is again a kernel and, dually, the pullback of a cokernel along arbitrary morphisms is again a cokernel. A quasi-abelian...

back or pullback may refer to: Pullback, a name given to two different mathematical processes Pullback (cohomology), a term in topology Pullback (differential...

the close. This was repeated the next trading day before another major pullback for the year. It took until Monday, June 4, 2018 (nearly three months)...

Graeme Segal in 1974. A Segal space is a simplicial space satisfying some pullback conditions, making it look like a homotopical version of a category. More...

is also feasible with during manual pullback.[citation needed] Advanced computer processing can utilise iFR-pullback data to predict the hemodynamic consequences...

most important one is the product of two smooth valuations. Together with pullback and pushforward, this operation extends to valuations on manifolds. Let...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

{\mathcal {M}}_{X}} , then this pullback can be used to define pullback of Cartier divisors. In terms of local sections, the pullback of { ( U i , f i ) } {\displaystyle...

of modules#Operations). The pullback of a vector bundle is a vector bundle of the same rank. In particular, the pullback of a line bundle is a line bundle...

f_{*}^{}\colon T_{x}M\to T_{f(x)}N} every such map induces a linear map (called the pullback) between the cotangent spaces, only this time in the reverse direction:...

all pullbacks, it has pushouts along monomorphisms, and pushout squares of monomorphisms are also pullback squares and are stable under pullback. C has...

} {\displaystyle f^{*}(E)=\{(a,e)\in A\times E\ |\ f(a)=p(e)\}} is the pullback and the projections of f ∗ ( E ) {\displaystyle f^{*}(E)} onto A {\displaystyle...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

from pullbacks and binary products (consider the pullback of (f, g) along the diagonal Δ), a category is complete if and only if it has pullbacks and products...

dictionary. The notion of pushforward in mathematics is "dual" to the notion of pullback, and can mean a number of different but closely related things. Pushforward...

general under pullbacks but Haefliger structures are. Indeed, given a continuous map f : X → Y {\displaystyle f:X\to Y} , one can take pullbacks of foliations...

s\subseteq w\Longrightarrow {\bar {s}}\subseteq {\bar {w}}} stability under pullback: f − 1 ( s ) ¯ ≡ f − 1 ( s ¯ ) {\displaystyle {\overline {f^{-1}(s)}}\equiv...

The Irrawaddy. 2 October 2025. "Resource, manpower shortages drove TNLA pullback from Mogok and Momeik, senior leader says". Nora Pyae (21 April 2025)....

R 1 ( n ) = ι ∗ η , {\displaystyle h_{R}^{1(n)}=\iota ^{*}\eta ,} the pullback of the Minkowski metric η {\displaystyle \eta } under inclusion, is a Riemannian...

v)={P_{u}}(u,v)\mathbf {e} _{u}+{P_{v}}(u,v)\mathbf {e} _{v}.} This is the pullback of F along ψ, and, by the above, it satisfies ∮ ∂ Σ F ( x ) ⋅ d l = ∮ γ...

structure in which additionally weak equivalences are preserved under pullback (fiber product) along fibrations, called right proper, and pushouts (cofiber...

Digital creating five different mattes for the final scene of the film—a pullback depicting the destroyed Three Mile Island—and Gavin Hood handing company...

nonautonomous and random dynamical systems, particularly the development of pullback attractors, and for co-authoring a foundational text on the numerical solution...

{\displaystyle f\colon T\to A^{\vee }} so that L is isomorphic to the pullback of P along the morphism 1 A × f : A × T → A × A ∨ {\displaystyle 1_{A}\times...

on X×t is closed. Moreover if this set is the whole of T then L is the pullback of a line bundle on T. Mumford (2008, section 10) also gave a more precise...

topological basis. In a more general set-up the restrictions are replaced with pullbacks; fibred categories then make a good framework to discuss the possibility...

{\displaystyle \mathrm {Sub} (X)} have "finite" unions which are stable under pullback, then S u b ( X ) {\displaystyle \mathrm {Sub} (X)} is an upper semilattice...

by f {\displaystyle f} gives a sieve on Y {\displaystyle Y} called the pullback of S {\displaystyle S} along f {\displaystyle f} , denoted by f ∗ S {\displaystyle...

variety over one field determines a variety over a bigger field, or the pullback of a family of varieties, or a fiber of a family of varieties. Base change...

there were six models at that time. In the year 2002, Tomy again produced pullback models. From time to time, Tomy produces shorter runs of cars with sound...

denotes the category-theoretic kernel. Any category with fibre products (pullbacks) and products has equalisers. In Top where objects are topological spaces...

'Wayne', Pilot 'Dark Cargo' Seek New Homes As YouTube Steps Up Scripted Pullback". Deadline Hollywood. Archived from the original on August 17, 2019. Retrieved...

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Aoun unveils US proposal, demands disarmament of armed groups and Israeli pullback". LBCIV7. Retrieved 31 July 2025. Mroue, Bassem (13 August 2025). "Lebanon...

original on 22 November 2018. Retrieved 21 November 2018. "The [Ivanhoe] pullback investors have been waiting for". Mining Journal. London, UK: Aspermont...

by Takara for the Sega Saturn. It is based on Takara's Choro Q line of pullback racer toys. Reception Two reviewers from Sega Saturn Magazine found the...

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{\displaystyle {\tilde {p}}} is defined w.r.t. scaled Hausdorff measure. The pullback and Hausdorff measures agree, so that: p ( θ ∣ μ , Σ ) = p ~ ( v ∣ μ ,...

many applications. At a basic level, this has to do with functions and pullbacks in geometric situations: given spaces X {\displaystyle X} and Y {\displaystyle...

BG, such that every bundle with the given structure group G over M is a pullback by means of a continuous map M → BG. When the definition of the classifying...

Black's King's Head Vanguard Pawn (玉頭位取り gyokutou kuraidori). Iijima Bishop Pullback ☖ pieces in hand: – ☗ pieces in hand: – The Bishop-Exchange Fourth File...

morphism Z → X {\displaystyle Z\to X} , and the second homomorphism is pullback with respect to the flat morphism X − Z → X {\displaystyle X-Z\to X} ....

(also called a Doolittle diagram) is a diagram that is simultaneously a pullback square and a pushout square. It is a self-dual concept. Adámek, Jiří; Herrlich...

morphism A ′ → A {\displaystyle A'\to A} , the pullback is an I {\displaystyle I} -indexed coproduct of the pullbacks: ( ∐ i ∈ I B i ) × A A ′ ≅ ∐ i ∈ I ( B i...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

singularities on compact Riemann surfaces having finite monodromy, by a pullback from the hypergeometric equation on the Riemann sphere by a complex analytic...

χ {\displaystyle \chi } in a “purely categorical way”, one can take a pullback Y → { 1 } ↓ ↓ X → χ { 0 , 1 } {\displaystyle {\begin{array}{lcl}&Y&\rightarrow...

M\times M} , and p r i ∗ {\displaystyle \mathrm {pr} _{i}^{*}} denotes the pullback of the respective bundles. In coordinate notation, a bitensor T {\displaystyle...

Thai fans who were unhappy with the portrayal of the playerbase. This pullback, however, faced another backlash from a different portion of fans who were...

spectral sequence addresses the calculation of the homology groups of a pullback over a fibration. The spectral sequence formulates the calculation from...

{\displaystyle d\varphi _{x}} is invertible, and the inverse gives the pullback of T φ ( x ) N . {\displaystyle T_{\varphi (x)}N.} The differential is...

reportedly did not feel a sense of urgency in making the film amidst a wider "pullback" of the superhero genre. Feige confirmed that three or four iterations...

Isn't Done With Live-Action Disney+ Shows Despite Reports Of Major TV Pullback". The Playlist. Archived from the original on August 21, 2026. Retrieved...

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crossings, tractor trailer mounted drills capable of 1,320,000 lbs (thrust/pullback force) and 150,000 ft-lbs (rotary force) may be used [600 tonnes- 204,000...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

'Wayne', Pilot 'Dark Cargo' Seek New Homes As YouTube Steps Up Scripted Pullback". Deadline Hollywood. August 16, 2019. Archived from the original on August...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

space is convex. A variety X {\displaystyle X} is called convex if the pullback of the tangent bundle to a stable rational curve f : C → X {\displaystyle...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

(pseudo-)metric in the sense that g {\displaystyle g} is equal to the pullback of h {\displaystyle h} by f {\displaystyle f} , i.e. g = f ∗ h {\displaystyle...

landing on the foot/feet. Notable variations are single pullback, double pullback, alternating pullback, and other variations including other steps. riff:...

Fury design by adding larger, more highway friendly front rubber, more pullback on the handle bars and classic, cruiser styled fenders; and the Interstate...

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exit by way of the southern end. Rutherford Road passes over the two hump pullback tracks at the north end of the yard, which curve to the west to end at...

the pullback. It may be determined using the following formula (using the Einstein summation convention), which is the component form of the pullback operation:...

al-Jir Base". Welat TV. 2025-10-29. "Syria takes control of Shaddadi as US pullback reshapes power balance". Middle East Online. 15 February 2026. "Syrian...

flaps, flap heel, cramp-roll, buffalo, Maxi Ford, Maxi Ford with a pullback, pullbacks, wings, Cincinnati, the shim sham shimmy (also called the Lindy)...

Kyushu Univ. Ser. A, 46 (2): 307–339, MR 1195472 Tamotsu, Ikeda (2006), "Pullback of the lifting of elliptic cusp forms and Miyawaki's conjecture", Duke...

many concepts related to random dynamical systems, it is defined in the pullback sense, which means they are understood through their long-term behavior...

principal bundles on algebraic varieties—those that become trivial after pullback by a finite étale map—are important. This acted as one important source...

detailed using renderings by medical illustrator Katherine Jones. The pullback sequence from within the brain to the outside of the skull included neurons...

{\displaystyle p^{*}\colon H^{*}(X)\rightarrow H^{*}(Y)} is injective, and the pullback bundle p ∗ ξ : p ∗ E → Y {\displaystyle p^{*}\xi \colon p^{*}E\rightarrow...

→ W is called a symplectic map if the pullback preserves the symplectic form, i.e. f∗ρ = ω, where the pullback form is defined by (f∗ρ)(u, v) = ρ(f(u)...

X {\displaystyle X} to a diffeological space Y {\displaystyle Y} , the pullback diffeology on X {\displaystyle X} consists of those maps p : U → X {\displaystyle...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

Formally, D {\displaystyle D} is the pullback connection γ ∗ ∇ {\displaystyle \gamma ^{*}\nabla } on the pullback bundle γ ∗ T M {\displaystyle \gamma...

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(Super Bust-a-Move 2) (2002) Ultra Puzzle Bobble (Ultra Bust-a-Move) (2004) Pullback!! Puzzle Bobble (Bust-a-Move DS) (2005) Ultra Puzzle Bobble Pocket (Bust-a-Move...

pullback. We say an L in Pic X / S ⁡ ( T ) {\displaystyle \operatorname {Pic} _{X/S}(T)} has degree r if for any geometric point s → T the pullback s...

Benmour, Eric (June 14, 1996). "Chi-Chi's closes oldest store here as pullback continues". Business First of Louisville. Retrieved July 2, 2010. "Salsafication...

'Wayne', Pilot 'Dark Cargo' Seek New Homes As YouTube Steps Up Scripted Pullback". Deadline Hollywood. August 16, 2019. Archived from the original on August...

Retrieved 19 January 2020. "EXCLUSIVE: US military offers Iraq a partial pullback". Middle East Eye. 14 February 2020. "U.S. service members killed in Iraq"...

called a pullback because it "pulls back" the gradient on R n {\displaystyle \mathbb {R} ^{n}} to a gradient on M {\displaystyle M} . The pullback is independent...

Internal category theory: Internalization of categories in a category V with pullbacks is replacing the category Set (same for classes instead of sets) by V...

shield; split five-spoke cast aluminum wheels with diamond cut highlights; pullback handlebar with polished finish; inverted front forks in silver and polished...

estimate has “slim odds” of passing. Furthermore, this might lead to a pullback in credit card lending. Trump sought a great amount of control over US...

2022. Balmforth, Tom; Hunder, Max (30 June 2022). "Ukraine fetes Russian pullback from strategic Snake Island outpost". Reuters. Retrieved 19 January 2023...

Companies". Medical Product Outsourcing. July 26, 2018. "Wait For The Pullback To Buy Edwards Lifesciences". Seeking Alpha. April 28, 2020. Whooley, Sean...

coherent), but pullbacks of coherent sheaves are coherent if X {\displaystyle X} is locally Noetherian. An important special case is the pullback of a vector...

example, it says that the pushout square above behaves like a homotopy pullback up to dimension m + n {\displaystyle m+n} . The generalization of the connectivity...

_{1}^{2}\hookrightarrow \Delta ^{2}} is a weak categorical equivalence, but its pullback along the isofibration Δ 1 ≅ { 0 → 2 } ↪ Δ 2 {\displaystyle \Delta ^{1}\cong...

{v} \wedge \alpha .} Suppose that T : V → V is a linear transformation. Pullback by the (n − 1)th exterior power of T induces a morphism of Hom spaces....

Walker's triumph at the Home Run Derby, the month of July marked another pullback in the team's overall performance, starting the month 8.5 games behind...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

a topological space X to another topological space Y is associated the pullback functor taking bundles on Y to bundles on X. Fibred categories formalise...

any G principal bundle over a paracompact manifold is isomorphic to a pullback of the principal bundle E G → B G {\displaystyle EG\to BG} . As explained...

general partners. Johnson has said he launched the fund in response to a pullback in federal support of research and development, and because of a general...

the distribution of (2n−2)-planes which, at the unit vector u, is the pullback of the orthogonal complement of u in the tangent space of M. This is a...

Retrieved December 4, 2024. "Joann files for bankruptcy amid consumer pullback, but plans to keep stores open - CBS News". www.cbsnews.com. March 18,...

gov.in. Retrieved 9 July 2026. Lt Gen YK Joshi Speaks On The Pangong Tso Pullback | Exclusive Interview | CNN News18. CNN-News18. 17 February 2021. Archived...

(SPO) approach. Other sub-approaches include the sesqui-pushout and the pullback approach. From the perspective of the DPO approach a graph rewriting rule...

from T into some scheme M (better: arises from a universal family through pullback), we say M is a fine moduli space. Denote Γ ( n ) = ker ⁡ [ Sp 2 g ⁡ (...

{\displaystyle 0\to B\xrightarrow {f'} E'\xrightarrow {g'} A\to 0,} first form the pullback over A {\displaystyle A} , Γ = { ( e , e ′ ) ∈ E ⊕ E ′ | g ( e ) = g ′...

Julian E.; Spiegel, Peter (15 August 2007). "Top general may propose pullbacks". Los Angeles Times. Retrieved 22 May 2012. "U.S. Department of Defense"...

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functions), sending a map f : X → Y {\displaystyle f\colon X\to Y} to the pullback operation f ∗ : b G ( Y ) → b G ( X ) {\displaystyle f^{*}\colon b_{G}(Y)\to...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

relation between two objects of a category. When the category has all pullbacks (and satisfies a small number of other conditions), spans can be considered...

∗ ( B ) {\displaystyle H_{*}(E)\to H_{*}(B)} and a contravariant map (pullback) on cohomology H ∗ ( B ) → H ∗ ( E ) . {\displaystyle H^{*}(B)\to H^{*}(E)...

commanders' talks were held on 30 June; India reiterated its demand for the pullback of the Chinese troops from all key areas including Pangong Tso, Galwan...

inaugural member of the Combat Robot Hall of Fame. It also has its own pullback toy, pullback minibot and DVD. Team Chaos had a small rivalry with Team Mace....

Δ m → Δ n {\displaystyle f:\Delta ^{m}\to \Delta ^{n}} , a choice of a pullback of p {\displaystyle p} along f {\displaystyle f} . Now, a conjecture of...

Rafael da Silva's mishit cross, and then he fired home Antonio Valencia's pullback to level the game. However, United went on to lose the game 3–2. In the...

HELOC Mortgage?". Forbes. Retrieved 2022-09-22. "Two years after HELOC pullback, JPMorgan again eyes the business". American Banker. 2022-05-23. Retrieved...

defines their dynamics by the generalized transfer operator (GTO)—the pullback averaged over noise. GTO commutes with the exterior derivative, which is...

inclusion I is an exact functor. This occurs if and only if C is closed under pullbacks of epimorphisms and pushouts of monomorphisms. The exact sequences in...

{\displaystyle f\colon X'\to X} , where f ∗ E {\displaystyle f^{*}E} denotes the pullback vector bundle. The uniqueness of these classes is proved for example, in...

September, Sarkozy and Medvedev signed another agreement on a Russian pullback from Georgia. After meeting with the French president, Medvedev said the...

are called free paths. The path space P X {\displaystyle PX} is then the pullback of X I → X , χ ↦ χ ( 0 ) {\displaystyle X^{I}\to X,\,\chi \mapsto \chi...

Bishop Pullback (hiki kaku), Gangi Castle Static Rook Anaguma (with Bishop Pullback, Static Bishop, or Bishop Exchange) Left Mino (with Bishop Pullback, Static...

dolly pullback required by the effects team, who needed a steady shot to blend a computer-generated version of Picard's eye with the pullback. The 135-foot...

a special case of the fact that differential forms transform through a pullback F ∗ {\displaystyle F^{*}} as F ∗ ( u d y 1 ∧ ⋯ ∧ d y n ) = ( u ∘ F ) det...

only battle, it was directly replaced by Tough As Nails.[citation needed] Pullback and Friction toys were made of all the House Robots, with the exception...

field to γ generates a horizontal vector field in the total space of the pullback bundle γ*E. By the Picard–Lindelöf theorem, this vector field is integrable...

2025. Steenhuysen, Julie; Lapid, Nancy (February 3, 2025). "CDC orders pullback of new scientific papers involving its researchers, source says". Reuters...

outbreak of the American Civil War, the post was abandoned, partly as a pullback of federal troops to the north, and partly due to the fort's unreliable...

U+27C6 ⟆ RIGHT S-SHAPED BAG DELIMITER U+27D3 ⟓ LOWER RIGHT CORNER WITH DOT ⟓pullback...pushout⟔ U+27D4 ⟔ UPPER LEFT CORNER WITH DOT U+27E6 ⟦ MATHEMATICAL LEFT...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

represented as a pullback of the universal line bundle on C P ∞ {\displaystyle \mathbf {CP} ^{\infty }} , meaning there is a pullback square L → L ↓ ↓...

h(x)\mid x\in X\rbrace .\,} This property is related to the notion of a pullback. Span (category theory) Pushout (category theory) Joint embedding property...

In the United States and its territories, Community Action Agencies (CAA) are local private and public non-profit organizations that carry out the Community...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

embedding, then Z | Q {\displaystyle Z\vert _{Q}\,} is a section of the pullback bundle i Q ∗ ( T E ) → Q {\displaystyle i_{Q}^{\ast }(TE)\to Q\,} , where...

that X {\displaystyle X} is parallel with respect to the pullback connection on the pullback bundle ⁠ γ ∗ T M {\displaystyle \gamma ^{*}TM} ⁠. However...

2022. Retrieved 11 September 2022. "Ukraine's Zelenskyy says Russia's pullback from Kharkiv region 'a good decision'". CBC News. Associated Press. 10...

on 2013-07-29. "Molina to close Midwest Health Center in primary care pullback". August 2017. Alacrastore. "Molina Health Care in New Mexico". Retrieved...

Retrieved October 7, 2019. Nissenbaum, Dion (October 7, 2019). "U.S. Begins Pullback From Northern Syria, Clearing Way for Turkish Offensive". Wall Street Journal...

categories of the category of simplicial sets. On them, postcomposition and pullbacks (due to its application in algebraic geometry also known as base change)...

Andrew E.; Troianovski, Anton (22 April 2021). "Russia Orders Partial Pullback From Ukraine Border Region". The New York Times. ISSN 0362-4331. Retrieved...

avec P. Marcellini, Birkhäuser, PNLDE Series, Boston, 37 (1999). PDF The pullback equation for differential forms; with G. Csato et O. Kneuss, Birkhäuser...

X# defined by f ↦ f ∘ u. The resulting functional u#(f) is called the pullback of f by u. The following relation characterizes the algebraic adjoint of...

connection 1-form on a surface embedded in Euclidean space E3 is just the pullback under the Gauss map of the connection 1-form on S2. Using the identification...

whereas μ ( T ( A ) ) {\displaystyle \mu (T(A))} is generically called a pullback. Almost all properties and behaviors of dynamical systems are defined in...

transition, most of the Arab political openings closed, causing an inevitable pullback. In particular in Egypt, the democratically elected government pushed for...

(h)(R_{h}^{*}\omega _{e}),{\text{ where }}h=g^{-1},} where Rh* is the pullback of forms along the right-translation in the group and Ad(h) is the adjoint...

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During the 1989 Tiananmen Square protests in Beijing, the People's Liberation Army (PLA) played a decisive role in enforcing martial law, using force to...

N . {\displaystyle F_{*}:TM\to TN.} The dual to the pushforward is the pullback, which "pulls" covectors on N {\displaystyle N} back to covectors on M...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

'Wayne', Pilot 'Dark Cargo' Seek New Homes As YouTube Steps Up Scripted Pullback/". Deadline Hollywood. Archived from the original on August 17, 2019. Retrieved...

{\displaystyle \operatorname {BSO} (n)} . The isomorphism is given by pullback. A particular application are principal SO(2)-bundles. There is a canonical...

the flatness assumption, provided that the pullback X ′ {\displaystyle X'} is replaced by the homotopy pullback. In the easiest case when X, S, and S ′ {\displaystyle...

diagonal modulo higher order terms. The cotangent sheaf is defined as the pullback of this sheaf to M {\displaystyle M} : Γ T ∗ M = Δ ∗ ( I / I 2 ) . {\displaystyle...

(August 20, 2024). "Time Magazine Lays Off 22 Staffers Amid Advertising Pullback, Restructuring". The Hollywood Reporter. Retrieved August 5, 2025. "Time...

corresponds to the invariant measure. The adjoint to the push-forward is the pullback; as an operator on spaces of functions on measurable spaces, it is the...

2012. Nesi, Ted (September 3, 2019). "Sen. Reed urged to push for US pullback in Yemen". WPRI.com. Providence. Retrieved September 3, 2019. Shaw, Donald...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

Gibbons, Robert (28 December 2011). "Oil falls on dollar's rise, Wall Street pullback". Reuters. Archived from the original on 8 January 2012. Retrieved 8 January...

oscillating mixture of abrasiveness and balm, of harsh satire and compassionate pullback." Peter Travers of Rolling Stone gave the film 3.5 out of 4 stars and noted...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

The New York Times. p. 4. Fox Butterfield (15 November 1972). "Enemy pullbacks reported near Saigon and the DMZ". The New York Times. p. 1. James P....

f : A → B be isogeny between two algebraic groups. This mapping induces a pullback mapping f* : K(B) → K(A) between their rational function fields. Since...

'Wayne', Pilot 'Dark Cargo' Seek New Homes As YouTube Steps Up Scripted Pullback". Deadline Hollywood. Patten, Dominic (February 18, 2019). "'The Punisher'...

isomorphism. One can define the pullback of vector-valued forms by smooth maps just as for ordinary forms. The pullback of an E-valued form on N by a smooth...

question is whether there is a local diffeomorphism φ:M→N such that the pullback of the coframe on N satisfies ϕ ∗ γ i ( y ) = g j i ( x ) θ j ( x ) ,  ...

∗ , f ∗ {\displaystyle f_{*},f^{*}} denote the pushforward as well the pullback for quasi-coherent sheaves (here, for simplicity, assume f ∗ : QCoh ( X...

because the invariant forms (ωi,ωji) pullback along φ, and the structural equations are preserved under this pullback. Consequently, the resulting system...

version has rider floorboards, different shaped silencers (mufflers) and 'pullback' handlebars. More colour choices were added and the pillion seat was modified...

low stress where force was applied up and down, and in simulations of "pullback". Due to the relative weakness of the skull at the sides and middle, these...

\mathbb {R} ^{n}} ⁠ is parallelizable, the pullback of its tangent bundle to M is trivial; since this pullback is the direct sum of the (intrinsically defined)...

Guardian. Sparks, Allister (17 August 1986). "Moves by Botha Telegraph Pullback From Compromise". The Washington Post. Cowell, Alan (22 May 1986). "South...

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D(X×Y). Most natural functors, including basic ones like pushforwards and pullbacks, are of this type. These kinds of functors were introduced by Mukai (1981)...

{\mathfrak {X}}\to B} such that any deformation can be found as a unique pullback square X → X ↓ ↓ S → B {\displaystyle {\begin{matrix}X&\to &{\mathfrak...

series. The Borg Cube is revealed in the first episode with an "ambitious pullback reveal" inspired by a similar shot from the film Star Trek: First Contact...

improved fitting methodology also allows it to be fit to larger trend pullbacks. The indicator is designed to forecast the highs and lows in normal asset...

the Sochi Agreement. By 4 December, the US had completed its military pullback from northeastern Syria and had consolidated its troop presence in the...

expression Ψ t ∗ ( g 0 ) {\displaystyle \Psi _{t}^{\ast }(g_{0})} refers to the pullback of the metric g 0 {\displaystyle g_{0}} by the diffeomorphism Ψ t {\displaystyle...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

Retrieved 29 March 2026. "Joint press release: ECtHR judgment on Italy-Libya 'pullback' policy—S.S. and Others v. Italy". de:border // migration justice collective...

sense that when a line bundle L gives a factorization f = p ∘ g, L is the pullback of O(-1) along g. See also Cone#O(1) for a more explicit construction of...

released, along with other themed merchandise, such as "80's Bobbleheads," "Pullback Custom Cruisers" and "Wrestling Buddies". There have been many graphic...

one typically waits for crossovers occurring together with an extreme pullback, after a peak or trough in the %D line. If price volatility is high, an...

persecution. Despite international standards, some countries engage in 'pullbacks,' which are measures to prevent people from leaving a country and returning...

principal G-bundle over a space S is (up to natural isomorphisms) the pullback of the universal bundle E G → B G {\displaystyle EG\to BG} along some map...

maps is a locally regular category: it has pullbacks, equalizers, and images that are stable under pullback. This is enough to study relations in Map(A)...

December 2021. "City officials, Neihu residents welcome Tzu Chi's project pullback | Society | FOCUS TAIWAN – CNA ENGLISH NEWS". Archived from the original...

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original Thunderjet 500 and Tuff Ones chassis. Playing Mantis added more pullback cars with bodies that were exact fits to the original Aurora AF/X chassis...

finite rank). D-modules on different algebraic varieties are connected by pullback and pushforward functors comparable to the ones for coherent sheaves. For...

was the first competitor robot recreated in toy form when the Robot Wars pullback toys were released. Hypno-Disc's debut battle was against fellow newcomers...

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Specifically, lower indices are covariant indices, and transform via pullbacks, while upper indices are contravariant, transforming under pushforwards...

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deletes the last m-n coordinates of a point is a fibration and therefore the pullback map π m , n ∗ : Ω ∙ ( X n ) → Ω ∙ ( X m ) {\displaystyle \pi _{m,n}^{\ast...

legitimate aspirations and concerns of the Syrian people”, cease hostilities, pullback military concentrations from towns, while simultaneously the Envoy would...

an orthonormal tetrad. That is, the metric tensor can be written as a pullback of the Minkowski metric η i j {\displaystyle \eta _{ij}} : g μ ν = η i...

Euscirrhopterus poeyi, the pullback moth, is a moth of the family Noctuidae. The species was first described by Augustus Radcliffe Grote in 1866. It is...

most generic definition writes the Lagrangian as the metric trace of the pullback of the metric tensor on a Riemannian manifold. For ϕ : M → Φ {\displaystyle...

"friction motor" to the device. As the flywheel, unlike the spring of a pullback motor, is continuously rotating, the motor may be "pumped up" by pushing...

immersed submanifold or an embedded submanifold of M {\displaystyle M} . The pullback i ∗ g {\displaystyle i^{*}g} of g {\displaystyle g} is a Riemannian metric...

submanifold or an embedded submanifold (with or without boundary), the pullback i ∗ g {\displaystyle i^{*}g} of g {\displaystyle g} is a Riemannian metric...

Retrieved 23 August 2026. "The Best of BoF 2024: Fashion's Sustainability Pullback". The Business of Fashion. 2024-12-26. Retrieved 2025-02-12. Guilbault...

defines a Riemannian metric called the quantum metric (equivalently, the pullback of the Fubini–Study metric on projective Hilbert space), while the imaginary...

(1944) (in Hebrew) Kibbutz Society (1954) (in Hebrew) There is No Where to Pullback To (1968) (in Hebrew) Lessons of the Six Day War (1970) (in Hebrew) Issues...

vector spaces. This functor assigns to each space its dual space, and the pullback construction assigns to each arrow f: V → W its dual f∗: W∗ → V∗. In the...

the one used in category theory because it is the covectors that have pullbacks in general and are thus contravariant, whereas vectors in general are...

a Darboux chart, then ω {\displaystyle \omega } can be written as the pullback of the standard symplectic form ω 0 {\displaystyle \omega _{0}} on C n...

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differentials for the cofiber of τ from purely algebraic data. One can then pullback these motivic Adams differentials to the motivic sphere, and then use the...

to μ f {\displaystyle \mu _{f}} . Because f is a finite morphism, the pullback measure f ∗ μ f {\displaystyle f^{*}\mu _{f}} is also defined, and μ f...

tropical Indo-Pacific region. 27 species are accepted. Pisonia aculeata L. – pullback (pantropical) Pisonia albida (Heimerl) Britton ex Standl. – corcho bobo...

the stochastic evolution operator defined as the stochastically averaged pullback induced on differential forms by SDE-defined diffeomorphisms of the phase...

Ryan J. (May 28, 2025). ""Trump's pardons highlight Justice Department's pullback from public corruption cases"". NBC News. "Callahan Pardon Warrant". Department...

of every compact set is compact. Let f: Y → X be such a map; then the pullback f ∗ : Ω c q ( X ) → Ω c q ( Y ) ∑ I g I d x i 1 ∧ … ∧ d x i q ↦ ∑ I ( g...

{\displaystyle TM\cong f^{*}{\widetilde {\gamma }}_{\mathbb {R} }^{4}} is the pullback bundle of the oriented tautological bundle along it) to a continuous map...

Cartesian closed category – Type of category in category theory Categorical pullback – Most general completion of a commutative square given two morphisms with...

2009. Herszenhorn, David M. (March 25, 2003). "Columbia Is Sued Over Pullback on Biosphere". The New York Times. p. 13. Retrieved June 5, 2009. "Science...

G)} corresponding to the identity. The above bijection is given by the pullback of that element f ↦ f ∗ u {\displaystyle f\mapsto f^{*}u} . This is similar...

kinesthetically of actual dance ... Accompanying this movement is a breathless pullback into a high crane shot that takes place at the same time Kelly is swinging...

the quick pursuit of a military pullback from Beirut to Israel's south Lebanon security belt. A partial Israeli pullback had earlier been approved in 1983...

the gold standard test in diagnosing nutcracker syndrome. A renocaval pullback mean gradient of >3 mmHg is considered diagnostic. Although this method...

unofficial term commonly used to differentiate it from the "Special," which has pullback bars, a teardrop tank, and other differences in appearance). The Es and...

sheaf or pullback sheaf. If f is the inclusion of a subspace X of Y, f*(E) is the restriction of E to X, often just called E again, and the pullback of a...

space using the notion of a pullback bundle. If πF:F→ N is a fiber bundle over N and f:M→ N is a continuous map, then the pullback of F by f is a fiber bundle...

Amrith (June 1, 2022). "SeatGeek and Forbes Nix SPAC Deals During Market Pullback". The Wall Street Journal. Archived from the original on May 13, 2023....

semigroups. The Hall–Yamada pullback theorem describes this construction. The construction requires the concepts of pullbacks (in the category of semigroups)...

Rump, 2001. Rump, 2001. Bonet, J.; Dierolf, S. (1 January 2006). "The Pullback for bornological and ultrabornological spaces". Note di Matematica. 25...

X {\displaystyle X} to P r {\displaystyle \mathbf {P} ^{r}} , and the pullback of the dual of the tautological bundle under this map is L {\displaystyle...

}}(0)&\rho (0)\end{pmatrix}}.} Because the Wigner function evolves by the pullback of the classical flow for quadratic Hamiltonians, W ( x , t ) = W 0 ( S...

{\displaystyle {\underline {\mathbb {Q} }}_{X}^{Hdg}} which is defined as the pullback of its corresponding object in Q H d g ∈ MHM ( { p t } ) {\displaystyle...

seen in a freer light, as the site for an integral transform composed as pullback onto the incidence graph and then push forward. The positive real numbers...

Gaza Strip," "... Mr. Arafat had asked the Israelis to delay their total pullback for the 21 days allowed in the accord because the Palestinians were not...

\phi } parametrises rotation about the z {\displaystyle z} -axis. The pullback of the standard Cartesian metric d s 2 = d x 2 + d y 2 + d z 2 {\displaystyle...

via Internet Archive. "Ethiopians and Somalis A gree To Border Truce and Pullback". The New York Times. 1964-03-31. ISSN 0362-4331. Retrieved 2022-09-08...

G} , the metric tensor on the manifold N {\displaystyle N} becomes the pullback of the metric tensor B m n {\displaystyle B_{mn}} on the Lie group G {\displaystyle...

for diversifying their sound, saying "change is good, and I think the pullback from the hardcore is the right one" and "there are still plenty of mean...

border committee would be the appropriate place to plan a coordinated pullback. The ICJ ruled on 11 November 2013 that the land adjacent to the temple...

pre-orders were taken for the product. The company has cited Intel's pullbacks/downsizing in Android development as a reason for its discontinuation...

every point p ∈ N {\displaystyle \textstyle p\in N} is annihilated by (the pullback of) each ⁠ α i {\displaystyle \textstyle \alpha _{i}} ⁠. A maximal integral...

installed by technicians. He described this effect as resembling a "giant pullback" that created the impression of being transported backwards through different...

{\displaystyle f:X\to Y} between two topological spaces, pushforward and pullback relate sheaves on X {\displaystyle X} to those on Y {\displaystyle Y} and...

and a pullback track in a middle tunnel at its northern end. This track descends underground and curves more than 180° west to join the pullback track...

epimorphism) and N → M ″ {\displaystyle N\to M''} is any arrow in E. Then their pullback exists and its projection to N {\displaystyle N} is also an admissible...

Rn is a homeomorphism onto an open set in Rn, and such that Ck|U is the pullback of the sheaf of k-times continuously differentiable functions on Rn. In...

to the pullback, by f, of a universal bundle over the classifying space, and the Chern classes of V can therefore be defined as the pullback of the Chern...

crisis. Turkish banking authorities warned state-run banks against the pullback of loans from the larger financial sectors. Turkey's economy resumed its...

(February 6, 2013). "DreamWorks Animation Layoffs Could Reach 500 Amid Slate Pullback". Deadline Hollywood. Retrieved January 31, 2016. McNary, Dave (July 31...

either key-wound, as were many 20th-century model trains, or a simpler pullback motor. Most photographic camera leaf shutters use a clockwork mechanism...

American retreat, Lafayette rallied the troops, allowing a more orderly pullback, before being treated for his wound. After the battle, Washington cited...

η−1F) on Y; in many cases where the Penrose transform is of interest, this pullback turns out to be an isomorphism. One then pushes the resulting cohomology...

corrections are short-lived and shallow. Anyone looking to "get in on a pullback" will likely miss the boat. As wave three starts, the news is probably...

to a 2009 estimate from the World Factbook. In 2010, in a significant pullback to derussification, Armenia voted to re-introduce Russian-medium schools...

scalar s, that is σsx = sx, then σs defines an action on functions via pullback: σ s ∗ f = f ∘ σ s . {\displaystyle \sigma _{s}^{*}f=f\circ \sigma _{s}...

sized to Matchbox or Hot Wheels) at speeds of up to 30 mph (50 km/h). The pullback motor is wound up by pressing down the rear of the car and rolling it forwards...

north Gaza town". BBC. Retrieved 31 May 2024. "Israeli military confirms pullback from Jabalia". Mackenzie, James (31 May 2024). "Israel completes combat...

the detailed description of the free group situation above. Products, pullbacks, equalizers, and kernels are all examples of the categorical notion of...

first condition means that X is parallel with respect to the pullback connection on the pullback bundle γ∗TM. However, in a local trivialization it is a first-order...

*-autonomous V-categories for all symmetric monoidal categories V with pullbacks, whose objects became known a decade later as Chu spaces. In a biclosed...

morphism over X 1 {\displaystyle X_{1}} from E 1 {\displaystyle E_{1}} to the pullback bundle g ∗ E 2 {\displaystyle g^{*}E_{2}} . Given a vector bundle π: E...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

Fury design by adding larger, more highway friendly front rubber, more pullback on the handle bars and classic, cruiser style fenders. The Interstate took...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

then a diagram of type J (A → B ← C) is a cospan, and its limit is a pullback. The index J = 0 ⇉ 1 {\displaystyle J=0\rightrightarrows 1} is called "two...

{\displaystyle (p,q)} . We can integrate α {\displaystyle \alpha } over Z using the pullback function i ∗ : X → Z {\displaystyle i^{*}\colon X\to Z} , ∫ Z i ∗ α {\displaystyle...

ceasefire with the military junta. "Resource, manpower shortages drove TNLA pullback from Mogok and Momeik, senior leader says". Burma News International. Retrieved...

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conformal. Without appeal to an auxiliary metric, consider the effect of the pullback under f of the usual Euclidean metric. The resulting metric is then given...

\cdot [e],[e]\rangle _{f}} on C ∗ ( G ) {\displaystyle C^{*}(G)} is the pullback of a state on C 0 ( G ^ ) {\displaystyle C_{0}({\widehat {G}})} , which...

the universal bundle since any vector bundle (over a compact space) is a pullback of the tautological bundle; this is to say a Grassmannian is a classifying...

R {\displaystyle R} -module ρ ∗ V {\displaystyle \rho ^{*}V} with the pullback R {\displaystyle R} -action R × V ⟶ M ( x , v ) ⟼ ρ ( x ) ⋅ v {\displaystyle...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

(May 21, 2024). "Skydance TV Expands: Doubles Series Output Amid Industry Pullback, Sets First-Look Pact With Undisputed Cinema". Variety. Retrieved May 31...

July 2026. "RSF regains control of strategic West Darfur town after army pullback". Sudan Tribune. 10 July 2026. Retrieved 11 July 2026. "Sudan Army Shoots...

the size of the gearbox (housing the spring drive). Wind-up doll joke Pullback motor "Windup Toys and". accelerateu.org. Retrieved 3 February 2022.{{cite...

marvel of Peru (Mirabilis jalapa) Mexican devil's-claws (Pisonia capitata) pullback (Pisonia aculeata) purple spiderling (Boerhavia purpurascens) scarlet four...

General Vladimir Boldyrev, commander of Russian land forces, claimed that pullback of forces present outside the security zones to Russia would last for 10...

rise to a subobject f ∗ ( u ) : S → A {\displaystyle f^{*}(u):S\to A} by pullback. For well-powered C {\displaystyle {\mathcal {C}}} , this gives rise to...

{\displaystyle F} . Abstractly, the functor F {\displaystyle F} gives a pullback map F ∗ : [ B , C ] → [ A , C ] {\displaystyle F^{*}:[\mathbf {B} ,\mathbf...

later in the United States, leading to the orderly evacuation (Operation Pullback) of the Dachen Islands by the United States Navy in February. At the time...

its tangent space at each point (cf. Gauss map). The Maslov index is the pullback via this mapping, in H 1 ( M , Z ) {\displaystyle H^{1}(M,\mathbb {Z} )}...

differential forms, any holomorphic 1-form on V {\displaystyle V} is a pullback of translation-invariant 1-form on the Albanese variety, coming from the...

group G. A moving frame on a submanifold M of G/H is a section of the pullback of the tautological bundle to M. Intrinsically a moving frame can be defined...

president's son, Donald Trump Jr. Despite a brief reprieve following the pullback of federal agents in late July-early August, tensions between protesters...

of torsion abelian groups; Coherent/geometric theories are preserved by pullback along geometric morphisms between topoi (MacLane & Moerdijk 1992, chapter...

classes of Z {\displaystyle Z} . This construction is functorial by taking pullbacks of families. Given f : T ′ → T {\displaystyle f:T'\to T} , there is a...

spectrum of X. homotopy pullback A homotopy pullback is a special case of a homotopy limit that is a homotopically-correct pullback. homotopy quotient If...

Paying for Israel's makeover: U.S. funds for a controversial settlement pullback could help advance a peace agreement. Gershom Gorenberg. Los Angeles Times...

low stress where force was applied up and down, and in simulations of "pullback". Due to the relative weakness of the skull at the sides and midline, these...

F_{f}} this is because computing the homotopy limit amounts to finding the pullback of the diagram B I ↓ A × ∗ → f B × B {\displaystyle {\begin{matrix}&&B^{I}\\&&\downarrow...

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} . In particular, the pullback of any form on X / G {\displaystyle X/G} is G {\displaystyle G} -invariant. Also, the pullback is an injective morphism...

Bennett, James (28 June 2003). "Mideast Leaders Test Compromise Israeli Pullback, Hamas Truce in Plan". New York Times. ProQuest 387857733. "Tanzim Terrorists...

take a path γ : I → S k {\displaystyle \gamma :I\to S^{k}} and take the pullback M I → S n + k ↓ ↓ f I x → γ S k {\displaystyle {\begin{matrix}M_{I}&\to...

three-day ultimatum to the U.K., demanding an arbitration of issues and a pullback of troops from the borders between the Republic and the adjoining Cape...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

be exactly the same as pullback along f {\displaystyle f} followed by pullback along g {\displaystyle g} . However, pullback involves an arbitrary choice...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

{\displaystyle f^{*}\omega '=\omega ,} where f ∗ {\displaystyle f^{*}} is the pullback of f {\displaystyle f} . The symplectic diffeomorphisms from M {\displaystyle...

(isotony). The Poincaré group acts continuously on Mink. There exists a pullback of this action, which is continuous in the norm topology of A ( M ) {\displaystyle...

landing that would take the Croatan work in reverse, so he ordered a general pullback to the Fort Thompson line. Thus, when the Federal army came upon the first...

over an open subset U {\displaystyle U} of M {\displaystyle M} . Then the pullback s*ω of a principal connection is a 1-form on U {\displaystyle U} with values...

concessions to the United States on trade and the environment, which included a pullback on global warming. West Germany had been pushing for a summit declaration...

the study of harmonic maps. In terms of the trace, interior product, and pullback operations, the biharmonic map equation can be written as Δ Δ f + tr g...

a_{2})=F(a_{1})\cap F(a_{2}).} Categorically, this means that it preserves the pullback: In order to be considered stable, functions of two arguments must satisfy...

it defines. The differential is also used to define the dual concept of pullback. Stochastic calculus provides a notion of stochastic differential and an...

}^{-1}s_{x_{0}}^{*}{\star }} , and s x 0 ∗ {\displaystyle s_{x_{0}}^{*}} is the pullback along the constant map s x 0 : x → x 0 {\displaystyle s_{x_{0}}:x\rightarrow...

border committee would be the appropriate place to plan a coordinated pullback. On July 23, 2011, one Cambodian soldier was killed along the Cambodian-Thai...

title. 2009 (37th Annual Shogi Awards): Eiji Iijima for the Iijima Bishop Pullback. 2010 (38th Annual Shogi Awards): Yoshitaka Hoshino for the Super High...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

face F of the nef cone of X, namely the intersection of Nef(X) with the pullback f ∗ ( N 1 ( Y ) ) ⊂ N 1 ( X ) {\displaystyle f^{*}(N^{1}(Y))\subset N^{1}(X)}...

suggested in these findings that Deinonychus may have fed by using neck-driven pullback movements to dismember carcasses when feeding, akin to modern varanid lizards...

from the original on November 5, 2025. Retrieved September 7, 2025. The pullback reflects a broader American retreat from international bodies and Mr. Trump's...

{\displaystyle A} such that A / B {\displaystyle A/B} is elementary. Then the pullback of a Schwartz–Bruhat function on A / B {\displaystyle A/B} is a Schwartz–Bruhat...

constructions (e.g., tensor products, differential forms, tangent spaces, pullbacks, exterior derivatives, cube and chains) are introduced in quick succession...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

f\colon X\rightarrow Y} are isomorphisms for all n {\displaystyle n} . Pullback (cohomology) Allen Hatcher, Algebraic topology. Cambridge University Press...

Illinois have been scrutinizing police practices. Data of the supposed pullback was reflected with an 80 percent decrease in the number of street stops...

Schwirtz, Michael; Engelbrecht, Cora; Specia, Megan (7 May 2022). "Russian Pullback Seen Near Kharkiv, Despite Victory Day Push for Gains". The New York Times...

the notion of the pullback of a differential form. Roughly speaking, when a differential form is integrated, applying the pullback transforms it in a...

(c. 122), through the building of the Antonine Wall (c. 142), until the pullback to Hadrian's Wall in 164. Ptolemy's Geography was written within this timeframe...

incorporates some or all of E {\displaystyle E} ; it is essentially the pullback of V {\displaystyle V} in cohomology. To pursue blow-up in its greatest...

attention to the pullback action as to the extension of the main punch. Different karate styles will have slightly different pullback chambering positions...

resulting closed subschemes are relative Schubert varieties, and their pullbacks by sections give degeneracy loci. On the complete flag bundle, put U 0...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

2021 – via France 24. Gross, Judah Ari (16 October 2019). "US Mideast pullback didn't start with the Kurds, and it won't end there either". The Times...

that cost through rate increases, Frazier said. That's helping drive the pullback from the state, he added. Darmiento, Laurence (July 30, 2024). "L.A. consumer...

_{S^{n}}\omega _{n}=1} . Since d ω n = 0 {\displaystyle d\omega _{n}=0} , the pullback φ ∗ ω n {\displaystyle \varphi ^{*}\omega _{n}} is a closed differential...

parameterize universal classes of flat morphisms, and every flat morphism is the pullback from some Hilbert scheme. I.e., if f : X → S {\displaystyle f\colon X\to...

then applying the ordinary Laplacian. The Laplacian is equivariant under pullback by every Euclidean transformation. More precisely, if g ( x ) = U x + a...

an isomorphism between them. The composition of morphisms is given by pullback. Define a topological space B + C {\displaystyle B^{+}C} by B + C = Ω B...

hangers when very high, or may drop a few inches below, called clubman bars. Pullback, the distance grips are behind their mounting location, may vary from 4...

and it was the loss rate in crews and not materiel that brought about a pullback from the strategic offensive in the autumn of 1943. The Eighth Air Force...

in the day, but just received. As a result of the miscommunication, the pullback did not occur, and the two regiments were ultimately surrounded with most...

the sense that the product above is essentially the fibered product or pullback X × f Y {\displaystyle X\times _{f}Y} which is dual to the pushout X ⊔...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

X_{2}=S_{2}^{2}=K(\mathbb {Z} ,2)} , and X 3 {\displaystyle X_{3}} comes from a pullback sequence X 3 → ∗ ↓ ↓ X 2 → K ( Z , 4 ) , {\displaystyle {\begin{matrix}X_{3}&\to...

category with pullbacks and a terminal object 1 the points of B can be identified with morphisms p:1→B and the fiber of p is obtained as the pullback of p and...

agentic AI eats up to 1,000x more tokens than standard AI, sparks corporate pullback at Microsoft, Meta, and Amazon". Tom's Hardware. Retrieved 28 May 2026...

threatened VRS-held Trebinje in eastern Herzegovina. As a result of the JNA pullback, the Prevlaka peninsula was demilitarized and placed under United Nations...

2026 that they had met their fundraising goals despite the 2025 corporate pullback. Several veteran contractors are employed to take on specific roles for...

Hopf bundle I-bundle Natural bundle Principal bundle Projective bundle Pullback bundle Quasifibration Universal bundle Vector bundle Wu–Yang dictionary...

} induces a map in cohomology H ∗ {\displaystyle H^{\ast }} called its pullback π ∗ {\displaystyle \pi ^{\ast }} π ∗ : H ∗ ( M ) ⟶ H ∗ ( E ) . {\displaystyle...

Alexandra (22 June 2022). "Ecuador indigenous groups condition talks on pullback of security forces". Reuters. Archived from the original on 2022-06-21...

28, 2018). "Forest City Sells Brooklyn Building for $156M Amid Borough Pullback". Commercial Observer. Retrieved July 4, 2024. Warerkar, Tanay (September...

be homomorphisms. The fiber product of G and H over Q, also known as a pullback, is the following subgroup of G × H: G × Q H = { ( g , h ) ∈ G × H : φ...

initial proposal. The most glaring omission from the initial plan due to the pullback in federal support was and is the future Sepulveda line connecting the...

Perspectives. Springer Science & Business Media. p. 10. ISBN 978-0-8176-4186-3. Pullbacks in Category of Sets and Partial Functions Pointed set at PlanetMath. Pointed...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

low stress where force was applied up and down, and in simulations of "pullback". Due to the relative weakness of the skull at the sides and middle, these...

Schlossberg, Tatiana (December 16, 2016). "As Trump Signals Climate Action Pullback, Local Leaders Push Forward". The New York Times. Archived from the original...

N/V/D (Counterstrike Zentraedi Remix) - Dieselboy O.D. - Demo The Big Pullback - Noah D Machine March - SPKTRM Load Rocket (Gridlok Remix) - Computer...

dark brown loam or sandy loam of strong to extreme acidity; Breakneck and Pullback series are most common. The climate of the summit of Kuwohi is humid continental...

algebra–valued) differential forms on E {\displaystyle E} and through pullback along smooth sections B ↪ E {\displaystyle B\hookrightarrow E} differ by...

the tangent bundle of M to the pullback of the vertical bundle of E along the distinguished section, where the pullback bundle is defined as o*VE = M ×...

fighters in their own words, Dec. 10, 2014 Medical Missionaries' Ebola Pullback: No More Kent Brantlys?, Deann Alford/ Nov. 21, 2014 Tryggestad, Erik (2015-02-06)...

3 December 2019. Retrieved 10 February 2022. "U.S. military completes pullback from northeast Syria, Esper says". Reuters. 4 December 2019. Retrieved...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

f:\mathbb {A} ^{n}\to \mathbb {A} ^{m},} then consider the (homotopy) pullback diagram Z → A n ↓ ↓ f { p t } → 0 A m {\displaystyle {\begin{matrix}Z&\to...

California Press, p 203. Joel Brinkley, 'Mideast Turmoil:Israel Promises a Pullback As Death Toll Keeps Rising,' New York Times, March 15, 2002 Nazir Majally...

and Y, a map f: X → Y is a weak homotopy equivalence if and only if the pullback homomorphism f*: Hn(Y,Z) → Hn(X,Z) on singular cohomology is bijective...

Product (category theory) Equaliser (mathematics) Kernel (category theory) Pullback (category theory)/fiber product Inverse limit Pro-finite group Colimit...

original on 28 May 2022. Retrieved 2 May 2022. "Live Updates: Russian Pullback Seen Near Kharkiv, Despite Victory Day Push for Gains". The New York Times...

established, there was no joint command of the ARBiH and the HVO. The ARBiH pullback was completed by 11 am on 3 November, while the right flank of the ARBiH...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

subsets of R > 0 , {\displaystyle \mathbb {R} _{>0},} corresponding to the pullback of the usual Lebesgue measure on the real numbers under the logarithm:...

GL1, the formula d F F {\displaystyle {\frac {dF}{F}}} is therefore a pullback of the invariant form.[citation needed] Exponential growth and exponential...

are module homomorphisms, then they are said to form a fiber square (or pullback square), denoted by M ×B N, if it fits into 0 → M × B N → M × N → ϕ B →...

C on S D•C > 0. Ample divisors have a nice property such as it is the pullback of some hyperplane bundle of projective space, whose properties are very...

sunny Los Angeles setting of the show, and the signature sweeping aerial pullbacks. Brooks, Tim and Marsh, Earle, The Complete Directory to Prime Time Network...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

^{n+1}:|x|=a\right\}} with g S n ( a ) {\displaystyle g_{S^{n}(a)}} given by the pullback of the standard Riemannian structure on R n + 1 {\displaystyle \mathbb...

figure of ertzainas, while the Spanish PP's Ministry of Interior rejects a pullback of Spanish police bodies, as demanded by the large majority of the political...

Satkhira axis. The corps moved to its present location in January 1985. The pullback of over four lakh troops along with heavy armored and artillery formations...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

original on 11 December 2013. Sen, Sudhi Ranjan (7 May 2013). "India-China pullback: what happened behind the scenes". NDTV News. Defence News. "India Destroyed...

morphism in C, and is a pullback, then the coequalizer of p0, p1 exists. The pair (p0, p1) is called the kernel pair of f. Being a pullback, the kernel pair...

original on 15 August 2008. Philippe Naughton (14 August 2008). "Russian pullback in doubt as Condoleezza Rice and US aid troops head for Georgia". The Times...

the perturbation metric may be defined as the difference between the pullback of g μ ν {\displaystyle g_{\mu \nu }} and the Minkowski metric: h μ ν =...

groupoid μ ∗ G ⇉ N {\displaystyle \mu ^{*}G\rightrightarrows N} , called its pullback groupoid or induced groupoid, where μ ∗ G ⊆ N × G × N {\displaystyle \mu...

\quad R=\pi _{*}E} , let f = m ∗ ( t ) {\displaystyle f=m^{*}(t)} be the pullback of t along m. It lives in E ∗ ( C P ∞ × C P ∞ ) = lim ← ⁡ E ∗ ( C P n ×...

Michael (23 August 2008). "Georgia Prepares for Refugees; Russians Declare Pullback Finished". The New York Times. "Russian troops to patrol Georgian port...

granted $5 billion in aid to 16 European nations. Postwar anti-Communism, pullback to American isolationism, and general conservative backlash led U.S. Republican...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

Attrition that had continued after the 1967 Six-Day War and a partial pullback of Israeli forces from occupied territory. The six dissenters, led by future...

a fad in the early 2000s. In 1978, Takara developed the Choro-Q, mini pullback cars. Internationally, they have been sold as "Penny Racers". Takara also...

models. In 1981, they developed small elaborate gearboxes suitable for pullback motor, which were used for many companies' products. Under the nostalgia...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

such that R ↪ B × A {\displaystyle R\hookrightarrow B\times A} is the pullback of ( ∈ ) ↪ A × P ( A ) {\displaystyle (\in )\hookrightarrow A\times {\mathcal...

deterministic case. It is necessary to "rewind time", as in the definition of a pullback attractor, so that the noise close to the final time remains consistent...

attacked its troops". AP NEWS. "Kurdish forces start Syria-Turkey border pullback". Arab News. 24 October 2019. Malsin, Jared; Osseiran, Nazih (24 October...

space. Analytic mappings induce pushforward maps on tangent spaces and pullback maps on cotangent spaces. The dimension of the tangent space at x is called...

{\mathbf {x} }},\dots ,\mathbf {x} ^{(n)}} attached to the point at x. The pullback of the Maurer–Cartan form along this map gives a complete set of affine...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

}\alpha =\int _{\varphi (U)}(\varphi ^{-1})^{*}\alpha \,,} i.e., via the pullback of α {\displaystyle \alpha } to ⁠ R n {\displaystyle \mathbb {R} ^{n}}...

sections of ω Y {\displaystyle \omega _{Y}} . In local coordinates, this pullback operation is given by the Jacobian determinant of f. When f : Y → X {\displaystyle...

of maritime pushbacks, or by a third country, in which case they are pullbacks. Some international requirements require boat patrols by transit countries...

{\Lambda ^{2}}{2}}|F|^{2}\right),} where π ∗ {\displaystyle \pi ^{*}} is the pullback of the fiber bundle projection π : P → M {\displaystyle \pi :P\to M} ....

discontinued shortly after. A range titled Pull Back and Go! featuring pullback versions of Thomas, Percy, Toby, and Bertie were released under Shining...

^{-1}(U)\to U\times \mathbb {R} ^{n}} : the bundle metric can be taken as the pullback of the inner product of a metric on R n {\displaystyle \mathbb {R} ^{n}}...

{\displaystyle i} . Note that g i {\displaystyle g_{i}} is also known as the pullback. If F : R → R 2 {\displaystyle F:\mathbb {R} \rightarrow \mathbb {R} ^{2}}...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

11 that Petraeus had "warned in stark terms against the kind of rapid pullback favored by the Democratic majorities in the House and Senate". Reid stated...

Herispehe. The next day, January 8, Hitler ordered the German Army's first pullback from the Battle of the Bulge. In fighting a numerically superior foe with...

Howard University Law School closed its evening classes, during a financial pullback because of the Great Depression. That same year, George A. Parker, Philip...

-form ω f := f ∗ ω G , {\displaystyle \omega _{f}:=f^{*}\omega _{G},} the pullback of ω G {\displaystyle \omega _{G}} by f {\displaystyle f} . The map f {\displaystyle...

{\displaystyle \mathbb {P} ^{1}} . The category of schemes admits finite pullbacks and in some cases finite pushouts; they both are constructed by gluing...

Stephen (4 November 2025). "Wall St ends lower as bank CEOs warn of possible pullback, fueling tech bubble jitters". Reuters. Retrieved 5 November 2025. D Duffy...

of a fiber bundle Σ → X {\displaystyle \Sigma \to X} , if any. Then the pullback bundle Y h = h ∗ Y {\displaystyle Y^{h}=h^{*}Y} over X {\displaystyle X}...

manifold (the action of the transformation on differential forms is just the pullback). More generally, the exterior derivative       d : Ω n ( M ) → Ω n + 1...

Riemannian connection on a surface embedded in Euclidean space E3 is just the pullback under the Gauss map of the Riemannian connection on S2. Using the identification...

and for every morphism h : Z → Y {\displaystyle h:Z\rightarrow Y} in the pullback diagram P → g ′ Z ↓ h ′ ↓ h X → g Y {\displaystyle {\begin{array}{ccc}P&{\xrightarrow...

Koning Beals (April 25, 2019). "U.S. oil prices fall, Brent turns lower in pullback from recent multimonth highs". Market Watch. Myra P. Saefong (May 24, 2019)...

{\displaystyle d\alpha =\pi ^{*}\omega } ; since exterior derivative and pullbacks commute, ω {\displaystyle \omega } is automatically closed. Using Chern-Weil...

game in April. Psyonix partnered with Zag Toys to produce a series of pullback toy cars based on the Rocket League vehicles, which released in June 2017...

Here π is the projection of the cotangent bundle T*M to M, and π* is the pullback of a vector bundle. Chain complex Atiyah, M. F.; Singer, I. M. (1968)....

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

operators x and p defined above, these are multiplication by eitx and pullback by translation x → x + s.) A formal computation (using a special case of...

\colon G\to B} is a fibration if and only if the following square is a pullback (dually, φ {\displaystyle \varphi } is an opfibration if and only if the...

Miller, Rich (April 12, 2023). "Brainard, Unlike Yellen, Sees Signs of a Pullback in Bank Credit". Bloomberg News. Archived from the original on April 14...

original on 9 December 2008. Retrieved 2008-11-20. "Congo rebels announce pullback to help peace bid". Reuters. 2008-11-18. Retrieved 2008-11-20. Louis Charbonneau...

towards, and end the use of heavy weapons in, population centres, and begin pullback of military concentrations in and around population centres. As these actions...

series include Mt. Rogers at the northern end in Virginia; Breakneck and Pullback on Clingman's Dome in Tennessee; Burton and Craggey on Mount Mitchell in...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

ultimatum to the United Kingdom, demanding an arbitration of issues and a pullback of troops from the borders between the Republic and the adjoining Cape...

pair of a morphism f : X → Y {\displaystyle f:X\to Y} is defined as the pullback on this morphism paired with itself. It can be visualized with the commutative...

Because of this, the object a {\displaystyle a} is often thought of as the pullback of z {\displaystyle z} and is sometimes even denoted as f ∗ z {\displaystyle...

Grothendieck's relative point of view. To move from one slice to another by "pullback" therefore requires base change. The related operation in the opposite...

S factors through S′, this factorization sends x′ to s′, and that the pullback of M to X′ admits a total S′-dévissage at x′ in dimensions between n and...

submanifold N ⊂ M {\displaystyle N\subset M} having the property that the pullback to N {\displaystyle N} of all differential forms contained in I {\displaystyle...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

M} ; that is, there is a unique symplectic form on the quotient whose pullback to μ − 1 ( 0 ) {\displaystyle \mu ^{-1}(0)} equals the restriction of ω...

directorship at the National Radio and Television Administration. Another pullback from China's official support for Wolf Warrior diplomacy occurred in January...

be seen as a natural vector bundle isomorphism vl:(πTM)*TM→VTM from the pullback bundle of (TM,πTM,M) over πTM:TM→M onto the vertical tangent bundle V T...

field Tensor field Differential form Exterior derivative Lie derivative pullback (differential geometry) pushforward (differential) jet (mathematics) Contact...

differential operator between two vector bundles E and F is a section of the pullback of the bundle Hom(E, F) to the cotangent space of X. The differential operator...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

ISBN 978-1-4008-2887-6 Deeptiman Tiwary, India said no to China proposal on pullback from Hot Springs, The Indian Express, 10 April 2022. PTI, India, China...

Given a ring homomorphism f : R → S the kernel pair of f (this is just the pullback of f with itself) is a congruence relation on R. The ideal determined by...

backwards, usually under motorized control at a pullback speed of 0.5 mm/s. (The motorized pullback tends to be smoother than hand movement by the physician...

nastier war began in 2346, sparked by a rebellion of mutants. This led to a pullback of the humans from their maximum expansion, isolating many colonies. The...

scheme of finite type over k. A morphism f: X → Y of schemes determines a pullback homomorphism on the rings of regular functions, f*: O(Y) → O(X). In the...

inclusions of open subsets. That is, for U open in X, there is a natural pullback or restriction homomorphism H i B M ( X ) → H i B M ( U ) . {\displaystyle...

is a principal H-bundle over B/H. If σ : X → B/H is a section, then the pullback bundle BH = σ−1B is a reduction of B. Every vector bundle of dimension...

rights violations and presumably responsible for thousands of illegal pullbacks in the Mediterranean. In February 2020, Spindelegger joined around fifty...

were also available in commemorative packaging as a Radio Times exclusive Pullback-action toys – Thunderbirds 1, 2 and 4 Thunderbird 2 pod vehicles – the...

tangent bundle on M {\displaystyle M} to N {\displaystyle N} (properly, the pullback i ∗ T M {\displaystyle i^{*}\mathrm {T} M} of the tangent bundle on M {\displaystyle...

губернатора Пермского края о прямых эфирах в Instagram "Russia Signals Pullback in Business Support as Budget Strains Mount" The Moscow Times (April 18...

_{ab}I^{a}dE^{b})=0} holds, where φ ∗ {\displaystyle \varphi ^{*}} is the pullback of φ {\displaystyle \varphi } . The manifold E {\displaystyle {\mathcal...

to invoke the Federal Marketing Order out of the realization that any pullback in supply by U.S. growers would easily be filled by Canadian production...

associated a unique morphism f: T → Av so that L is isomorphic to the pullback of P along the morphism 1A×f: A×T → A×Av. Applying this to the case when...

[in particular] a strong opening." He also cites the big ending, and "pullback and reveal", whereby the audience or reader is led along a specific path...

Schwirtz, Michael; Engelbrecht, Cora; Specia, Megan (7 May 2022). "Russian Pullback Seen Near Kharkiv, Despite Victory Day Push for Gains". The New York Times...

canonical bundle formula implies that KX is Q-linearly equivalent to the pullback of some Q-divisor on S; it is essential here that the elliptic surface...

of his troops supporting the Imperial cause in Mexico. This strategic pullback was a potentially fatal blow to the infant Mexican monarchy; at the end...

1 X / Y → L 0 X / Y {\displaystyle L_{1}^{X/Y}\to L_{0}^{X/Y}} is the pullback along i of the inclusion of J in the structure sheaf O V {\displaystyle...

covering of Z {\displaystyle Z} . The output of MAPPER is the nerve of the pullback cover M ( U , f ) := N ( f − 1 ( U ) ) {\textstyle M(\mathbb {U} ,f):=N(f^{-1}(\mathbb...

(August 20, 2024). "Time Magazine Lays Off 22 Staffers Amid Advertising Pullback, Restructuring". The Hollywood Reporter. Retrieved August 5, 2025. Caitlin...

which normalizes H/Z(G) and H/Z(G) is a proper subgroup of it. Therefore, pullback this subgroup to the subgroup in G and it normalizes H. (This proof is...

trivializations of P given as sections sU : U → P and letting θU = s*η be the pullbacks of the Cartan connection along the sections. Another way in which to define...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

f(u_{0})=\left(\mathrm {D} g(u_{0})\right)^{*}(\lambda ),} where (Dg(u0))∗(λ) is the pullback of λ by Dg(u0), i.e. the action of the adjoint map (Dg(u0))∗ on λ, as defined...

products of the curve, together with a compatibility condition involving pullbacks to the complement of various diagonals. Any translation-equivariant chiral...

Universal constructions Limits Terminal objects Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels...

the military force. Other modern scholars (Ferrill et al.) also see the pullback as a strategic mistake, arguing that it left lower quality "second string"...

{Z} }^{n}} , we let O ( 1 ) {\displaystyle {\mathcal {O}}(1)} denote the pullback of O ( 1 ) {\displaystyle {\mathcal {O}}(1)} to P S n {\displaystyle \mathbb...

Reuters. 31 May 2017. Retrieved 8 September 2017. "Barclays continues pullback with final exit from European retail banking". Financial Times. "Barclays...