Hopf is a German surname. Notable people with the surname include: Eberhard Hopf (1902–1983), Austrian mathematician Hans Hopf (1916–1993), German tenor...

In differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space)...

The Hopf theorem (named after Heinz Hopf) is a statement in differential topology, saying that the topological degree is the only homotopy invariant of...

the Hopf invariant is a homotopy invariant of certain maps between n-spheres. In 1931 Heinz Hopf used Clifford parallels to construct the Hopf map η...

In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously a (unital associative) algebra and a (counital coassociative)...

mathematics, the Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important...

In geometry, the Killing–Hopf theorem states that complete connected Riemannian manifolds of constant curvature are isometric to a quotient of a sphere...

In complex geometry, a Hopf manifold (Hopf 1948) is obtained as a quotient of the complex vector space (with zero deleted) ( C n ∖ 0 ) {\displaystyle...

In mathematical knot theory, the Hopf link is the simplest nontrivial link with more than one component. It consists of two circles linked together exactly...

The Hopf–Rinow theorem is a set of statements about the geodesic completeness of Riemannian manifolds. It is named after Heinz Hopf and his student Willi...

In complex geometry, a Hopf surface is a compact complex surface obtained as a quotient of the complex vector space (with zero deleted) C 2 ∖ { 0 } {\displaystyle...

Heinz Hopf (19 November 1894 – 3 June 1971) was a German mathematician who worked on the fields of dynamical systems, topology and geometry. Hopf was born...

The Heinz Hopf Prize is awarded every two years at ETH Zurich. The prize honours outstanding scientific work in the field of pure mathematics. It is named...

the theory of Hopf algebras, a Hopf algebroid is a generalisation of weak Hopf algebras, certain skew Hopf algebras and commutative Hopf k-algebroids....

In algebra, the Pareigis Hopf algebra is the Hopf algebra over a field k whose left comodules are essentially the same as complexes over k, in the sense...

In algebraic topology, the Hopf construction constructs a map from the join X ∗ Y {\displaystyle X*Y} of two spaces X {\displaystyle X} and Y {\displaystyle...

mathematics, Hopf conjecture may refer to one of several conjectural statements from differential geometry and topology attributed to Heinz Hopf. The Hopf conjecture...

The Hopf maximum principle is a maximum principle in the theory of second order elliptic partial differential equations and has been described as the "classic...

In the mathematics of dynamical systems and differential equations, a Hopf bifurcation is said to occur when varying a parameter of the system causes the...

Eberhard Frederich Ferdinand Hopf (April 4, 1902, in Salzburg, Austria-Hungary – July 24, 1983, in Bloomington, Indiana, USA) was a German mathematician...

In mathematics, the Hopf lemma, named after Eberhard Hopf, states that if a continuous real-valued function in a domain in Euclidean space with sufficiently...

Heinz Willy Gustav Hopf (11 November 1934 – 23 January 2001) was a Swedish actor. He was born in Stockholm but moved to Lund where he studied medicine...

In physics, the Einstein–Hopf drag (named after Albert Einstein and Ludwig Hopf) is a velocity-dependent drag force upon charged particles that are being...

89–90) introduced an example of an infinite-dimensional Hopf algebra, and Sweedler's Hopf algebra H4 is a certain 4-dimensional quotient of it that...

Hans Hopf (August 2, 1916, Nuremberg – June 25, 1993, Munich) was a German operatic tenor, one of the leading heldentenors of the immediate postwar period...

Eduard Hopf (10 January 1901 – 19 November 1973) was a German painter. His work was part of the painting event in the art competition at the 1928 Summer...

Wiener–Hopf method is a mathematical technique widely used in applied mathematics. It was initially developed by Norbert Wiener and Eberhard Hopf as a method...

Karl Hopf (26 March 1863 – 23 March 1914) was a German serial killer. He was sentenced to death by a Frankfurt jury on 19 January 1914 for the murder of...

Karl Hopf may refer to: Karl Hopf (historian) Karl Hopf (serial killer) This disambiguation page lists articles about people with the same name. If an...

mathematics, the group Hopf algebra of a given group is a certain construct related to the symmetries of group actions. Deformations of group Hopf algebras are...

The Cole–Hopf transformation is a change of variables that allows to transform a special kind of parabolic partial differential equations (PDEs) with a...

In mathematics, the Hopf decomposition, named after Eberhard Hopf, gives a canonical decomposition of a measure space (X, μ) with respect to an invertible...

quasi-Hopf algebra is a generalization of a Hopf algebra, which was defined by the Ukrainian mathematician Vladimir Drinfeld in 1989. A quasi-Hopf algebra...

In algebra, the Malvenuto–Poirier–Reutenauer Hopf algebra of permutations or MPR Hopf algebra is a Hopf algebra with a basis of all elements of all the...

Annie Stebler-Hopf (4 September 1861 – 30 January 1918), also known as Anny Hopf or Anna Hopf, was a Swiss painter. She trained in Basel, Berlin, and...

Theodore Hopf (born 1959) is an American academic and a leading figure in constructivism in international relations theory. He was a Provost Chair Professor...

Ludwig Hopf (23 October 1884 in Nuremberg, Germany – 23 December 1939 in Dublin) was a German-Jewish theoretical physicist who made contributions to mathematics...

Per Johannes Hopf (born 16 June 1987) is a Swedish former professional footballer who played as a goalkeeper. He played professionally in Sweden with Hammarby...

Ernest Hopf (1910 - 1999) was a German-American artist known for his silk screen prints. Hopf was born February 2, 1910 in Germany. In 1935, he married...

In mathematics, especially algebraic topology and homotopy theory, the Hopf–Whitney theorem is a result relating the homotopy classes between a CW complex...

These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital...

In algebra, a Taft Hopf algebra is a Hopf algebra introduced by Earl Taft (1971) that is neither commutative nor cocommutative and has an antipode of large...

path-connected H-space with finitely generated and free cohomology groups is a Hopf algebra. Also, one can define the Pontryagin product on the homology groups...

In physics, the Landau–Hopf theory of turbulence, named for Lev Landau and Eberhard Hopf, was until the mid-1970s,[clarification needed] the accepted...

In mathematics, a braided Hopf algebra is a Hopf algebra in a braided monoidal category. The most common braided Hopf algebras are objects in a Yetter–Drinfeld...

Genet. 10 (11): 783–796. doi:10.1038/nrg2664. PMID 19834483. Bernstein H, Hopf FA, Michod RE (1987). "The Molecular Basis of the Evolution of Sex". Molecular...

In mathematics, a Hopf algebra, H, is quasitriangular if there exists an invertible element, R, of H ⊗ H {\displaystyle H\otimes H} such that R   Δ ( x...

Maria Hopf (13 September 1913 – 24 August 2008) was a pioneering archaeobotanist, based at the RGZM, Mainz. Hopf studied botany from 1941 to 1944, receiving...

deformed but always conserves an integer Hopf topological invariant. It is named after the German mathematician, Heinz Hopf. A model that supports hopfions was...

Pitchfork bifurcation Period-doubling (flip) bifurcation Hopf bifurcation Neimark–Sacker (secondary Hopf) bifurcation Global bifurcations occur when "larger"...

name "quantum double" come from the Drinfeld double of a finite groups and Hopf algebras. The most well-known example is the toric code model, which is a...

giving the 3-sphere the structure of a principal circle bundle known as the Hopf bundle. If one thinks of S3 as a subset of C2, the action is given by ( z...

In quantum group and Hopf algebra, the bicrossed product is a process to create new Hopf algebras from the given ones. It's motivated by the Zappa–Szép...

In mathematics, a shuffle algebra is a Hopf algebra with a basis corresponding to words on some set, whose product is given by the shuffle product X ⧢...

Karl Hopf (February 19, 1832, in Hamm, Westphalia – August 23, 1873, in Wiesbaden) or Carl Hermann Friedrich Johann Hopf was a historian and an expert...

solvability of statistical mechanical models. He also generalized Hopf algebras to quasi-Hopf algebras and introduced the study of Drinfeld twists, which can...

Alice Lightner Hopf (1904–1988) was an American writer who wrote young adult science fiction under the name of A. M. Lightner and youth nature books under...

simple for values n {\displaystyle n} ≤ 4 {\displaystyle 4} . There are four Hopf fibrations of hyperspheres: S 0 ↪ S 1 → S 1 , S 1 ↪ S 3 → S 2 , S 3 ↪ S 7...

spirit, weak Hopf algebras are weak bialgebras together with a linear map S satisfying specific conditions; they are generalizations of Hopf algebras. These...

categories, Hopf algebroids etc. Ross Street, Brian Day, "Quantum categories, star autonomy, and quantum groupoids", in "Galois Theory, Hopf Algebras, and...

the pseudonym Alex Fridolinski, and starring Christina Lindberg and Heinz Hopf. It tells the story of a mute young woman who is forced into heroin addiction...

is important in a certain noncommutative Galois theory, which generates Hopf algebroids in place of the more classical Galois groups, whereas the notion...

directed by Arne Sucksdorff, starring Tomas Bolme, Anders Henrikson, Heinz Hopf and Björn Gustafson. It tells the story of a troubled 16-year-old boy who...

783–796. doi:10.1038/nrg2664. PMID 19834483. S2CID 771357. Bernstein, H.; Hopf, F. A.; Michod, R. E. (1987). "The Molecular Basis of the Evolution of Sex"...

{\displaystyle T_{p}M} , the entire tangent space at p {\displaystyle p} . The Hopf–Rinow theorem gives alternative characterizations of completeness. Let (...

structure of a Z2-graded Hopf algebra. Likewise the representations of this Hopf algebra turn out to be Z2-graded comodules. This Hopf algebra gives the global...

first interesting example is the group π3(S2) which is generated by the Hopf fibration. The problem of computing the groups πn+k(Sn) for positive k is...

representation of a Hopf algebra is a representation of its underlying associative algebra. That is, a representation of a Hopf algebra H over a field...

Memorable skateboarders such as Dylan Rieder and Kenny Hopf have performed at the venue, with Hopf filming a video there during the COVID-19-lockdown in...

economies across Eurasia. As originally defined by Daniel Zohary and Maria Hopf, they consisted of three cereals (emmer wheat, einkorn wheat, and barley)...

In mathematics, an exp algebra is a Hopf algebra Exp(G) constructed from an abelian group G, and is the universal ring R such that there is an exponential...

are all zero. A stronger form of the theorem, also known as the Lefschetz–Hopf theorem, states that, if f {\displaystyle f} has only finitely many fixed...

In quantum group, Hopf algebra and weak Hopf algebra, the Doi-Hopf module is a crucial construction that has many applications. It's named after Japanese...

the Hopf algebras of functions. A finite commutative group scheme over a field corresponds to a finite dimensional commutative cocommutative Hopf algebra...

(graded commutator if C is graded). If A is a connected graded cocommutative Hopf algebra over a field of characteristic zero, then the Milnor–Moore theorem...

monoidal category. It consists of modules over a Hopf algebra which satisfy some additional axioms. Let H be a Hopf algebra over a field k. Let Δ {\displaystyle...

them as "Hopf monads", while in works of Bruguières and Virelizier they are called "bimonads", by analogy to "bialgebra", reserving the term "Hopf monad"...

g., semisimple complex Lie group), then the coordinate ring of G is the Hopf algebra A corresponding to G. Many structures of G translate to those of...

Hopf Bifurcation...

Lie algebras and Malcev groups are both equivalent to complete Hopf algebras, i.e., Hopf algebras H endowed with a filtration so that H is isomorphic to...

}{1-\alpha }}} At that critical value of the parameter K, the system undergoes a Hopf bifurcation. It comes as counterintuitive (hence the term 'paradox') because...

algebra over a field has a further structure of a Hopf algebra; in this case, it is thus called a group Hopf algebra. The apparatus of group rings is especially...

vector space (with the braiding often induced by a finite group) is a braided Hopf algebra which is denoted by B ( V ) {\displaystyle {\mathfrak {B}}(V)} and...

with his thesis Stabilitätswechsel und globale Hopf-Verzweigung (Stability transformation and global Hopf bifurcation), written under the direction of Willi...

mathematician specializing in abstract algebra. He is the namesake of the Taft Hopf algebra which he introduced in a 1971 publication, and he was the founding...

article. Bialgebras can often be extended to Hopf algebras, if an appropriate antipode can be found; thus, all Hopf algebras are examples of bialgebras. Similar...

Hopf bifurcation, the limit cycle should have size ∝ ε 1 / 2 , {\displaystyle \propto \varepsilon ^{1/2},} we may attempt to convert this to a Hopf bifurcation...

transformation semigroups, ring theory, and Hopf algebra,[A][B] including the proof of the Nichols–Zoeller freeness theorem in Hopf algebra.[A] With her husband, Thomas...

coproduct and a bilinear form making it into a positive selfadjoint graded Hopf algebra that is both commutative and cocommutative. The study of symmetric...

the Carathéodory–Fréchet extension theorem, the Carathéodory–Hopf extension theorem, the Hopf extension theorem and the Hahn–Kolmogorov extension theorem...

yields a bialgebra, and can be extended by giving an antipode to create a Hopf algebra structure. Note: In this article, all algebras are assumed to be...

Oxford University Press.[ISBN missing] Bernstein, Harris; Byerly, Henry C.; Hopf, Frederic A.; Michod, Richard E. (20 September 1985). "Genetic Damage, Mutation...

equivalent to the representation category of some weak Hopf algebra. Adding more structures onto the weak Hopf algebras corresponds to adding more structures...

comultiplications that turn them into Hopf algebras. This is made precise in the article on the tensor algebra: the tensor algebra has a Hopf algebra structure on it...

intersection of algebraic topology and algebraic geometry, there is the notion of a Hopf algebroid which encodes the information of a presheaf of groupoids whose...

defined by George W. Whitehead (1942), extending a construction of Heinz Hopf (1935). Whitehead's original homomorphism is defined geometrically, and gives...

{\displaystyle \operatorname {diam} (M,d_{g})=\sup\{d_{g}(p,q):p,q\in M\}.} The Hopf–Rinow theorem shows that if ( M , d g ) {\displaystyle (M,d_{g})} is complete...

current research interests concern noncommutative algebras: in particular, Hopf algebras, their structure and representations, and their actions on other...

their sycamore trees.[why?] According to botanists Daniel Zohary and Maria Hopf, cultivation of this species was "almost exclusively" by the ancient Egyptians...

Hopf algebra ( A , ∇ , η , Δ , ε , S , R , ν ) {\displaystyle (A,\nabla ,\eta ,\Delta ,\varepsilon ,S,{\mathcal {R}},\nu )} is a quasitriangular Hopf...

cocommutative Hopf algebra A over a field of characteristic zero with dim ⁡ A n < ∞ {\displaystyle \dim A_{n}<\infty } for all n, the natural Hopf algebra homomorphism...

isomorphic to any of its proper subgroups. Hopfian groups are named after Heinz Hopf. Every finite group, by an elementary counting argument. More generally,...

This latter pentagonal symmetry of the 600-cell is captured by the set of Hopf coordinates (𝜉i, 𝜂, 𝜉j) given as: ({<10}⁠𝜋/5⁠, {≤5}⁠𝜋/10⁠, {<10}⁠𝜋/5⁠)...

2014. Retrieved 19 August 2014. McKinnon Riehm & Hoffman 2011, p. 212 H. Hopf. Proceedings of the International Congress of Mathematicians 1958. Archived...

Semisimple Hopf Algebras, was supervised by Nicolás Andruskiewitsch. She is also the author of the monograph Semisolvability of Semisimple Hopf Algebras...

(1977). "Solutions of the Maxwell and Yang–Mills equations associated with Hopf fibrings". International Journal of Theoretical Physics. 16 (9): 561–565...

showing that the renormalization of Feynman diagrams can be described by a Hopf algebra. Combinatorial physics can be characterized by the use of algebraic...

Dirk Kreimer (born 12 July 1960) is a German physicist who pioneered the Hopf-algebraic approach to perturbative quantum field theory with Alain Connes...

Sakuntabhai A, MacSween R, et al. (February 2003). "Acrokeratosis verruciformis of Hopf is caused by mutation in ATP2A2: evidence that it is allelic to Darier's...

operation. They were introduced by J. Frank Adams (1960) in his solution to the Hopf invariant problem. Similarly, one can define tertiary cohomology operations...

crossings (the Hopf link [1]). Patching the trefoil P() = A × P() + P() gives the unknot and, again, the Hopf link. Patching the Hopf link P() = A × P()...

nontrivial example of a link with more than one component is called the Hopf link, which consists of two circles (or unknots) linked together once. The...

Eisenbud–Levine–Khimshiashvili signature formula gives a way of computing the Poincaré–Hopf index of a real, analytic vector field at an algebraically isolated singularity...

results in algebra and category theory, notably for his theory of braided Hopf algebras and for a new view of the octonions. Although many regard Majid...

studied there under Heinz Hopf, obtaining his Ph.D. in 1941. His dissertation, on homotopy theory, was jointly supervised by Heinz Hopf and Ferdinand Gonseth...

cohomologous to a Lie bialgebra on a coboundary. They are also called Poisson-Hopf algebras, and are the Lie algebra of a Poisson–Lie group. Lie bialgebras...

circle/ Hopf circle/ fold cycle supercritical Andronov-Hopf Hopf/ circle Hopf/ homoclinic Hopf/ Hopf Hopf/ fold cycle subcritical Andronov-Hopf subHopf/ circle...

presented at a congress in 1891. Hopf fibration Toric section Vesica piscis Coxeter 1969. Hirsch 2002. Dorst 2019, §6. Hopf Fibration and Stereographic Projection...

geometry. He received his Ph.D. degree under the supervision of Hopf and George Pólya. Hopf later recommended Stoker to Richard Courant. In 1937 Stoker,...

career Country Indian Police Service Department Director General of Police, HoPF, Former Intelligence Chief, Telangana State - 2014-2016 and 2023-present...

1111/j.1365-2583.2009.00948.x. PMID 20167026. S2CID 11617147. Bernstein, H.; Hopf, F. A.; Michod, R. E. (1987). "The Molecular Basis of the Evolution of Sex"...

Muzaka Condisa Muzaka Muzaka family Principality of Muzaka Elsie 2003, p. 42. Hopf 1873, p. 532. Elsie 2003, p. 47. Anamali 2002, p. 295. Anamali, Skënder (2002)...

April 1942, in Brooklyn) is an American mathematician, known for Sweedler's Hopf algebra, Sweedler's notation, measuring coalgebras, and his proof, with Harry...

in symplectic geometry. The concept is due to Charles Ehresmann and Heinz Hopf in the 1940s. Let M be a smooth manifold. An almost complex structure J on...

involution (see Milne's lecture notes on abelian varieties). Involutive Hopf algebras are important examples of *-algebras (with the additional structure...

commonly referred to as the Hopf fibration of S3, a topological construction pointed out by Heinz Hopf (1931). But Hopf’s procedure was explicitly based...

to the circular fibers of a Hopf fibration SU(2) → S2. As such, the Berger metrics can also be constructed via the Hopf fibration, by scaling the tangent...

importance of the fixed-point index is largely due to its role in the Lefschetz–Hopf theorem, which states: ∑ x ∈ F i x ( f ) i n d ( f , x ) = Λ f , {\displaystyle...

elements of a Hopf algebra do form a group. A primitive element is an element x that satisfies Δ(x) = x ⊗ 1 + 1 ⊗ x. The primitive elements of a Hopf algebra...

a group of isometries of the 3-sphere. The conjecture was posed by Heinz Hopf in 1926 after determining the fundamental groups of three-dimensional spherical...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

at the University of Greifswald. He retired in 1972. The Hopf–Rinow theorem is named after Hopf and Rinow. In 1959, he became the director of the Institute...

several branches of mathematics, including a list of ten conjectures on Hopf algebras. They are usually known as Kaplansky's conjectures. Let K be a field...

imaging system. Strehl ratio Hopf, Johannes. "Kurt Hopf – Astronomie – Karl Strehl Strehlwert Definitionshelligkeit". www.kurt-hopf.de. Archived from the original...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

is the terminal object in category of graded Hopf algebras with a single character. Hence any such Hopf algebra has a morphism to the ring of quasisymmetric...

Sciences, and the recipient of the 1999 Ostrowski Prize and the 2013 Heinz Hopf Prize. Since 2009, he has been a faculty member at the Institute for Advanced...

Mathematics at Ben-Gurion University of the Negev whose main areas of research are Hopf algebras, quantum groups and Noncommutative rings. Miriam Cohen (née Hirsch)...

Gugelhupf (also Kugelhupf, Guglhupf, Gugelhopf, pronounced [ˈɡuːɡl̩.hʊp͡f, -hɔp͡f, ˈkuːɡl̩-], in Czech bábovka [ˈbaːbofka], and, in France, kouglof [kuɡlɔf]...

long before their introduction into cultivation", according to Zohary and Hopf. Although they point to finds of pears in sites in Neolithic and Bronze Age...

contributions of historian and professor Carl Hermann Friedrich Johann Hopf (1832–1873). Hopf's publications, particularly "Urkunden und Zusätze zur Geschichte...

subgroups. The notion is dual to that of a Hopfian group, named after Heinz Hopf. A group G is called co-Hopfian if whenever φ : G → G {\displaystyle \varphi...

1086/386552. PMID 15266388. S2CID 15042207. Bernstein, Harris; Byerly, Henry C.; Hopf, Frederic A.; Michod, Richard E. (1985). "Sex and the emergence of species"...

the Gay-Lussac Humboldt Prize, and he is the recipient of the 2011 Heinz Hopf Prize. In 1994, he was an Invited Speaker (with talk Non-Archimedean period...

metaphor for the personal secrets and conflicts within relationships. Scholars Hopf and Creighton have argued that the metaphor works both ways, with the series...

In mathematical analysis, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral...

noncommutative symmetric functions form a Hopf algebra NSymm analogous to the Hopf algebra of symmetric functions. The Hopf algebra NSymm was introduced by Israel...

no archival evidence that Voisava was part of the Brankovic family. Karl Hopf (1832–1873), a German historian and expert in Byzantine studies, in Chroniques...

Henry C. Wente (1986). It is a counterexample to the conjecture of Heinz Hopf that every closed, compact, constant-mean-curvature surface is a sphere (though...

beginning with Supercritical All pages with titles containing Supercritical Hopf bifurcation, in mathematics, a local bifurcation; when the first Lyapunov...

with no singularities comes from considering the flow along the lines of a Hopf fibration. Let r {\textstyle r} be a constant radius of the inner coil. One...

Centennial Planetarium 1970 R. Hopf...

corresponding to a 1-parameter group of automorphisms σt of A = L∞(X,μ), then by the Hopf decomposition either every St with t ≠ 0 is dissipative or every St with...

In 2004, he and Uwe Abresch extended the classical Hopf differential, discovered by Heinz Hopf in the 1950s, from the setting of surfaces in three-dimensional...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

Bochner Alfred Brauer Richard Brauer Lothar Collatz Alexander Dinghas Michael Golomb Guido Hoheisel Eberhard Hopf Heinz Hopf Martin Kneser Wilhelm Specht...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

Samantha; Ferrari, Carlotta; Suarez, Guillaume; Sauvain, Jean-Jacques; Hopf, Nancy B. (2016). "Locating bomb factories by detecting hydrogen peroxide"...

C. A. Wunderlich. Violinzithers have been manufactured luthier C. Robert Hopf since the 1920s. Bowed psaltery D.R.G.M Patent No. 903152 Mühlemann, Lorenz...

Hamburg and Göttingen. In 1935 he received his doctorate from ETH under Heinz Hopf, with a dissertation entitled Richtungsfelder und Fernparallelismus in n-dimensionalen...

93A. doi:10.1126/science.aan0032. PMID 28684525. S2CID 19943904. Zohary & Hopf 2000, p. 46 Weide, Alexander (21 June 2015). "On the Identification of Domesticated...

{\displaystyle \tau _{V,W}} , most importantly the modules over quasitriangular Hopf algebras and Yetter–Drinfeld modules over finite groups (such as Z 2 {\displaystyle...

4D rotations, an even more useful coordinate system for 4D is provided by Hopf coordinates {ξ1, η, ξ2}, which are a set of three angular coordinates specifying...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

kernel. Example: the Hopf fibration. Let B equal S 2 {\displaystyle S^{2}} and E equal S 3 . {\displaystyle S^{3}.} Let p be the Hopf fibration, which has...

A quasi-triangular quasi-Hopf algebra is a specialized form of a quasi-Hopf algebra defined by the Ukrainian mathematician Vladimir Drinfeld in 1989. It...

Bergman Prize from the American Mathematical Society in 2015, and the Heinz Hopf Prize from ETH in 2021. Demailly was elected a correspondent of the French...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

coefficients from integers to the rational numbers. To any group ring or Hopf algebra is associated its representation ring or "Green ring". The representation...

Schollin Marika Lindström Stefan Ekman Bertil Norström Lena Endre Heinz Hopf Willie Andréason Johan Hedenberg Composer Anders Neglin Country of origin...

during which Werner Hopf, a 30-year-old electronics engineer from the Stanford Research Institute, fell and was seriously injured. Hopf died despite the...

on the occasion of the re-appointment of Hermann Weyl, Schur says of Hopf: Hopf is a very excellent teacher, a mathematician of strong temperament and...

102.6600D. doi:10.1073/pnas.0502030102. PMC 1131873. PMID 15851674. Hopf, F. A.; Hopf, F. W. (1985). "The role of the Allee effect on species packing"....

the space of all continuous mappings with the compact-open topology. The Hopf fibration S 1 → S 3 → S 2 {\displaystyle S^{1}\to S^{3}\to S^{2}} is a non-trivial...

comultiplication, counit, and antipode structures in the Hopf algebra. The unit and multiplication structures in the Hopf algebra are intrinsic to the underlying scheme...

Retrieved 11 January 2026. from Old High German, from ein one + korn grain Hopf, M.; Zohary, Daniel (2000). Domestication of Plants in the Old World: The...

finite-dimensional Hopf algebra, by a 1969 theorem of Larson-Sweedler on Hopf modules and integrals. Note: the coalgebra structure for the Hopf algebra is different...

visited the University of Paris. He completed his thesis work with Heinz Hopf at Berlin, defended a thesis on the ends of topological groups in 1930, and...

Retrieved 2025-11-25. D. C. Youla, H. A. Jabr, J. J. Bongiorno: Modern Wiener-Hopf design of optimal controllers: part II, IEEE Trans. Automat. Contr., AC-21...

This link cobordism between the Hopf link and the unlink is topologically a pair of pants....

is the dual vector space. The Hopf algebras associated to groups have a commutative algebra structure, and so general Hopf algebras are known as quantum...

Championship Forfeited Palla Dapples Winner (8 times) Top goalscorer League: All: Pietro Lana Carlo Hopf Luigi Forlano (2) Home colours ← 1906–07 1908–09 →...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

Werner Fenchel Hans Freudenthal Helmut Grunsky Maximilian Herzberger Heinz Hopf Rudolf Kochendörffer Karl Reinhardt Willi Rinow Kurt Schröder [de] Wilhelm...

work was later put into the setting of a boundary value problem by Eberhard Hopf. A breakthrough came with work of Vladimir Scheffer in the 1970s. He showed...

convolution of distributions is again a distribution and thus they form the Hopf algebra on G, denoted by Dist(G), which contains the Lie algebra Lie(G) associated...

of Uppsala in 2017. In 2013 Eliashberg shared with Helmut Hofer the Heinz Hopf Prize from the ETH, Zurich, for their pioneering research in symplectic topology...

geodesic flow on Riemannian manifolds, starting with the results of Eberhard Hopf for Riemann surfaces of negative curvature. Markov chains form a common context...

J} is the connect-sum of a non-trivial knot K ′ {\displaystyle K'} with a Hopf link. If the link K ′ ∪ J {\displaystyle K'\cup J} is the Whitehead link...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

there must be at least one zero. This is a consequence of the Poincaré–Hopf theorem. In the case of the torus, the Euler characteristic is 0; and it...

(1999) pointed out that the Butcher group is the group of characters of the Hopf algebra of rooted trees that had arisen independently in their own work on...

Michel Barbaza, David Geddes, Jean-Louis Vernet, Miguel Llongueras & Maria Hopf (1982). "Prehistoric Human Adaptations in Catalonia (Spain)", Journal of...

noncommutative Hopf algebra which is cocommutative, meaning its comultiplication is cocommutative. This implies if we take the dual Hopf algebra, denoted...

National Laboratory Review, Charles Butcher in The Chemical Engineer, Henning Hopf in Angewandte Chemie, George Morton in The Book Report, Arlene Perly Rae...

free product of the link groups of the components. The link group of the Hopf link, the simplest non-trivial link – two circles, linked once – is the free...

is also a juggler and magician. Ehrenborg, Richard (1996). "On posets and Hopf algebras". Advances in Mathematics. 119 (1): 1–25. doi:10.1006/aima.1996...

Library of Medicine. 1 August 2020. Retrieved 11 May 2024. Zohary, Daniel; Hopf, Maria; Weiss, Ehud (2012). Domestication of Plants in the Old World: The...

free group on n generators, and is used in classifying Brunnian links. The Hopf link is a simple example of a link with two components that is not an unlink...

Drabeck) The boy treble The mother mezzo-soprano The teacher baritone Otto Hopf First student treble or tenor Second student treble or tenor Third student...

Director General of Police (DGP), who serves as the head of the police force (HoPF). The remaining DG-ranked officers in a state or UT may be appointed to various...

Affine symmetric group, a braid group on an annulus Artin–Tits group Braided Hopf algebra Braided monoidal category Braided vector space Knot theory Non-commutative...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

General Carlsson Rosie Jauckens as Fru Carlsson Lenore Zann as Viveka Heinz Hopf as David Mark Dowling as Silenski Pontus Platin as Sandberg Olle Björling...

Collection. Christina Lindberg ... Lena Svensson (as Cristina Lindberg) Heinz Hopf... Helge Björn Adelly ... Jan, Lena's boyfriend Siv Ericks ... Jan's Mother...

quantization Landau theory Landau–Squire jet Landau–Levich problem Landau–Hopf theory of turbulence Ginzburg–Landau theory Darrieus–Landau instability Landau–Lifshitz...

whether these were domesticated or wild forms of B. vulgaris. Zohary and Hopf note that beetroot is "linguistically well identified". They state the earliest...

for example by the Soviet physicist Lev Landau who developed the Landau-Hopf theory of turbulence. David Ruelle and Floris Takens later predicted, against...

In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle;...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

Laboratory. Archived from the original on 2009-03-12. Bernstein H, Byerly HC, Hopf FA, Michod RE. Genetic damage, mutation, and the evolution of sex. Science...

Bibcode:1997CurrA..38..651H. doi:10.1086/204651. S2CID 144151770. Daniel Zohary; Maria Hopf (2000). Domestication of Plants in the Old World. Oxford University Press...

zeroes and poles in the right half plane (RHP). This is called the Wiener–Hopf factorization. Divide S x , s ( s ) e α s {\displaystyle S_{x,s}(s)e^{\alpha...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

Germain Prize (2003) Satter Prize (2007) Clay Research Award (2008) Heinz Hopf Prize (2015) CNRS Gold medal (2016) Shaw Prize (2017) L'Oréal-UNESCO Award...

{\displaystyle p} , the Steenrod algebra A p {\displaystyle A_{p}} is the graded Hopf algebra over the field F p {\displaystyle \mathbb {F} _{p}} of order p {\displaystyle...

took his place. Following the departure of Anderson, Kilmister bought a Hopf Studio bass off Hawkwind synth player Del Dettmar. He used Rickenbacker basses...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

Research by the American Mathematical Society. In 2009 he received the Heinz Hopf Prize from ETH Zurich. In 2012, he became a fellow of the American Mathematical...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

Andhra Pradesh. In the past, he held the position of Head of Police Force (HoPF) Andhra Pradesh Police from 6 May 2024 through 19 June 2024. Harish Kumar...

have started". The Washington Post. Bernstein, Harris; Byerly, Henry C.; Hopf, Frederick A.; Michod, Richard A.; Vemulapalli, G. Krishna (1983). "The Darwinian...

(midfielder) Virgilio Fossati (midfielder) Achille Gama (forward) Carlo Hopf (forward) Kappler (defender) Werner Kummer (midfielder) Hernst Marktl (defender)...

continuous motion, the two curves are said to be linked. For example, the Hopf link is formed by two circles that each pass through the disk spanned by...

foxtail millet; wild or weedy forms of foxtail millet also exist. Zohary and Hopf note that the primary difference between the wild and cultivated forms is...

Archived from the original on 8 September 2015. Retrieved 26 August 2017. Hopf, Ted (2016). "'Crimea is ours': A discursive history". International Relations...

the equivalence of these four properties is given in the article on the Hopf decomposition. Suppose that μ ( X ) < ∞ {\displaystyle \mu (X)<\infty } and...

1038/scientificamerican0481-88. PMID 6164094. Bernstein, Harris; Byerly, Henry C.; Hopf, Frederick A.; et al. (June 1983). "The Darwinian Dynamic". The Quarterly...

the Ludwig-Maximilians-Universität München, Sommerfeld's students Ludwig Hopf and Werner Heisenberg would write their Ph.D. theses on this topic. For his...

under and over each other. This contrasts with two crossings in the simpler Hopf link. In most artistic representations, the parts of the loops that alternately...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

inédits relatifs à l'histoire de la Grèce au moyen âge, IX (Paris), p. 159 Hopf, Carlo, ed. (1873). "Breve Memoria de li Discendenti de Nostra Casa Musachi"...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

fibered manifolds are a special case, is attributed to Herbert Seifert, Heinz Hopf, Jacques Feldbau, Whitney, Norman Steenrod, Charles Ehresmann, Jean-Pierre...

A = B, the measuring coalgebra has a natural structure of a Hopf algebra, called the Hopf algebra of the algebra A. Hazewinkel, Michiel; Gubareni, Nadiya;...

Surface Class Surface Charts n-spheres n-sphere Sn Hopf chart Hyperspherical coordinates Sphere S2 Spherical coordinates Stereographic chart Central projection...

state space C 2 {\displaystyle \mathbb {C} ^{2}} to the Bloch sphere is the Hopf fibration, with each ray of spinors mapping to one point on the Bloch sphere...

Harder, N.; Hartmann, D.; Helander, P.; Heinemann, B.; Hirsch, M.; Höfel, U.; Hopf, C.; Ida, K.; Isobe, M.; Jakubowski, M. W.; Kazakov, Y. O.; Killer, C.; Klinger...

Chuck Gaspar Deprecated link archived 2014-04-26 at archive.today Werner Hopf[link removed] John D. Lowry[link removed] Dr. Jürgen Noffke[link removed]...

viscous Burgers' equation can be converted to a linear equation by the Cole–Hopf transformation, u ( x , t ) = − 2 ν ∂ ∂ x ln ⁡ φ ( x , t ) , {\displaystyle...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

John Moore, was titled The cohomology of restricted Lie algebras and of Hopf algebras: Application to the Steenrod algebra. From 1964 to 1967, May taught...

pre-pottery Neolithic levels of the Nahal Hemar caves in Israel. Zohary and Hopf speculate, "these finds indicate that the wild colocynth was very probably...

Zero fret on a Hopf Saturn 63 electric guitar....

constructivist IR scholars include Michael Barnett, Martha Finnemore, Ted Hopf, Peter Katzenstein, Kathryn Sikkink, and Alexander Wendt. Post-structuralist...

anime Shuffle (dominoes), to mix the tiles in dominoes Shuffle algebra, a Hopf algebra with a basis corresponding to words on some set whose product is...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

Two-dimensional topological manifolds have triangulations. 1926 Heinz Hopf Poincaré–Hopf theorem, the sum of the indexes of a vector field with isolated zeroes...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

of the variables. Another example shows how a center manifold models the Hopf bifurcation that occurs for parameter a ≈ 4 {\displaystyle a\approx 4} in...

[citation needed] The symmetric algebra can be given the structure of a Hopf algebra. See Tensor algebra for details. The symmetric algebra S(V) is the...

question of whether it has a complex structure is known as the Hopf problem, after Heinz Hopf.) Using an almost complex structure we can make sense of holomorphic...

413H. doi:10.1007/s10722-013-0046-5. ISSN 0925-9864. Zohary, Daniel and Hopf, Maria (2000). Domestication of Plants in the Old World, third edition. Oxford:...

of the Wiener-Hopf technique that impinge on finance and probability. This has led to developments, for example in relating Wiener-Hopf factorisation...

shared with Charles Fefferman. In the same year, he was awarded the Heinz Hopf Prize, the Lobachevsky Medal and Prize by Kazan Federal University, and the...

I Supposed to Believe That? Directed by Marran Gosov Written by Florian Hopf Klaus Lemke Marran Gosov Produced by Felix Hock Horst Wendlandt Starring...

is that it allowed the understanding of monopole quantization in terms of Hopf fibrations. Equivalences between fiber bundle theory and gauge theory were...

half-time position at the University of Rochester. His most-cited paper is on Hopf algebras, co-authored with John Milnor. As a faculty member at Princeton...

National Register of Historic Places listings in Newport County, Rhode Island Hopf, John T. (1976). The Complete Book of Newport Mansions. Paul L. Veeder, II...

"Scherenschnitte and Fraktur." Pennsylvania Folklife 37.4 (Summer 1988): 190–192. Hopf, Claudia. Papercutting: Tips, Tools, and Techniques for Learning the Craft...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

PMID 2185476. Birdsell & Wills 2003, pp. 113–117 Bernstein H, Byerly HC, Hopf FA, Michod RE. Genetic damage, mutation, and the evolution of sex. Science...

each other naturally due to the Hopf fibration.[failed verification] The collective of edges forms another discrete Hopf fibration of 12 rings with 10 vertices...

records 51418, 57909. Hopf 1856, p. 103. Hopf 1856, p. 104. Hopf 1856, p. 105. Hopf 1856, p. 106. Hopf 1856, p. 107. Hopf 1856, p. 108. Hopf, Carlo (1856). Dissertazione...

Examples of limit cycles branching from fixed points near Hopf bifurcation. Trajectories in red, stable structures in dark blue, unstable structures in...

Barak, Färberin, Amme) Conductor, Opera house and orchestra Label 1955 Hans Hopf Leonie Rysanek Ludwig Weber Christel Goltz Elisabeth Höngen Karl Böhm Vienna...

May, J. Peter (1965), "The cohomology of restricted Lie algebras and of Hopf algebras", Bulletin of the American Mathematical Society, 71: 372–377, doi:10...

Freeman and Company. ISBN 0-7167-1766-2 Bernstein, Harris; Byerly, Henry C.; Hopf, Frederick A.; et al. (June 1983). "The Darwinian Dynamic". The Quarterly...

antipode of a Hopf algebra can be expressed in terms of structure constants. The connecting axiom, which defines a consistency condition on the Hopf algebra...

org/nlab/show/image (Definition 3.1 and Remarks 3.2) in Gabriella Böhm, Hopf algebroids, in Handbook of Algebra (2008) arXiv:0805.3806 paragraph 2-14...

in the books of Morrey and Smoller, following the original statement of Hopf (1927): Let M be an open subset of Euclidean space ℝn. For each i and j between...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

In mathematics, a quantum affine algebra (or affine quantum group) is a Hopf algebra that is a q-deformation of the universal enveloping algebra of an...

original on 20 January 2008. Retrieved 14 August 2008. P. Pulkkinen; S. Hopf b; A. Jutila (2012). "Conceptual design of the Chenab Bridge in India" (PDF)...

construction based on Clifford parallelism that was pointed out by Heinz Hopf in 1931 The lines on 1 in elliptic space are described by versors with a...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

group Hall algebra Hecke algebra of a locally compact group Heyting algebra Hopf algebra Hurwitz algebra Hypercomplex algebra Incidence algebra Iwahori–Hecke...

Grids on SO(3) Using the Hopf Fibration". The International Journal of Robotics Research. 29 (7). Section 8 — Derivation of Hopf parametrisation. Bibcode:2010IJRR...

University of California at Davis. Retrieved 7 December 2023. Zohary D, Hopf M, Weiss E (2012). Domestication of Plants in the Old World: The origin and...

"Cyclic Cohomology and Hopf Algebras". Letters in Mathematical Physics. 48: 97–108. doi:10.1023/A:1007527510226. S2CID 117855160. (See Hopf algebra.) Connes...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

structure. Lie bialgebra: a Lie algebra with a compatible bialgebra structure. Hopf algebra: a bialgebra with a connection axiom (antipode). Clifford algebra:...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

applied. C() = C() + z C() gives the unknot and the Hopf link. Applying the relation to the Hopf link where indicated, C() = C() + z C() gives a link...

A Seifert surface for the Hopf link. This is an annulus, not a Möbius strip. It has two half-twists and is thus orientable....

Eberhard Hopf, Heinz Hopf, Herman Müntz, Wilhelm Meyer, and Abraham Plessner. Some emigrated to the United States, others to European countries; Heinz Hopf spent...

Language Film, 1975 Thriller – A Cruel Picture Alex Fridolinski Christina Lindberg, Heinz Hopf, Per-Axel Arosenius Exploitation Thriller – en grym film...

can be regarded as a family of circles parametrized by CPn: this is the Hopf fibration. Complex projective space carries a (Kähler) metric, called the...

from the original on 30 May 2004. Retrieved 17 May 2020. Zohary, Daniel; Hopf, Maria; Weiss, Ehud (2012). Domestication of Plants in the Old World: The...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

with glyphosate-containing herbicides considered effective. Zohary and Hopf note that the archaeological evidence for the ancient cultivation of the...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

Auge 3. (with Rinaldo Hopf) (2006) Schwule Orte. 150 berühmt-berüchtigte Schauplätze (2007) Mein schwules Auge 4. (with Rinaldo Hopf) (2007) Mein schwules...

Missourian. 15 December 1924. Retrieved 20 December 2017. 1913, poisoner Karl Hopf, arsenic in champagne, FAZ from June 24, 2017 "Peter Kürten: The Vampire...

1086/386552. PMID 15266388. S2CID 15042207. Bernstein, Harris; Byerly, Henry C.; Hopf, Frederic A.; Michod, Richard E. (1985). "Sex and the emergence of species"...

sphere. The case of n {\displaystyle n} odd is taken care of by the Poincaré–Hopf index theorem (see hairy ball theorem), so the case n {\displaystyle n} even...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

barley". Native Plant Trust. Retrieved 13 January 2024. Zohary, Daniel; Hopf, Maria (2000). Domestication of Plants in the Old World: The Origin and Spread...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

pinching. This result is known as the differentiable sphere theorem. Heinz Hopf conjectured that a simply connected manifold with pinched sectional curvature...

reflect her influence. The transition is also attributed to the work of Heinz Hopf, who was influenced by Noether, and to Leopold Vietoris and Walther Mayer...

Gustavus died of epilepsy on 9 January 1641, at 8 years of age. Georg Wilhelm Hopf: Bayerische Geschichte in Zeittafeln, Schmid, 1865, S. 134 Carl Eduard Vehse:...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

Lyubov Sokolova as Olga Fyodorovna, doctor Yuri Timoshenko as Operator Hopf p.34 Hopf, Ted. Reconstructing the Cold War: The Early Years, 1945-1958. Oxford...

a Lie algebra, both of which are also cocommutative Hopf algebras. In general cocommutative Hopf algebras behave very much like groups. For simplicity...

intégrale généralisée et homotopie, was written under the direction of Heinz Hopf and Beno Eckmann. Kervaire was a professor at New York University's Courant...

manifold that is compact but not complete, a combination of properties that the Hopf–Rinow theorem disallows for Riemannian manifolds. Causality conditions Globally...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

Opera house and orchestra Label 1954 Elisabeth Grümmer, Rita Streich, Hans Hopf, Kurt Böhme Wilhelm Furtwängler, Vienna Philharmonic and Vienna State Opera...

German academic publisher founded in 1980. Its managing director is Wilhelm Hopf. Its principal place of publication is Münster; further publishing offices...

Model Theory was given by Thomas Scanlon. In 2019 he was awarded the Heinz Hopf Prize and in 2022 the Shaw Prize in Mathematical Sciences. Hrushovski is...

Archive.org. April 1942. p. 94. Retrieved 31 May 2026. Zohary, Daniel; Hopf, Maria; Weiss, Ehud (2012). Domestication of Plants in the Old World (Fourth ed...

General of Police (DGP), who is designated as the Head of Police Force (HoPF). The DGP may be assisted by special and additional DGPs. The various functional...

Position Player Club GK Johannes Hopf Hammarby TFF DF Haris Devic Bodens BK MF Joakim Persson Lunds BK FW Nedim Halilović Dalkurd FF...

November 2024. "Cydonia oblonga Quince". Plants For A Future. Zohary, Daniel; Hopf, Maria; Weiss, Ehud (2012). Domestication of Plants in the Old World: The...

Ankara 20:00 EEST Tošić 23' (o.g.) Skúlason  38' Kahveci  44' Djalma  69' Hopf  88' Report Şahan  45' Gómez  54' Necip Uysal  58' Töre 67' Gülüm  83' Stadium:...

introduction to quaternions to elucidate the Hopf fibration as a mapping on unit quaternions. He writes "the fibers of the Hopf map are circles in S3 ". Versors have...

respect to this partial order. (See also poset topology.) Alexandrov and Hopf first introduced the grid cell topology, for the two-dimensional case, within...

very little is known about her. The 19th-century German medievalist Karl Hopf proposed a reconstructed genealogy, whereby she was the daughter of Guibert...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

Decapitation by guillotine An expensive cigar and a cup of Brazilian coffee. Karl Hopf Serial murder 1914 Sausages, bread and beer. Mathias Kneißl Murder and robbery...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

algebra, noncommutative algebraic geometry, symmetry in quantum mechanics, Hopf algebras, and quantum groups. She is a full professor at Rice University...

geometry) Hilbert's theorem (differential geometry) Hopf–Rinow theorem (differential geometry) Killing–Hopf theorem (Riemannian geometry) Lee Hwa Chung theorem...

translated by Karl Hopf. His translations contained several mistakes that led him to conclusions which were later corrected. Hopf misidentified Alexander...

Hackett William Rowan Hamilton Edward Hincks Nathaniel Hone the Younger Ludwig Hopf John Kells Ingram John Hewitt Jellett John Joly William Johnston Gregorios...

compound of a class of 2-ladderane-like molecules containing cyclobutenes Hopf, Henning; Joel F. Liebman; H. Mark Perks (2009). "Cubanes, Fenestranes, Ladderanes...

Italian). Archived from the original on 11 May 2024. Retrieved 12 May 2024. Hopf-Sulc, Adrian (8 May 2024). "Ideenlabor Brainstore in Biel – Wie Nemos Eltern...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

celery accompanies buffalo wings and similar dishes. Daniel Zohary and Maria Hopf note that celery leaves and inflorescences were part of the garlands found...

425–428. doi:10.1016/0065-2571(65)90067-1 M. Mincheva., M.R. Roussel., Turing-Hopf instability in biochemical reaction networks arising from pairs of subnetworks...

accidentally confuse bitter vetch with red lentils. According to Zohary and Hopf, this crop is consumed only by the poorest people or in times of famine....

Karl Hopf thought that the Greek name derived from the French form Véligourt, in turn possibly a corruption of Valaincourt/Walincourt, which Hopf proposed...

de li discendenti de nostra casa Musachi. The work was published in Karl Hopf's Chroniques gréco-romaines, Paris 1873, pp. 270–340. According to his memoirs...

fundamental theorem of algebra is a corollary of Hopf's theorem. Dropping the requirement of commutativity, Hopf generalized his result: Any finite-dimensional...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

"Cumin". Encyclopaedia Britannica. 2018. Retrieved 24 February 2018. Zohary D, Hopf M (2000). Domestication of plants in the Old World (first ed.). Oxford: Oxford...

Göttingen, where topologists such as Pavel Sergeevich Alexandrov and Heinz Hopf were working. In 1930 he received his doctorate with his work on three-dimensional...

from one fixed point to three fixed points. Pitchfork bifurcations, like Hopf bifurcations, have two types – supercritical and subcritical. In continuous...

 5367–5368. Butz 2007, pp. 534–553. Stover & Simmonds 1987, pp. 106–126. Zohary & Hopf 2000, pp. 20–22. Floros, Newsome & Fisher 2010. Schoening 2005. Acharya &...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

In representation theory, a Yangian is an infinite-dimensional Hopf algebra, a type of a quantum group. Yangians first appeared in physics in the work...

İstanbul Başakşehir 2010–17 Sebastian Holmén – Çaykur Rizespor 2021–22 Johannes Hopf – Gençlerbirliği, MKE Ankaragücü 2015–19 Andreas Isaksson – Kasımpaşa 2012–16...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

American Society of Agronomy. p. 765. ISBN 978-0-89118-091-3. Zohary, Daniel; Hopf, Maria (2000). Domestication of Old World plants: the origin and spread of...

doi:10.1142/S0129167X94000048. Kuperberg, Greg (1996). "Non-involutory Hopf algebras and 3-manifold invariants". Duke Mathematical Journal. 84: 83–129...

land-mass, is seldom found in natural stands there today. Zohary, Daniel; Hopf, Maria (2000). Domestication of plants in the old world: the origin and spread...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

ft 10 in (2.08 m) 255 lb (116 kg) Sr Driehuis, Netherlands F/C 52 Clint Hopf 6 ft 8 in (2.03 m) 256 lb (116 kg) Sr Ferdinand, Indiana Head coach Marty...

SC27 — September 20, 1998 Xinglong SCAP  · 2.6 km MPC · JPL 25142 Hopf 1998 SA28 Hopf September 26, 1998 Prescott P. G. Comba  · 4.9 km MPC · JPL 25143...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

1073/pnas.0701572104. PMC 1871816. PMID 17409186. Bernstein H, Byerly HC, Hopf FA, Michod RE (September 1985). "Genetic damage, mutation, and the evolution...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

made a breakthrough in solving the KPZ equation by an extension of the Cole–Hopf transformation and constructing approximations using Feynman diagrams. In...

1111/j.1365-2583.2009.00948.x. PMID 20167026. S2CID 11617147. Bernstein, H.; Hopf, F. A.; Michod, R. E. (1987). "The Molecular Basis of the Evolution of Sex"...

Archived from the original on 2021-12-06. Massimiliano Rizzato, Michael Hopf (2023-03-13). "Towards FRMCS in Switzerland". globalrailwayreview.com. "Private...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

C {\displaystyle \mathbb {C} } ) into the category of finite dimensional Hopf algebras, so that the Pontryagin duality functor G ↦ G ^ {\displaystyle G\mapsto...

original (PDF) on 2016-02-07. Retrieved 2012-03-23. Daniel Zohary; Maria Hopf (2000). Domestication of Plants in the Old World (3rd ed.). Oxford University...

Never Tarnished". The New York Times. Retrieved June 12, 2026. Roof Tour Hopf, John T. (1995). The Complete Book of Newport Mansions (10th ed.). Newport...

Max-Planck-Institut für Mathematik Doctoral advisor Heinrich Behnke Heinz Hopf Doctoral students Egbert Brieskorn Detlef Gromoll Matthias Kreck Winfried...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

ISBN 978-3-662-46220-1. Weierstrass eta-function Böhm, Gabriella (2019). Hopf algebras and their generalizations from a category theoretical point of view...

2012 Root C (2007). Domestication. Greenwood Publishing Groups. Zohary D, Hopf M, Weiss E (2012). Domestication of Plants in the Old World: The origin and...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

the Whitney embedding theorem, the hairy ball theorem, the Hopf theorem, the Poincaré–Hopf theorem, Donaldson's theorem, and the Poincaré conjecture....

doi:10.1371/journal.pone.0214519. PMC 6438500. PMID 30921415. Zohary D, Hopf M, Weiss E (2012). Domestication of Plants in the Old World: The Origin and...

from the original on 27 May 2012. Retrieved 4 January 2026. Zohary, Daniel; Hopf, Maria (2000). Domestication of Plants in the Old World: The Origin and Spread...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

(88 kg) RS Jr Lexington Catholic High School Lexington, Kentucky F 42 Curt Hopf 6 ft 8 in (2.03 m) 225 lb (102 kg) RS Jr Barr-Reeve High School Montgomery...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

which it is linearly unstable. The corresponding bifurcation may be either a Hopf bifurcation to a globally oscillating homogeneous state with a dominant wave...

used as a bifurcation parameter, then the Hodgkin–Huxley model undergoes a Hopf bifurcation. As with most neuronal models, increasing the injected current...

{\displaystyle \eta \colon S^{3}\to S^{2}} is the Hopf map. This can be shown by observing that the Hopf invariant defines an isomorphism π 3 ( S 2 ) ≅ Z...

kingdom (PDF). London: John Murray. Bernstein, Harris; Byerly, Henry C.; Hopf, Frederic A.; Michod, Richard E. (20 September 1985). "Genetic Damage, Mutation...

Topological K-theory has been applied in John Frank Adams’ proof of the “Hopf invariant one” problem via Adams operations. Adams also proved an upper bound...

relying on a key theorem from differential topology known as the Poincaré–Hopf theorem. It can be summarized as follows. From the locality assumption, the...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

the Davis Mountains and the Marathon Basin, Texas", p. 111 Zohary, Daniel; Hopf, Maria; Weiss, Ehud (2012). Domestication of Plants in the Old World: The...

although this minimizing sequence need not converge to a geodesic. The metric Hopf-Rinow theorem provides situations where a length space is automatically a...

Swimming Women's 50m freestyle S7  Gold Yvonne Hopf Swimming Women's 100m backstroke B3  Gold Yvonne Hopf Swimming Women's 100m freestyle B3  Gold Claudia...

in 1936 for Zurich, Switzerland, where he studied with the geometer Heinz Hopf and received his doctorate in 1940 from the Swiss Federal Institute of Technology...

Robert; A Greek–English Lexicon at the Perseus Project. Zohary, Daniel; Hopf, Maria; Weiss, Ehud (2012). Domestication of Plants in the Old World: The...

doi:10.1111/tpj.12496. PMID 24597605. Bernstein, Harris; Byerly, Henry C.; Hopf, Frederic A.; Michod, Richard E. (20 September 1985). "Genetic Damage, Mutation...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

Archived from the original (Photograph) on 7 June 2023. Retrieved 10 June 2025. Hopf, John T (2 July 1965). "AERIAL VIEW OF THE STAGE AT "FESTIVAL FIELD" (Photograph)...

Kingdon Clifford and is closely related to Clifford parallelism and the Hopf fibration. A flat 2-torus admits no C2 (in particular, no smooth) isometric...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

1614/0890-037x(2002)016[0901:yncels]2.0.co;2. S2CID 85720525. Daniel Zohary and Maria Hopf, Domestication of plants in the Old World, third edition (Oxford: University...

PMID 9351519. Roman Furtmüller; Michael G Schlag; Michael Berger; Rudolf Hopf; Sigismund Huck; Werner Sieghart; Heinz Redl (April 2002). "Tranexamic Acid...

Nonfiction". The New York Times. November 26, 2023. Retrieved November 28, 2024. Hopf, Andrew (November 20, 2023). "An Index of Everything (and Everyone) Mentioned...

is found in a truly wild state only in northern India ... Zohary, Daniel; Hopf, Maria; Weiss, Ehud (2012). Domestication of plants in the old world: The...

other neurosurgeons are not capable of'. Professor of Neurosurgery Nikolai J Hopf of University of Mainz, Germany, described Teo as 'one of the most important...

2007–2009† Jan Thilo Haux [de] Eva Herman, 1989–2007† Jan Hofer, 1985–2020† Georg Hopf [de], 1975–1985 Horst Jaedicke [de] Silke Jürgensen [de], 2002–2005 Karolin...

1007/s12304-015-9250-3. PMC 4978442. PMID 27525048. Bernstein, H.; Byerly, H. C.; Hopf, F. A.; Michod, R. E. (September 1985). "Genetic damage, mutation, and the...

Elsevier Science. 2015. p. 387. ISBN 978-0-12-384953-3. Zohary, Daniel; Hopf, Maria (2000). Domestication of Plants in the Old World (3rd ed.). Oxford...

⁠. In 1958 J. Frank Adams published a further generalization in terms of Hopf invariants on H-spaces that still limits the dimension to 1, 2, 4, or 8....

George David Birkhoff, and Ernst Witt Poincaré–Hopf theorem Mathematics Henri Poincaré and Heinz Hopf Poincaré recurrence theorem Poincaré conjecture...

doi:10.1037/0003-066x.59.1.20. ISSN 1935-990X. PMID 14736317. S2CID 6296189. Hopf SM (2010). "Risk and Resilience in Children Coping with Parental Divorce"...

15th-century traveller Nompar de Caumont and repeated as late as the works of Karl Hopf in the 19th century, ascribed the name to the Navarrese Company, but that...

Vectors, and Sectors (Washington: CQ Press, 2013) excerpt and text search Hopf, Ted, ed. Understandings of Russian Foreign Policy (1999) Kanet, Roger E...

University Press. p. 149. ISBN 978-0-19-537222-9. Murawski 2010, p. 209. Hopf, Eberhard (1939). "Statistik der geodätischen Linien in Mannigfaltigkeiten...

example: The unknot, trefoil knot, and figure-eight knot are fibered knots. The Hopf link is a fibered link. The Alexander polynomial of a fibered knot is monic...

mathematical symbols, read mathematical books and papers (notably those of Heinz Hopf, J. H. C. Whitehead, and Hassler Whitney) to him, and later worked as his...

originally described as a nephew of the Venetian Doge Enrico Dandolo by Karl Hopf, on the basis of erroneous identifications with homonyms, cf. Loenertz 1970...

doi:10.3389/fpls.2020.00638. PMC 7261834. PMID 32523597. Zohary, Daniel; Hopf, Maria; Weiss, Ehud (2012). Domestication of Plants in the Old World (Fourth ed...

In mathematics, a Nichols algebra is a Hopf algebra in a braided category assigned to an object V in this category (e.g. a braided vector space). The Nichols...

considered in the literature. Another explanation is that speed wobble is a Hopf bifurcation, a mathematical phenomenon in which a stable fixed point of a...

Madden 1997, p. 17. Robert de Clari, La Prise de Constantinople, xi–xii, in Hopf, Chroniques Greco-Romaines, pp. 7–9. Old French. Phillips 2004, p. 57. Zara...

alpha-galactosyltransferase, and raffinose-raffinose alpha-galactotransferase. Hopf H, Gruber G, Zinn A, Kandler O (1984). "Physiology and biosynthesis of lychnose...

developed. The building blocks of Brunnian links therein turn out to be Hopf -links, hyperbolic Brunnian links, and hyperbolic Brunnian links in unlink-complements...

The Boy in the Tree Arne Sucksdorff Tomas Bolme, Anders Henrikson, Heinz Hopf Drama Pojken i trädet The Cat and the Canary Jan Molander Märta Dorff, Lena...

1126/science.163.3868.671. PMID 17742735. S2CID 34052655. Zohary, Daniel; Hopf, Maria; Weiss, Ehud (2012). Domestication of Plants in the Old World. Oxford:...

Ottoman Captive to Albanian Hero. I.B. Tauris. p. 240. ISBN 978-1-85043-941-7. Hopf, Karl (1873). Chroniques gréco-romanes: inédites ou peu connues, pub. avec...

Ottoman Conquest. University of Michigan Press. ISBN 978-0-4720-8260-5. Hopf, Karl (1873). Chroniques greco-romanes inedites ou peu connues [Unpublished...

Engineering as major subjects. He served as the Director general of police (HoPF - Head of Police Force) of Andhra Pradesh. Prior to DGP, he was vice-chairman...

Canada (ed. 2) i–910. New York Botanical Garden, Bronx. Zohary, Daniel; Hopf, Maria; Weiss, Ehud (2012). Domestication of Plants in the Old World. Oxford...

fixed-point theorem", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Hopf, H. (1944). "Eine Verallgemeinerung bekannter Abbildungs-und Überdeckungssätze"...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

encodes the notion of Temperley–Lieb algebra. A semisimple and cosemisimple Hopf algebra over an algebraically closed field is encoded in a planar algebra...

operators Vector space Linear algebra Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra v t e...

Tanusio was mentioned as Count of Mat (conte di Matia). According to Karl Hopf, Tanusio's son or brother Andrea I, as told by Gjon Muzaka (fl. 1510), had...

journal}}: CS1 maint: multiple names: authors list (link) Zohary, Daniel; Hopf, Maria; Weiss, Ehud (2012). Domestication of plants in the Old World: the...

bronze-coloured specialty), and Andechser. Regional brands in Bavaria are Hopf, Unertl, Ayinger, Schweiger and Plank. Aventinus is an example of Weizen...

Grichka Bogdanov's construction yields a bialgebra which is not necessarily a Hopf algebra, the latter being a type of mathematical object which must satisfy...

Literacy Project. 2015-08-24. Retrieved 2021-07-09. Daniel Zohary; Maria Hopf; Ehud Weiss (2012). Domestication of Plants in the Old World: The Origin...

von Machtausübung und Ausgrenzung in der SBZ und der DDR LIT Verlag Dr. W. Hopf, Berlin (2010) pp. 356-357. ISBN 978-3-643-10429-8. Retrieved July 18, 2011...

others for $23 million". Market Screener. 2015-01-05. Retrieved 2026-01-12. Hopf, Engelbert. "Balu Balakrishnan: »Mit 70 sollte man es als CEO gut sein lassen«"...

{\displaystyle e(F(X))=\infty } . Hans Freudenthal and independently Heinz Hopf established in the 1940s the following two facts: For any finitely generated...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

ISBN 978-0-470-01590-2, retrieved 2025-03-17 Bernstein, H; Byerly, HC; Hopf, FA; Michod, RE (1985). "Genetic damage, mutation, and the evolution of sex"...

{\displaystyle x\in G} . Strictly speaking, this does not make C(G) into a Hopf algebra, unless G is finite. On the other hand, a finite-dimensional representation...

Claude Chevalley, can be defined as the group of complex characters of the Hopf algebra of representative functions, i.e. the matrix coefficients of finite-dimensional...

(1st ed.). New York: Dodd, Mead. Flora of North America Zohary, Daniel; Hopf, Maria; Weiss, Ehud (2012). Domestication of Plants in the Old World: The...

0.co;2. PMID 12038534. S2CID 20943704. Bernstein, H.; Byerly, H. C.; Hopf, F. A.; Michod, R. E. (1985). "Genetic damage, mutation, and the evolution...

conjectures in commutative algebra commutative algebra n/a Hopf conjectures geometry Heinz Hopf 476 Ibragimov–Iosifescu conjecture for φ-mixing sequences...

cohomology essentially appeared in works of Heinz Hopf and Egbert van Kampen on obstructions. Hopf invented an obstruction to homotopy (and homotopy classification)...

Tree of Life, planted on the threshold between life and death. Zohary and Hopf note that "the fruit and the timber, and sometimes even the twigs, are richly...

Theory. The textbook Topologie I, written together with Heinz Hopf in German (Alexandroff P., Hopf H. (1935) Topologie Band 1 — Berlin) became the classic course...

negative linear damping and positive non-linear damping terms, leading to a Hopf bifurcation and the appearance of limit cycles. The van der Pol oscillator...

categories used by the arXiv, and is a unification of algebraic deformations, Hopf algebras, category theory, topology, noncommutative geometry, and quantum...

Euclidean space whose boundary forms a closed curve of given length The Hopf conjectures relating the curvature and Euler characteristic of higher-dimensional...

doi:10.1093/genetics/131.3.745. PMC 1205045. PMID 1628815. Bernstein, H.; Hopf, F.A.; Michod, R.E. (1987). "The Molecular Basis of the Evolution of Sex"...

promontorio, e del venerabile tempio di Santa Maria di Leuca, etc (in Italian). Hopf, Carlo, ed. (1873). "Breve Memoria de li Discendenti de Nostra Casa Musachi"...

Text list Hopf, Matt (2016-01-08). "Liberty School District seeks voter approval for property tax hike". Herald-Whig. Retrieved 2025-06-02. Hopf, Matt (2016-02-22)...

813022Z. doi:10.1038/s41598-018-31467-6. PMC 6115419. PMID 30158541. Zohary D, Hopf M, eds. (2000). Domestication of Plants in the Old World (3rd ed.). Oxford...

classical case. He used this spectral sequence to attack the celebrated Hopf invariant one problem, which he completely solved in a 1960 paper by making...

(2006). "Static Equilibria of Rigid Bodies: Dice, Pebbles, and the Poincare-Hopf Theorem". Journal of Nonlinear Science. 16 (3): 255. Bibcode:2006JNS....16...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

Mayoral Candidate Vote % Karl Hopf 101 48.79 Graham Vaughan 78 37.68 Roy Hoffman (X) 28 13.53...

Zetterberg Gunilla Larsson - Eliz Zetterberg Gino Samil - Länsman Heinz Hopf - Hans Thomsen Runo Sundberg - Eklund Bjørn Aronsson - Fredriksson Tomas...

doi:10.1007/s00497-013-0234-7. PMC 3825497. PMID 23995700. Bernstein, H.; Hopf, F.A.; Michod, R.E. (1987). ""The Molecular Basis of the Evolution of Sex"...

hdl:2263/19269. PMID 22497583. S2CID 36059683. Bernstein, H.; Byerly, H. C.; Hopf, F. A. & Michod, R. E. (1985). "Genetic damage, mutation, and the evolution...

classical harmonic and complex analysis (ISBN 0262230925); Vol. 3, The Hopf-Wiener integral equation; Prediction and filtering; Quantum mechanics and...

801–810. doi:10.1111/brv.12367. PMID 28913952. S2CID 4764175. Bernstein H, Hopf FA, Michod RE (1987). "The molecular basis of the evolution of sex". Molecular...

equation describes the behavior of a nonlinear oscillating system near the Hopf bifurcation, named after John Trevor Stuart and Lev Landau. In 1944, Landau...

S^{n}\right]=\pi _{n}S^{n}} and Z {\displaystyle \mathbf {Z} } . Moreover, the Hopf theorem states that for any n {\displaystyle n} -dimensional closed oriented...

555–564. doi:10.1002/ajim.20481. PMID 17516558. Ward EM, Schulte PA, Straif K, Hopf NB, Caldwell JC, Carreón T, DeMarini DM, Fowler BA, Goldstein BD, Hemminki...

doi:10.1007/s00122-003-1232-1. PMID 12835927. S2CID 11868237. Zohary, Daniel; Hopf, Maria (2000). Domestication of Plants in the Old World (3rd ed.). Oxford...

Leon J. (2023). A History of the Music for Wind Bands, Part I. Berlin: Lit Verlag Dr. W. Hopf. ISBN 9783643966544. OCLC 1447092479. Retrieved 2026-05-31....

irregularity q is 1, and h1,0 = 0. All plurigenera are 0. Hodge diamond: Hopf surfaces are quotients of C2−(0,0) by a discrete group G acting freely, and...

result, which can be proved using the Gauss–Bonnet theorem, is the Poincaré-Hopf index theorem for vector fields on M which vanish at only a finite number...

der Wissenschaften und Künste, 1868, S. 162 Carl Hermann Friedrich Johann Hopf, S. 293 Musachi, Giovanni. Breve memoria de li discendenti de nostra casa...

has a natural structure of a Hopf algebra, with a coproduct Δ. The ring S used above is just a completion of this Hopf algebra. A related combinatoric...

{\displaystyle d_{k}:E_{p,q}^{k}\to E_{p-k,q-1+k}^{k}} . Recall that the Hopf fibration is given by S 1 ↪ S 3 → S 2 {\displaystyle S^{1}\hookrightarrow...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

1953(1953-09-28) (aged 88) Pasadena, California Party Republican Spouse Laura Elise Hopf (m. 1893) Alma mater University of Vermont (1886) Profession Engineer...

(88 kg) RS So Lexington Catholic High School Lexington, Kentucky F 42 Curt Hopf 6 ft 8 in (2.03 m) 225 lb (102 kg) Jr Barr-Reeve High School Montgomery,...

Arianiti family Fine 1994, p. 599. Elsie 2003, p. 43. Sainty 2018, p. 495. Hopf 1873, p. 534-535. Fine 1994, p. 556. Fine 1994, p. 561 & 599. Sainty 2018...

critical value, both equilibrium points lose stability through a subcritical Hopf bifurcation. When ρ = 28, σ = 10, and β = ⁠8/3⁠, the Lorenz system has chaotic...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

gravitational waves. In 1977, Trautman identified the Dirac monopole with the Hopf fibration. In 1981, Trautman became a founding member of the World Cultural...

doi:10.1093/jhered/esab052. PMC 8683835. PMID 34718632. Bernstein, H.; Hopf, F.A.; Michod, R.E. (1987). "The Molecular Basis of the Evolution of Sex"...

Fußballbiographien und Fußballkulturen heute (1 ed.). Berlin: LIT Verlag, Dr. Wilhelm Hopf. p. 139. ISBN 978-3-8258-0194-6. "GDR » Oberliga 1988/1989 » Attendance »...

Artin, E. (1965). Collected Papers. Addison Wesley, New York. pp. 499–501. Hopf, E. (1937). Ergodentheorie. Springer, Berlin. p. 67. doi:10.1007/978-3-642-86630-2...

S^{4n+3}\to \mathbb {HP} ^{n}.} This bundle is sometimes called a (generalized) Hopf fibration. There is also a construction of H P n {\displaystyle \mathbb {HP}...

){\overline {p(\zeta )}}} is also called the spectral factorization (or Wiener-Hopf factorization) of w ( ζ ) {\displaystyle w(\zeta )} . Rudin 1987, p. 88 Powell...

properties are isometric to each other. It is a consequence of the Killing–Hopf theorem. To prove the existence of such a space as described above one can...

algebra, noncommutative algebraic geometry, symmetry in quantum mechanics, Hopf algebras, and quantum groups Zhouping Xin (Chinese: 辛周平; born 13 July 1959)...

* Chairman: Rudy den Outer Secretary: Nancy Schoof Treasurer: Sebastiaan Hopf Opened by Mayor of Medemblik Theo van Eijk Competitors Competitors 128 Competing...

Cornell University (1955–68) where he started his work on Toeplitz and Wiener-Hopf operators, partly inspired by Mark Kac. Widom was appointed in the Department...

Corporation. April 19, 1999. Retrieved January 27, 2009. Daniel Zohary; Maria Hopf & Ehud Weiss (2012). Domestication of Plants in the Old World: The Origin...

x_{0}:=v-\lambda p_{0}} is the minimizer in the primal formulation and vice versa. By Hopf–Lax formula, the Moreau envelope is a viscosity solution to a Hamilton–Jacobi...

Williams, Harris Bernstein, Carol Bernstein, Michael M. Cox, Frederic A. Hopf and Richard E. Michod – have suggested competing explanations for how a vast...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

Dirichlet boundary condition Neumann boundary condition Stefan problem Wiener–Hopf problem Separation of variables Green's function Elliptic partial differential...

for example by the Soviet physicist Lev Landau, who developed the Landau-Hopf theory of turbulence. David Ruelle and Floris Takens later predicted, against...

Good times create weak men. And weak men create hard times." — G. Michael Hopf, Those Who Remain "Fear leads to anger. Anger leads to hate. Hate leads to...

1038/s44185-026-00146-5. ISSN 2731-4243. PMC 13350911. PMID 42380584. Adeleye MA, Hopf F, Haberle SG, Stannard GL, Mcwethy DB, Harris S, Bowman DM (15 November...

path-connected as well, providing a homotopy to the identity map. The Lefschetz–Hopf theorem states that the sum of the indices (in this context, multiplicity)...