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id stringlengths 40 40	title stringlengths 15 120	text stringlengths 41 3.14k	source stringclasses 2 values
b620ae8ea7d384346118b65436516262c6c42e3b	from 1942 he participated in the manhattan project,	from 1942 he participated in the manhattan project, working initially at the university of chicago, but after 1943, and for the rest of his career, at oak ridge, tennessee. there he introduced the use of ion-exchange chromatography for separation of isotopes needed for developing the atomic bomb. on account of the secr...	wikipedia
6a88eba3d85769b68b22bacfae635be25a44bc7e	he was born in san francisco, california, on	he was born in san francisco, california, on 28 june 1910, and studied at the university of california, berkeley, where he worked under the supervision of d. m. greenberg, and received his ph.d. on the basis of a thesis on radioactive phosphorus (p) produced in the cyclotron and its effects in rats, work later publishe...	wikipedia
7aa209bf6644ae11b2973045cf531f6d8c83e16b	peter alfred gorer frs was a british immunologist,	peter alfred gorer frs was a british immunologist, pathologist and geneticist who pioneered the field of transplant immunology. peter gorer was born in london to edgar and rachel née cohen gorer. he died of lung cancer in 1961.	wikipedia
44fb7382ed50080c8263514cf9b06c62fd9ad643	gorer is credited with the co-discovery of histocompatibility	gorer is credited with the co-discovery of histocompatibility antigens and the elucidation of their genetic regulation. together with george snell, he helped discover the murine histocompatibility 2 locus, or h-2, which is analogous to the human leukocyte antigen. gorer also identified antigen ii and determined its rol...	wikipedia
4070cdd13deabb7f087d8724c96ec5b42dbdb5a6	he was educated at charterhouse. he graduated from	he was educated at charterhouse. he graduated from guy's hospital, london in 1929 and then studied genetics under j.b.s. haldane at university college, london. from 1933 to 1940 gorer worked at the lister institute before returning to guy's hospital to work as a pathologist.	wikipedia
9bf09118293dd4ca2a1674286824d6d7901fb810	levan kobiashvili is a georgian former professional footballer	levan kobiashvili is a georgian former professional footballer and the current president of the georgian football federation and a member of parliament of georgia. he played primarily as a left wingback or left winger. during his career, levan played for gorda rustavi, dinamo tbilisi, alania vladikavkaz and three germa...	wikipedia
d4571f14cd5925f0205e16ee15f64fde077c96f5	in 2011, kobiashvili became his country's first 100-cap	in 2011, kobiashvili became his country's first 100-cap player and received a special award from the uefa. that game against greece was the last for kobiashvili's international career. he is still the most-capped georgian player. kobiashvili captained the national team for 16 times and has scored 12 goals during his in...	wikipedia
1b590b6adf9d4796408c2031b388ce09385d4fba	during a relegation playoff game against 2. bundesliga	during a relegation playoff game against 2. bundesliga team fortuna düsseldorf, kobiashvili punched referee wolfgang stark after the final whistle. hertha lost the playoff 4–3 on aggregate goals and was relegated from the bundesliga as a result. kobiashvili was banned for one year, retroactively beginning 16 may 2012. ...	wikipedia
3a86b75f6ac081b3d535c249998ca8cb34895c1f	one of the best games of kobiashvili's career	one of the best games of kobiashvili's career came against psv eindhoven in 2005–06 uefa champions league season where he scored a hat-trick. two of them were from penalty kicks. after the game he was praised by the manager ralf rangnick and teammate frank rost, who labeled kobiashvili as a true professional, who was a...	wikipedia
efb6bed015db834ab506304d1c3f44a1e26604b9	kobiashvili became the starting member of his new	kobiashvili became the starting member of his new club during the first season. schalke coach jupp heynckes used him as a left-back. upon the arrival of ralf rangnick, kobiashvili was moved back to midfield, becoming one of the key links between schalke's defence and attack. two years after joining the gelsenkirchen -b...	wikipedia
7eb54bafc5ac686b401a7c5fc1197b70596e58b6	during summer 2003, kobiashvili's contract with freiburg expired	during summer 2003, kobiashvili's contract with freiburg expired and he decided to leave the club. he received an offer from the future uefa cup winners cska moscow. the coach of the russian team, valeri gazzaev, was interested in signing the georgian midfielder with whom he worked in alania five years earlier. however...	wikipedia
3738c2d68c0fa12a9352aada9025a57b3f3627eb	sc freiburg finished sixth in the 2000–01 bundesliga	sc freiburg finished sixth in the 2000–01 bundesliga season which granted them a qualification for 2001–02 uefa cup. this was the second time the club has ever participated in a uefa tournament. sc freiburg were eliminated in the third round by the future champions feyenoord, on a 3–2 aggregate loss. kobiashvili played...	wikipedia
ca77c3e93cabdf1e05b5c70944c198fa341ee5b6	after spending a half season on a loan	after spending a half season on a loan at sc freiburg, kobi signed a deal with the german club in 1998. during his spell with the breisgau-brasilianer ("breisgau brazilians"), kobiashvili became one of the key players of volker finke 's system. he was joined some georgian players in germany as well, alexander iashvili ...	wikipedia
f12126c20ebb31702b0243a57823fcd178c8a1ca	at the start of the year 1997, alania	at the start of the year 1997, alania vladikavkaz declared their interest in georgian midfielder. dinamo tbilisi let kobiashvili leave the club on a season long loan deal. kobiashvili joined a few of his compatriots there, including mikheil ashvetia, giorgi gakhokidze and kakhaber tskhadadze. he made 21 appearances for...	wikipedia
0b1a1f396f5986414aaddc7f7b810f0dee1845eb	kobiashvili began his career in hometown club avaza	kobiashvili began his career in hometown club avaza tbilisi. his first professional club was gorda rustavi where he made his debut in the umaglesi liga in 1993. after spending two years with the rustavi -based club, kobiashvili moved to dinamo tbilisi in 1995. under the guidance of famous former player and then-dinamo ...	wikipedia
4313b759ce400786c46978c7cf482ff53135eb78	he played primarily as a left wingback or	he played primarily as a left wingback or left winger. during his career, levan played for gorda rustavi, dinamo tbilisi, alania vladikavkaz and three german clubs: sc freiburg, schalke 04 and hertha bsc.	wikipedia
39001ed00829d29547f8220c2e8daac7d1ea8fd8	levan kobiashvili (georgian: ლევან კობიაშვილი, born 10 july	levan kobiashvili (georgian: ლევან კობიაშვილი, born 10 july 1977) is a georgian former professional footballer and the current president of the georgian football federation and a member of parliament of georgia.	wikipedia
f5ab497a75ce5a470b3bb4003fda00447929f16b	the 2021–22 brooklyn nets season was the 46th	the 2021–22 brooklyn nets season was the 46th season of the franchise in the national basketball association (nba), 55th season overall, and its 10th season playing in the new york city borough of brooklyn. on april 2, 2022, the nets clinched a spot in the play-in tournament. on april 12, the nets clinched a playoff sp...	wikipedia
bbf9199cce0620dcf515f3051984c0d63c3de5cf	the nets entered the draft holding one first	the nets entered the draft holding one first round pick and three second round picks. the 44th overall pick was acquired on july 7, 2016, in a trade with the indiana pacers. the 49th overall pick was acquired on july 6, 2019, in a trade with the atlanta hawks. the 59th overall pick was acquired on july 20, 2018, in a t...	wikipedia
f5ab497a75ce5a470b3bb4003fda00447929f16b	the 2021–22 brooklyn nets season was the 46th	the 2021–22 brooklyn nets season was the 46th season of the franchise in the national basketball association (nba), 55th season overall, and its 10th season playing in the new york city borough of brooklyn. on april 2, 2022, the nets clinched a spot in the play-in tournament. on april 12, the nets clinched a playoff sp...	wikipedia
25b10e90da9cb843fea5219dd790d48b2009a104	in the theory of lie groups, the exponential	in the theory of lie groups, the exponential map is a map from the lie algebra g of a lie group g to the group, which allows one to recapture the local group structure from the lie algebra. the existence of the exponential map is one of the primary reasons that lie algebras are a useful tool for studying lie groups. th...	wikipedia
4185fa595d96a3bbc527cab96c18ff994f18613d	remark: the open cover { u g \|	remark: the open cover { u g \| g ∈ g } {\displaystyle \{ug\|g\in g\}} gives a structure of a real-analytic manifold to g such that the group operation (g, h) ↦ g h − 1 {\displaystyle (g,h)\mapsto gh^{-1}} is real-analytic.	wikipedia
58d00bcf3bb8f4f6d9700253e7dfffa7fcb34a31	given a lie group g {\displaystyle g} with	given a lie group g {\displaystyle g} with lie algebra g {\displaystyle {\mathfrak {g}}}, each choice of a basis x 1, …, x n {\displaystyle x_{1},\dots,x_{n}} of g {\displaystyle {\mathfrak {g}}} determines a coordinate system near the identity element e for g, as follows. by the inverse function theorem, the exponenti...	wikipedia
ed62188f27d870d41c6849bb50fbe3c23a67bb4b	in particular, when applied to the adjoint action	in particular, when applied to the adjoint action of a lie group g {\displaystyle g}, since ad ∗ = ad {\displaystyle \operatorname {ad} _{*}=\operatorname {ad} }, we have the useful identity:	wikipedia
778a4522a6a12bdf889300af6b990377449b8a36	let ϕ: g → h {\displaystyle \phi \colon	let ϕ: g → h {\displaystyle \phi \colon g\to h} be a lie group homomorphism and let ϕ ∗ {\displaystyle \phi _{*}} be its derivative at the identity. then the following diagram commutes:	wikipedia
1bf412d2d49038d3b75188bdd94de97b2c1dbd10	the image of the exponential map of the	the image of the exponential map of the connected but non-compact group sl (r) is not the whole group. its image consists of c -diagonalizable matrices with eigenvalues either positive or with modulus 1, and of non-diagonalizable matrices with a repeated eigenvalue 1, and the matrix − i {\displaystyle -i}. (thus, the i...	wikipedia
d3a603be50d729c85b8212e2afe449b9443caa15	globally, the exponential map is not necessarily surjective.	globally, the exponential map is not necessarily surjective. furthermore, the exponential map may not be a local diffeomorphism at all points. for example, the exponential map from s o {\displaystyle {\mathfrak {so}}} (3) to so(3) is not a local diffeomorphism; see also cut locus on this failure. see derivative of the ...	wikipedia
f44cf50950241dce980c4ba6d38d5c87b5b80743	it is then not difficult to show that	it is then not difficult to show that if g is connected, every element g of g is a product of exponentials of elements of g {\displaystyle {\mathfrak {g}}}: g = exp (x 1) exp (x 2) ⋯ exp (x n), x j ∈ g {\displaystyle g=\exp(x_{1})\exp(x_{2})\cdots \exp(x_{n}),\quad x_{j}\in {\mathfrak {g}}}.	wikipedia
8740de572daad8490ada1af6204eaf1f460935e3	it follows from the inverse function theorem that	it follows from the inverse function theorem that the exponential map, therefore, restricts to a diffeomorphism from some neighborhood of 0 in g {\displaystyle {\mathfrak {g}}} to a neighborhood of 1 in g {\displaystyle g}.	wikipedia
9aada24571274e063f2928b04ff2b1cd38e1ca3a	the exponential map exp: g → g {\displaystyle	the exponential map exp: g → g {\displaystyle \exp \colon {\mathfrak {g}}\to g} is a smooth map. its differential at zero, exp ∗: g → g {\displaystyle \exp _{*}\colon {\mathfrak {g}}\to {\mathfrak {g}}}, is the identity map (with the usual identifications).	wikipedia
ae55b3d6c32ee35a5c34b9a7d8cdab9de0fb8ff2	for all x ∈ g {\displaystyle x\in {\mathfrak	for all x ∈ g {\displaystyle x\in {\mathfrak {g}}}, the map γ (t) = exp (t x) {\displaystyle \gamma (t)=\exp(tx)} is the unique one-parameter subgroup of g {\displaystyle g} whose tangent vector at the identity is x {\displaystyle x}. it follows that:	wikipedia
0e1bf3ad7e66a972f0cf2fa45c5a56db4dc4e287	from the quotient by the lattice. since x	from the quotient by the lattice. since x {\displaystyle x} is locally isomorphic to c n {\displaystyle \mathbb {c} ^{n}} as complex manifolds, we can identify it with the tangent space t 0 x {\displaystyle t_{0}x}, and the map	wikipedia
0d98f4b1e430a1dc5f9f9577bd866e8e5622bb93	for a general g, there will not exist	for a general g, there will not exist a riemannian metric invariant under both left and right translations. although there is always a riemannian metric invariant under, say, left translations, the exponential map in the sense of riemannian geometry for a left-invariant metric will not in general agree with the exponen...	wikipedia
e816ee71a937b55d0ae5d88861b9ca742f908104	where i {\displaystyle i} is the identity matrix.	where i {\displaystyle i} is the identity matrix. thus, in the setting of matrix lie groups, the exponential map is the restriction of the matrix exponential to the lie algebra g {\displaystyle {\mathfrak {g}}} of g {\displaystyle g}.	wikipedia
d0ac37c2d2f754d2b42b8a0bc91c565306efbbe6	it follows easily from the chain rule that	it follows easily from the chain rule that exp (t x) = γ (t) {\displaystyle \exp(tx)=\gamma (t)}. the map γ {\displaystyle \gamma } may be constructed as the integral curve of either the right- or left-invariant vector field associated with x {\displaystyle x}. that the integral curve exists for all real parameters fol...	wikipedia
ae66f93919a5502109425c14a46d3abdd87f3cdd	let g {\displaystyle g} be a lie group	let g {\displaystyle g} be a lie group and g {\displaystyle {\mathfrak {g}}} be its lie algebra (thought of as the tangent space to the identity element of g {\displaystyle g}). the exponential map is a map	wikipedia
15f930d367573e6acb864a1882f5c40e148a6989	the ordinary exponential function of mathematical analysis is	the ordinary exponential function of mathematical analysis is a special case of the exponential map when g {\displaystyle g} is the multiplicative group of positive real numbers (whose lie algebra is the additive group of all real numbers). the exponential map of a lie group satisfies many properties analogous to those...	wikipedia
275a7be421dab450a6c67de24a522cdaa50a94c7	in the theory of lie groups, the exponential	in the theory of lie groups, the exponential map is a map from the lie algebra g {\displaystyle {\mathfrak {g}}} of a lie group g {\displaystyle g} to the group, which allows one to recapture the local group structure from the lie algebra. the existence of the exponential map is one of the primary reasons that lie alge...	wikipedia
fc024fb73ecdd5d947817578d2c66462562ab39b	the 2020–21 season was lori fc's third and	the 2020–21 season was lori fc's third and final season in the armenian premier league, and they also participated in the armenian cup. lori submitted their resignation from the league in april, with the remaining games being awarded as 3-0 technical defeats, leaving lori in 8th in the league at the end of the season, ...	wikipedia
f1793fbb530b9dd0db2ffb16bcfe456298138e31	on 16 march, lori walked off at the	on 16 march, lori walked off at the start of their match against ararat yerevan in protest of their matchday 1 fixture being awarded to urartu after lori where unable to field a team due to covid-19. with the match later being awarded to ararat yerevan 3–0.	wikipedia