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561214738a391962de0aaecdc4c6d50b66ea3ca6
until a few decades ago, most united states
until a few decades ago, most united states professional sports leagues' contracts retained clauses contracts that essentially prevented players from leaving their original teams by their own choice. these "reserve clauses" were upheld because courts found that these sports leagues did not operate in interstate trade o...
wikipedia
7aa60091982c376240c60e4ee9f95120b2792212
the first body to assist agents in learning
the first body to assist agents in learning the ins and outs of contract negotiations, endorsements and media relations was the association for representatives of athletes (arpa). the co-founders and leaders of arpa, since absorbed into the nfl players association, were professor william weston of the university of bal...
wikipedia
45ba1ff6936b044a6a0ccc954372e85b8adb4f75
sports agents are generally certified by each sport's
sports agents are generally certified by each sport's players' association. once certified, agents or contract advisors may negotiate individual player contracts. agents who are entrusted to conduct business on a player's behalf owe a fiduciary duty, i.e., a duty to remain loyal, act honestly, behave ethically, and act...
wikipedia
07753e02da2a62366da5112df8e4681b023ada9a
in nearly all professional sports, the issue of
in nearly all professional sports, the issue of limits on the use of performance-enhancing drugs has become an integral aspect of cba negotiations. drug policies are not uniform for all professional sports. typically, each cba explains the policy regarding drug testing, list of banned drugs, violations, penalties, priv...
wikipedia
56350e62f7710a5314f16fa84dc3e060e283558e
in 1967, the national labor relations board accepted
in 1967, the national labor relations board accepted that players have the right to form unions or players' associations. it is now common for professional athletes to organize into associations or unions in order to negotiate collective bargaining agreements ' (cbas) with their sport's owners. under federal labor law,...
wikipedia
8d5801a73347be6f51357f6981bf76063e5bead5
in 1995 the gender in equity disclosure act
in 1995 the gender in equity disclosure act was passed to require schools to make an annual, public report on male-female athletic participation rates, recruiting by gender, and financial support. the u.s. supreme court's decision in brown university v. cohen, is an important aspect of litigation for women sports.
wikipedia
ac8d37328017be32658c1636dec2c3d671c9fd6d
title ix is an increasingly important issue in
title ix is an increasingly important issue in college sports law. the act, passed in 1972, makes it illegal for a federally funded institution to discriminate on the basis of sex or gender. in sports law, the piece of legislation often refers to the effort to achieve equality for women's sports in colleges. the office...
wikipedia
0dd179f0229aca7c4c8734cf03adb8c336b7cd21
membership is voluntary. the ncaa operates along a
membership is voluntary. the ncaa operates along a series of bylaws that govern the areas of ethical conduct, amateur eligibility, financial aid, recruiting, gender equity, championship events, and academic standards. the ncaa has enforcement power and can introduce a series of punishments up to the death penalty, the ...
wikipedia
7042ed171c1d7fc1a19dbabb1d6415f26704ee31
sports law in the united states overlaps substantially
sports law in the united states overlaps substantially with labor law, contract law, competition or antitrust law, and tort law. issues like defamation and privacy rights are also integral aspects of sports law. this area of law was established as a separate and important entity only a few decades ago, coinciding with ...
wikipedia
f46d3c329c20e18748e805ce2649fd1302e33a61
1849 kresák is a carbonaceous eos asteroid from
1849 kresák is a carbonaceous eos asteroid from the outer region of the asteroid belt, approximately 24 kilometers in diameter. it was discovered by german astronomer karl reinmuth at heidelberg observatory in the middle of world war ii on 14 january 1942. the asteroid was later named after slovak astronomer Ľubor kres...
wikipedia
228100f84795ecb52e542959bfb5cf2c23b99a71
according to the survey carried out by nasa's
according to the survey carried out by nasa's wide-field infrared survey explorer with its subsequent neowise mission, kresák measures 21.7 kilometers in diameter, and its surface has an albedo of 0.114, while the collaborative asteroid lightcurve link assumes a standard albedo for carbonaceous asteroids of 0.057 and c...
wikipedia
2d6ab736daff3f0edd75550715685fd69de65ff6
in january 2012, a rotational lightcurve of kresák
in january 2012, a rotational lightcurve of kresák was obtained from photometric observations at the palomar transient factory in california. in the r-band, it gave a rotation period of 19.10 hours with a brightness variation of 0.19 magnitude (u=2).
wikipedia
218440ad45120ade4fd5ea91c6a30193c130968a
kresák is known for his theoretical work on
kresák is known for his theoretical work on meteors and the question of their relationship with comets and minor planets, as well as for the rediscovery of the short-period comet 41p/tuttle–giacobini–kresák at the skalnaté pleso observatory in 1951. the official naming citation was published by the minor planet center ...
wikipedia
4093a79bdaca8ab5820773b8210997e6c1bb94c0
this minor planet was named in honor of
this minor planet was named in honor of slovak astronomer Ľubor kresák (1927–1994) from the slovak academy of sciences in bratislava and president of iau 's commission 20 in the 1970s.
wikipedia
54e803181868d7313e0f6985f210065c5ce6a062
kresák is a member of the eos family
kresák is a member of the eos family (606), the largest asteroid family in the outer main belt consisting of nearly 10,000 asteroids. it orbits the sun in the outer main-belt at a distance of 3.0–3.1 au once every 5 years and 4 months (1,950 days). its orbit has an eccentricity of 0.02 and an inclination of 11 ° with r...
wikipedia
540676c487bc8d7f4fbe8b4f393cd3b5595c1240
1849 kresák (prov. designation: 1942 ab) is a
1849 kresák (prov. designation: 1942 ab) is a carbonaceous eos asteroid from the outer region of the asteroid belt, approximately 24 kilometers in diameter. it was discovered by german astronomer karl reinmuth at heidelberg observatory in the middle of world war ii on 14 january 1942. the asteroid was later named after...
wikipedia
6e9db0ef49e7b165d49ea9f6db72216cabe2a500
the beaver bridge in beaver, arkansas, is a
the beaver bridge in beaver, arkansas, is a historic one-lane suspension bridge carrying arkansas highway 187 over the white river at table rock lake. built in 1949 by the pioneer construction company, the structure is the only suspension bridge open to traffic in arkansas. the beaver bridge was added to the national r...
wikipedia
233c2321b0eb41123490d90cb023c5d0ca2e00a2
since the construction was coincident with the building
since the construction was coincident with the building of table rock dam, completion was delayed until 1949 as the united states army corps of engineers required the bridge to be raised 40 feet (12 m). upon completion, the bridge remained a vital link for the citizens of beaver until its closure for major deck rehabil...
wikipedia
64af4d8a1895a6dc5910f23033404d440ff7cab9
the bridge was bid on december 19, 1947,
the bridge was bid on december 19, 1947, to pioneer construction company of malvern, arkansas. the construction foreman who led the project was m. r. blair (1914-2014), who later served as lead foreman on numerous bridge and highway projects across arkansas, missouri, and tennessee, and who led the construction of nume...
wikipedia
6e9db0ef49e7b165d49ea9f6db72216cabe2a500
the beaver bridge in beaver, arkansas, is a
the beaver bridge in beaver, arkansas, is a historic one-lane suspension bridge carrying arkansas highway 187 over the white river at table rock lake. built in 1949 by the pioneer construction company, the structure is the only suspension bridge open to traffic in arkansas. the beaver bridge was added to the national r...
wikipedia
4355b7be874afa680f7171229dc3214285eee0ef
the 2014–15 season was galatasaray's 111th in existence
the 2014–15 season was galatasaray's 111th in existence and 57th consecutive season in the süper lig. the club were aiming for an unprecedented twentieth league title, after finishing in second place in the previous season. in europe, galatasaray competed in the uefa champions league for a fourteenth season. they also ...
wikipedia
b968bcbdff2dd1a95e9305ff5f468af9ad327fc1
last updated: 3 june 2015 source: http://www.ntvspor.net/istatistik only
last updated: 3 june 2015 source: http://www.ntvspor.net/istatistik only competitive matches = number of bookings; = number of sending offs after a second yellow card; = number of sending offs by a direct red card.
wikipedia
040d31b72fa15fd0d98b2425beeae666644632fb
includes all competitive matches. in the case of
includes all competitive matches. in the case of a tie in total number of goals, players with more goals in champions league are ranked higher, followed by league, super cup and turkish cup goals respectively. if all stats are the same, then the younger player is ranked higher.
wikipedia
ba5ce582568627796b69bc86b4bb3adca8b11d26
the 2014–15 season was galatasaray ' s 111th
the 2014–15 season was galatasaray ' s 111th in existence and 57th consecutive season in the süper lig. the club were aiming for an unprecedented twentieth league title, after finishing in second place in the previous season.
wikipedia
1c34bbd4dc282007f89e7fd516bba9e10af0cedb
passarge's theories of racial geography (expounded in the
passarge's theories of racial geography (expounded in the 1920s in das judentum als landschaftskundlich-ethnologisches problem) were embraced by the nazi party after 1933. on 11 november 1933, he was among the signatories of the commitment of the professors at german universities and colleges to adolf hitler and the na...
wikipedia
ed2d7e7f77fb4e0653f307e4f62decc8d291e470
from 1904–1905 passarge held the post of associate
from 1904–1905 passarge held the post of associate professor of geography in berlin and in 1905 he became professor of geography in breslau. in 1908 he joined the colonial institute in hamburg, where he worked until 1936. he theorised that it should be possible for geographers to set up a taxonomic system for landforms...
wikipedia
d252e1bc8615ea204825584aea6322663f8c0336
in 1894 passarge took part in an expedition
in 1894 passarge took part in an expedition to adamawa, at the northern boundary of the former german colony of cameroon. from 1896 to 1899 passarge worked as a geologist and surveyor for the british west charterland company in south africa, during which time he made extensive ethnographic studies of the khoisan and ba...
wikipedia
85192c4dd5ef5a095a4f9f84b44a889c5cb62fda
siegfried passarge was born in königsberg, the son
siegfried passarge was born in königsberg, the son of travel writer ludwig passarge. he attended collegium fridericianum, and after graduation studied geography in berlin and jena. he also trained in medicine, and worked as a doctor during his military service.
wikipedia
94ba2eac8a0bd18bf56ba93afddacbeccfb52aa6
ruzhentsev was a member of the russia national
ruzhentsev was a member of the russia national under-18 team that took the 6th place at the 2019 fiba u18 european championship in volos, greece. over six tournament games, he averaged team-high 12.3 points, 3.2 rebounds, and an assist per game.
wikipedia
d9b0542f73da36a97960aef828c4a67549385b2c
on 17 june 2021, ruzhentsev signed a contract
on 17 june 2021, ruzhentsev signed a contract with mega basket of the basketball league of serbia and the aba league. in the aba league, samson played 21 matches, averaging 6.8 points (with 40% from the field and 50% from behind the arc) and making 3 rebounds in 16 minutes of playing time. and in the basketball league ...
wikipedia
eb4df5083abe75549c922b872929ad361d274aae
ruzhentsev played high school basketball with hamilton heights
ruzhentsev played high school basketball with hamilton heights christian academy in chattanooga, tennessee as a senior. he averaged 19.3 points and 6.3 rebounds per game, helping lead the team to a 28–3 record. also, ruzhentsev helped hamilton heights to three straight naca national championships.
wikipedia
eff6e7fe004038bd495672aa853aa6b4aa3e5670
samson ruzhentsev (russian: Самсон Руженцев; born 23 october
samson ruzhentsev (russian: Самсон Руженцев; born 23 october 2001) is a russian professional basketball player for cska moscow of the vtb united league. he played college basketball for the florida gators.
wikipedia
5b970eb7f4074c33cbf4bd0ea8b6ea2e7327fe2e
the baillie–psw primality test is a probabilistic or
the baillie–psw primality test is a probabilistic or possibly deterministic primality testing algorithm that determines whether a number is composite or is a probable prime. it is named after robert baillie, carl pomerance, john selfridge, and samuel wagstaff. the baillie–psw test is a combination of a strong fermat pr...
wikipedia
cee0fe7f99344fea5a03a38c0e9a4434bc67ae44
the baillie–psw primality test is a probabilistic or
test is a deterministic primality test on numbers below that bound. there are also no known composite numbers above that bound that pass the test, in other words, there are no known baillie–psw pseudoprimes. in 1980, the authors pomerance, selfridge, and wagstaff offered $30 for the discovery of a counterexample, that...
wikipedia
92f5dbd6bf05310e5e181e6f45c99c725981bd16
have constructed a set s of 1248 primes
have constructed a set s of 1248 primes such that, among the nearly 21248 products of distinct primes in s, there may be about 740 counterexamples. however, they are talking about the weaker psw test that substitutes a fibonacci test for the lucas test.
wikipedia
b1e1ebc5c6a0aaf1462617ebec10e64542c67dbc
cryptographic libraries often have prime-testing functions. albrecht et
cryptographic libraries often have prime-testing functions. albrecht et al. discuss the tests used in these libraries. some use a combined fermat and lucas test; many do not. for some of the latter, albrecht, et al. were able to construct composite numbers that the libraries declared to be prime.
wikipedia
d84f157b71d13a4bfc468784a59a7fcf4eb747be
as of 6.2.0, gnu multiple precision arithmetic library
as of 6.2.0, gnu multiple precision arithmetic library 's mpz_probab_prime_p function uses a strong lucas test and a miller–rabin test; previous versions did not make use of baillie–psw. magma 's isprobableprime and isprobablyprime functions use 20 miller–rabin tests for numbers > 34·10, but do not combine them with a ...
wikipedia
38e4bfbd5533bea62e2f855a38a7d251077dc31c
in perl, the math::primality and math::prime::util modules have
in perl, the math::primality and math::prime::util modules have functions to perform the strong baillie–psw test as well as separate functions for strong pseudoprime and strong lucas tests. in python, the nzmath library has the strong pseudoprime and lucas tests, but does not have a combined function. the sympy library...
wikipedia
617d79fbcf7178175cdc5df4a798ce6a2ba1a7d8
the biginteger class in standard versions of java
the biginteger class in standard versions of java and in open-source implementations like openjdk has a method called isprobableprime. this method does one or more miller–rabin tests with random bases. if n, the number being tested, has 100 bits or more, this method also does a non-strong lucas test that checks whether...
wikipedia
c723ba7b462384ab2780d1a7b00e03a859176331
maple 's isprime function, mathematica 's primeq function
maple 's isprime function, mathematica 's primeq function (that already uses 2020's version of baillie–psw), pari/gp 's isprime and ispseudoprime functions, and sagemath 's is_pseudoprime function all use a combination of a fermat strong probable prime test and a lucas test. maxima 's primep function uses such a test f...
wikipedia
ee431519b5b21b78152dbf20f6effd2f20e9e87b
there is also overlap among strong pseudoprimes to
there is also overlap among strong pseudoprimes to different bases.for example, 1373653 is the smallest strong pseudoprime to bases 2 through 4, and 3215031751 is the smallest strong pseudoprime to bases 2 through 10.arnault gives a 397-digit carmichael number n that is a strong pseudoprime to all prime bases less than...
wikipedia
3273971700aaa5cfa71d23ff3cf72a13c49a79a1
the number 29341 is the smallest pseudoprime to
the number 29341 is the smallest pseudoprime to bases 2 through 12.all of this suggests that probable prime tests to different bases are not independent of each other, so that performing fermat probable prime tests to more and more bases will give diminishing returns.on the other hand, the calculations in and the calcu...
wikipedia
7d5afdedf25d39c5f1968f335920fb47659793b1
therefore, if n is a pseudoprime to base
therefore, if n is a pseudoprime to base a, then n is more likely than average to be a pseudoprime to some other base. for example, there are 21853 pseudoprimes to base 2 up to 25·10.this is only about two out of every million odd integers in this range.however:
wikipedia
d2df0469b881334b94f218f690cdd9d8eae64456
for example, n = 341 is a pseudoprime
for example, n = 341 is a pseudoprime to base 2. it follows from theorem 1 on page 1392 of that there are 100 values of a (mod 341) for which 341 is a pseudoprime base a.(the first ten such a are 1, 2, 4, 8, 15, 16, 23, 27, 29, and 30).the proportion of such a compared to n is usually much smaller.
wikipedia
0d95ed3d96f171e5b058f106400e828f539de1b1
in 1980, the authors pomerance, selfridge, and wagstaff
in 1980, the authors pomerance, selfridge, and wagstaff offered $30 for the discovery of a counterexample, that is, a composite number that passed this test. richard guy incorrectly stated that the value of this prize had been raised to $620, but he was confusing the lucas sequence with the fibonacci sequence, and his ...
wikipedia
f5c6d9f0dcb06fb293b7096bfd8af46ca7972247
no composite number below 2 (approximately 1.845·10) passes
no composite number below 2 (approximately 1.845·10) passes the strong or standard baillie–psw test, that result was also separately verified by charles greathouse in june 2011. consequently, this test is a deterministic primality test on numbers below that bound. there are also no known composite numbers above that bo...
wikipedia
001740ac704bb48fdf30ad5ea7e222a041848ea6
there is no known overlap between these lists,
there is no known overlap between these lists, and there is even evidence that the numbers tend to be of different kind, in fact even with standard and not strong lucas test there is no known overlap. for example, fermat pseudoprimes to base 2 tend to fall into the residue class 1 (mod m) for many small m, whereas luca...
wikipedia
f17dd1a42e3720a165cb14fea33517922fe63a30
the baillie–psw test is a combination of a
the baillie–psw test is a combination of a strong fermat probable prime test to base 2 and a standard or strong lucas probable prime test. the fermat and lucas test each have their own list of pseudoprimes, that is, composite numbers that pass the test. for example, the first ten strong pseudoprimes to base 2 are
wikipedia
b781cd95bf35252218296a1827f0f4857fba741c
the baillie–psw primality test is a probabilistic or
the baillie–psw primality test is a probabilistic or possibly deterministic primality testing algorithm that determines whether a number is composite or is a probable prime. it is named after robert baillie, carl pomerance, john selfridge, and samuel wagstaff.
wikipedia
e373bd015bcffcebee29ceb2498b0e8e617b4940
benzoyl-coa 2,3-dioxygenase is an enzyme with systematic name
benzoyl-coa 2,3-dioxygenase is an enzyme with systematic name benzoyl-coa,nadph:oxygen oxidoreductase (2,3-hydroxylating). this enzyme catalyses the following chemical reaction benzoyl-coa 2,3-dioxygenase is involved in aerobic benzoate metabolism in azoarcus evansii.
wikipedia
af6a7ae4bdb4a9a4dcd5b9ccc0fdc35d3150b2e2
benzoyl-coa 2,3-dioxygenase (ec 1.14.12.21, benzoyl-coa dioxygenase/reductase, boxba, boxa/boxb
benzoyl-coa 2,3-dioxygenase (ec 1.14.12.21, benzoyl-coa dioxygenase/reductase, boxba, boxa/boxb system) is an enzyme with systematic name benzoyl-coa,nadph:oxygen oxidoreductase (2,3-hydroxylating). this enzyme catalyses the following chemical reaction
wikipedia
01d903ad8b70cbcb9e5248a2ebe08c6fba6f86e0
four simultaneous by-elections were held in samoa on
four simultaneous by-elections were held in samoa on 29 july 2011. they followed on from the general election on 4 march, after which the results in several constituencies had been challenged. the supreme court voided the election of va'ai papu vailupe in the vaisigano no.1 constituency due to bribery and treating,
wikipedia
e328dae86ebf8ef2effca878f604f029da879a0c
the election of tavu'i tiafau salevao in the
the election of tavu'i tiafau salevao in the satupaitea constituency due to bribery and treating. consequently, by-elections were held for those four seats to the legislative assembly. the governing human rights protection party won all four by-elections, giving it a total of 37 seats out of 49 in the assembly, one mor...
wikipedia
d9de6b5a98dfedfcee5cd6798c3257bf07464786
consequently, by-elections were held for those four seats
consequently, by-elections were held for those four seats to the legislative assembly. the governing human rights protection party won all four by-elections, giving it a total of 37 seats out of 49 in the assembly, one more than it had had following the general election. the opposition tautua samoa party was left with ...
wikipedia
7f136c7aae21b82b3b1b90ae2ac869c6ce974825
the 1993–94 season was sport lisboa e benfica's
the 1993–94 season was sport lisboa e benfica's 90th season in existence and the club's 60th consecutive season in the top flight of portuguese football. it involved benfica competing in the primeira divisão and the taça de portugal. benfica qualified for the european cup winners' cup by winning previous portuguese cup...
wikipedia
675ea895916a382854f64dca18dde23fce73b388
carlos mozer, an undisputed starter during the season,
carlos mozer, an undisputed starter during the season, narrated the events in the club almanac: "we won the title with great difficulty, because sporting had a young but good team, while porto had the experience. at benfica, our squad was strong. there were veterans like william, veloso and isaías, that taught the youn...
wikipedia
62498516de18bccf63976e0f6b904896053b7787
benfica entered the derby de lisboa on 14
benfica entered the derby de lisboa on 14 may with just a one-point advantage in the league table, knowing that a loss would cost them first place. joão pinto had one of his best performances with benfica, scoring a hat-trick that effectively ended the title race in his club's favour. only a few days later, away agains...
wikipedia
ce82a51327d2c3f67c1299ab49a98663cd66ebf2
in the first month of 1994, the club
in the first month of 1994, the club lost points against gil vicente and was eliminated from the taça de portugal by belenenses, though this was not enough to stop their momentum, continuing to defend their first place with consecutive wins. in early march, with successive draws in the league and a hard-fought 4–4 draw...
wikipedia
de35e8f251da6cb89fc534e5b387653d759a5140
with almost no new signings, and having lost
with almost no new signings, and having lost sousa, pacheco and paulo futre, the team led by toni was not seen as favourite in the title race. the season opened with the 1993 supertaça cândido de oliveira, and with a win for both sides, a third match would be necessary. in the league, benfica started by sharing points ...
wikipedia
d937d1e816c030a634931349615f666dfbfd2eca
sousa had been a frequent starter for benfica,
sousa had been a frequent starter for benfica, playing 35 games in the previous season and having joined the club as a 16-year-old. pacheco was utilized more as a substitute, but had still amassed over 160 league games for benfica. the players' "betrayal" and the increase in tension between the old rivals was labelled ...
wikipedia
09c4dc1cd022e57a74aaec75c29e148d036ff149
the season that celebrated its 90th anniversary was
the season that celebrated its 90th anniversary was also one of the club most tumultuous periods in recent history. in the summer, paulo sousa, joão pinto and antónio pacheco unilaterally terminated their contracts, claiming unpaid salaries. while pinto was successfully resigned with a pay increase, both sousa and pach...
wikipedia
e8c9945c10baa2f8ccad0bceb6e9fa00844a2862
the season was marked by the events in
the season was marked by the events in his pre-season, as the club only made three signings. more importantly, however, the club lost regular starter paulo sousa and common substitute antónio pacheco to sporting cp due to unpaid salaries. expectations around benfica were not high, as sporting and porto were deemed the ...
wikipedia
1bfc1734727a96b98a142113a9729b2f618a4978
the 1993–94 season was sport lisboa e benfica
the 1993–94 season was sport lisboa e benfica 's 90th season in existence and the club 's 60th consecutive season in the top flight of portuguese football. it involved benfica competing in the primeira divisão and the taça de portugal. benfica qualified for the european cup winners' cup by winning previous portuguese c...
wikipedia
e47601a678b8b90ee003c1fb78db7689904332c8
rebecca (becca) peixotto is an american archaeologist who
rebecca (becca) peixotto is an american archaeologist who is best known for her contribution to the rising star expedition as one of the six underground astronauts, a group of scientists tasked with excavating the rising star cave system. she has also participated in the great dismal swamp landscape study and is an exp...
wikipedia
ef60e8c54808e144a1634361837e73c5734cca13
as a child, peixotto enjoyed searching her grandparents’
as a child, peixotto enjoyed searching her grandparents’ old vermont farmhouse for artifacts. she initially studied engineering at college, but according to peixotto, "when i took my first archaeology course, it was like a lightbulb turned on! i could combine all my experiences and interests in science, the outdoors, t...
wikipedia
d3c9ae9053e91990f533d7ec7bba80d4648d18c7
since this expedition, peixotto has continued to work
since this expedition, peixotto has continued to work with a team to learn more about homo naledi. as of 2021, this team has discovered two dozen naledi individuals and evidence that suggests this cave system might have served as burial grounds for homo naledi.
wikipedia
b340f606c1881fa85e56843c44051d906238ea9b
peixotto, hannah morris, marina elliott, alia gurtov, k.
peixotto, hannah morris, marina elliott, alia gurtov, k. lindsay eaves, and elen feuerriegel, along with a team of sixty international scientists, excavated "one of the richest collections of hominin fossils ever discovered—some 1,550 fossil fragments, belonging to at least 15 individual skeletons."
wikipedia
63518c1eb4f7864d249ea66fbd45c83cfa228dcb
the critical skills and physical attributes sought for
the critical skills and physical attributes sought for the excavation team by lead scientist and university of the witwatersrand professor lee berger were a "master's degree or higher in palaeontology, archeology or an associated field; caving experience; and the ability to fit through an 18-centimeter (about 7-inch) s...
wikipedia
73626d6596f8d4e9664dec3e51bc914a60766567
in october 2013, peixotto and five others were
in october 2013, peixotto and five others were chosen to be part of a specialized excavation team for the rising star expedition. the purpose of the 21-day expedition, sponsored by the national geographic society and the university of the witwatersrand, johannesburg, was to excavate fossils which had been recently foun...
wikipedia
95c9ec7566478da040055cd03ac588e3070da5e8
peixotto received her ph.d. in anthropology, archaeology specialization,
peixotto received her ph.d. in anthropology, archaeology specialization, in 2017 from american university with her dissertation against the map: resistance landscapes of the great dismal swamp. peixotto obtained a b.a. in slavic area studies and mathematics from the university of alabama in huntsville. she pursued furt...
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e47601a678b8b90ee003c1fb78db7689904332c8
rebecca (becca) peixotto is an american archaeologist who
rebecca (becca) peixotto is an american archaeologist who is best known for her contribution to the rising star expedition as one of the six underground astronauts, a group of scientists tasked with excavating the rising star cave system. she has also participated in the great dismal swamp landscape study and is an exp...
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d88644183053d1f387d0366a23491033e8b2e147
in mathematics, particularly in abstract algebra, a semigroup
in mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism, which—roughly speaking—brings it closer to a group because this involution, considered as unary operator, exhibits certain fundamental properties of the operation ...
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16524d07a9c318d0bc930f770a6cb187a0d60c2c
the same interaction law with the binary operation
the same interaction law with the binary operation as in the case of the group inverse. it is thus not a surprise that any group is a semigroup with involution. however, there are significant natural examples of semigroups with involution that are not groups. an example from linear algebra is the multiplicative monoid ...
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522baaff1a11c1df5967a62a78e90c5b95d93d1b
a baer *-semigroup is a *-semigroup with (two-sided)
a baer *-semigroup is a *-semigroup with (two-sided) zero in which the right annihilator of every element coincides with the right ideal of some projection; this property is expressed formally as: for all x ∈ s there exists a projection e such that
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b0874ad66ecb338ec1566fa5e76d86575e36f174
the construction of a free group is not
the construction of a free group is not very far off from that of a free monoid with involution. the additional ingredient needed is to define a notion of reduced word and a rewriting rule for producing such words simply by deleting any adjacent pairs of letter of the form x x † {\displaystyle xx^{\dagger }} or x † x {...
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e6fe2428b46828eb63e74d4c35b2d01076a06c39
the construction of a free group is not
— eli shamir —although more recently it has been called the involutive monoid generated by x. (this latter choice of terminology conflicts however with the use of "involutive" to denote any semigroup with involution—a practice also encountered in the literature.)
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ab7bcd67818df9093e273993bca12854eb074c7d
the construction above is actually the only way
the construction above is actually the only way to extend a given map θ {\displaystyle \theta \,} from x {\displaystyle x\,} to x † {\displaystyle x^{\dagger }\,}, to an involution on y + {\displaystyle y^{+}\,} (and likewise on y ∗ {\displaystyle y^{*}\,}). the qualifier "free" for these constructions is justified in ...
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9ba7f026211a171386b63941f99071db81e984be
if in the above construction instead of y
if in the above construction instead of y + {\displaystyle y^{+}\,} we use the free monoid y ∗ = y + ∪ { ε } {\displaystyle y^{*}=y^{+}\cup \{\varepsilon \}}, which is just the free semigroup extended with the empty word ε {\displaystyle \varepsilon \,} (which is the identity element of the monoid y ∗ {\displaystyle y^...
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4b60486cd78c76150c0dd086073103bc61006b17
this map is an involution on the semigroup
this map is an involution on the semigroup y + {\displaystyle y^{+}\,}. thus, the semigroup (x ⊔ x †) + {\displaystyle (x\sqcup x^{\dagger })^{+}} with the map † {\displaystyle {}^{\dagger }\,} is a semigroup with involution, called a free semigroup with involution on x. (the irrelevance of the concrete identity of x †...
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53c1433bb5297cbf3e1ba35069c287ae05e24f9b
the bijection † {\displaystyle \dagger } on y
the bijection † {\displaystyle \dagger } on y {\displaystyle y} is then extended as a bijection †: y + → y + {\displaystyle {}^{\dagger }:y^{+}\rightarrow y^{+}} defined as the string reversal of the elements of y + {\displaystyle y^{+}\,} that consist of more than one letter:
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caf46c62206a7519f7fe3e0be3ae7896cfc6f84c
now construct y + {\displaystyle y^{+}\,} as the
now construct y + {\displaystyle y^{+}\,} as the free semigroup on y {\displaystyle y\,} in the usual way with the binary (semigroup) operation on y + {\displaystyle y^{+}\,} being concatenation:
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c564e8d3778065c2a740514802f585f6afd21c31
the generators of a free semigroup with involution
the generators of a free semigroup with involution are the elements of the union of two (equinumerous) disjoint sets in bijective correspondence: y = x ⊔ x † {\displaystyle y=x\sqcup x^{\dagger }}. (here the notation ⊔ {\displaystyle \sqcup \,} emphasized that the union is actually a disjoint union.) in the case were t...
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65b510cd4fc88f0e3a638ceda003b5fe6df9fadc
as with all varieties, the category of semigroups
as with all varieties, the category of semigroups with involution admits free objects. the construction of a free semigroup (or monoid) with involution is based on that of a free semigroup (and respectively that of a free monoid). moreover, the construction of a free group can easily be derived by refining the construc...
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39b4dc09949ab57b4a3788034f41aabbbea1b52c
in the multiplicative semigroup m (c) of square
in the multiplicative semigroup m (c) of square matrices of order n, the map which assigns a matrix a to its hermitian conjugate a * is an involution. the semigroup m (c) is a *-regular semigroup with this involution. the moore–penrose inverse of a in this *-regular semigroup is the classical moore–penrose inverse of a...
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60275495bbb093e2c5479a2d42db89d16d586ad0
one motivation for studying these semigroups is that
one motivation for studying these semigroups is that they allow generalizing the moore–penrose inverse's properties from r {\displaystyle \mathbb {r} } and c {\displaystyle \mathbb {c} } to more general sets.
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a56ea11209a3300471f674adf95b354dbfc3332d
a semigroup s with an involution * is
a semigroup s with an involution * is called a *-regular semigroup (in the sense of drazin) if for every x in s, x * is h -equivalent to some inverse of x, where h is the green's relation h. this defining property can be formulated in several equivalent ways. another is to say that every l -class contains a projection....
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8601dda60719dbfd4fafe6dd6d59c099772977c7
a regular semigroup s is a *-regular semigroup,
a regular semigroup s is a *-regular semigroup, as defined by nordahl & scheiblich, if and only if it has a p-system f(s). in this case f(s) is the set of projections of s with respect to the operation ° defined by f(s). in an inverse semigroup the entire semilattice of idempotents is a p-system. also, if a regular sem...
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86c502c32d63512b4dfeeb844a6b38422f80f4b3
the problem of characterizing when a regular semigroup
the problem of characterizing when a regular semigroup is a regular *-semigroup (in the sense of nordahl & scheiblich) was addressed by m. yamada (1982). he defined a p-system f(s) as subset of the idempotents of s, denoted as usual by e(s). using the usual notation v(a) for the inverses of a, f(s) needs to satisfy the...
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fb78a7bcf80e67839dabff3f7f5486163bc1fa86
it is a simple calculation to establish that
it is a simple calculation to establish that a regular *-semigroup is also a regular semigroup because x * turns out to be an inverse of x. the rectangular band from example 7 is a regular *-semigroup that is not an inverse semigroup. it is also easy to verify that in a regular *-semigroup the product of any two projec...
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2362517124b297792a407716a8a81dfa78790121
the first of these looks like the definition
the first of these looks like the definition of a regular element, but is actually in terms of the involution. likewise, the second axiom appears to be describing the commutation of two idempotents. it is known however that regular semigroups do not form a variety because their class does not contain free objects (a re...
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63f0b60138ba190134a3913bed57c43ce4a7cf90
as mentioned in the previous examples, inverse semigroups
as mentioned in the previous examples, inverse semigroups are a subclass of *-semigroups. it is also textbook knowledge that an inverse semigroup can be characterized as a regular semigroup in which any two idempotents commute. in 1963, boris m. schein showed that the following two axioms provide an analogous character...
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f39e48fa62e832d7abc8724bdd02b133a6a02632
the partial isometries in a c*-algebra are exactly
the partial isometries in a c*-algebra are exactly those defined in this section. in the case of m (c) more can be said. if e and f are projections, then e ≤ f if and only if im e ⊆ im f. for any two projection, if e ∩ f = v, then the unique projection j with image v and kernel the orthogonal complement of v is the mee...
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b4684222c267c6d6f643540d6ac220d80be78d6b
partial isometries can be partially ordered by s
partial isometries can be partially ordered by s ≤ t defined as holding whenever s = ss * t and ss * = ss * tt *. equivalently, s ≤ t if and only if s = et and e = ett * for some projection e. in a *-semigroup, pi(s) is an ordered groupoid with the partial product given by s ⋅ t = st if s * s = tt *.
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43d201d436dc7c03971eea46a7e5fe9b18bf4df3
certain basic concepts may be defined on *-semigroups
certain basic concepts may be defined on *-semigroups in a way that parallels the notions stemming from a regular element in a semigroup. a partial isometry is an element s such that ss * s = s; the set of partial isometries of a semigroup s is usually abbreviated pi(s). a projection is an idempotent element e that is ...
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6d52837dc9e2ce948525feff294f909df174d11a
an element x of a semigroup with involution
an element x of a semigroup with involution is sometimes called hermitian (by analogy with a hermitian matrix) when it is left invariant by the involution, meaning x * = x. elements of the form xx * or x * x are always hermitian, and so are all powers of a hermitian element. as noted in the examples section, a semigrou...
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0232c820f66cc15a9dc0719883a64f3e44c70e0d
in some applications, the second of these axioms
in some applications, the second of these axioms has been called antidistributive. regarding the natural philosophy of this axiom, h.s.m. coxeter remarked that it "becomes clear when we think of and as the operations of putting on our socks and shoes, respectively."
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dcc7d9aec7a9381fa73b7f1c787f269e7e660504
an example from linear algebra is the multiplicative
an example from linear algebra is the multiplicative monoid of real square matrices of order n (called the full linear monoid). the map which sends a matrix to its transpose is an involution because the transpose is well defined for any matrix and obeys the law (ab) = b a, which has the same form of interaction with mu...
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327282358da4260ad86e2597a8ac10d3300e88d7
in mathematics, particularly in abstract algebra, a semigroup
in mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism, which—roughly speaking—brings it closer to a group because this involution, considered as unary operator, exhibits certain fundamental properties of the operation ...
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95ccc20e6413e199bf658f25c7df7c7b4d47965d
slitrk1 is a human gene that codes for
slitrk1 is a human gene that codes for a transmembrane and signalling protein that is part of the slitrk gene family, which is responsible for synapse regulation and presynaptic differentiation in the brain. expression of the gene has been linked to early formation of excitatory synapses through binding with receptor t...
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36324c6b445f4ba7bd3da2a4574df6c1b749d0eb
a study was done in which 44 families
a study was done in which 44 families with individuals who had trichotillomania had their slitrk1 gene sequenced. two new non-synonymous mutations were discovered about 9 base pairs apart from each other, in an area separate from the one where the tourette mutations were found. these results were compared to a control ...
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