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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... | 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 |
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 ... | wikipedia |
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 ... | wikipedia |
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 | wikipedia |
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 {... | wikipedia |
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.) | wikipedia |
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 ... | wikipedia |
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^... | wikipedia |
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 †... | wikipedia |
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: | wikipedia |
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: | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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. | wikipedia |
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.... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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 *. | wikipedia |
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 ... | wikipedia |
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... | wikipedia |
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." | wikipedia |
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... | wikipedia |
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 ... | wikipedia |
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... | wikipedia |
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 ... | wikipedia |
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