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#( Going down ) If B is an integral extension of A, and B is a domain, and A is integrally closed in its field of fractions, then the extension ( in addition to going-up, lying-over and incomparability ) satisfies the going-down property.
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#( Going up ) If B is an integral extension of A, then the extension satisfies the going-up property ( and hence the lying over property ), and the incomparability property.
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#( Betti numbers ) If X is a ( good ) " reduction mod p " of a non-singular projective variety Y defined over a number field embedded in the field of complex numbers, then the degree of P < sub > i </ sub > is the i < sup > th </ sup > Betti number of the space of complex points of Y.
#( a property of Delaunay triangulations ): If there is a circle with two of the input points on its boundary which contains no other input points, the line between those two points is an edge of every Delaunay triangulation.
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#( Desargues ) Given seven distinct points A, A ', B, B ', C, C ', O, such that AA ', BB ', and CC ' are distinct lines through O and AB is parallel to A ' B ' and BC is parallel to B ' C ', then AC is parallel to A ' C '.
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#( A « B and A « C ) ⇒ A « B ∩ C
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#( Crypto -) CatharAccording to this thesis, troubadour poetry is a reflection of Cathar religious doctrine.
#( Affine axiom of parallelism ) Given a point A and a line r, not through A, there is at most one line through A which does not meet r.
#( Rationality ) ζ ( X, s ) is a rational function of T = q < sup >− s </ sup >.
#( Functional equation and Poincaré duality ) The zeta function satisfies < dl >< dd ></ dl > or equivalently < dl >< dd ></ dl > where E is the Euler characteristic of X.
#( All ) y is a Z
#( the cycle property of minimum spanning trees ): For any cycle C in the graph, if the weight of an edge e of C is larger than the weights of other edges of C, then this edge cannot belong to a MST.
#( TR 3 ) Given a map between two morphisms, there is a morphism between their mapping cones ( which exist by axiom ( TR 1 )), that makes everything commute.
#( TR 4 ) This is called the octahedral axiom.
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The diagonal lemma also requires that there be a systematic way of assigning to every formula θ a natural number #( θ ) called its Gödel number.
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#( Senior ) Project Manager: Has overall responsibility for design, implementation, and management of research projects.
#( Riemann hypothesis ) | α < sub > i, j </ sub >| = q < sup > i / 2 </ sup > for all and all j.
#( Later ) Jin and Korea will not violate each other's territory.
#( Polonaise ) in D minor, BWV Anh.
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#( For men only ) Doing istibra ' before ghusl janabat.
#( TR 2 ) The rotations of any distinguished triangle are distinguished.
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#( 2 ). 50 caliber sniper rifles
#( probably ) Dietrich I, Count of Wettin, d. 976
#( a ) Minimal usage not an issue here.
Going and down
Going " down " to Egypt is derived from the Biblical origin, where Egypt is consistently perceived as being " below " other lands, with going to Egypt being " down " while going away from Egypt is " up ".
Although the poem states that he fled " from home in Spain / Going down to Rome with heavy spirit ," this does not resolve the question of what intermediate journeys Ibn Ezra may have made before settling in Rome, possibly in the company of R ' Yehudah HaLevi.
Going in the opposite direction, English-to-French, provides an example of how a compound word may be calqued by first breaking it down into its component roots.
Going down the stretch, the injuries of Stephen Jackson and Tyrus Thomas killed any chances of Charlotte trying to catch the Indiana Pacers, who swept them 0 – 4 in the regular season, for the eighth spot in the east.
Going into the Australian Open, Mirza went down fighting to former world no.
Going layer by layer from his surroundings and through his ( now tattered ) clothes and down to the grime and dirt he is covered in, he soon realizes that he has no scent at all.
Going into his fifteenth season in the VFL, Matthews showed no signs of slowing down in 1983.
The recording career of the 4 Tunes wound down with an LP on the ARA label in 1969 ( which not only contained a version of " I Love You For Sentimental Reasons ," but also " Whole Lot Of Shaking Going On ").
Going up Morrow Mountain ( or going down ) is a decent climb and for the rest of the trail ( blue triangle blazes ) the trail rolls up and down hills.
Going southeast, it widens to four-lane near Marshall, merging farther down with I-26 / US 19 / US 23 going into Asheville.
* Lồng tồng ( literally: " Going down the rice paddy ") celebrated after New Lunar Year Festival to pray for yield.
Going into the Wehrseifen slight right hand / sharp left hand turn, Marimón's Maserati 250F failed to negotiate the corner while going down the downhill run to the corner, plunged down an embankment, the car somersaulted and he was killed instantly.
Going a goal down early on in the game at the Swedish national stadium, Llanelli rallied and won the game 2 – 1 thanks to a debut goal from Rhys Griffiths and a goal from fans favourite, Jacob Mingorance.
Diamond Jim Brady once lived in the house known as the South Branch Hotel, which he purchased for his mistress, Edna Maculey in 1903 paying $ 68, 000 for it and altering it to suit his taste, " Going down to Brady's Farm " became the fashionable thing to do and Anna Held, Flo Ziegfeld, Lillian Russell and other famous personalities of the days were frequent guests.
I'm Going Home ( Je rentre à la maison ) stars Michel Piccoli as Gilbert Valence, an aging stage actor that never achieved great success who deals with the sudden deaths of his wife, daughter and son-in-law after a car accident, turning down undignified roles in commercial TV shows and raising his 9-year-old grandson.
: Going to sit down by my Jesus
: Going to sit down by my Jesus, Lord.
Going further down the tape, the last two stationary head tracks carried control and time code information, respectively.
Going over the Chilkoot Pass, his party built rafts and floated down the Yukon River to its mouth in the Bering Sea, naming many geographic features along the way.
When the Post Office burns down in Going Postal Moist goes back into the burning Post Office to save Mr. Tiddles.
# REDIRECT Going up and going down
1.170 seconds.