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https://en.wikipedia.org/wiki/Rinat%20Shakirov | Rinat Shakirov (; born 1962 in Karaganda, Kazakhstan) is a Kazakh pianist.
Education
Shakirov graduated from the Physics & Mathematics School in 1979 and entered the Leningrad Polytechnic Institute's Department of Nuclear Physics while dabbling in music.
Shakirov decided to become a musician in 1981. He studied at the music school with the famous piano teacher Alfred Rippe (working in Marburg, Germany).
He repeatedly won regional piano competitions during his studies. (Alma-Ata, Frunze).
He continued his studies at the St. Petersburg Conservatory with Stanislav Igolinsky and at the Moscow Conservatory with Lev Vlasenko from 1985 to 1992.
In 1994 he took part in the Xth International Competition after P.I. Tchaikovsky, Moscow (I, II rounds).
Career
On graduating from the conservatory, Shakirov was engaged in concert and teaching activities. His concert programs were based on Bach, Schubert, Rachmaninov, Tchaikovsky, Chopin, Debussy, Ravel, and Gershwin. His works have been widely recognized by the public and critics. The music of contemporary composers—Messiaen, Stravinsky, Hindemith, Ligeti, Satie, Bartok, Copland—also makes up a significant part of Shakirov's repertoire, as does the music of Tatarstan composers—Yarullin, Yakhin, Kalimullin, Monasypov, and Enikeev, among others.
Shakirov is the author of the piano suite based on Farit Yarullin's Shurale ballet, published in Moscow in 2005 and 2011 in the Composer Publishing House.
Shakirov has recorded nine discs and records of piano classics in studios in Russia, Tatarstan and Kazakhstan.
Since 1990, Shakirov has performed more than 600 solo concerts in Russia, Italy, Finland, France, Germany, Sweden, Belgium, Switzerland. He has performed in the halls of Moscow, St. Petersburg, Kazan, Voronezh, Orel, Astana, Almaty, Milan, Paris, Stockholm, Helsinki, Zurich, Basel, Kassel, Stuttgart, and Brussels.
Shakirov works with many orchestras and conductors, including Fuat Mansurov, Ravil Martynov, Alexander Kantorov, Mikhail Sinkevich, Dmitry Khokhlov, Andrei Anikhanov, Fabio Mastrangelo, Sergei Stadler, Alexander Sladkovsky, Igor Manasherov and Rustem Abyazov.
Shakirov has taken part in international music festivals such as Geteborg Art Sound, Europe-Asia, St. Petersburg Musical Spring, Other Space, Japanese Spring in St. Petersburg, Panorama of Russian Music, Moscow Autumn, Names of St. Petersburg and many others.
He has been an award panelist in various international piano competitions.
References
External links
1962 births
Living people
Kazakhstani pianists
Artistic directors (music)
Honored Artists of the Russian Federation
21st-century pianists
Moscow Conservatory alumni |
https://en.wikipedia.org/wiki/David%20Dalglish | David Dalglish (born April 2, 1984) is an American writer of epic fantasy fiction.
Early life and education
Dalglish graduated with a degree in Mathematics from Missouri Southern State University in 2006.
Career
Dalglish used to live in Missouri where he worked odd jobs before self-publishing his first novel, The Weight of Blood, in 2010. In 2013, after releasing fifteen novels as e-books and more than 200,000 sales, Dalglish signed a publishing deal with Orbit Books to re-release his Shadowdance Series of novels. Later that year, he also signed an agreement with 47North, part of Amazon Publishing, to publish a new series, The Breaking World. In 2019 he, along with his family, moved to South Carolina, where he has written the series "The Keepers".
Work
Most of Dalglish's work takes place within his invented world of Dezrel, and much was originally self-published: The Half-Orcs, an R.A. Salvatore-inspired series starring a pair half-orc brothers; The Shadowdance Series, a lengthy adventure starring thieves and assassins; The Paladins; and The Breaking World (published by 47North, which chronicles the creation of his world and the war between gods that is referenced in all his earlier works.) Dalglish also served as editor and main contributor to A Land of Ash, a short story compilation dealing with the fallout from the eruption of the Yellowstone Caldera. Publishers Weekly wrote that, "Dalglish puts familiar pieces together with a freshness and pleasure that are contagious." According to fantasy author Sam Sykes, "Dalglish concocts a heady cocktail of energy, breakneck pace, and excitement."
Bibliography
The Half-Orcs series (Self-Published)
The Weight of Blood (January 31, 2010)
The Cost of Betrayal (March 25, 2010)
The Death of Promises (May 30, 2010)
The Shadows of Grace (October 7, 2010)
A Sliver of Redemption (January 19, 2011)
A Prison of Angels (November 29, 2012)
The King of the Vile (January 26, 2015)
The King of the Fallen (August 3, 2020)
The Shadowdance Series
A Dance of Cloaks (self published 2011, with Orbit Books October 8, 2013)
A Dance of Blades (self published 2011, with Orbit Books November 5, 2013)
A Dance of Mirrors (self published as A Dance of Death 2012, with Orbit Books December 3, 2013)
A Dance of Shadows (self published as Blood of the Father 2012, with Orbit Books May 20, 2014)
A Dance of Ghosts (Orbit Books, November 11, 2014)
A Dance of Chaos (Orbit Books, May 12, 2015)
Cloak and Spider: A Shadowdance Novella (Orbit Books, December 3, 2013)
The Paladins (Self-Published)
Night of Wolves (May 31, 2011)
Clash of Faiths (July 24, 2011)
The Old Ways (December 30, 2011)
The Broken Pieces (August 19, 2012)
The Breaking World (47North, written with Robert J. Duperre)
Dawn of Swords (January 14, 2014)
Wrath of Lions (April 22, 2014)
Blood of Gods (October 14, 2014)
The Seraphim Trilogy (Orbit Books)
Skyborn (November 17, 2015)
Fireborn (November 22, 2016)
Shadowborn (November 7, 20 |
https://en.wikipedia.org/wiki/3-3%20duoprism | In the geometry of 4 dimensions, the 3-3 duoprism or triangular duoprism is a four-dimensional convex polytope. It can be constructed as the Cartesian product of two triangles and is the simplest of an infinite family of four-dimensional polytopes constructed as Cartesian products of two polygons, the duoprisms.
It has 9 vertices, 18 edges, 15 faces (9 squares, and 6 triangles), in 6 triangular prism cells. It has Coxeter diagram , and symmetry , order 72. Its vertices and edges form a rook's graph.
Hypervolume
The hypervolume of a uniform 3-3 duoprism, with edge length a, is . This is the square of the area of an equilateral triangle, .
Graph
The graph of vertices and edges of the 3-3 duoprism has 9 vertices and 18 edges. Like the Berlekamp–van Lint–Seidel graph and the unknown solution to Conway's 99-graph problem, every edge is part of a unique triangle and every non-adjacent pair of vertices is the diagonal of a unique square. It is a toroidal graph, a locally linear graph, a strongly regular graph with parameters (9,4,1,2), the rook's graph, and the Paley graph of order 9.
This graph is also the Cayley graph of the group with generating set .
Images
Symmetry
In 5-dimensions, some uniform 5-polytopes have 3-3 duoprism vertex figures, some with unequal edge-lengths and therefore lower symmetry:
The birectified 16-cell honeycomb also has a 3-3 duoprism vertex figure. There are three constructions for the honeycomb with two lower symmetries.
Related complex polygons
The regular complex polytope 3{4}2, , in has a real representation as a 3-3 duoprism in 4-dimensional space. 3{4}2 has 9 vertices, and 6 3-edges. Its symmetry is 3[4]2, order 18. It also has a lower symmetry construction, , or 3{}×3{}, with symmetry 3[2]3, order 9. This is the symmetry if the red and blue 3-edges are considered distinct.
Related polytopes
3-3 duopyramid
The dual of a 3-3 duoprism is called a 3-3 duopyramid or triangular duopyramid. It has 9 tetragonal disphenoid cells, 18 triangular faces, 15 edges, and 6 vertices.
It can be seen in orthogonal projection as a 6-gon circle of vertices, and edges connecting all pairs, just like a 5-simplex seen in projection.
orthogonal projection
Related complex polygon
The regular complex polygon 2{4}3 has 6 vertices in with a real representation in matching the same vertex arrangement of the 3-3 duopyramid. It has 9 2-edges corresponding to the connecting edges of the 3-3 duopyramid, while the 6 edges connecting the two triangles are not included. It can be seen in a hexagonal projection with 3 sets of colored edges. This arrangement of vertices and edges makes a complete bipartite graph with each vertex from one triangle is connected to every vertex on the other. It is also called a Thomsen graph or 4-cage.
See also
3-4 duoprism
Tesseract (4-4 duoprism)
5-5 duoprism
Convex regular 4-polytope
Duocylinder
Notes
References
Regular Polytopes, H. S. M. Coxeter, Dover Publications, Inc., 1973, New York, p. 124.
Co |
https://en.wikipedia.org/wiki/3-4%20duoprism | In geometry of 4 dimensions, a 3-4 duoprism, the second smallest p-q duoprism, is a 4-polytope resulting from the Cartesian product of a triangle and a square.
The 3-4 duoprism exists in some of the uniform 5-polytopes in the B5 family.
Images
Related complex polygons
The quasiregular complex polytope 3{}×4{}, , in has a real representation as a 3-4 duoprism in 4-dimensional space. It has 12 vertices, and 4 3-edges and 3 4-edges. Its symmetry is 3[2]4, order 12.
Related polytopes
The birectified 5-cube, has a uniform 3-4 duoprism vertex figure:
3-4 duopyramid
The dual of a 3-4 duoprism is called a 3-4 duopyramid. It has 12 digonal disphenoid cells, 24 isosceles triangular faces, 12 edges, and 7 vertices.
See also
Polytope and polychoron
Convex regular polychoron
Duocylinder
Tesseract
Notes
References
Regular Polytopes, H. S. M. Coxeter, Dover Publications, Inc., 1973, New York, p. 124.
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999, (Chapter 5: Regular Skew Polyhedra in three and four dimensions and their topological analogues)
Coxeter, H. S. M. Regular Skew Polyhedra in Three and Four Dimensions. Proc. London Math. Soc. 43, 33–62, 1937.
John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, (Chapter 26)
Norman Johnson Uniform Polytopes, Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
External links
The Fourth Dimension Simply Explained—describes duoprisms as "double prisms" and duocylinders as "double cylinders"
Polygloss - glossary of higher-dimensional terms
Exploring Hyperspace with the Geometric Product
4-polytopes |
https://en.wikipedia.org/wiki/Four-spiral%20semigroup | In mathematics, the four-spiral semigroup is a special semigroup generated by four idempotent elements. This special semigroup was first studied by Karl Byleen in a doctoral dissertation submitted to the University of Nebraska in 1977. It has several interesting properties: it is one of the most important examples of bi-simple but not completely-simple semigroups; it is also an important example of a fundamental regular semigroup; it is an indispensable building block of bisimple, idempotent-generated regular semigroups. A certain semigroup, called double four-spiral semigroup, generated by five idempotent elements has also been studied along with the four-spiral semigroup.
Definition
The four-spiral semigroup, denoted by Sp4, is the free semigroup generated by four elements a, b, c, and d satisfying the following eleven conditions:
a2 = a, b2 = b, c2 = c, d2 = d.
ab = b, ba = a, bc = b, cb = c, cd = d, dc = c.
da = d.
The first set of conditions imply that the elements a, b, c, d are idempotents. The second set of conditions imply that a R b L c R d where R and L are the Green's relations in a semigroup. The lone condition in the third set can be written as d ωl a, where ωl is a biorder relation defined by Nambooripad. The diagram below summarises the various relations among a, b, c, d:
Elements of the four-spiral semigroup
General elements
Every element of Sp4 can be written uniquely in one of the following forms:
[c] (ac)m [a]
[d] (bd)n [b]
[c] (ac)m ad (bd)n [b]
where m and n are non-negative integers and terms in square brackets may be omitted as long as the remaining product is not empty. The forms of these elements imply that Sp4 has a partition Sp4 = A ∪ B ∪ C ∪ D ∪ E where
A = { a(ca)n, (bd)n+1, a(ca)md(bd)n : m, n non-negative integers }
B = { (ac)n+1, b(db)n, a(ca)m(db) n+1 : m, n non-negative integers }
C = { c(ac)m, (db)n+1, (ca)m+1(db)n+1 : m, n non-negative integers }
D = { d(bd)n, (ca)m+1(db)n+1d : m, n non-negative integers }
E = { (ca)m : m positive integer }
The sets A, B, C, D are bicyclic semigroups, E is an infinite cyclic semigroup and the subsemigroup D ∪ E is a nonregular semigroup.
Idempotent elements
The set of idempotents of Sp4, is {an, bn, cn, dn : n = 0, 1, 2, ...} where, a0 = a, b0 = b, c0 = c, d0 = d, and for n = 0, 1, 2, ....,
an+1 = a(ca)n(db)nd
bn+1 = a(ca)n(db)n+1
cn+1 = (ca)n+1(db)n+1
dn+1 = (ca)n+1(db)n+ld
The sets of idempotents in the subsemigroups A, B, C, D (there are no idempotents in the subsemigoup E) are respectively:
EA = { an : n = 0,1,2, ... }
EB = { bn : n = 0,1,2, ... }
EC = { cn : n = 0,1,2, ... }
ED = { dn : n = 0,1,2, ... }
Four-spiral semigroup as a Rees-matrix semigroup
Let S be the set of all quadruples (r, x, y, s) where r, s, ∈ { 0, 1 } and x and y are nonnegative integers and define a binary operation in S by
The set S with this operation is a Rees matrix semigroup over the bicyclic semigroup, and th |
https://en.wikipedia.org/wiki/Stan%20Wawrinka%20career%20statistics | This is a list of the main career statistics of Swiss professional tennis player, Stan Wawrinka. To date, Wawrinka has won sixteen ATP singles titles, including three Grand Slam singles titles at the 2014 Australian Open, the 2015 French Open, and the 2016 US Open, and one ATP Masters 1000 title at the 2014 Monte-Carlo Rolex Masters. He was also a semifinalist at the 2013 US Open, the 2015 Australian Open, the 2015 US Open, and the 2013, 2014 and 2015 ATP World Tour Finals. He also has reached the quarterfinals at 2014 and 2015 Wimbledon. Wawrinka also won a gold medal partnering Roger Federer in men's doubles for Switzerland in the 2008 Summer Olympics in Beijing, beating Swedish team Simon Aspelin and Thomas Johansson. In 2014 Wawrinka was part of the Swiss National Team, winning the Davis Cup for the first time.
His best singles ranking to date is World No. 3, achieved for the first time on 27 January 2014.
Performance timelines
Singles
Current through the 2023 Paris Masters.
Significant finals
Grand Slam finals
Singles: 4 (3 titles, 1 runner-up)
Olympics finals
Doubles: 1 (1 gold medal)
Masters 1000 finals
Singles: 4 (1 title, 3 runner-ups)
Doubles: 1 (1 runner-up)
ATP career finals
Singles: 31 (16 titles, 15 runner-ups)
Doubles: 7 (3 titles, 4 runner–ups)
Team competition: 1 (1 title)
Junior Grand Slam finals
Singles: 1 (1 title)
Records accomplished in the Open Era (Post 1968)
Best Grand Slam results details
Record against other players
Record against top 10 players
Wawrinka's match record against those who have been ranked in the top 10, with those who have been No. 1 in boldface
Marin Čilić 12–2
Tomáš Berdych 11–5
Andy Murray 9–13
Grigor Dimitrov 7–4
Kei Nishikori 7–4
David Ferrer 7–7
Marcos Baghdatis 6–0
David Nalbandian 6–3
Nicolás Almagro 6–3
Novak Djokovic 6–21
Fabio Fognini 5–1
Milos Raonic 5–3
Gilles Simon 5–3
Jo-Wilfried Tsonga 5–3
Kevin Anderson 5–4
Juan Mónaco 4–1
James Blake 3–0
Pablo Carreno Busta 3–0
Frances Tiafoe 3–0
Andy Roddick 3–1
Marat Safin 3–1
Dominic Thiem 3–1
David Goffin 3–2
Juan Carlos Ferrero 3–3
Richard Gasquet 3–3
Ivan Ljubičić 3–3
Gaël Monfils 3–3
Fernando Verdasco 3–3
Mikhail Youzhny 3–3
Juan Martín del Potro 3–4
Radek Štěpánek 3–4
Tommy Robredo 3–6
Rafael Nadal 3–19
Roger Federer 3–23
Guillermo Cañas 2–0
Taylor Fritz 2–0
Sébastien Grosjean 2–0
Ernests Gulbis 2–0
Nicolás Massú 2–1
Lleyton Hewitt 2–2
Karen Khachanov 2–2
Nicolas Kiefer 2–2
Daniil Medvedev 2–2
Jürgen Melzer 2–2
Robin Söderling 2–2
John Isner 2–3
Jannik Sinner 2–3
Roberto Bautista Agut 1–0
Tim Henman 1–0
Lucas Pouille 1–0
Jack Sock 1–0
Janko Tipsarević 1–0
Stefanos Tsitsipas 1–0
Nicolás Lapentti 1–1
Mariano Puerta 1–1
Holger Rune 1–1
Paradorn Srichaphan 1–1
Mario Ančić 1–2
Nikolay Davydenko 1–2
Greg Rusedski 1–2
Félix Mantilla 0–1
Carlos Moyá 0–1
Gastón Gaudio 0–1
Tommy Haas 0–2
Mardy Fish 0–3
A |
https://en.wikipedia.org/wiki/List%20of%20Sumgayit%20FK%20records%20and%20statistics | Sumgayit FK is an Azerbaijani professional football club based in Sumqayit.
This list encompasses the major records set by the club and their players in the Azerbaijan Premier League. The player records section includes details of the club's goalscorers and those who have made more than 50 appearances in first-team competitions.
Player
Most appearances
Players played over 50 competitive, professional matches only. Appearances as substitute (goals in parentheses) included in total.
Overall scorers
Competitive, professional matches only, appearances including substitutes appear in brackets.
Internationals
This is a list of all full international footballers to play for Sumgayit FK. Players who were capped while a Sumgayit player are marked in bold. Players who gained their first International cap after leaving Sumgayit are not included.
Current players
Former players
Team
Record wins
Record win: 4–0
v Turan Tovuz, 2012–13 Azerbaijan Premier League , 11 March 2013
Record League win: 4–0
v Turan Tovuz, 2012–13 Azerbaijan Premier League , 11 March 2013
Record Azerbaijan Cup win: 2–0
v Lokomotiv-Bilajary, 26 October 2011
Record away win: 2–3
v Ravan Baku, 2012–13 , 16 December 2012
Record home win 4–0
v Turan Tovuz, 2012–13 Azerbaijan Premier League , 11 March 2013
Record defeats
Record defeat: 1–8
v Neftchi Baku, 2012-13 Azerbaijan Premier League, 17 November 2012
Record League defeat: 1–8
v Neftchi Baku, 2012-13 Azerbaijan Premier League, 17 November 2012
Record away defeat: 1–8
v Neftchi Baku, 2012-13 Azerbaijan Premier League, 17 November 2012
Record Azerbaijan Cup defeat: 0–3
v Qarabağ, 2011-12 Azerbaijan Cup, 30 November 2011
Record home defeat: 1–6
v Qarabağ, 2012-13 Azerbaijan Premier League, 19 August 2012
Wins/draws/losses in a season
Most wins in a league season: 9 – 2012–13
Most draws in a league season: 8 – 2012–13
Most defeats in a league season: 20 – 2011-12
Fewest wins in a league season: 6 – 2011-12
Fewest draws in a league season: 6 – 2011-12
Fewest defeats in a league season: 15 – 2012–13
Goals
Most League goals scored in a season: 32 – 2012–13
Most Premier League goals scored in a season: 31 – 2012–13
Fewest League goals scored in a season: 29 – 2011–12
Most League goals conceded in a season: 52 – 2011–12
Fewest League goals conceded in a season: 49 – 2012–13
Points
Most points in a season:
35 in 32 matches, Azerbaijan Premier League, 2012-13
Fewest points in a season:
24 in 32 matches, Azerbaijan Premier League, 2011-12
References
Sumgayit FK
Sumgayit FK |
https://en.wikipedia.org/wiki/1961%E2%80%9362%20Galatasaray%20S.K.%20season | The 1961–62 season was Galatasaray's 58th in existence and the 4th consecutive season in the 1. Lig. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
Players in / out
In
Out
Milli Lig
Standings
Matches
Kick-off listed in local time (EET)
Balkans Cup
Group A
Friendly Matches
Kick-off listed in local time (EET)
Tournament
Eski Muharip Kupası
Doğuya Yardim Kampanyasi
Friendly match in Ankara
Attendances
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1961–62 season
Turkish football championship-winning seasons
1960s in Istanbul |
https://en.wikipedia.org/wiki/2013%20DPR%20Korea%20Football%20League | Statistics of DPR Korea Football League in the 2013 season.
Overview
The Highest Class Football League was played as a single round robin in October, with ten teams taking part. April 25 won the championship, finishing with 18 points (5 wins, 3 draws, 1 loss) in the nine matches played; Man'gyŏnbong were runners-up, and Hwaebul – a new addition to the competition established in May 2013 – finished in third place.
Table
Clubs
Although all clubs have a home stadium, all matches of the Highest Class Football League tournament were played at Kim Il-sung Stadium in P'yŏngyang.
Results
Round 1
Round 2
Round 3
Round 4
Round 5
Round 6
Round 7
Round 8
Round 9
Cup competitions
Hwaebul Cup
The Hwaebul Cup competition was held for the first time in 2013, with all matches played at Kim Il-sung Stadium in P'yŏngyang. The first stage was made up of two groups, with the first and second place finishers qualifying for the semi-finals. The semi-finals were held on (probably) 26 August, with Sŏnbong defeating Hwaebul, and April 25 defeating Amrokkang 3–1 on penalties, after regular time ended 2–2. The final was played on 28 August, between Sŏnbong and April 25. Regular play ended with the sides level at 2–2, and Sŏnbong won 6–5 on penalties. However, after the match, Sŏnbong was deemed to have fielded an ineligible player, and April 25 was awarded the victory.
Man'gyŏngdae Prize
The 2013 edition of the Man'gyŏngdae Prize was held in P'yŏngyang, with matches played at the Kim Il-sung Stadium and the Sosan Football Stadium from early March. Fourteen teams entered, including Kigwanch'a, Kyŏnggong'ŏp, Maebong, Rimyŏngsu, Sobaeksu, Myohyangsan, Man'gyŏnbong, P'yŏngyang City, and Amrokkang. The final, held on 29 April, saw Rimyŏngsu defeat Amrokkang by a score of 2–1. Having won the Man'gyŏngdae Prize, Rimyŏngsu were invited to take part in the 2014 AFC President's Cup – the first time a North Korean side would take part in an Asian club competition since April 25's last appearance in the 1991 Asian Club Championship.
Poch'ŏnbo Torch Prize
The fourth edition of the Poch'ŏnbo Torch Prize was played in two stages between 20 May and 10 July, the first being a double round-robin league phase, followed by a North American-style knock-out play-off phase. The top four finishers in the league phase qualified for the semi-finals. The final was played on 10 July, in which Hwaebul defeated Kyŏnggong'ŏp 2–1.
60th Anniversary of the Victory in the Fatherland Liberation War
A one-off competition was held for the 60th anniversary of the end of the Korean War, which is referred to as the "Fatherland Liberation War" in North Korea. April 25, Hwaebul, Rimyŏngsu, and Amrokkang took part in the competition, which was won by Amrokkang.
References
DPR Korea Football League seasons
1
Korea
Korea |
https://en.wikipedia.org/wiki/Trigonal%20trapezohedral%20honeycomb | In geometry, the trigonal trapezohedral honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. Cells are identical trigonal trapezohedra or rhombohedra. Conway, Burgiel, and Goodman-Strauss call it an oblate cubille.
Related honeycombs and tilings
This honeycomb can be seen as a rhombic dodecahedral honeycomb, with the rhombic dodecahedra dissected with its center into 4 trigonal trapezohedra or rhombohedra.
It is analogous to the regular hexagonal being dissectable into 3 rhombi and tiling the plane as a rhombille. The rhombille tiling is actually an orthogonal projection of the trigonal trapezohedral honeycomb. A different orthogonal projection produces the quadrille where the rhombi are distorted into squares.
Dual tiling
It is dual to the quarter cubic honeycomb with tetrahedral and truncated tetrahedral cells:
See also
Architectonic and catoptric tessellation
References
Honeycombs (geometry) |
https://en.wikipedia.org/wiki/P-space | In the mathematical field of topology, there are various notions of a P-space and of a p-space.
Generic use
The expression P-space might be used generically to denote a topological space satisfying some given and previously introduced topological invariant P. This might apply also to spaces of a different kind, i.e. non-topological spaces with additional structure.
P-spaces in the sense of Gillman–Henriksen
A P-space in the sense of Gillman–Henriksen is a topological space in which every countable intersection of open sets is open. An equivalent condition is that countable unions of closed sets are closed. In other words, Gδ sets are open and Fσ sets are closed. The letter P stands for both pseudo-discrete and prime. Gillman and Henriksen also define a P-point as a point at which any prime ideal of the ring of real-valued continuous functions is maximal, and a P-space is a space in which every point is a P-point.
Different authors restrict their attention to topological spaces that satisfy various separation axioms. With the right axioms, one may characterize P-spaces in terms of their rings of continuous real-valued functions.
Special kinds of P-spaces include Alexandrov-discrete spaces, in which arbitrary intersections of open sets are open. These in turn include locally finite spaces, which include finite spaces and discrete spaces.
P-spaces in the sense of Morita
A different notion of a P-space has been introduced by Kiiti Morita in 1964, in connection with his (now solved) conjectures (see the relevant entry for more information). Spaces satisfying the covering property introduced by Morita are sometimes also called Morita P-spaces or normal P-spaces.
p-spaces
A notion of a p-space has been introduced by Alexander Arhangelskii.
References
Further reading
External links
General topology
Properties of topological spaces |
https://en.wikipedia.org/wiki/Yang%20Hae-joon | Yang Hae-Joon (Hangul: 양해준; born 4 October 1990) is a South Korean football player.
Club Statistics
References
External links
1990 births
Living people
Men's association football midfielders
South Korean men's footballers
South Korean expatriate men's footballers
J2 League players
Kataller Toyama players
Expatriate men's footballers in Japan
South Korean expatriate sportspeople in Japan |
https://en.wikipedia.org/wiki/Rempei%20Uchida | is a Japanese football player.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at Kataller Toyama
1991 births
Living people
Kanazawa Seiryo University alumni
Association football people from Hokkaido
Japanese men's footballers
J2 League players
J3 League players
Kataller Toyama players
Men's association football defenders
People from Asahikawa |
https://en.wikipedia.org/wiki/Intersection | In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their intersection is the point at which they meet. More generally, in set theory, the intersection of sets is defined to be the set of elements which belong to all of them. Unlike the Euclidean definition, this does not presume that the objects under consideration lie in a common space.
Intersection is one of the basic concepts of geometry. An intersection can have various geometric shapes, but a point is the most common in a plane geometry. Incidence geometry defines an intersection (usually, of flats) as an object of lower dimension that is incident to each of original objects. In this approach an intersection can be sometimes undefined, such as for parallel lines. In both cases the concept of intersection relies on logical conjunction. Algebraic geometry defines intersections in its own way with intersection theory.
Uniqueness
There can be more than one primitive object, such as points (pictured above), that form an intersection. The intersection can be viewed collectively as all of the shared objects (i.e., the intersection operation results in a set, possibly empty), or as several intersection objects (possibly zero).
In set theory
The intersection of two sets A and B is the set of elements which are in both A and B. Formally,
.
For example, if and , then . A more elaborate example (involving infinite sets) is:
A = {x is an even integer}
B = {x is an integer divisible by 3}
As another example, the number 5 is not contained in the intersection of the set of prime numbers {2, 3, 5, 7, 11, …} and the set of even numbers {2, 4, 6, 8, 10, …}, because although 5 is a prime number, it is not even. In fact, the number 2 is the only number in the intersection of these two sets. In this case, the intersection has mathematical meaning: the number 2 is the only even prime number.
In geometry
Notation
Intersection is denoted by the from Unicode Mathematical Operators.
The symbol was first used by Hermann Grassmann in Die Ausdehnungslehre von 1844 as general operation symbol, not specialized for intersection. From there, it was used by Giuseppe Peano (1858–1932) for intersection, in 1888 in Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann.
Peano also created the large symbols for general intersection and union of more than two classes in his 1908 book Formulario mathematico.
See also
Constructive solid geometry, Boolean Intersection is one of the ways of combining 2D/3D shapes
Dimensionally Extended 9-Intersection Model
Meet (lattice theory)
Intersection (set theory)
Union (set theory)
References
External links
zh-yue:交點
Broad-concept articles |
https://en.wikipedia.org/wiki/Indigenous%20health%20in%20Australia | Indigenous health in Australia examines health and wellbeing indicators of Indigenous Australians compared with the rest of the population. Statistics indicate that Aboriginal Australians and Torres Strait Islanders are much less healthy than other Australians. Various government strategies have been put into place to try to remediate the problem; there has been some improvement in several areas, but statistics between Indigenous Australians and the rest of the Australian population still show unacceptable levels of difference.
Colonisation and ongoing disadvantage
Prior to European colonisation, it is likely that the health of Indigenous Australians was better than that of the inhabitants of poorer sections of Europe. Colonisation impacted the health of Indigenous Australians via land dispossession, social marginalisation, political oppression, incarceration, acculturation and population decline. The process of colonisation began with the arrival of the First Fleet in 1788. In the following decades, foreign diseases, dispossession, exploitation, warfare and violence proved devastating for the Indigenous population, and the immediate effect was a widespread increase in mortality and disease. By the end of the 19th century, Indigenous Australians were greatly reduced in numbers and the survivors were largely confined to remote reserves and missions. They were associated in the public mind with disease, which led to exclusion from institutions and isolation from non-Indigenous society for fear of contamination. These colonial policies resulted in segregated oppression and a lack of access to adequate medical care, leading to further disease and mortality.
The Australian government proceeded to deny the Indigenous people of their civil rights, including property rights; the ability to work and receive wages; and access to medical care and educational institutions. Legislation also allowed for the separation of Indigenous families, with guardianship being awarded to government officials called Protectors of Aborigines. Indigenous children forcibly removed from their families under Protection legislation in the first half of the 20th century are referred to as the Stolen Generations. Many of these children were neglected, abused, and denied of an education. The Australian government forced the Indigenous populations to assimilate into the colonisers’ culture through schools and programs, where Indigenous languages were banned and any resistance to these practices could result in imprisonment or death. This process of acculturation has led to trauma, including historical, inter-generational, and social trauma. Issues such as anxiety, stress, grief, and sadness are produced from this trauma, which have led to higher suicide rates, violence, substance abuse and incarceration of Indigenous peoples today.
Social, political and economic factors that result from colonisation present barriers to quality healthcare, health education, and health behaviours. |
https://en.wikipedia.org/wiki/2014%20Moldovan%20census | The 2014 Moldovan census was held between 12 and 25 May 2014. It was organized by National Bureau of Statistics of the Republic of Moldova.
On 31 March 2017 the National Bureau of Statistics officially announced a part of the census results. The census covered people with habitual residence (living in Moldova over 12 months regardless citizenship) and citizens gone from the country for more than 12 months. Accordingly, the census covered 2,998,235 people. In addition, estimated 193,434 persons were not covered by the census. In Chișinău municipality as many as 41% of population were not covered. The total population in Moldova covered is 2,804,801, of which about 209,000 (7.5%) were non-residents (living mostly abroad for over 12 months). The number of habitual residents in Moldova was 2,595,771.
2,754.7 thousand people (98.2%) reported their ethnicity, and the distribution is as follows:
75.1% Moldovans
7.0% Romanians
6.6% Ukrainians
4.6% Gagauz
4.1% Russians
1.9% Bulgarians
0.3% Roma
0.5% other
The 2014 census for the first time collected the information about the language they usually speak. 2,720.3 thousand reported these data as follows:
54.6% Moldovan,
24.0% Romanian,
14.5% Russian,
2.7% Ukrainian,
2,7% Gagauz
1.7% Bulgarian
0.5% other
About religion, 96.8% reported to be of Christian Orthodox faith.
By gender, population structure is as follows: 48.2% are men, while 51.8% are women. As many as 1,452,702 of the registered persons were females, exceeding the number of males by 100 thousand. Countrywide, for every 100 females there are 93 males.
The number of households registered in the 2014 census was of 959.2 thousand. The average size of a household is decreasing and was 2.9 persons, compared with 3.0 persons in 2004. Similar trends are typical of the residential environments: an urban household is made up, on average, of 2.7 persons, compared with 2.8 persons in 2004, while a rural household of average size was of 3.0 persons, compared with 3.1 persons in 2004.
The cost of the 2014 census was 89 million MDL. The finances for organizing and conducting the census, processing the data and publishing the results came from the state budget, as well as from Moldova's development partners – Swiss Development and Cooperation (SDC), Government of Romania, Government of the Czech Republic, UNICEF, UNDP and the European Union, with the support of the United Nations Population Fund (UNFPA).
The census did not cover the breakaway republic of Transnistria, which approximately corresponds to the Administrative-Territorial Units of the Left Bank of the Dniester of Moldova. At the same time, Transnistria postponed its census for at least 2 years citing financial difficulties. Its estimated population as of the beginning of 2014 was 505.1 thousand.
See also
2004 Moldovan census
References
Censuses in Moldova
Census
Moldova |
https://en.wikipedia.org/wiki/Moduli%20stack%20of%20principal%20bundles | In algebraic geometry, given a smooth projective curve X over a finite field and a smooth affine group scheme G over it, the moduli stack of principal bundles over X, denoted by , is an algebraic stack given by: for any -algebra R,
the category of principal G-bundles over the relative curve .
In particular, the category of -points of , that is, , is the category of G-bundles over X.
Similarly, can also be defined when the curve X is over the field of complex numbers. Roughly, in the complex case, one can define as the quotient stack of the space of holomorphic connections on X by the gauge group. Replacing the quotient stack (which is not a topological space) by a homotopy quotient (which is a topological space) gives the homotopy type of .
In the finite field case, it is not common to define the homotopy type of . But one can still define a (smooth) cohomology and homology of .
Basic properties
It is known that is a smooth stack of dimension where is the genus of X. It is not of finite type but locally of finite type; one thus usually uses a stratification by open substacks of finite type (cf. the Harder–Narasimhan stratification), also for parahoric G over curve X see and for G only a flat group scheme of finite type over X see.
If G is a split reductive group, then the set of connected components is in a natural bijection with the fundamental group .
The Atiyah–Bott formula
Behrend's trace formula
This is a (conjectural) version of the Lefschetz trace formula for when X is over a finite field, introduced by Behrend in 1993. It states: if G is a smooth affine group scheme with semisimple connected generic fiber, then
where (see also Behrend's trace formula for the details)
l is a prime number that is not p and the ring of l-adic integers is viewed as a subring of .
is the geometric Frobenius.
, the sum running over all isomorphism classes of G-bundles on X and convergent.
for a graded vector space , provided the series on the right absolutely converges.
A priori, neither left nor right side in the formula converges. Thus, the formula states that the two sides converge to finite numbers and that those numbers coincide.
Notes
References
J. Heinloth, Lectures on the moduli stack of vector bundles on a curve, 2009 preliminary version
J. Heinloth, A.H.W. Schmitt, The Cohomology Ring of Moduli Stacks of Principal Bundles over Curves, 2010 preprint, available at http://www.uni-essen.de/~hm0002/.
E. Arasteh Rad, U. Hartl, Uniformizing The Moduli Stacks of Global G-Shtukas, 2013 preprint, available at .
Gaitsgory, D; Lurie, J.; Weil's Conjecture for Function Fields. 2014,
Further reading
Tamagawa number for functional fields
C. Sorger, Lectures on moduli of principal G-bundles over algebraic curves
See also
Geometric Langlands conjectures
Ran space
Moduli stack of vector bundles
Algebraic geometry |
https://en.wikipedia.org/wiki/Behrend%27s%20trace%20formula | In algebraic geometry, Behrend's trace formula is a generalization of the Grothendieck–Lefschetz trace formula to a smooth algebraic stack over a finite field conjectured in 1993 and proven in 2003 by Kai Behrend. Unlike the classical one, the formula counts points in the "stacky way"; it takes into account the presence of nontrivial automorphisms.
The desire for the formula comes from the fact that it applies to the moduli stack of principal bundles on a curve over a finite field (in some instances indirectly, via the Harder–Narasimhan stratification, as the moduli stack is not of finite type.) See the moduli stack of principal bundles and references therein for the precise formulation in this case.
Pierre Deligne found an example that shows the formula may be interpreted as a sort of the Selberg trace formula.
A proof of the formula in the context of the six operations formalism developed by Yves Laszlo and Martin Olsson is given by Shenghao Sun.
Formulation
By definition, if C is a category in which each object has finitely many automorphisms, the number of points in is denoted by
with the sum running over representatives p of all isomorphism classes in C. (The series may diverge in general.) The formula states: for a smooth algebraic stack X of finite type over a finite field and the "arithmetic" Frobenius , i.e., the inverse of the usual geometric Frobenius in Grothendieck's formula,
Here, it is crucial that the cohomology of a stack is with respect to the smooth topology (not etale).
When X is a variety, the smooth cohomology is the same as etale one and, via the Poincaré duality, this is equivalent to Grothendieck's trace formula. (But the proof of Behrend's trace formula relies on Grothendieck's formula, so this does not subsume Grothendieck's.)
Simple example
Consider , the classifying stack of the multiplicative group scheme (that is, ). By definition, is the category of principal -bundles over , which has only one isomorphism class (since all such bundles are trivial by Lang's theorem). Its group of automorphisms is , which means that the number of -isomorphisms is .
On the other hand, we may compute the l-adic cohomology of directly. We remark that in the topological setting, we have (where now denotes the usual classifying space of a topological group), whose rational cohomology ring is a polynomial ring in one generator (Borel's theorem), but we shall not use this directly. If we wish to stay in the world of algebraic geometry, we may instead "approximate" by projective spaces of larger and larger dimension. Thus we consider the map induced by the -bundle corresponding to This map induces an isomorphism in cohomology in degrees up to 2N. Thus the even (resp. odd) Betti numbers of are 1 (resp. 0), and the l-adic Galois representation on the (2n)th cohomology group is the nth power of the cyclotomic character. The second part is a consequence of the fact that the cohomology of is generated by algebraic cycle |
https://en.wikipedia.org/wiki/List%20of%20Western%20Sydney%20Wanderers%20FC%20records%20and%20statistics | Western Sydney Wanderers Football Club is an Australian professional association football club based in Rooty Hill, Sydney. The club was formed and admitted into the A-League Men in 2012.
The list encompasses the honours won by Western Sydney Wanderers, records set by the club, their managers and their players. The player records section itemises the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Western Sydney Wanderers players on the international stage. Attendance records at Parramatta Stadium, Stadium Australia and Western Sydney Stadium are also included.
Western Sydney Wanderers have won two top-flight titles and are the only Australian team to win the AFC Champions League. The club's record appearance maker is Mark Bridge, who made 141 appearances between 2012 and 2019. Brendon Santalab is the Western Sydney Wanderers' record goalscorer, scoring 41 goals in total.
All figures are correct as of the match played on 22 October 2023.
Honours and achievements
Domestic
A-League Men Premiership
Winners (1): 2012–13
Runners-up (2): 2013–14, 2015–16
A-League Men Championship
Runners-up (3): 2013, 2014, 2016
AFC
AFC Champions League
Winners (1): 2014
Player records
Appearances
Most A-League Men appearances: Mark Bridge, 121
Most Australia Cup appearances: Kearyn Baccus, 12
Most Asian appearances: Shannon Cole, 20
Youngest first-team player: Alusine Fofanah, 15 years, 189 days (against Adelaide United, A-League, 19 January 2014)
Oldest first-team player: Ante Covic, 39 years, 326 days (against Guangzhou Evergrande Taobao, AFC Champions League, 5 May 2015)
Most consecutive appearances: Mitch Nichols, 52 (from 11 August 2015 to 28 January 2017)
Most appearances
Competitive matches only, includes appearances as substitute. Numbers in brackets indicate goals scored.
a. Includes goals and appearances (including those as a substitute) in the FIFA Club World Cup.
Goalscorers
Most goals in a season: Brendon Santalab, 16 goals (in the 2016–17 season)
Most league goals in a season: Oriol Riera, 15 goals in the A-League, 2017–18)
Youngest goalscorer: Alexander Badolato, 16 years, 260 days (against Broadmeadow Magic, FFA Cup, 10 November 2021)
Oldest goalscorer: Miloš Ninković, 38 years, 247 days (against Adelaide United, Australian Cup, 29 August 2023)
Top goalscorers
Competitive matches only. Numbers in brackets indicate appearances made.
a. Includes goals and appearances (including those as a substitute) in the FIFA Club World Cup.
International
This section refers to caps won while a Western Sydney Wanderers player.
First capped player: Aaron Mooy for Australia against Guam on 7 December 2012
Most capped player: Tomi Juric with 13 caps.
First player to play in the World Cup finals: Matthew Spiranovic, for Australia against Chile on 13 June 2014
Managerial records
First full-time manager: Tony Popovic managed the Western Sydney Wanderer |
https://en.wikipedia.org/wiki/Harder%E2%80%93Narasimhan%20stratification | In algebraic geometry and complex geometry, the Harder–Narasimhan stratification is any of a stratification of the moduli stack of principal G-bundles by locally closed substacks in terms of "loci of instabilities". In the original form due to Harder and Narasimhan, G was the general linear group; i.e., the moduli stack was the moduli stack of vector bundles, but, today, the term refers to any of generalizations. The scheme-theoretic version is due to Shatz and so the term "Shatz stratification" is also used synonymously. The general case is due to Behrend.
References
Further reading
Nitin Nitsure, Schematic Harder-Narasimhan Stratification
Algebraic geometry
Stratifications |
https://en.wikipedia.org/wiki/2014%20Fujieda%20MYFC%20season | The 2014 Fujieda MYFC season sees Fujieda MYFC compete in J. League Division 3 for the first team.
Players
First team squad
As of 13 February 2014
J3 League
League table
Results
Squad statistics
Appearances and goals
|}
Top scorers
Disciplinary record
References
Fujieda MYFC
Fujieda MYFC seasons |
https://en.wikipedia.org/wiki/Giovanni%20Battista%20Guccia | Giovanni Battista Guccia (21 October 1855 – 29 October 1914) was an Italian mathematician.
Biography
Guccia was born in Palermo in a rich and aristocratic family. He graduated in mathematics in 1880 at the University of Rome, where he was a student of Luigi Cremona. His doctoral thesis was presented at the Reims scientific congress and then published with the title "On a class of surfaces representable point by point on a plane" in the
"Comptes-rendus de l'Association française pour l'avancement des sciences". In 1887 the French journal Comptes Rendus published his article "Theorem on the singular points of an algebraic surface".
In 1889, having applied for a chair, he was appointed full professor of geometry at the University of Palermo, a position which he held for the rest of his life.
In 1884 he founded, personally contributing both financially and intellectually, the "Circolo Matematico di Palermo" (Mathematical Society of Palermo). The Circolo produced a journal called Rendiconti del Circolo di Palermo that attracted quality manuscripts from mathematicians. Michele Gebbia (1854-1929), Giovanni Maisano (1851-1929), Michele Luigi Albeggiani (1852-1943) and Francesco Paolo Paternò (1852-1927) were instrumental in assisting Guccia in bringing the Rendiconti to press.
Guccia was the Mathematical Society's director and essence until his death.
His scientific work consists of about 50 papers on algebraic geometry, in particular Cremona transformations, classification of curves and projective properties of curves.
Notes
External links
An Italian short biography of Giovanni Battista Guccia in Edizione Nazionale Mathematica Italiana online.
1855 births
1914 deaths
Algebraic geometers
19th-century Italian mathematicians
20th-century Italian mathematicians
Sapienza University of Rome
University of Palermo
Mathematicians from Sicily |
https://en.wikipedia.org/wiki/Directional%20symmetry | Directional symmetry may refer to:
Isotropy
Directional statistics
Directional symmetry (time series) |
https://en.wikipedia.org/wiki/Polar%20representation | In mathematics, polar representation may refer to:
Representations of points in the Euclidean plane via the polar coordinate system
Polar actions on Euclidean spaces |
https://en.wikipedia.org/wiki/Albert%20C.%20Reynolds | Dr. Albert C. Reynolds is McMan Chair Professor of Petroleum Engineering and Professor of Mathematics at the University of Tulsa, where he is the Director of the Tulsa University Petroleum Reservoir Exploitation Projects (TUPREP). He is known for his research in the areas of reservoir characterization, well testing and reservoir simulation.
Education
Reynolds received a BA degree from the University of New Hampshire in 1966, an MS degree from Case Institute of Technology in 1968, and a PhD degree from Case Western Reserve University in 1970, all in mathematics.
Career
Reynolds joined the faculty of the University of Tulsa in 1970. He has at various times filled the posts of Associate Graduate Dean, Associate Director of Research, and Chairman of the Department of Petroleum Engineering.
Reynolds received the 1983 SPE Distinguished Achievement Award for Petroleum Engineering Faculty, 2003 SPE Reservoir Description and Dynamics Award, and 2005 SPE Formation Evaluation Award. In 2013 he was presented with the John Franklin Carll Award. He has been a SPE Distinguished Member since 1999.
Current Research
Gradient-Based History Matching with Optimal Parameterization
Covariance Localization for Ensemble Kalman Filter
Iterative forms of EnKF and Ensemble Smoother
Combining Ensemble Kalman Filter and Markov Chain Monte Carlo
Ensemble Kalman Filter Method with KPCA and DCT Parameterization
Production Optimization Under Linear and Nonlinear Constraints
Derivative-Free Production Optimization Algorithms
Optimal Well Placement
Numerical Well Testing and History Matching Using Commercial Reservoir Simulators
Stochastic Optimization for Automatic History Matching
References
External links
Profile at the University of Tulsa
Google Scholar report
Year of birth missing (living people)
Living people
University of Tulsa faculty
University of New Hampshire alumni
Case Western Reserve University alumni |
https://en.wikipedia.org/wiki/Artin%E2%80%93Schreier%20curve | In mathematics, an Artin–Schreier curve is a plane curve defined over an algebraically closed field of characteristic by an equation
for some rational function over that field.
One of the most important examples of such curves is hyperelliptic curves in characteristic 2, whose Jacobian varieties have been suggested for use in cryptography. It is common to write these curves in the form
for some polynomials and .
Definition
More generally, an Artin-Schreier curve defined over an algebraically closed field of characteristic is a branched covering
of the projective line of degree . Such a cover is necessarily cyclic, that is, the Galois group of the corresponding algebraic function field extension is the cyclic group . In other words, is an Artin–Schreier extension.
The fundamental theorem of Artin–Schreier theory implies that such a curve defined over a field has an affine model
for some rational function that is not equal for for any other rational function . In other words, if we define polynomial , then we require that .
Ramification
Let be an Artin–Schreier curve.
Rational function over an algebraically closed field has partial fraction decomposition
for some finite set of elements of and corresponding non-constant polynomials defined over , and (possibly constant) polynomial .
After a change of coordinates, can be chosen so that the above polynomials have degrees coprime to , and the same either holds for or it is zero. If that is the case, we define
Then the set is precisely the set of branch points of the covering .
For example, Artin–Schreier curve , where is a polynomial, is ramified at a single point over the projective line.
Since the degree of the cover is a prime number, over each branching point lies a single ramification point with corresponding different (not to confused with the ramification index) equal to
Genus
Since does not divide , ramification indices are not divisible by either. Therefore, the Riemann–Roch theorem may be used to compute that the genus of an Artin–Schreier curve is given by
For example, for a hyperelliptic curve defined over a field of characteristic by equation with decomposed as above,
Generalizations
Artin–Schreier curves are a particular case of plane curves defined over an algebraically closed field of characteristic by an equation
for some separable polynomial and rational function . Mapping yields a covering map from the curve to the projective line . Separability of defining polynomial ensures separability of the corresponding function field extension . If , a change of variables can be found so that and . It has been shown that such curves can be built via a sequence of Artin-Schreier extension, that is, there exists a sequence of cyclic coverings of curves
each of degree , starting with the projective line.
See also
Artin–Schreier theory
Hyperelliptic curve
Superelliptic curve
References
Algebraic curves |
https://en.wikipedia.org/wiki/Transparency%20report | A transparency report is a statement issued semesterly or annually by a company or government, which discloses a variety of statistics related to requests for user data, records, or content. Transparency reports generally disclose how frequently and under what authority governments have requested or demanded data or records over a certain period of time. This form of corporate transparency allows the public to discern how much user information governments have requested through search warrants, court orders, emergency requests, subpoenas, etc. Additionally, companies report data related to requests for user information regarding national security matters, including national security letters and FISA Requests. In 2010, Google was the first company to release a transparency report, with Twitter following in 2012. Additional companies began releasing transparency reports in light of the Edward Snowden leaks in 2013, and the number of companies issuing them has increased rapidly ever since. Additionally, the United States Intelligence Community began releasing their Annual Statistical Transparency Report in 2013, in an attempt to raise public opinion following the leaks. Today, transparency reports are issued by a variety of technology and communications companies, including Google, Microsoft, Verizon, AT&T, Twitter, Apple, Dropbox, Facebook, Yahoo, Uber, Amazon, T-Mobile, Discord, Reddit, and CloudFlare. As of July 2021, 88 companies have provided transparency reports. Due to the optional nature of transparency reporting, some companies' transparency reports include information related to the government's involvement in copyright takedowns, while others do not. Critics claim that these descrepencies in various companies' reports results in confusion rather than clarification regarding government requesting and censorship practices, and many agree that systematic transparency reporting practices should be implemented across every company that receives requests for user information or takedown notices. Additionally, companies are required by the government to report the number of national security requests they received in bands of 500 or 1000 (0-499) (0-999). Several companies and advocacy groups have lobbied the U.S. government to change this policy and allow the exact number of national security requests to be released, and Twitter is raising this issue in the ongoing legal battle,Twitter v. Garland.
Purpose
Transparency reports are primarily provided to shed light on surveillance practices of government law enforcement in order to enable stakeholders to understand the operations of the company, to help identify areas where companies and organizations can improve policies and practices, and to serve as a tool for advocacy and public change. Access Now claims that transparency reports are "one of the strongest ways for technology companies to disclose threats to user privacy and free expression," and are tools vital to safeguard against abuses of |
https://en.wikipedia.org/wiki/Bogdan%20Suceav%C4%83 | Bogdan Suceavă (born September 27, 1969) is a Romanian-American mathematician and writer, working as professor of mathematics at California State University Fullerton. He is also a honorary research professor with the STAR-UBB Institute, Babeș-Bolyai University, Cluj-Napoca, Romania.
Biography
He was born in Curtea de Argeș, Romania. Growing up, Suceavă spent his holidays with his maternal grandparents at Nucșoara, a remote community that maintained its traditions, unbroken by the collectivisation elsewhere of Nicolae Ceaușescu's regime. There he absorbed Balkan folk-tales and myths, which would inform some of his literary works. Suceavă mentioned his maternal grandmother was a cousin of Elisabeta Rizea, a figure of the Romanian anti-communist resistance movement.
Suceavă went to school in Pitești, Găești, Târgoviște, and Bucharest, as his family moved several times. After the Romanian Revolution of 1989, he attended the University of Bucharest, where he obtained his undergraduate degree in mathematics and master's degree in mathematics, with a focus on geometry. He then moved to the United States to study at the Michigan State University for his doctorate. His thesis, titled New Riemannian and Kählerian Curvature Invariants and Strongly Minimal Submanifolds, was written under the supervision of Bang-Yen Chen.
Following his doctorate in 2002, Suceavă was hired by California State University, Fullerton. In the spring of 2023 Suceavă was presented at California State University, Fullerton with the L. Donald Shields Excellence in Scholarship and Creativity Award.
Career
Mathematics
At the age of 13, Suceavă won a prize at the Romanian National Mathematical Olympiad, following which he was encouraged to pursue mathematics as a viable career. During his undergraduate years he studied mathematical analysis with Solomon Marcus and Ion Colojoară, algebra with Constantin Vraciu and Constantin Niță, geometry with Adriana Turtoi, Stere Ianuș, and Liviu Nicolescu, among others. At Michigan State University he took courses with Selman Akbulut, Bang-Yen Chen, John D. McCarthy, Thomas Parker, Baisheng Yan, and others.
Since 2002, Suceavă is a Professor of Mathematics at California State University, Fullerton. He specialises in differential geometry, metric geometry, and the history of mathematics.
Suceavă is active in the encouragement of mathematical research among young students in California. He has established a mathematics circle involving undergraduates, and extensively published in gazettes of mathematical problems aimed at high school students.
His mathematical works appeared in Houston Journal of Mathematics, Taiwanese Journal of Mathematics, American Mathematical Monthly, Mathematical Intelligencer, Beiträge zur Algebra und Geometrie, Differential Geometry and Its Applications, Czechoslovak Mathematical Journal, Publicationes Mathematicae, Results in Mathematics, Tsukuba Journal of Mathematics, Notices of the American Mathematical Society, Co |
https://en.wikipedia.org/wiki/Bikash%20Bista | Bikash Bista (Nepali: बिकास बिस्ट; born 3 December 1965) is a Nepalese Economist and Statistician, and the former Director General of Central Bureau of Statistics of Nepal.
Biography
Early years
Bista was born in Palung VDC of Makwanpur District in Nepal to father Om Bahadur Bista and mother Durga Devi Bista. Graduating from Chitwan High School, he enrolled in Tribhuvan University to study Bachelor of Arts and later obtained a master's degree in Economics in 1988. After working in the Central of Bureau of Statistics for nearly 18 years, he became the Deputy Director General (DDG) of the bureau in 2007. He was appointed the Director General of the bureau in 2012.
Career
Bista started his early career as an officer of statistics for Central Bureau of Statistics. Later, he was involved in Social Statistics Division of the CBS as a Deputy Director General. The National Population and Housing Census 2011 was successfully conducted under his supervision as the bureau deputy. The census included major improvements compared to the previous censuses, introducing the geographical GPS Mapping of settlements for data collection that helped to reinforce the authenticity of the new census. In the past, CBS used to rely on political divisions for population census.
This census also became the first census in Nepal to recognize the country's third gender population.
In addition, he has worked on the socio-economic surveys' design and implementation and system of price statistics studies, conducting several surveys in the field, like the Nepal Living Standards Survey- 2010/11.
Personal life
Bista is married to Beenu Bista, who is a professor at Tribhuvan University. The couple has a son, Bivash, who is an Aerospace engineer working for a Lockheed Martin company.
References
1965 births
Living people
Tribhuvan University alumni
People from Makwanpur District
Nepalese economists |
https://en.wikipedia.org/wiki/Record%20value | In statistics, a record value or record statistic is the largest or smallest value obtained from a sequence of random variables. The theory is closely related to that used in order statistics.
The term was first introduced by K. N. Chandler in 1952.
See also
Ladder height process
MinHash
References
Further reading
Nonparametric statistics |
https://en.wikipedia.org/wiki/Ladder%20height%20process | In probability theory, the ladder height process is a record of the largest or smallest value a given stochastic process has achieved up to the specified point in time.
The Wiener-Hopf factorization gives the transition probability kernel in the discrete time case.
See also
Record value
References
Queueing theory |
https://en.wikipedia.org/wiki/Mircea%20Grosaru | Mircea Grosaru (June 30, 1952 – February 3, 2014) was a Romanian politician, MP (2000–2014), and lawyer.
Born in Buhuși, he was a 1974 graduate in mathematics and physics from the Pedagogical Institute of Bacău He earned a law degree from the University of Craiova in 2000. According to a member of Romania's Italian community, he attended meetings of its organization, initially identifying as an ethnic Romanian. He later claimed, without evidence, that his wife's grandfather was Italian. When asked about the subject in 2012, he initially dismissed the question as "lacking relevance", and initially hesitated when asked to explain his Italian ancestry. Later, he stated that his grandfather was an Italian, Lorenzo Masseri, who changed his surname into a Romanian one.
Grosaru belonged to the National Liberal Party until 2010. During his time in office, he helped establish an collaboration agreement between the Italian Association of Romania and the European Democratic Party, which is now being continued by his son, Andi-Gabriel Grosaru. However, in 2010, the Suceava County chapter expelled him for inactivity and for voting "against the interests of Romanians and right-wing principles".
Grosaru hired his wife Ioana to work in his parliamentary office, when from 2008 to 2011, she earned 66,745 lei. In 2013, the National Integrity Agency accused him of a conflict of interest. He was found guilty during a first trial, but died before proceedings were finished. In 2015, prosecutors alleged that Grosaru was promised a bribe from businessman Marian Vlasov, in exchange for promoting a law that would be to the latter's benefit. Reportedly, the bribe consisted of an arbiter's post within the Romanian affiliate of the Court of International Commercial Arbitration; Grosaru was named to this post in March 2013.
Grosaru died on February 3, 2014, at the age of 61 from cardiac arrest. The funeral was held at the Romanian Orthodox Mirăuți Church in Suceava. At the 2016 election, his son Andi Gabriel Grosaru was elected to the same seat.
References
1952 births
2014 deaths
People from Buhuși
University of Craiova alumni
Members of the Chamber of Deputies (Romania)
Romanian jurists
Romanian people of Italian descent
Romanian politicians of ethnic minority parties |
https://en.wikipedia.org/wiki/Graded%20%28mathematics%29 | In mathematics, the term "graded" has a number of meanings, mostly related:
In abstract algebra, it refers to a family of concepts:
An algebraic structure is said to be -graded for an index set if it has a gradation or grading, i.e. a decomposition into a direct sum of structures; the elements of are said to be "homogeneous of degree i ".
The index set is most commonly or , and may be required to have extra structure depending on the type of .
Grading by (i.e. ) is also important; see e.g. signed set (the -graded sets).
The trivial (- or -) gradation has for and a suitable trivial structure .
An algebraic structure is said to be doubly graded if the index set is a direct product of sets; the pairs may be called "bidegrees" (e.g. see Spectral sequence).
A -graded vector space or graded linear space is thus a vector space with a decomposition into a direct sum of spaces.
A graded linear map is a map between graded vector spaces respecting their gradations.
A graded ring is a ring that is a direct sum of additive abelian groups such that , with taken from some monoid, usually or , or semigroup (for a ring without identity).
The associated graded ring of a commutative ring with respect to a proper ideal is .
A graded module is left module over a graded ring that is a direct sum of modules satisfying .
The associated graded module of an -module with respect to a proper ideal is .
A differential graded module, differential graded -module or DG-module is a graded module with a differential making a chain complex, i.e. .
A graded algebra is an algebra over a ring that is graded as a ring; if is graded we also require .
The graded Leibniz rule for a map on a graded algebra specifies that .
A differential graded algebra, DG-algebra or DGAlgebra is a graded algebra that is a differential graded module whose differential obeys the graded Leibniz rule.
A homogeneous derivation on a graded algebra A is a homogeneous linear map of grade d = |D| on A such that acting on homogeneous elements of A.
A graded derivation is a sum of homogeneous derivations with the same .
A DGA is an augmented DG-algebra, or differential graded augmented algebra, (see Differential graded algebra).
A superalgebra is a -graded algebra.
A graded-commutative superalgebra satisfies the "supercommutative" law for homogeneous x,y, where represents the "parity" of , i.e. 0 or 1 depending on the component in which it lies.
CDGA may refer to the category of augmented differential graded commutative algebras.
A graded Lie algebra is a Lie algebra that is graded as a vector space by a gradation compatible with its Lie bracket.
A graded Lie superalgebra is a graded Lie algebra with the requirement for anticommutativity of its Lie bracket relaxed.
A supergraded Lie superalgebra is a graded Lie superalgebra with an additional super -gradation.
A differential graded Lie algebra is a graded vector space over a field of characteristic zero toge |
https://en.wikipedia.org/wiki/Sheila%20Bird | Sheila Macdonald Bird OBE FRSE FMedSci ( Gore; born 18 May 1952) is a Scottish biostatistician whose assessment of misuse of statistics in the British Medical Journal (BMJ) and BMJ series ‘Statistics in Question’ led to statistical guidelines for contributors to medical journals. Bird's doctoral work on non-proportional hazards in breast cancer found application in organ transplantation where beneficial matching was the basis for UK's allocation of cadaveric kidneys for a decade. Bird led the Medical Research Council (MRC) Biostatistical Initiative in support of AIDS/HIV studies in Scotland, as part of which Dr A. Graham Bird and she pioneered Willing Anonymous HIV Surveillance (WASH) studies in prisons. Her work with Cooper on UK dietary bovine spongiform encephalopathy (BSE) exposure revealed that the 1940–69 birth cohort was the most exposed and implied age-dependency in susceptibility to clinical vCJD progression from dietary BSE exposure since most vCJD cases were younger, born in 1970–89. Bird also designed the European Union's robust surveillance for transmissible spongiform encephalopathies in sheep which revolutionised the understanding of scrapie.
Record linkage studies in Scotland were central to Bird's work (with others) on the late sequelae of Hepatitis C virus infection and on the morbidity and mortality of opioid addiction. Her team first quantified the very high risk of drugs-related death in the fortnight after prison-release, in response to which Bird and Hutchinson proposed a prison-based randomized controlled trial of naloxone, the opioid antagonist, for prisoners-on-release who had a history of heroin injection. Bird introduced the Royal Statistical Society’s statistical seminars for journalists and awards for statistical excellence in journalism. She is the first female statistician to have been awarded four medals by the Royal Statistical Society (Guy bronze, 1989; Austin Bradford Hill, 2000; Chambers, 2010, Howard, 2015).
Early life and education
Bird was born in Inverness, Scotland on 18 May 1952 to Isabella Agnes Gordon (née Macdonald) and Herbert Gore. She was educated at Elgin Academy in Scotland, where the mathematics master, Lewis Grant, introduced her to statistics. She graduated with a joint-honours in mathematics and statistics from the University of Aberdeen. From 1974-1976 she was a research assistant in medical statistics at the University of Edinburgh where she, Jones and Rytter quantified the misuse of statistics in the BMJ. In his editorial, Stephen Lock "took on the chin" their 1977 paper and championed statistical guidelines for contributors to medical journals. Doctoral work followed, begun at the University of Edinburgh and supervised by Stuart Pocock, on the analysis of survival in breast cancer which Bird undertook part-time during a lectureship in statistics at the University of Aberdeen (1976–80) before joining the Medical Research Council's Biostatistics Unit in Cambridge in 1980.
Career
Bird |
https://en.wikipedia.org/wiki/Mutation%20%28algebra%29 | In the theory of algebras over a field, mutation is a construction of a new binary operation related to the multiplication of the algebra. In specific cases the resulting algebra may be referred to as a homotope or an isotope of the original.
Definitions
Let A be an algebra over a field F with multiplication (not assumed to be associative) denoted by juxtaposition. For an element a of A, define the left a-homotope to be the algebra with multiplication
Similarly define the left (a,b) mutation
Right homotope and mutation are defined analogously. Since the right (p,q) mutation of A is the left (−q, −p) mutation of the opposite algebra to A, it suffices to study left mutations.
If A is a unital algebra and a is invertible, we refer to the isotope by a.
Properties
If A is associative then so is any homotope of A, and any mutation of A is Lie-admissible.
If A is alternative then so is any homotope of A, and any mutation of A is Malcev-admissible.
Any isotope of a Hurwitz algebra is isomorphic to the original.
A homotope of a Bernstein algebra by an element of non-zero weight is again a Bernstein algebra.
Jordan algebras
A Jordan algebra is a commutative algebra satisfying the Jordan identity . The Jordan triple product is defined by
For y in A the mutation or homotope Ay is defined as the vector space A with multiplication
and if y is invertible this is referred to as an isotope. A homotope of a Jordan algebra is again a Jordan algebra: isotopy defines an equivalence relation. If y is nuclear then the isotope by y is isomorphic to the original.
References
Non-associative algebras |
https://en.wikipedia.org/wiki/Addison%20Alves | Addison Alves de Oliveira (born March 20, 1981) is a retired Brazilian footballer who played as a striker and is the current assistant manager of Bali United.
Career statistics
Club
References
External links
Profile at liga-indonesia.co.id
1981 births
Living people
Footballers from Brasília
Brazilian men's footballers
Men's association football forwards
Segunda División B players
Tercera División players
CD Huracán Z players
Cultural y Deportiva Leonesa players
Hércules CF players
FC Cartagena footballers
Burgos CF footballers
Coruxo FC players
Liga 1 (Indonesia) players
PSIS Semarang players
Persela Lamongan players
Persipura Jayapura players
Persija Jakarta players
Addison Alves
Addison Alves
Addison Alves
Brazilian expatriate men's footballers
Brazilian expatriate sportspeople in Spain
Brazilian expatriate sportspeople in Indonesia
Brazilian expatriate sportspeople in Thailand
Expatriate men's footballers in Spain
Expatriate men's footballers in Indonesia
Expatriate men's footballers in Thailand |
https://en.wikipedia.org/wiki/Generalized%20iterative%20scaling | In statistics, generalized iterative scaling (GIS) and improved iterative scaling (IIS) are two early algorithms used to fit log-linear models, notably multinomial logistic regression (MaxEnt) classifiers and extensions of it such as MaxEnt Markov models and conditional random fields. These algorithms have been largely surpassed by gradient-based methods such as L-BFGS and coordinate descent algorithms.
See also
Expectation-maximization
References
Optimization algorithms and methods
Log-linear models |
https://en.wikipedia.org/wiki/Cenk%20Ahmet%20Alk%C4%B1l%C4%B1%C3%A7 | Cenk Ahmet Alkılıç (born 9 December 1987) is a Turkish footballer who plays as a defender for Karşıyaka. He made his professional debut in 2006 with Beylerbeyi.
Career statistics
References
1987 births
People from Karşıyaka
Sportspeople from İzmir Province
Living people
Turkish men's footballers
Turkey men's B international footballers
Men's association football defenders
Galatasaray S.K. footballers
Beylerbeyi S.K. footballers
Altay S.K. footballers
Çaykur Rizespor footballers
Kayseri Erciyesspor footballers
İstanbul Başakşehir F.K. players
Alanyaspor footballers
Erzurumspor F.K. footballers
Eyüpspor footballers
Boluspor footballers
Karşıyaka S.K. footballers
Süper Lig players
TFF First League players
TFF Second League players
TFF Third League players |
https://en.wikipedia.org/wiki/Cyclic%20sieving | In combinatorial mathematics, cyclic sieving is a phenomenon by which evaluating a generating function for a finite set at roots of unity counts symmetry classes of objects acted on by a cyclic group.
Definition
Let C be a cyclic group generated by an element c of order n. Suppose C acts on a set X. Let X(q) be a polynomial with integer coefficients. Then the triple (X, X(q), C) is said to exhibit the cyclic sieving phenomenon (CSP) if for all integers d, the value X(e2id/n) is the number of elements fixed by cd. In particular X(1) is the cardinality of the set X, and for that reason X(q) is regarded as a generating function for X.
Examples
The q-binomial coefficient
is the polynomial in q defined by
It is easily seen that its value at q = 1 is the usual binomial coefficient , so it is a generating function for the subsets of {1, 2, ..., n} of size k. These subsets carry a natural action of the cyclic group C of order n which acts by adding 1 to each element of the set, modulo n. For example, when n = 4 and k = 2, the group orbits are
(of size 2)
and
(of size 4).
One can show that evaluating the q-binomial coefficient when q is an nth root of unity gives the number of subsets fixed by the corresponding group element.
In the example n = 4 and k = 2, the q-binomial coefficient is
evaluating this polynomial at q = 1 gives 6 (as all six subsets are fixed by the identity element of the group); evaluating it at q = −1 gives 2 (the subsets {1, 3} and {2, 4} are fixed by two applications of the group generator); and evaluating it at q = ±i gives 0 (no subsets are fixed by one or three applications of the group generator).
List of cyclic sieving phenomena
In the Reiner–Stanton–White paper, the following example is given:
Let α be a composition of n, and let W(α) be the set of all words of length n with αi letters equal to i. A descent of a word w is any index j such that . Define the major index on words as the sum of all descents.
The triple exhibit a cyclic sieving phenomenon, where is the set of non-crossing (1,2)-configurations of [n − 1].
Let λ be a rectangular partition of size n, and let X be the set of standard Young tableaux of shape λ. Let C = Z/nZ act on X via promotion. Then exhibit the cyclic sieving phenomenon. Note that the polynomial is a q-analogue of the hook length formula.
Furthermore, let λ be a rectangular partition of size n, and let X be the set of semi-standard Young tableaux of shape λ. Let C = Z/kZ act on X via k-promotion. Then exhibit the cyclic sieving phenomenon. Here, and sλ is the Schur polynomial.
An increasing tableau is a semi-standard Young tableau, where both rows and columns are strictly increasing, and the set of entries is of the form for some .
Let denote the set of increasing tableau with two rows of length n, and maximal entry . Then
exhibit the cyclic sieving phenomenon, where act via K-promotion.
Let be the set of permutations of cycle type λ and exactly j exceedan |
https://en.wikipedia.org/wiki/Marc%20Rieffel | Marc Aristide Rieffel is a mathematician noted for his fundamental contributions to C*-algebra and quantum group theory. He is currently a professor in the department of mathematics at the University of California, Berkeley.
In 2012, he was selected as one of the inaugural fellows of the American Mathematical Society.
Contributions
Rieffel earned his doctorate from Columbia University in 1963 under Richard Kadison with a dissertation entitled A Characterization of Commutative Group Algebras and Measure Algebras.
Rieffel introduced Morita equivalence as a fundamental notion in noncommutative geometry and as a tool for classifying C*-algebras. For example, in 1981 he showed that if Aθ denotes the noncommutative torus of angle θ, then Aθ and Aη are Morita equivalent if and only if θ and η lie in the same orbit of the action of SL(2, Z) on R by fractional linear transformations. More recently, Rieffel has introduced a noncommutative analogue of Gromov-Hausdorff convergence for compact metric spaces which is motivated by applications to string theory.
References
External links
Living people
20th-century American mathematicians
21st-century American mathematicians
Columbia Graduate School of Arts and Sciences alumni
Fellows of the American Mathematical Society
University of California, Berkeley faculty
1937 births |
https://en.wikipedia.org/wiki/Equivariant%20sheaf | In mathematics, given an action of a group scheme G on a scheme X over a base scheme S, an equivariant sheaf F on X is a sheaf of -modules together with the isomorphism of -modules
that satisfies the cocycle condition: writing m for multiplication,
.
Notes on the definition
On the stalk level, the cocycle condition says that the isomorphism is the same as the composition ; i.e., the associativity of the group action. The condition that the unit of the group acts as the identity is also a consequence: apply to both sides to get and so is the identity.
Note that is an additional data; it is "a lift" of the action of G on X to the sheaf F. Moreover, when G is a connected algebraic group, F an invertible sheaf and X is reduced, the cocycle condition is automatic: any isomorphism automatically satisfies the cocycle condition (this fact is noted at the end of the proof of Ch. 1, § 3., Proposition 1.5. of Mumford's "geometric invariant theory.")
If the action of G is free, then the notion of an equivariant sheaf simplifies to a sheaf on the quotient X/G, because of the descent along torsors.
By Yoneda's lemma, to give the structure of an equivariant sheaf to an -module F is the same as to give group homomorphisms for rings R over ,
.
There is also a definition of equivariant sheaves in terms of simplicial sheaves. Alternatively, one can define an equivariant sheaf to be an equivariant object in the category of, say, coherent sheaves.
Linearized line bundles
A structure of an equivariant sheaf on an invertible sheaf or a line bundle is also called a linearization.
Let X be a complete variety over an algebraically closed field acted by a connected reductive group G and L an invertible sheaf on it. If X is normal, then some tensor power of L is linearizable.
Also, if L is very ample and linearized, then there is a G-linear closed immersion from X to such that is linearized and the linearlization on L is induced by that of .
Tensor products and the inverses of linearized invertible sheaves are again linearized in the natural way. Thus, the isomorphism classes of the linearized invertible sheaves on a scheme X form an abelian group. There is a homomorphism to the Picard group of X which forgets the linearization; this homomorphism is neither injective nor surjective in general, and its kernel can be identified with the isomorphism classes of linearizations of the trivial line bundle.
See Example 2.16 of for an example of a variety for which most line bundles are not linearizable.
Dual action on sections of equivariant sheaves
Given an algebraic group G and a G-equivariant sheaf F on X over a field k, let be the space of global sections. It then admits the structure of a G-module; i.e., V is a linear representation of G as follows. Writing for the group action, for each g in G and v in V, let
where and is the isomorphism given by the equivariant-sheaf structure on F. The cocycle condition then ensures that is a group homo |
https://en.wikipedia.org/wiki/Quot%20scheme | In algebraic geometry, the Quot scheme is a scheme parametrizing sheaves on a projective scheme. More specifically, if X is a projective scheme over a Noetherian scheme S and if F is a coherent sheaf on X, then there is a scheme whose set of T-points is the set of isomorphism classes of the quotients of that are flat over T. The notion was introduced by Alexander Grothendieck.
It is typically used to construct another scheme parametrizing geometric objects that are of interest such as a Hilbert scheme. (In fact, taking F to be the structure sheaf gives a Hilbert scheme.)
Definition
For a scheme of finite type over a Noetherian base scheme , and a coherent sheaf , there is a functorsending towhere and under the projection . There is an equivalence relation given by if there is an isomorphism commuting with the two projections ; that is,is a commutative diagram for . Alternatively, there is an equivalent condition of holding . This is called the quot functor which has a natural stratification into a disjoint union of subfunctors, each of which is represented by a projective -scheme called the quot scheme associated to a Hilbert polynomial .
Hilbert polynomial
For a relatively very ample line bundle and any closed point there is a function sending
which is a polynomial for . This is called the Hilbert polynomial which gives a natural stratification of the quot functor. Again, for fixed there is a disjoint union of subfunctorswhereThe Hilbert polynomial is the Hilbert polynomial of for closed points . Note the Hilbert polynomial is independent of the choice of very ample line bundle .
Grothendieck's existence theorem
It is a theorem of Grothendieck's that the functors are all representable by projective schemes over .
Examples
Grassmannian
The Grassmannian of -planes in an -dimensional vector space has a universal quotientwhere is the -plane represented by . Since is locally free and at every point it represents a -plane, it has the constant Hilbert polynomial . This shows represents the quot functor
Projective space
As a special case, we can construct the project space as the quot schemefor a sheaf on an -scheme .
Hilbert scheme
The Hilbert scheme is a special example of the quot scheme. Notice a subscheme can be given as a projectionand a flat family of such projections parametrized by a scheme can be given bySince there is a hilbert polynomial associated to , denoted , there is an isomorphism of schemes
Example of a parameterization
If and for an algebraically closed field, then a non-zero section has vanishing locus with Hilbert polynomialThen, there is a surjectionwith kernel . Since was an arbitrary non-zero section, and the vanishing locus of for gives the same vanishing locus, the scheme gives a natural parameterization of all such sections. There is a sheaf on such that for any , there is an associated subscheme and surjection . This construction represents the quot functor
Quadrics in |
https://en.wikipedia.org/wiki/Tatsuya%20Ide | is a former Nippon Professional Baseball outfielder.
External links
Career statistics - NPB.jp
87 Tatsuya Ide PLAYERS2021 - Fukuoka SoftBank Hawks Official site
1971 births
Living people
Baseball people from Yamanashi Prefecture
Japanese baseball players
Nippon Professional Baseball outfielders
Nippon Ham Fighters players
Yomiuri Giants players
Fukuoka SoftBank Hawks players
Japanese baseball coaches
Nippon Professional Baseball coaches |
https://en.wikipedia.org/wiki/Eleanor%20Jones | Eleanor Green Dawley Jones (10 August 1929 - 1 March 2021) was an American mathematician. She was one of the first African-American women to achieve a Ph.D. in mathematics. Jones worked as a consultant for the development of college mathematics curriculums, and as a speaker at events to encourage women and minorities to pursue careers in science and mathematics.
Early life
Jones was born to George Herbert Green and Lillian Vaughn Green on August 10 of 1929 in Norfolk, Virginia. She was the second of six children, all of whom went on to earn, at minimum, a bachelor's degree. Jones attended Booker T. Washington High School, a segregated public school. Jones began her academic career early, after graduating as valedictorian of her high school in 1945 at the age of 15. She then attended Howard University with two scholarships, one from the university and one from the Pepsi-Cola Corporation. Jones was fortunate to be mentored by Elbert Frank Cox, the first African-American person to receive a Ph.D. in mathematics, as well as David Blackwell, another notable African-American mathematician. In addition to Jones majoring in mathematics, she minored in physics and education. She graduated cum laude from Howard University in 1949 and completed her master's degree the following year.
Career
After completing her master's degree, Jones went back to Booker T. Washington High School, this time to teach. In addition to her role as an educator, she developed a new curriculum for the high school's mathematics program. Jones wed Edward Dawley, Jr. in 1951 and took time off from teaching in 1953 to start a family. She returned to teaching in 1955, this time as a mathematics instructor at Hampton Institute (presently Hampton University), near Norfolk.
In 1957, when all-white public schools were integrated, the segregated public schools in Norfolk were closed. This left many African-American youth with no place to attend school, leading Jones to begin tutoring these students at Norfolk's First Baptist Church. Jones also became active in the civil rights movement, achieving the rank of vice chair in Virginia's branch of CORE (Congress for Racial Equality) from 1958 to 1960.
Following a divorce, Jones decided to pursue a doctorate, as Hampton Institute would only give tenure to instructors with doctorates. At the time, Virginia did not permit black students to pursue doctorates in the state, so Jones relocated with her two sons to Syracuse University in New York in 1962. She received a National Science Foundation fellowship in 1963 and began to work as a teaching assistant at Syracuse University. Jones received her doctorate in 1966.
As an associate professor, Jones returned to the Hampton Institute for the 1966–67 academic year, until she joined the Norfolk State University mathematics department in 1967. Jones continued to teach at NSU for more than 30 years, where she continued her education through summer postgraduate courses at New York State University in 1957 |
https://en.wikipedia.org/wiki/Margherita%20Piazzola%20Beloch | Margherita Beloch Piazzolla (12 July 1879, in Frascati – 28 September 1976, in Rome) was an Italian mathematician who worked in algebraic geometry, algebraic topology and photogrammetry.
Biography
Beloch was the daughter of the German historian Karl Julius Beloch, who taught ancient history for 50 years at Sapienza University of Rome, and American Bella Bailey.
Beloch studied mathematics at the Sapienza University of Rome and wrote her undergraduate thesis under the supervision of Guido Castelnuovo. She received her degree in 1908 with Laude and "dignità di stampa" which means that her work was worthy of publication, and in fact her thesis "Sulle trasformazioni birazionali nello spazio" (On Birational Transformations in Space) was published in the Annali di Matematica Pura ed Applicata.
Guido Castelnuovo was very impressed with her talent and offered her the position of assistant which Margherita took and held until 1919, when she moved to Pavia. In 1920 she moved to Palermo to work under Michele De Franchis, an important figure of the Italian school of algebraic geometry at the time.
In 1924, Beloch completed her "libera docenza" (a degree that at that time had to be obtained before one could become a professor), and three years later she became a full professor at the University of Ferrara
where she taught until her retirement (1955).
Piazzolla is Beloch's married surname.
Scientific work
Her main scientific interests were in algebraic geometry, algebraic topology and photogrammetry.
After her thesis, she worked on the classification of algebraic surfaces by studying the configurations of lines that could lie on surfaces. The next step was to study rational curves lying on surfaces and in this framework Beloch obtained the following important result: "Hyperelliptic surfaces of rank 2 are characterised by having 16 rational curves."
Beloch also made some contributions to the theory of skew algebraic curves. She continued working on topological properties of algebraic curves either planar or lying on ruled or cubic surfaces for most of her life, writing about a dozen papers on these subjects.
Around 1940 Beloch become more and more interested in photogrammetry and the application of mathematics, and in particular algebraic geometry, to it. She is also known for her contribution to the mathematics of paper folding: In particular she seems to have been the first to formalise an origami move which allows, when possible, to construct by paper folding the common tangents to two parabolas. As a consequence she showed how to extract cubic roots by paper folding, something that is impossible to do by ruler and compass. The move she used has been called the Beloch fold.
References
1879 births
1976 deaths
People from Frascati
Italian mathematicians
Women mathematicians |
https://en.wikipedia.org/wiki/Suslin%20homology | In mathematics, the Suslin homology is a homology theory attached to algebraic varieties. It was proposed by Suslin in 1987, and developed by . It is sometimes called singular homology as it is analogous to the singular homology of topological spaces.
By definition, given an abelian group A and a scheme X of finite type over a field k, the theory is given by
where C is a free graded abelian group whose degree n part is generated by integral subschemes of , where is an n-simplex, that are finite and surjective over .
References
Algebraic geometry |
https://en.wikipedia.org/wiki/Smooth%20topology | In algebraic geometry, the smooth topology is a certain Grothendieck topology, which is finer than étale topology. Its main use is to define the cohomology of an algebraic stack with coefficients in, say, the étale sheaf .
To understand the problem that motivates the notion, consider the classifying stack over . Then in the étale topology; i.e., just a point. However, we expect the "correct" cohomology ring of to be more like that of as the ring should classify line bundles. Thus, the cohomology of should be defined using smooth topology for formulae like Behrend's fixed point formula to hold.
Notes
References
Unfortunately this book uses the incorrect assertion that morphisms of algebraic stacks induce morphisms of lisse-étale topoi. Some of these errors were fixed by .
Algebraic geometry |
https://en.wikipedia.org/wiki/Bruno%20D%27Amore | Bruno D’Amore (Born in Bologna, 28 September 1946) is an Italian mathematician and author.
Education
He has degrees in mathematics, pedagogy, philosophy, and a postgraduate qualification in Elementary Mathematics from a higher point of view, all obtained at the University of Bologna (Italy). D'Amore also has a Ph.D. in mathematics education from the University “Constantine the Philosopher” of Nitra in Slovakia.
Career
Formerly professor in mathematics education at the University of Bologna, D'Amore currently holds seminars and supervises doctoral theses at the Universidad Distrital “Francisco José de Caldas” of Bogotá in Colombia. He also teaches postgraduate courses at other Colombian universities.
He is a member of many research groups in Italy (NRD of Bologna), Spain (GRADEM, Barcelona) and Colombia (MESCUD, Bogotá) as well as the editorial boards of numerous scientific research journals in many countries. He is also a member of the Scientific Committee of International Research Groups and International Conferences.
He is the author of two collections of stories, one of which won the “Arturo Loria 2003” literary prize from the municipality of Carpi, while the other won the “Il Ceppo 2003” literary prize from the municipality of Pistoia. He has also authored numerous publications. Since 1977 he has been a member of the Association International des Critiques d’Art. He has been the secretary of a Quadriennale d’arte in the Venetian Region, the director of a private art gallery in Bologna and a consultant at private and public art galleries in Italy.
In 1986 he founded the National Conference “Incontri con la Matematica” (Meetings with Mathematics) whose first edition was held in Bologna. From the month of November of the following year the conference "Meetings with math" has always done, and is held annually, during the same period, in Castel San Pietro Terme - Bologna. The event, which has collected over the years more than 20000 teachers participating, is currently headed by Professor D'Amore and by Professors Silvia Sbaragli and Martha Isabel Fandiño Pinilla (his wife).
Awards
D'Amore has been awarded various prizes for his studies and research, including “Lo Stilo d’Oro”, 2000 edition; a nomination at “Pianeta Galileo 2010”; a Ph.D. ad honorem in Social Sciences and Education from the University of Cyprus, at Nicosia, on 15 October 2013, for the international relevance of his research in mathematics education (ceremony in Cyprus, ceremony in Bogota); the “Premio a la Contribución Científica Internacional en Ciencia y Tecnología” from the University of Medellín, on 10 May 2013. He has also been awarded honorary citizenship of Castel San Pietro Terme (Bologna) on 27 September 1997, and honorary citizenship of Cerchio (L’Aquila) on 5 September 2005.
External links
Personal website
Incontri con la Matematica: Official Conference Website History of the Conference History of the Congress' Proceedings
Mathematics Education Research Group: NRD, |
https://en.wikipedia.org/wiki/Curling%20at%20the%202014%20Winter%20Olympics%20%E2%80%93%20Statistics | This is a statistical synopsis of the curling tournaments at the 2014 Winter Olympics.
A total of thirty-three curlers are Olympic veterans. Two female curlers from the inaugural Olympic curling event in Nagano in 1998 returned to the Olympics. Seven female curlers and one male curler who competed in Salt Lake City in 2002 have qualified again. Ten curlers from the Torino Olympics in 2006 are competing at these Olympics, and fifteen women and eighteen men who participated in the 2010 Vancouver Olympics have returned.
Percentages
In curling, each player is graded on their shots on a scale of zero to four. Their cumulative point total is then marked as a percentage out of the total points possible. This score is just for statistical purposes, and has nothing to do with the outcome of the game.
Men's tournament
Percentages by draw.
Leads
Seconds
Thirds
Fourths
Team totals
Women's tournament
Percentages by draw.
Leads
Seconds
Thirds
Fourths
Team totals
References
Men's statistics
Women's statistics
Statistics |
https://en.wikipedia.org/wiki/Indicator%20vector | In mathematics, the indicator vector or characteristic vector or incidence vector of a subset T of a set S is the vector such that if and if
If S is countable and its elements are numbered so that , then where if and if
To put it more simply, the indicator vector of T is a vector with one element for each element in S, with that element being one if the corresponding element of S is in T, and zero if it is not.
An indicator vector is a special (countable) case of an indicator function.
Example
If S is the set of natural numbers , and T is some subset of the natural numbers, then the indicator vector is naturally a single point in the Cantor space: that is, an infinite sequence of 1's and 0's, indicating membership, or lack thereof, in T. Such vectors commonly occur in the study of arithmetical hierarchy.
Notes
Basic concepts in set theory
Vectors (mathematics and physics) |
https://en.wikipedia.org/wiki/Stochastic%20Processes%20and%20Their%20Applications | Stochastic Processes and Their Applications is a monthly peer-reviewed scientific journal published by Elsevier for the Bernoulli Society for Mathematical Statistics and Probability. The editor-in-chief is Sylvie Méléard. The principal focus of this journal is theory and applications of stochastic processes. It was established in 1973.
Abstracting and indexing
The journal is abstracted and indexed in:
According to the Journal Citation Reports, Stochastic Processes and Their Applications has a 2020 impact factor of 1.467.
References
Probability journals
Elsevier academic journals
English-language journals
Monthly journals
Academic journals established in 1973 |
https://en.wikipedia.org/wiki/Lucky%20Pierre%20%28film%29 | Lucky Pierre (; also known as I'm Losing My Temper) is a 1974 French comedy film written and directed by Claude Zidi, starring Pierre Richard and Jane Birkin.
Plot
Pierre Durois is a mathematics teacher at an all-girls high school in Aix-en-Provence. He also works as a ghostwriter for his father the mayor, who is seeking re-election, and for his friend who works for a tabloid newspaper.
When Pierre's students sitch the contents of his folders as a joke, a speech for the mayor, an article on Jackie Logan, a famous Hollywood actress, and his students' papers all end up in the wrong hands.
Pierre finds himself on a film set trying to resolve the mix-up, and ends up spending the night at Jackie Logan's house. The tabloids catch wind, and the next day's headlines provoke dismay for the mayor and for Pierre's fiancée.
Cast
Notes
References
External links
1974 films
1974 comedy films
1970s French films
1970s French-language films
Films about actors
Films about educators
Films about tabloid journalism
Films directed by Claude Zidi
Films scored by Vladimir Cosma
Films set in Provence-Alpes-Côte d'Azur
Films shot at Victorine Studios
Films shot in Bouches-du-Rhône
French comedy films |
https://en.wikipedia.org/wiki/Groupoid%20object | In category theory, a branch of mathematics, a groupoid object is both a generalization of a groupoid which is built on richer structures than sets, and a generalization of a group objects when the multiplication is only partially defined.
Definition
A groupoid object in a category C admitting finite fiber products consists of a pair of objects together with five morphisms
satisfying the following groupoid axioms
where the are the two projections,
(associativity)
(unit)
(inverse) , , .
Examples
Group objects
A group object is a special case of a groupoid object, where and . One recovers therefore topological groups by taking the category of topological spaces, or Lie groups by taking the category of manifolds, etc.
Groupoids
A groupoid object in the category of sets is precisely a groupoid in the usual sense: a category in which every morphism is an isomorphism. Indeed, given such a category C, take U to be the set of all objects in C, R the set of all arrows in C, the five morphisms given by , , and . When the term "groupoid" can naturally refer to a groupoid object in some particular category in mind, the term groupoid set is used to refer to a groupoid object in the category of sets.
However, unlike in the previous example with Lie groups, a groupoid object in the category of manifolds is not necessarily a Lie groupoid, since the maps s and t fail to satisfy further requirements (they are not necessarily submersions).
Groupoid schemes
A groupoid S-scheme is a groupoid object in the category of schemes over some fixed base scheme S. If , then a groupoid scheme (where are necessarily the structure map) is the same as a group scheme. A groupoid scheme is also called an algebraic groupoid, to convey the idea it is a generalization of algebraic groups and their actions.
For example, suppose an algebraic group G acts from the right on a scheme U. Then take , s the projection, t the given action. This determines a groupoid scheme.
Constructions
Given a groupoid object (R, U), the equalizer of , if any, is a group object called the inertia group of the groupoid. The coequalizer of the same diagram, if any, is the quotient of the groupoid.
Each groupoid object in a category C (if any) may be thought of as a contravariant functor from C to the category of groupoids. This way, each groupoid object determines a prestack in groupoids. This prestack is not a stack but it can be stackified to yield a stack.
The main use of the notion is that it provides an atlas for a stack. More specifically, let be the category of -torsors. Then it is a category fibered in groupoids; in fact, (in a nice case), a Deligne–Mumford stack. Conversely, any DM stack is of this form.
See also
Simplicial scheme
Notes
References
Algebraic geometry
Scheme theory
Category theory |
https://en.wikipedia.org/wiki/Torsor%20%28algebraic%20geometry%29 | In algebraic geometry, a torsor or a principal bundle is an analogue of a principal bundle in algebraic topology. Because there are few open sets in Zariski topology, it is more common to consider torsors in étale topology or some other flat topologies. The notion also generalizes a Galois extension in abstract algebra. Though other notions of torsors are known in more general context (e.g. over stacks) this article will focus on torsors over schemes, the original setting where torsors have been thought for. The word torsor comes from the French torseur. They are indeed widely discussed, for instance, in Michel Demazure's and Pierre Gabriel's famous book Groupes algébriques, Tome I.
Definition
Let be a Grothendieck topology and a scheme. Moreover let be a group scheme over , a -torsor (or principal -bundle) over is the data of a scheme and a morphism with a -invariant action on that is locally trivial in i.e. there exists a covering in the sense that the base change is isomorphic to the trivial torsor
First remarks
A line bundle can be seen as a -torsor, and, more in general, a vector bundle can be seen as a -torsor, for some .
It is common to consider a torsor for not just a group scheme but more generally for a group sheaf (e.g., fppf group sheaf).
The category of torsors over a fixed base forms a stack. Conversely, a prestack can be stackified by taking the category of torsors (over the prestack).
Examples and basic properties
Examples
A -torsor on X is a principal -bundle on X.
If is a finite Galois extension, then is a -torsor (roughly because the Galois group acts simply transitively on the roots.) This fact is a basis for Galois descent. See integral extension for a generalization.
Remark: A G-torsor P over X is isomorphic to a trivial torsor if and only if is nonempty. (Proof: if there is an , then is an isomorphism.)
Let P be a G-torsor with a local trivialization in étale topology. A trivial torsor admits a section: thus, there are elements . Fixing such sections , we can write uniquely on with . Different choices of amount to 1-coboundaries in cohomology; that is, the define a cohomology class in the sheaf cohomology (more precisely Čech cohomology with sheaf coefficient) group . A trivial torsor corresponds to the identity element. Conversely, it is easy to see any class in defines a G-torsor on X, unique up to an isomorphism.
If G is a connected algebraic group over a finite field , then any G-bundle over is trivial. (Lang's theorem.)
The universal torsor of a scheme X and the fundamental group scheme
In this context torsors have to be taken in the fpqc topology. Let be a Dedekind scheme (e.g. the spectrum of a field) and a faithfully flat morphism, locally of finite type. Assume has a section . We say that has a fundamental group scheme if there exist a pro-finite and flat -torsor , called the universal torsor of , with a section such that for any finite -torsor with a section there i |
https://en.wikipedia.org/wiki/Manin%20conjecture | In mathematics, the Manin conjecture describes the conjectural distribution of rational points on an algebraic variety relative to a suitable height function. It was proposed by Yuri I. Manin and his collaborators in 1989 when they initiated a program with the aim of describing the distribution of rational points on suitable algebraic varieties.
Conjecture
Their main conjecture is as follows.
Let
be a Fano variety defined
over a number field ,
let
be a height function which is relative to the anticanonical divisor
and assume that
is Zariski dense in .
Then there exists
a non-empty Zariski open subset
such that the counting function
of -rational points of bounded height, defined by
for ,
satisfies
as
Here
is the rank of the Picard group of
and
is a positive constant which
later received a conjectural interpretation by Peyre.
Manin's conjecture has been decided for special families of varieties, but is still open in general.
References
Conjectures
Diophantine geometry
Unsolved problems in number theory |
https://en.wikipedia.org/wiki/Joe%20Busillo | Giuseppe Busillo (born May 13, 1970) is a former professional ice hockey player. Busillo represented Italy in the 1998 and 2006 Winter Olympics.
Career statistics
Regular season and playoffs
International
References
External links
1970 births
Living people
Canadian ice hockey left wingers
Eisbären Berlin players
HC Alleghe players
HC Varese players
Ice hockey people from Toronto
Ice hockey players at the 1998 Winter Olympics
Ice hockey players at the 2006 Winter Olympics
Kölner Haie players
Manchester Storm (1995–2002) players
Olympic ice hockey players for Italy
Oshawa Generals players
Sault Ste. Marie Greyhounds players
Schwenninger Wild Wings players
Canadian expatriate ice hockey players in England
Canadian expatriate ice hockey players in Italy
Canadian expatriate ice hockey players in Germany |
https://en.wikipedia.org/wiki/Marin%20%C4%8Cili%C4%87%20career%20statistics | This is a list of the main career statistics of Croatian professional tennis player Marin Čilić. To date, Čilić has won 20 ATP singles titles including one Grand Slam singles title at the 2014 US Open, one ATP Masters 1000 title at the 2016 Western & Southern Open and a record four titles at the PBZ Zagreb Indoors. Other highlights of Čilić's career thus far include finals at the 2017 Wimbledon Championships and 2018 Australian Open. Čilić achieved a career high singles ranking of World No. 3 on 29 January 2018.
Career achievements
In August 2008, Čilić reached his first career singles final at the Pilot Pen Tennis event in New Haven, where he defeated Mardy Fish in three sets to win his first ATP singles title. The following year, Čilić claimed the first of his four titles at the PBZ Zagreb Indoors with a straight sets victory over his compatriot Mario Ančić in the final before advancing to his first grand slam quarterfinal at the US Open after a straight sets win over then World No. 2 Andy Murray before losing to the eventual champion, Juan Martín del Potro in four sets after leading by a set and a break. However, Čilić avenged his defeat to Del Potro at the 2010 Australian Open, where he defeated the Argentine en route to his first grand slam semi-final where he lost to the eventual runner-up, Andy Murray despite winning the first set. By reaching this stage of the event, Čilić became the first Croatian to reach the Australian Open semi-finals and also entered the top ten of the ATP rankings for the first time in his career, thus becoming just the fourth player from his country to do so after his coach, Goran Ivanišević and his compatriots, Ivan Ljubičić and Mario Ančić.
Midway through 2012, Čilić claimed his first career singles titles on grass and clay respectively after a default over David Nalbandian in the final of the Queen's Club Championships and a straight sets victory over Marcel Granollers in the final of the ATP Studena Croatia Open before reaching his third grand slam quarterfinal at the US Open, where he lost to the eventual champion, Andy Murray after leading by a set and 5–1.
In July 2014, Čilić reached his first quarterfinal at the Wimbledon Championships, defeating 2010 runner-up Tomáš Berdych en route before losing in five sets to the top seed and eventual champion, Novak Djokovic. In September, Čilić recorded the third hundred singles win of his career by winning his first grand slam singles title at the US Open, defeating five-time champion, Roger Federer en route and fellow first time grand slam finalist, Kei Nishikori in the final. In doing so, he became the first Croatian player to win a major since his coach, Goran Ivanišević and the first player outside of the top ten to win the last grand slam of the year since Pete Sampras in 2002. Čilić also joined Juan Martín del Potro and Stanislas Wawrinka as the only players outside of the Big Four to have won a grand slam since 2005.
In 2016, Čilić won his first Masters |
https://en.wikipedia.org/wiki/2014%20Indonesia%20Super%20League%20statistics | This is a list of players' statistics for 2014 Indonesia Super League. It consists of lists of goal-scorers, hat-tricks, own goals, clean sheets and disciplines.
Scoring
First goal of the season: Lukas Mandowen for Persipura Jayapura against Persela Lamongan (1 February 2014)
Fastest goal of the season: 20 seconds - Lukas Mandowen for Persipura Jayapura against Persebaya ISL (Bhayangkara) (15 April 2014)
Last goal of the season:
Widest winning margin: 5 goals
Arema Cronus 5–0 Persik Kediri (6 February 2014)
Putra Samarinda 5–0 Perseru Serui (9 February 2014)
Arema Cronus 5–0 Gresik United (8 May 2014)
Persib Bandung 5-0 Persijap Jepara (August 19, 2014)
Highest scoring game: 7 goals
Persiba Bantul 2–5 Persipura Jayapura (2 May 2014)
Most goals scored in a match by a single team: 5 goals
Arema Cronus 5–0 Persik Kediri (6 February 2014)
Putra Samarinda 5–0 Perseru Serui (9 February 2014)
Mitra Kukar 5–1 Persela Lamongan (20 February 2014)
Persik Kediri 5–1 Sriwijaya (26 April 2014)
Persiba Bantul 2–5 Persipura Jayapura (2 May 2014)
Arema Cronus 5–0 Gresik United (8 May 2014)
Persib Bandung 5-0 Persijap Jepara (August 19, 2014)
Most goals scored in a match by a losing team: 2 goals
Gresik United 3–2 Persijap Jepara (6 February 2014)
Persita Tangerang 3–2 Gresik United (10 February 2014)
Perseru Serui 3–2 Persiba Balikpapan (23 February 2014)
Persib Bandung 3–2 Arema Cronus (13 April 2014)
Persiba Bantul 2–5 Persipura Jayapura (2 May 2014)
Sriwijaya 4–2 Barito Putera (4 May 2014)
Persiba Bantul 2–3 Persela Lamongan (2 June 2014)
Persita Tangerang 2–4 Semen Padang (7 June 2014)
Widest home winning margin: 5 goals
Arema Cronus 5–0 Persik Kediri (6 February 2014)
Putra Samarinda 5–0 Perseru Serui (9 February 2014)
Arema Cronus 5–0 Gresik United (8 May 2014)
Persib Bandung 5-0 Persijap Jepara (August 19, 2014)
Widest away winning margin: 4 goals
Persita Tangerang 0–4 Persija Jakarta (12 June 2014)
Most goals scored by a home team: 5 goals
Arema Cronus 5–0 Persik Kediri (6 February 2014)
Putra Samarinda 5–0 Perseru Serui (9 February 2014)
Mitra Kukar 5–1 Persela Lamongan (20 February 2014)
Persik Kediri 5–1 Sriwijaya (26 April 2014)
Arema Cronus 5–0 Gresik United (8 May 2014)
Persib Bandung 5-0 Persijap Jepara (August 19, 2014)
Most goals scored by an away team: 5 goals
Persiba Bantul 2–5 Persipura Jayapura (2 May 2014)
Team records
Longest winning run: 5
Arema Cronus
Longest unbeaten run: 16
Persipura Jayapura
Longest winless run: 9
Persijap Jepara
Longest losing run: 9
Persijap Jepara
Longest clean sheet run: 5
Arema Cronus
Top scorers
In Italic is previous club on first half season.
Own goals
Hat-tricks
4 Player scored 4 goals
5 Player scored 5 goals
Clean Sheets
A number of 45 goalkeepers had appeared representing 22 clubs this season.
Updated to games played on 7 August 2014.
Players
Clubs
Most clean sheets: 11
Arema Cronus
Fewest clean sheets: 0
Persiba Bantul
Discipline
Player
Most yellow cards: 6
Elvis Herawan (Persiram)
Gera |
https://en.wikipedia.org/wiki/Robust%20geometric%20computation | In mathematics, specifically in computational geometry, geometric nonrobustness is a problem wherein branching decisions in computational geometry algorithms are based on approximate numerical computations, leading to various forms of unreliability including ill-formed output and software failure through crashing or infinite loops.
For instance, algorithms for problems like the construction of a convex hull rely on testing whether certain "numerical predicates" have values that are positive, negative, or zero. If an inexact floating-point computation causes a value that is near zero to have a different sign than its exact value, the resulting inconsistencies can propagate through the algorithm causing it to produce output that is far from the correct output, or even to crash.
One method for avoiding this problem involves using integers rather than floating point numbers for all coordinates and other quantities represented by the algorithm, and determining the precision required for all calculations to avoid integer overflow conditions. For instance, two-dimensional convex hulls can be computed using predicates that test the sign of quadratic polynomials, and therefore may require twice as many bits of precision within these calculations as the input numbers. When integer arithmetic cannot be used (for instance, when the result of a calculation is an algebraic number rather than an integer or rational number), a second method is to use symbolic algebra to perform all computations with exactly represented algebraic numbers rather than numerical approximations to them. A third method, sometimes called a "floating point filter", is to compute numerical predicates first using an inexact method based on floating-point arithmetic, but to maintain bounds on how accurate the result is, and repeat the calculation using slower symbolic algebra methods or numerically with additional precision when these bounds do not separate the calculated value from zero.
References
Computational geometry |
https://en.wikipedia.org/wiki/Order-5%20tesseractic%20honeycomb | In the geometry of hyperbolic 4-space, the order-5 tesseractic honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {4,3,3,5}, it has five 8-cells (also known as tesseracts) around each face. Its dual is the order-4 120-cell honeycomb, {5,3,3,4}.
Related polytopes and honeycombs
It is related to the Euclidean 4-space (order-4) tesseractic honeycomb, {4,3,3,4}, and the 5-cube, {4,3,3,3} in Euclidean 5-space. The 5-cube can also be seen as an order-3 tesseractic honeycomb on the surface of a 4-sphere.
It is analogous to the order-5 cubic honeycomb {4,3,5} and order-5 square tiling {4,5}.
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry) |
https://en.wikipedia.org/wiki/Order-4%20120-cell%20honeycomb | In the geometry of hyperbolic 4-space, the order-4 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {5,3,3,4}, it has four 120-cells around each face. Its dual is the order-5 tesseractic honeycomb, {4,3,3,5}.
Related honeycombs
It is related to the (order-3) 120-cell honeycomb, and order-5 120-cell honeycomb.
It is analogous to the order-4 dodecahedral honeycomb and order-4 pentagonal tiling.
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry) |
https://en.wikipedia.org/wiki/Order-5%20120-cell%20honeycomb | In the geometry of hyperbolic 4-space, the order-5 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {5,3,3,5}, it has five 120-cells around each face. It is self-dual. It also has 600 120-cells around each vertex.
Related honeycombs
It is related to the (order-3) 120-cell honeycomb, and order-4 120-cell honeycomb. It is analogous to the order-5 dodecahedral honeycomb and order-5 pentagonal tiling.
Birectified order-5 120-cell honeycomb
The birectified order-5 120-cell honeycomb constructed by all rectified 600-cells, with octahedron and icosahedron cells, and triangle faces with a 5-5 duoprism vertex figure and has extended symmetry [[5,3,3,5]].
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry)
Self-dual tilings |
https://en.wikipedia.org/wiki/Cubic%20honeycomb%20honeycomb | In the geometry of hyperbolic 4-space, the cubic honeycomb honeycomb is one of two paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite facets, whose vertices exist on 3-horospheres and converge to a single ideal point at infinity. With Schläfli symbol {4,3,4,3}, it has three cubic honeycombs around each face, and with a {3,4,3} vertex figure. It is dual to the order-4 24-cell honeycomb.
Related honeycombs
It is related to the Euclidean 4-space 16-cell honeycomb, {3,3,4,3}, which also has a 24-cell vertex figure.
It is analogous to the paracompact tesseractic honeycomb honeycomb, {4,3,3,4,3}, in 5-dimensional hyperbolic space, square tiling honeycomb, {4,4,3}, in 3-dimensional hyperbolic space, and the order-3 apeirogonal tiling, {∞,3} of 2-dimensional hyperbolic space, each with hypercube honeycomb facets.
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry) |
https://en.wikipedia.org/wiki/Order-4%2024-cell%20honeycomb | In the geometry of hyperbolic 4-space, the order-4 24-cell honeycomb is one of two paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol {3,4,3,4}, it has four 24-cells around each face. It is dual to the cubic honeycomb honeycomb.
Related honeycombs
It is related to the regular Euclidean 4-space 24-cell honeycomb, {3,4,3,3}, with 24-cell facets.
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry) |
https://en.wikipedia.org/wiki/Juninho%20Potiguar | Jarlesson Inácio Júnior (born 22 February 1990), commonly known as Juninho Potiguar, is a Brazilian footballer who plays as a forward for Brazilian club Caxias.
Career statistics
Honours
Sheriff Tiraspol
Moldovan National Division (1): 2013–14
References
External links
Sheriff Tiraspol profile
1990 births
Living people
Brazilian men's footballers
Footballers from Natal, Rio Grande do Norte
Men's association football forwards
Sport Club do Recife players
América Futebol Clube (PE) players
Sport Club Corinthians Alagoano players
Associação Desportiva Recreativa e Cultural Icasa players
FC Sheriff Tiraspol players
Al Shabab Al Arabi Club (Dubai) players
Fortaleza Esporte Clube players
América Futebol Clube (RN) players
Clube de Regatas Brasil players
Boa Esporte Clube players
União Recreativa dos Trabalhadores players
Ferroviário Atlético Clube (CE) players
Sociedade Esportiva e Recreativa Caxias do Sul players
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série C players
Campeonato Pernambucano players
Moldovan Super Liga players
UAE Pro League players
Brazilian expatriate men's footballers
Expatriate men's footballers in Moldova
Brazilian expatriate sportspeople in Moldova
Expatriate men's footballers in the United Arab Emirates
Brazilian expatriate sportspeople in the United Arab Emirates |
https://en.wikipedia.org/wiki/Ravi%20Agarwal | Ravi P. Agarwal (born July 10, 1947) is an Indian mathematician, Ph.D. sciences, professor, professor & chairman, Department of Mathematics Texas A&M University-Kingsville, Kingsville, U.S. Agarwal is the author of over 1000 scientific papers as well as 30 monographs. He was previously a professor in the Department of Mathematical Sciences at Florida Institute of Technology.
Monographs and books
R.P. Agarwal, Boundary Value Problems for Higher Order Differential Equations, World Scientific, Singapore, Philadelphia, 1986, p. 307.
R.P. Agarwal and R.C. Gupta, Essentials of Ordinary Differential Equations, McGraw-Hill Book Co., Singapore, New York, 1991, p. 467.
R.P. Agarwal, Difference Equations and Inequalities : Theory, Methods and Applications, Marcel Dekker, Inc., New York, 1992, p. 777.
R.P. Agarwal and V. Lakshmikantham, Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations, World Scientific, Singapore, 1993, p. 312.
R.P. Agarwal and P.J.Y. Wong, Error Inequalities in Polynomial Interpolation and Their Applications, Kluwer Academic Publishers, Dordrecht, 1993, p. 365.
R.P. Agarwal and R.C. Gupta, Solutions Manual to Accompany Essentials of Ordinary Differential Equations, McGraw-Hill Book Co., Singapore, New York, 1993, p. 209.
R.P. Agarwal and P.Y.H. Pang, Opial Inequalities with Applications in Differential and Difference Equations, Kluwer Academic Publishers, Dordrecht, 1995, p. 393.
R.P. Agarwal and P.J.Y. Wong, Advanced Topics in Difference Equations, Kluwer Academic Publishers, Dordrecht, 1997, p. 507.
R.P. Agarwal, Focal Boundary Value Problems for Differential and Difference Equations, Kluwer Academic Publishers, Dordrecht, 1998, p. 289.
R.P. Agarwal, D. O’Regan and P.J.Y. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 1999, p. 417.
R.P. Agarwal, Difference Equations and Inequalities: Second Edition, Revised and Expended, Marcel Dekker, New York, 2000, xv+980pp.
R.P. Agarwal, M. Meehan and D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press, Cambridge, 2001, 170pp.
R.P. Agarwal, S.R. Grace and D. O’Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, 2000, 337pp.
R.P. Agarwal and D. O’Regan, Infinite Interval Problems for Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 2001, 341pp.
R.P. Agarwal, M. Meehan and D. O’Regan, Nonlinear Integral Equations and Inclusions, Nova Science Publishers, New York, 2001, 362pp.
R.P. Agarwal, S.R. Grace and D. O’Regan, Oscillation Theory for Second Order Linear, Half–linear, Superlinear and Sublinear Dynamic Equations, Kluwer Academic Publishers, The Netherlands, 2002, 672pp.
R.P. Agarwal, S.R. Grace and D. O’Regan, Oscillation Theory for Second Order Dynamic Equations, Taylor & Francis, U.K., 2003, 404pp.
R.P. Agarwal and D. O’Regan, Singular Differential and Integra |
https://en.wikipedia.org/wiki/Carl%20Benedicks | Carl Axel Fredrik Benedicks (27 May 1875 – 16 July 1958) was a Swedish physicist whose work included geology, mineralogy, chemistry, physics, astronomy and mathematics.
Biography
Carl Benedicks was born 27 May 1875 in Stockholm, Sweden to Edward Otto Benedicks and Sofia Elisabet Tholander. He married Cecilia af Geijerstam on 6 October 1899.
Benedicks was a professor at Stockholm's technical university, Director of the Institute of Metallography, and was the first to study the yttrium silicate thalenite. In 1926 Benedicks argued to the Nobel Physics Committee that Jean Baptiste Perrin should receive the Nobel Prize in Physics for his work, over 15 years prior, on Brownian motion, a debate which led to Perrin's eventual nomination and award. Benedicks was awarded a Carnegie Gold medal for his work on the cooling power of liquids, quenching velocities, and the constituents of troostite and austenite.
Benedicks was critical of the Copenhagen interpretation put forward by Niels Bohr and Werner Heisenberg, saying he thought they had resigned themselves to never observing the effects of individual atoms, and that their arguments were no more than that of any pessimist.
References
20th-century Swedish physicists
1875 births
1958 deaths
Academic staff of Stockholm University
Scientists from Stockholm
Members of the Royal Society of Sciences in Uppsala |
https://en.wikipedia.org/wiki/Le%20Hochet | Le Hochet is a village located in the Pamplemousses District of Mauritius. According to the Statistics Mauritius census in 2011, the population was 15,034.
See also
Districts of Mauritius
List of places in Mauritius
References
Pamplemousses District
Populated places in Mauritius |
https://en.wikipedia.org/wiki/Clarence%20Lemuel%20Elisha%20Moore | Clarence Lemuel Elisha Moore (12 May 1876, in Bainbridge, Ohio – 5 December 1931) was an American mathematics professor, specializing in algebraic geometry and Riemannian geometry. He is chiefly remembered for the memorial eponymous C. L. E. Moore instructorship at the Massachusetts Institute of Technology; this prestigious instructorship has produced many famous mathematicians, including three Fields medal winners: Paul Cohen, Daniel Quillen, and Curtis T. McMullen.
C. L. E. Moore received his B.Sc. from Ohio State University (1901) and then his A.M. (1902) and Ph.D. (1904) from Cornell University. His doctoral dissertation was entitled Classification of the surfaces of singularities of the quadratic spherical complex with Virgil Snyder as thesis advisor. Moore also studied geometry at the University of Göttingen, the University of Turin with Corrado Segre, and the University of Bonn with Eduard Study. In 1904, Moore joined the MIT mathematics department as an instructor and was successively promoted to assistant professor, associate professor, and full professor. In 1920 he was one of the founders of the MIT Journal of Mathematics and Physics. He remained at MIT until his death in 1931 following a surgical operation.
Selected publications
References
19th-century American mathematicians
20th-century American mathematicians
Ohio State University alumni
Cornell University alumni
Massachusetts Institute of Technology faculty
1876 births
1931 deaths
Mathematicians from Ohio
People from Bainbridge, Ross County, Ohio |
https://en.wikipedia.org/wiki/Football%20records%20and%20statistics%20in%20the%20Netherlands |
Most successful clubs by titles
League
Titles
Most League titles: 35 (27 professional era), Ajax
Most consecutive League titles: 4, joint record:
Professional era
PSV (1985/86, 86/87, 87/88, 88/89) and (2004/05, 05/06, 06/07, 07/08)
Ajax (2010/11, 11/12, 12/13, 13/14)
Amateur era
HVV Den Haag (1899/1900, 00/01, 01/02, 02/03)
Cup
Titles
Most Cup titles: 20, Ajax
Most consecutive Cup titles: 3, joint record:
Ajax (1969/70, 70/71, 71/72)
PSV (1987/88, 88/89, 89/90)
Records |
https://en.wikipedia.org/wiki/Artin%27s%20criterion | In mathematics, Artin's criteria are a collection of related necessary and sufficient conditions on deformation functors which prove the representability of these functors as either Algebraic spaces or as Algebraic stacks. In particular, these conditions are used in the construction of the moduli stack of elliptic curves and the construction of the moduli stack of pointed curves.
Notation and technical notes
Throughout this article, let be a scheme of finite-type over a field or an excellent DVR. will be a category fibered in groupoids, will be the groupoid lying over .
A stack is called limit preserving if it is compatible with filtered direct limits in , meaning given a filtered system there is an equivalence of categoriesAn element of is called an algebraic element if it is the henselization of an -algebra of finite type.
A limit preserving stack over is called an algebraic stack if
For any pair of elements the fiber product is represented as an algebraic space
There is a scheme locally of finite type, and an element which is smooth and surjective such that for any the induced map is smooth and surjective.
See also
Artin approximation theorem
Schlessinger's theorem
References
Deformation theory and algebraic stacks - overview of Artin's papers and related research
Algebraic geometry |
https://en.wikipedia.org/wiki/Tantalit | Tantalit LLC “TOB” (, Russian: “Танталит“) is an originally Ukrainian association with limited liability. According to the State Committee of Statistics of Ukraine, the association was founded by the Austrian company Euro East Beteiligungs GmbH from Vienna and a native of Donetsk named Pavlo Lytovchenko (born in 1980, aged 41-42).
The company legally owns of the former state property Mezhyhirya, the former residence of former President Viktor Yanukovych. This is because in the 2000s, former President Viktor Yuschenko agreed the transfer of 139.7 hectares of land at Mezhyhirya for a 49-year lease to the Tantalit company. Before the Revolution of Dignity, a share in the company was owned by the pro-Russian Ukrainian politician Andriy Klyuyev, who was close to former President Viktor Yanukovych. Before fleeing Ukraine, Klyuyev sold his share in Tantalit.
The company has been implicated as one of the holdings used by Yanukovych to embezzle funds, as well as act as a cover for full ownership of the Mezhyhirya property, of which its privatisation in 2007 was alleged as illegal by opposition activists.
According to rumours, one of the current owners is a resident of the United Arab Emirates. In 2018, a lawyer from the company arrived at Mezhyhirya to allege that the protestors occupying the complex were “thugs” and that on 22 February 2014 protestors broke into Mezhyhirya in what was a criminal action and that they were now illegally occupying it. Though legal paperwork was prepared, a lawsuit was never filed, reportedly because of Ukrainian popular support for those occupying the complex.
Company ownership
The share capital of the company in 2010 consisted of ₴146,629,000 (over $18,320,000). About 0.03% or ₴44,000 was a capital of Lytovchenko, while 99.97% or ₴146,585,000 - part of the Euro East Beteiligungs (see :de:Beteiligung (Strafrecht)). On September 3, 2013 Serhiy Klyuyev bought Tantalit for $18.25 mln.
Pavlo Lytovchenko
Pavlo Lytovchenko, beside founding Talantit, also established another company Edelweiss, LLC (), shareholders of which are a son of Viktor Yanukovych, Oleksandr and a Donetsk lawyer Andriy Fedoruk.
Pavlo Lytovchenko is also a shareholder of another company Aqualine Plus, LLC () sharing its ownership with company Capital Building Corporation.
Pavlo Lytovchenko is also a trustee for Viktor Viktorovych Yanukovych, a son of the President of Ukraine Viktor Yanukovych, according to the 2010 declaration of income of Viktor Viktorovych Yanukovych.
Euro East Beteiligungs
Director of the company is Johann Wanovits who works as a stockbroker in the Euro Invest Bank AG who owns 65% of the Euro East Beteiligungs. The other 35% of Beteiligings belong to another company "BLYTHE (Europa) Ltd" (London), director of which is Reinhard Proksch who also is a director of yet another company Astute Partners Ltd.
In April 2013 Johann Wanovits was jailed for the next five years when he was found guilty of manipulating Telekom Austria's share |
https://en.wikipedia.org/wiki/Simona%20Halep%20career%20statistics | This is a list of the main career statistics of professional Romanian tennis player Simona Halep.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current after the 2022 US Open.
Doubles
This table is current through the 2022 Australian Open.
Grand Slam tournament finals
Singles: 5 (2 titles, 3 runner-ups)
Other significant finals
WTA Tour Championships finals
Singles: 1 (1 runner-up)
WTA 1000 finals
Singles: 18 (9 titles, 9 runner-ups)
Doubles: 1 (1 runner-up)
WTA career finals
Singles: 42 (24 titles, 18 runner-ups)
Doubles: 2 (1 title, 1 runner-up)
ITF Circuit finals
Singles: 8 (6 titles, 2 runner–ups)
Doubles: 4 (4 titles)
WTA Tour career earnings
Current after the 2022 US Open.
Career Grand Slam statistics
Grand Slam tournament seedings
The tournaments won by Halep are in boldface, and advanced into finals by Halep are in italics.
Best Grand Slam tournament results details
Grand Slam winners are in boldface, and runner–ups are in italics.
Record against other players
Record against top 10 players
Halep's record against players who have been ranked in the top 10. Active players are in boldface:
Record against No. 11–20 players
Halep's record against players who have been ranked world No. 11–20. Active ones are in boldface.
Anastasia Pavlyuchenkova 8–0
Kirsten Flipkens 6–0
Barbora Strýcová 6–1
Anastasija Sevastova 6–3
Alison Riske 4–0
Sabine Lisicki 4–1
Elise Mertens 4–2
Magdaléna Rybáriková 4–2
Alisa Kleybanova 3–0
Donna Vekić 3–0
Jennifer Brady 3–0
Beatriz Haddad Maia 3–1
Daria Gavrilova 3–1
Petra Martić 3–1
Ekaterina Alexandrova 3–2
Eleni Daniilidou 2–0
Mihaela Buzărnescu 2–0
Varvara Lepchenko 2–0
Wang Qiang 2–0
Kaia Kanepi 2–1
Klára Koukalová 2–1
Yanina Wickmayer 2–3
Alizé Cornet 2–4
Ana Konjuh 1–0
Anne Kremer 1–0
Karolína Muchová 1–0
Peng Shuai 1–0
Elena Vesnina 1–1
María José Martínez Sánchez 1–1
Tamarine Tanasugarn 1–1
Markéta Vondroušová 1–2
Anabel Medina Garrigues 1–4
Aravane Rezaï 0–1
Elena Bovina 0–1
Karolina Šprem 0–1
Sybille Bammer 0–1
Virginie Razzano 0–1
Mirjana Lučić-Baroni 0–2
* Statistics correct .
No. 1 wins
Top 10 wins
Double bagel matches (6–0, 6–0)
Longest winning streaks
17 match win streak (2020)
See also
2018 Simona Halep tennis season
2019 Simona Halep tennis season
Notes
References
External links
Simona Halep
Halep, Simona |
https://en.wikipedia.org/wiki/Order-7%20dodecahedral%20honeycomb | In the geometry of hyperbolic 3-space, the order-7 dodecahedral honeycomb a regular space-filling tessellation (or honeycomb).
Geometry
With Schläfli symbol {5,3,7}, it has seven dodecahedra {5,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many dodecahedra existing around each vertex in an order-7 triangular tiling vertex arrangement.
Related polytopes and honeycombs
It a part of a sequence of regular polytopes and honeycombs with dodecahedral cells, {5,3,p}.
It a part of a sequence of honeycombs {5,p,7}.
It a part of a sequence of honeycombs {p,3,7}.
Order-8 dodecahedral honeycomb
In the geometry of hyperbolic 3-space, the order-8 dodecahedral honeycomb a regular space-filling tessellation (or honeycomb). With Schläfli symbol {5,3,8}, it has eight dodecahedra {5,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many dodecahedra existing around each vertex in an order-8 triangular tiling vertex arrangement.
It has a second construction as a uniform honeycomb, Schläfli symbol {5,(3,4,3)}, Coxeter diagram, , with alternating types or colors of dodecahedral cells.
Infinite-order dodecahedral honeycomb
In the geometry of hyperbolic 3-space, the infinite-order dodecahedral honeycomb a regular space-filling tessellation (or honeycomb). With Schläfli symbol {5,3,∞}. It has infinitely many dodecahedra {5,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many dodecahedra existing around each vertex in an infinite-order triangular tiling vertex arrangement.
It has a second construction as a uniform honeycomb, Schläfli symbol {5,(3,∞,3)}, Coxeter diagram, , with alternating types or colors of dodecahedral cells.
See also
Convex uniform honeycombs in hyperbolic space
List of regular polytopes
Infinite-order hexagonal tiling honeycomb
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
The Beauty of Geometry: Twelve Essays (1999), Dover Publications, , (Chapter 10, Regular Honeycombs in Hyperbolic Space) Table III
Jeffrey R. Weeks The Shape of Space, 2nd edition (Chapters 16–17: Geometries on Three-manifolds I,II)
George Maxwell, Sphere Packings and Hyperbolic Reflection Groups, JOURNAL OF ALGEBRA 79,78-97 (1982)
Hao Chen, Jean-Philippe Labbé, Lorentzian Coxeter groups and Boyd-Maxwell ball packings, (2013)
Visualizing Hyperbolic Honeycombs arXiv:1511.02851 Roice Nelson, Henry Segerman (2015)
External links
John Baez, Visual insights: {7,3,3} Honeycomb (2014/08/01) {7,3,3} Honeycomb Meets Plane at Infinity (2014/08/14)
Danny Calegari, Kleinian, a tool for visualizing Kleinian groups, Geometry and the Imagination 4 March 2014.
{5,3,∞} Honeycomb in H^3 YouTube rotation of Poincare sphere
Honeycombs (geometry)
Infinite-order tilings |
https://en.wikipedia.org/wiki/Small%20stellated%20120-cell%20honeycomb | In the geometry of hyperbolic 4-space, the small stellated 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {5/2,5,3,3}, it has three small stellated 120-cells around each face. It is dual to the pentagrammic-order 600-cell honeycomb.
It can be seen as a stellation of the 120-cell honeycomb, and is thus analogous to the three-dimensional small stellated dodecahedron {5/2,5} and four-dimensional small stellated 120-cell {5/2,5,3}. It has density 5.
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry)
5-polytopes |
https://en.wikipedia.org/wiki/Pentagrammic-order%20600-cell%20honeycomb | In the geometry of hyperbolic 4-space, the pentagrammic-order 600-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {3,3,5,5/2}, it has five 600-cells around each face in a pentagrammic arrangement. It is dual to the small stellated 120-cell honeycomb. It can be considered the higher-dimensional analogue of the 4-dimensional icosahedral 120-cell and the 3-dimensional great dodecahedron. It is related to the order-5 icosahedral 120-cell honeycomb and great 120-cell honeycomb: the icosahedral 120-cells and great 120-cells in each honeycomb are replaced by the 600-cells that are their convex hulls, thus forming the pentagrammic-order 600-cell honeycomb.
This honeycomb can also be constructed by taking the order-5 5-cell honeycomb and replacing clusters of 600 5-cells meeting at a vertex with 600-cells. Each 5-cell belongs to five such clusters, and thus the pentagrammic-order 600-cell honeycomb has density 5.
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry)
5-polytopes |
https://en.wikipedia.org/wiki/Order-5%20icosahedral%20120-cell%20honeycomb | In the geometry of hyperbolic 4-space, the order-5 icosahedral 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {3,5,5/2,5}, it has five icosahedral 120-cells around each face. It is dual to the great 120-cell honeycomb.
It can be constructed by replacing the great dodecahedral cells of the great 120-cell honeycomb with their icosahedral convex hulls, thus replacing the great 120-cells with icosahedral 120-cells. It is thus analogous to the four-dimensional icosahedral 120-cell. It has density 10.
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry)
5-polytopes |
https://en.wikipedia.org/wiki/Great%20120-cell%20honeycomb | In the geometry of hyperbolic 4-space, the great 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {5,5/2,5,3}, it has three great 120-cells around each face. It is dual to the order-5 icosahedral 120-cell honeycomb.
It can be seen as a greatening of the 120-cell honeycomb, and is thus analogous to the three-dimensional great dodecahedron {5,5/2} and four-dimensional great 120-cell {5,5/2,5}. It has density 10.
See also
List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)
Honeycombs (geometry)
5-polytopes |
https://en.wikipedia.org/wiki/List%20of%20Newcastle%20Jets%20FC%20records%20and%20statistics | Newcastle Jets Football Club is an Australian professional association football club based in Newcastle, New South Wales. The club was formed in 2000 as Newcastle United before being renamed as Newcastle Jets in 2005. After spending their first four seasons participating in the National Soccer League, Newcastle became the first of three New South Wales members admitted to the A-League Men along with the Central Coast Mariners and Sydney FC.
The list encompasses the honours won by the Newcastle Jets at national and friendly level, records set by the club, their managers and their players. The player records section itemises the club's leading goalscorers and those who have made most appearances in first-team competitions.
Newcastle have won one top-flight title. The club's record appearance maker is Jason Hoffman, who has currently made 218 appearances from 2008 to the present day. Joel Griffiths is Newcastle Jets' record goalscorer, scoring 61 goals in total.
All figures are correct as of the match played on 27 January 2023.
Honours and achievements
Domestic
National Soccer League (until 2004) and A-League Men Premiership
Runners-up (1): 2001–02
National Soccer League (until 2004) and A-League Men Championship
Winners (1): 2007–08
Runners-up (1): 2017–18
Other
Pre-season
Surf City Cup
Runners-up (1): 2019
Player records
Appearances
Most league appearances: Jason Hoffman, 200
Most Australia Cup appearances: Jason Hoffman, 8
Youngest first-team player: Archie Goodwin, 16 years, 106 days (against Melbourne Victory, A-League, 21 February 2021)
Oldest first-team player: Wes Hoolahan, 37 years, 308 days (against Melbourne City, A-League, 23 March 2020)
Most consecutive appearances: Steven Ugarkovic, 113 (from 13 February 2017 — 27 March 2021)
Most appearances
Competitive matches only, includes appearances as substitute. Numbers in brackets indicate goals scored.
a. Includes the National Soccer League and A-League Men.
b. Includes the A-League Pre-Season Challenge Cup and Australia Cup
c. Includes goals and appearances (including those as a substitute) in the 2005 Australian Club World Championship Qualifying Tournament.
Goalscorers
First goalscorer: Anthony Surjan (against Eastern Pride, National Soccer League, 14 October 2000)
First A-League Men goalscorer: Ante Milicic (against Central Coast Mariners, 4 September 2005)
First hat-trick scorer: Joel Griffiths (against Northern Spirit, National Soccer League, 4 October 2002)
First A-League Men hat-trick scorer: Ante Milicic (against New Zealand Knights, A-League, 4 November 2005)
Youngest goalscorer: Archie Goodwin, 16 years, 151 days (against Melbourne City, A-League, 10 June 2021)
Oldest goalscorer: Wes Hoolahan, 37 years, 93 days (against Edgeworth, FFA Cup, 21 August 2019)
Top goalscorers
Competitive matches only. Numbers in brackets indicate appearances made.
a. Includes the National Soccer League and A-League Men.
b. Includes the A-League Pre-Season Challenge Cup |
https://en.wikipedia.org/wiki/Karen%20E.%20Smith | Karen Ellen Smith (born 1965 in Red Bank, New Jersey) is an American mathematician, specializing in commutative algebra and algebraic geometry. She completed her bachelor's degree in mathematics at Princeton University before earning her PhD in mathematics at the University of Michigan in 1993. Currently she is the Keeler Professor of Mathematics at the University of Michigan. In addition to being a researcher in algebraic geometry and commutative algebra, Smith with others wrote the textbook An Invitation to Algebraic Geometry.
Biography
Smith graduated in 1987 with a bachelor's degree in mathematics from Princeton University, where she was influenced in her freshman year by Charles Fefferman. She was a high school mathematics teacher in the academic year 1987/1988. In 1988 she became a graduate student at the University of Michigan, where in 1993 she earned her PhD with thesis Tight closure of parameter ideals and f-rationality under the supervision of Melvin Hochster. In the academic year 1993–1994 she was a postdoc at Purdue University working with Craig Huneke. In 1994 she became a C.L.E. Moore Instructor and then an associate professor at MIT. Since 1997 she has been a professor at the University of Michigan.
In 1991 she married the Finnish mathematician Juha Heinonen. He died in 2007.
Honors
In 2001 Smith won the Ruth Lyttle Satter Prize in Mathematics for her development of tight closure methods, introduced by Hochster and Huneke, in commutative algebra and her application of these methods in algebraic geometry. The prize committee specifically cited her papers "Tight closure of parameter ideals" (Inventiones Mathematicae 1994), "F-rational rings have rational singularities" (American J. Math. 1997, and, with Gennady Lyubeznik, "Weak and strong F-regularity are equivalent in graded rings" (American J. Math., 1999).
In addition to the Satter Prize, Smith was the recipient of a 1997 Sloan Research Fellowship, a Fulbright award, and a University of Michigan Faculty Recognition Award for outstanding contributions as a teacher, scholar and member of the University community.
Smith was selected to give the 2015 Earle Raymond Hedrick Lectures at the Mathematical Association of America's MathFest. Smith was chosen to give the Association for Women in Mathematics-American Mathematical Society 2016 Noether Lecture at the Joint Mathematics Meetings.
In 2015 she was elected as a fellow of the American Mathematical Society "for contributions to commutative algebra and algebraic geometry." She was named MSRI Clay Senior Scholar for 2012-2013. In 2019, she was elected to the National Academy of Sciences. The Association for Women in Mathematics has included her in the 2020 class of AWM Fellows for "her tireless support of women in mathematics; throughout her career, she has officially and unofficially mentored numerous female mathematicians at every level from undergraduate to full professor; she continues to be an incredibly strong role model f |
https://en.wikipedia.org/wiki/Patrik%20Blomberg | Patrick Blomberg (born 27 January 1994) is a Swedish professional ice hockey player. He is currently playing for HC Vita Hästen in HockeyAllsvenskan.
Career statistics
External links
1994 births
Living people
Borås HC players
Malmö Redhawks players
Swedish ice hockey left wingers
Timrå IK players
Tyringe SoSS players
VIK Västerås HK players
Ice hockey people from Stockholm |
https://en.wikipedia.org/wiki/Deductive%20lambda%20calculus | Deductive lambda calculus considers what happens when lambda terms are regarded as mathematical expressions. One interpretation of the untyped lambda calculus is as a programming language where evaluation proceeds by performing reductions on an expression until it is in normal form. In this interpretation, if the expression never reduces to normal form then the program never terminates, and the value is undefined. Considered as a mathematical deductive system, each reduction would not alter the value of the expression. The expression would equal the reduction of the expression.
History
Alonzo Church invented the lambda calculus in the 1930s, originally to provide a new and simpler basis for mathematics. However soon after inventing it major logic problems were identified with the definition of the lambda abstraction: The Kleene–Rosser paradox is an implementation of Richard's paradox in the lambda calculus. Haskell Curry found that the key step in this paradox could be used to implement the simpler Curry's paradox. The existence of these paradoxes meant that the lambda calculus could not be both consistent and complete as a deductive system.
Haskell Curry studied of illative (deductive) combinatory logic in 1941. Combinatory logic is closely related to lambda calculus, and the same paradoxes exist in each.
Later the lambda calculus was resurrected as a definition of a programming language.
Introduction
Lambda calculus is the model and inspiration for the development of functional programming languages. These languages implement the lambda abstraction, and use it in conjunction with application of functions, and types.
The use of lambda abstractions, which are then embedded into other mathematical systems, and used as a deductive system, leads to a number of problems, such as Curry's paradox. The problems are related to the definition of the lambda abstraction and the definition and use of functions as the basic type in lambda calculus. This article describes these problems and how they arise.
This is not a criticism of pure lambda calculus, and lambda calculus as a pure system is not the primary topic here. The problems arise with the interaction of lambda calculus with other mathematical systems. Being aware of the problems allows them to be avoided in some cases.
Terminology
For this discussion, the lambda abstraction is added as an extra operator in mathematics. The usual domains, such as Boolean and real will be available. Mathematical equality will be applied to these domains. The purpose is to see what problems arise from this definition.
Function application will be represented using the lambda calculus syntax. So multiplication will be represented by a dot. Also, for some examples, the let expression will be used.
The following table summarizes;
Interpretation of lambda calculus as mathematics
In the mathematical interpretation, lambda terms represent values. Eta and beta reductions are deductive steps that do no |
https://en.wikipedia.org/wiki/List%20of%20Perth%20Glory%20FC%20records%20and%20statistics | Perth Glory Football Club is an Australian professional association football club based in East Perth, Perth. The club was formed in 1995 and has played at its current home ground, Perth Oval, since its inception. The club played its first competitive match in the first round of the 1996–97 National Soccer League, in October 1996. Perth is one of the three National Soccer League clubs from the 2003–04 season that were implemented into the A-League Men for the inaugural 2005–06 season, and has since participated in every A-League Men season.
The list encompasses the honours won by Perth Glory, records set by the club, their managers and their players. The player records section itemises the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Perth Glory players on the international stage, and the highest transfer fees paid and received by the club. Attendance records at Lord Street, the Perth Oval, the club's home ground since 1996, and other temporary home grounds, such as Arena Joondalup in 2003, are also included.
Perth Glory have won six top-flight titles. The club's record appearance maker is Jamie Harnwell, who made 269 appearances between 1998 and 2011. Bobby Despotovski is Perth Glory's record goalscorer, scoring 116 goals in total.
All figures are correct as of 2 January 2023.
Honours and achievements
Domestic
National Soccer League (until 2004) and A-League Men Premiership
Winners (4): 1999–2000, 2001–02, 2003–04, 2018–19
Runners-up (1): 2002–03
National Soccer League (until 2004) and A-League Men Championship
Winners (2): 2002–03, 2003–04
Runners-up (4): 1999–2000, 2001–02, 2011–12, 2018–19
Australia Cup
Runners-up (2): 2014, 2015
A-League Pre-Season Challenge Cup
Runners-up (2): 2005, 2007
Player records
Appearances
Most league appearances: Jamie Harnwell, 256
Youngest first-team player: Daniel De Silva, 15 years, 361 days (against Sydney FC, A-League Men, 2 March 2013)
Oldest first-team player: Ante Covic, 40 years, 309 days (against Melbourne City, A-League Men Finals, 17 April 2016)
Most consecutive appearances: Danny Vukovic, 80 (from 9 October 2011 to 22 February 2014)
Most appearances
Competitive matches only, includes appearances as substitute. Numbers in brackets indicate goals scored.
a. Includes the National Soccer League and A-League Men.
b. Includes the A-League Pre-Season Challenge Cup and Australia Cup
c. Includes goals and appearances (including those as a substitute) in the 2005 Australian Club World Championship Qualifying Tournament.
Goalscorers
Most goals in a season: Damian Mori, 24 (in the 2002–03 season)
Most league goals in a season: Damian Mori, 24 (in the 2002–03 season)
Youngest goalscorer: Daniel De Silva, 17 years, 237 days (against Melbourne Victory, Australia Cup, 29 October 2014)
Oldest goalscorer: Diego Castro, 38 years, 325 days (against Macarthur FC, A-League Men, 23 May 2021)
Top goalsco |
https://en.wikipedia.org/wiki/List%20of%20road%20traffic%20accidents%20deaths%20in%20the%20Republic%20of%20Ireland%20by%20year | Official road traffic accident statistics in the Republic of Ireland are compiled by the Road Safety Authority (RSA) using data supplied by the Garda Síochána (police). While related data is collected by other organisations, including the National Roads Authority, local authorities, and the Health Service Executive, these are not factored into RSA statistics.
Footnotes
References
Sources
Citations
Road traffic accidents by year
Ireland, Republic |
https://en.wikipedia.org/wiki/Rational%20arrival%20process | In queueing theory, a discipline within the mathematical theory of probability, a rational arrival process (RAP) is a mathematical model for the time between job arrivals to a system. It extends the concept of a Markov arrival process, allowing for dependent matrix-exponential distributed inter-arrival times.
The processes were first characterised by Asmussen and Bladt and are referred to as rational arrival processes because the inter-arrival times have a rational Laplace–Stieltjes transform.
Software
Q-MAM a MATLAB toolbox which can solve queueing systems with RAP arrivals.
References
Queueing theory |
https://en.wikipedia.org/wiki/Matrix-exponential%20distribution | In probability theory, the matrix-exponential distribution is an absolutely continuous distribution with rational Laplace–Stieltjes transform. They were first introduced by David Cox in 1955 as distributions with rational Laplace–Stieltjes transforms.
The probability density function is (and 0 when x < 0), and the cumulative distribution function is where 1 is a vector of 1s and
There are no restrictions on the parameters α, T, s other than that they correspond to a probability distribution. There is no straightforward way to ascertain if a particular set of parameters form such a distribution. The dimension of the matrix T is the order of the matrix-exponential representation.
The distribution is a generalisation of the phase-type distribution.
Moments
If X has a matrix-exponential distribution then the kth moment is given by
Fitting
Matrix exponential distributions can be fitted using maximum likelihood estimation.
Software
BuTools a MATLAB and Mathematica script for fitting matrix-exponential distributions to three specified moments.
See also
Rational arrival process
References
Continuous distributions |
https://en.wikipedia.org/wiki/Mongolian%20Canadians | Mongolian Canadians are Canadian citizens who are descended from migrants from Mongolia. According to the 2021 Census by Statistics Canada, there were 9,090 Canadians who claimed full or partial Mongolian ancestry.
Canada Mongolia Chamber of Commerce, established by Mongolian Canadians, helps to connect business and people between the two countries.
See also
Canada–Mongolia relations
Asian Canadians
East Asian Canadians
References
Asian Canadian
Canada
East Asian Canadian |
https://en.wikipedia.org/wiki/Rees%20matrix%20semigroup | In mathematics, the Rees matrix semigroups are a special class of semigroups introduced by David Rees in 1940. They are of fundamental importance in semigroup theory because they are used to classify certain classes of simple semigroups.
Definition
Let S be a semigroup, I and Λ non-empty sets and P a matrix indexed by I and Λ with entries pi,λ taken from S.
Then the Rees matrix semigroup M(S; I, Λ; P) is the set I×S×Λ together with the multiplication
(i, s, λ)(j, t, μ) = (i, spλ,j t, μ).
Rees matrix semigroups are an important technique for building new semigroups out of old ones.
Rees' theorem
In his 1940 paper Rees proved the following theorem characterising completely simple semigroups:
That is, every completely simple semigroup is isomorphic to a semigroup of the form M(G; I, Λ; P) for some group G. Moreover, Rees proved that if G is a group and G0 is the semigroup obtained from G by attaching a zero element, then M(G0; I, Λ; P) is a regular semigroup if and only if every row and column of the matrix P contains an element that is not 0. If such an M(G0; I, Λ; P) is regular, then it is also completely 0-simple.
See also
Semigroup
Completely simple semigroup
David Rees (mathematician)
References
.
.
Semigroup theory |
https://en.wikipedia.org/wiki/Basic%20theorems%20in%20algebraic%20K-theory | In mathematics, there are several theorems basic to algebraic K-theory.
Throughout, for simplicity, we assume when an exact category is a subcategory of another exact category, we mean it is strictly full subcategory (i.e., isomorphism-closed.)
Theorems
The localization theorem generalizes the localization theorem for abelian categories.
Let be exact categories. Then C is said to be cofinal in D if (i) it is closed under extension in D and if (ii) for each object M in D there is an N in D such that is in C. The prototypical example is when C is the category of free modules and D is the category of projective modules.
See also
Fundamental theorem of algebraic K-theory
References
Ross E. Staffeldt, On Fundamental Theorems of Algebraic K-Theory
GABE ANGELINI-KNOLL, FUNDAMENTAL THEOREMS OF ALGEBRAIC K-THEORY
Tom Harris, Algebraic proofs of some fundamental theorems in algebraic K-theory
Algebraic K-theory
Theorems in algebraic topology |
https://en.wikipedia.org/wiki/Christian%20Genest | Christian Genest (; born January 11, 1957, in Chicoutimi, Quebec) is a professor in the Department of Mathematics and Statistics at McGill University (Montréal, Canada), where he holds a Canada Research Chair. He is the author of numerous research papers in multivariate analysis, nonparametric statistics, extreme-value theory, and multiple-criteria decision analysis.
He is a recipient of the Statistical Society of Canada's Gold Medal for Research and was elected a Fellow of the Royal Society of Canada in 2015.
Contributions
Genest is best known for developing models and statistical inference techniques for studying the dependence between variables through the concept of copula. He has designed, among others, various techniques for selecting, estimating and validating copula-based models through rank-based methods. His methodological contributions in multivariate analysis and extreme-value theory found numerous practical applications in finance, insurance, and hydrology.
Throughout his career, Genest also made significant contributions to the development of techniques for the reconciliation and use of expert opinions and pairwise comparison methods used to establish priorities in multiple-criteria decision analysis. He is the author or co-author of over 250 scientific publications, about half of which appeared in peer-reviewed journals. Part of his work is also concerned with the history of statistics and scientometrics. Christian Genest has given over 300 invited talks, including 75+ presentations for a general audience.
Birthplace and education
Christian Genest was born on January 11, 1957, in Chicoutimi (Québec, Canada). He was trained as a mathematician at the Université du Québec à Chicoutimi (B.Sp.Sc., 1977) and at the Université de Montréal (M.Sc., 1978) before completing graduate studies in statistics at the University of British Columbia (Ph.D., 1983). His thesis, entitled "Towards a Consensus of Opinion", was written under the supervision of James V. Zidek and earned him the Pierre Robillard Award from the Statistical Society of Canada (SSC) in 1984.
Academic career
After completing his PhD, Christian Genest was a postdoctoral fellow and visiting assistant professor at Carnegie Mellon University (Pittsburgh, Pennsylvania) in 1983–84. From 1984 to 1987, he was an assistant professor in the Department of Statistics and Actuarial Science at the University of Waterloo (Waterloo, ON). He was then hired by Université Laval (Québec, QC), where he was promoted to the ranks of associate in 1989 and professor in 1993. He joined McGill University (Montréal, QC) in 2010, where he holds a Canada Research Chair in Stochastic Dependence Modeling.
Honors and prizes
Christian Genest was the first recipient of the CRM-SSC Prize in 1999. He received the SUMMA Research Award from Université Laval the same year. In 2011, the Statistical Society of Canada awarded him its most prestigious distinction, the gold medal, "in recognition of his remarkable |
https://en.wikipedia.org/wiki/Cotriple%20homology | In algebra, given a category C with a cotriple, the n-th cotriple homology of an object X in C with coefficients in a functor E is the n-th homotopy group of the E of the augmented simplicial object induced from X by the cotriple. The term "homology" is because in the abelian case, by the Dold–Kan correspondence, the homotopy groups are the homology of the corresponding chain complex.
Example: Let N be a left module over a ring R and let . Let F be the left adjoint of the forgetful functor from the category of rings to Set; i.e., free module functor. Then defines a cotriple and the n-th cotriple homology of is the n-th left derived functor of E evaluated at M; i.e., .
Example (algebraic K-theory): Let us write GL for the functor . As before, defines a cotriple on the category of rings with F free ring functor and U forgetful. For a ring R, one has:
where on the left is the n-th K-group of R. This example is an instance of nonabelian homological algebra.
Notes
References
Further reading
Who Threw a Free Algebra in My Free Algebra?, a blog post.
Adjoint functors
Category theory
Homotopy theory |
https://en.wikipedia.org/wiki/Ernst%20Huth | Ernst Huth (27 December 1845, Potsdam – 5 August 1897) was a German naturalist and botanist.
He studied mathematics and natural sciences in Berlin, later working as a secondary school teacher in Frankfurt an der Oder. Beginning in 1883 he published the Monatliche Mittheilungen des Naturwissenschaftlichen Vereins Regierungsbezirkes Frankfurt, in which he was the author of numerous scientific articles.
He is known for his treatment of the botanical family Ranunculaceae, of which he was the taxonomic author of many species, especially plants within the genus Delphinium. In 1908 August Brand named the genus Huthia (synonym Cantua, family Polemoniaceae) in his honor.
Selected works
Ueber Geokarpe, Amphikarpe, und Heterokarpe Pflanzen, 1890 - On geocarp, amphicarp and heterocarp.
Monographie der Gattung Caltha, 1891 - Monograph on the genus Caltha.
Flora von Frankfurt a.Oder und Umgegend, 1895 - Flora of Frankfurt an der Oder and surrounding areas.
Monographie Der Gattung Delphinium, 1895 - Monograph on the genus Delphinium.
References
1845 births
1897 deaths
Scientists from Potsdam
German naturalists
19th-century German botanists
People involved with the periodic table |
https://en.wikipedia.org/wiki/Statistical%20and%20Applied%20Mathematical%20Sciences%20Institute | Statistical and Applied Mathematical Sciences Institute (SAMSI) is an applied mathematics and statistics research organization based in Research Triangle Park, North Carolina. It is funded by the National Science Foundation, and is partnered with Duke University, North Carolina State University, the University of North Carolina at Chapel Hill, and the National Institute of Statistical Sciences.
SAMSI was founded in 2002. In 2012, the National Science Foundation renewed SAMSI's funding for an additional five years. SAMSI is offering programs in bioinformatics and statistical ecology in 2014–15.
SAMSI closed its doors in August of 2021, after 19 years of work.
References
National Science Foundation mathematical sciences institutes
2002 establishments in North Carolina |
https://en.wikipedia.org/wiki/Saud%20Al-Farsi | Saud Khamis Al-Farsi (; born 3 April 1993), commonly known as Saud Al-Farsi, is an Omani footballer who plays for Al-Oruba SC.
Club career statistics
International career
Saud is part of the first team squad of the Oman national football team. He was selected for the national team for the first time in 2014. He made his first appearance for Oman on 25 December 2013 against Bahrain in the 2014 WAFF Championship. He has made an appearance in the 2014 WAFF Championship.
Honours
Sur
Oman Professional League Cup: 2007
References
External links
Saud Al Farsi at Goalzz.com
Saud Al Farsi at Kooora.com
1993 births
Living people
People from Sur, Oman
Omani men's footballers
Oman men's international footballers
Men's association football midfielders
Sur SC players
Oman Professional League players
Footballers at the 2014 Asian Games
Asian Games competitors for Oman |
https://en.wikipedia.org/wiki/Rudolf%20Fueter | Karl Rudolf Fueter (30 June 1880 – 9 August 1950) was a Swiss mathematician, known for his work on number theory.
Biography
After a year of graduate study of mathematics in Basel, Fueter began study in 1899 at the University of Göttingen and completed his Promotion in 1903 with dissertation Der Klassenkörper der quadratischen Körper und die komplexe Multiplikation under David Hilbert. After his Promotion, Fueter studied for 1 year in Paris, 3 months in Vienna, and 6 months in London. In 1905 he completed his Habilitierung at the University of Marburg. Fueter worked as a docent in 1907/1908 at Marburg and in the winter of 1907/1908 at the Bergakademie Clausthal. He was called to positions as professor ordinarius in 1908 at Basel, in 1913 at the Technische Hochschule Karlsruhe, and in 1916 at the University of Zurich. From 1920 to 1922 he was the rector of the University of Zurich.
Fueter did research on algebraic number theory and quaternion analysis proposing a definition of ‘regular’ for quaternionic functions similar to the definition of holomorphic function by means of an analogue of the Cauchy-Riemann equations. He also published a proof of the Fueter–Pólya theorem with George Pólya.
In 1910 he was one of the founders of the Swiss Mathematical Society and he became its first president. With Andreas Speiser he was instrumental in the editing and publication of the collected works of Leonhard Euler and from 1927 he was the head of the Euler Commission. He gave plenary lectures at the International Congress of Mathematicians in 1932 at Zurich (Idealtheorie und Funktionentheorie) and in 1936 at Oslo (Die Theorie der regulären Funktionen einer Quaternionenvariablen). During WWII he was a colonel of artillery in the Swiss army, an outspoken opponent of German National Socialism, and an advocate for freedom of the press. Fueter was an editor for the Commentarii Mathematici Helvetici.
Fueter married in 1908 and had a daughter.
Selected works
Synthetische Zahlentheorie. 3rd edition DeGruyter, Berlin 1930 (1st edition 1917).
Vorlesungen über die singulären Moduln und die komplexe Multiplikation der elliptischen Funktionen. Teubner, Leipzig 1924/1927
142 pages 1924.
pp. 144–358. 1927.
Das mathematische Werkzeug des Chemikers, Biologen, Statistikers und Soziologen. Vorlesung über die höheren mathematischen Begriffe in Verbindung mit ihren Anwendungen (publ. Schweizerische Mathematische Gesellschaft; vol. 3). 3rd edition Orell Füssli, Zürich 1947 (1st edition 1926).
Der Klassenkörper der quadratischen Körper und die complexe Multiplication. Dieterich, Göttingen 1903 (Dissertation, Universität Göttingen 1903).
Die Theorie der Zahlenstrahlen. Reimer, Berlin 1905 (Habilitationsschrift, University of Marburg 1905).
Sources
Siegfried Gottwald, Hans-Joachim Ilgauds, Karl-Heinz Schlote (eds.): Lexikon bedeutender Mathematiker. Verlag Deutsch, Thun 1990, .
References
External links
1880 births
1950 deaths
20th-century Swiss mathematicians
Number theor |
https://en.wikipedia.org/wiki/Esteban%20Sachetti | Esteban Fernando Sachetti (born 21 November 1985) is an Argentine footballer who plays as a defensive midfielder for Alki Oroklini.
Career statistics
External links
1985 births
Living people
Argentine men's footballers
Argentine expatriate men's footballers
Men's association football midfielders
Tercera División players
Sevilla FC C players
CD San Fernando players
Cypriot First Division players
Cypriot Second Division players
Doxa Katokopias FC players
AEL Limassol players
Apollon Limassol FC players
Alki Oroklini players
Argentine expatriate sportspeople in Spain
Argentine expatriate sportspeople in Cyprus
Expatriate men's footballers in Spain
Expatriate men's footballers in Cyprus
Footballers from Tucumán Province |
https://en.wikipedia.org/wiki/Cosheaf | In topology, a branch of mathematics, a cosheaf with values in an ∞-category C that admits colimits is a functor F from the category of open subsets of a topological space X (more precisely its nerve) to C such that
(1) The F of the empty set is the initial object.
(2) For any increasing sequence of open subsets with union U, the canonical map is an equivalence.
(3) is the pushout of and .
The basic example is where on the right is the singular chain complex of U with coefficients in an abelian group A.
Example: If f is a continuous map, then is a cosheaf.
See also
sheaf (mathematics)
Notes
References
Algebraic topology
Category theory
Sheaf theory |
https://en.wikipedia.org/wiki/Order-7%20heptagrammic%20tiling | In geometry, the order-7 heptagrammic tiling is a tiling of the hyperbolic plane by overlapping heptagrams.
Description
This tiling is a regular star-tiling, and has Schläfli symbol of {7/2,7}. The heptagrams forming the tiling are of type {7/2}, . The overlapping heptagrams subdivide the hyperbolic plane into isosceles triangles, 14 of which form each heptagram.
Each point of the hyperbolic plane that does not lie on a heptagram edge belongs to the central heptagon of one heptagram, and is in one of the points of exactly one other heptagram. The winding number of each heptagram around its points is one, and the winding number around the central heptagon is two, so adding these two numbers together, each point of the plane is surrounded three times; that is, the density of the tiling is 3.
In the Euclidean plane, a heptagram of type {7/2} would have angles of 3/7 at its vertices, but in the hyperbolic plane heptagrams can have the sharper vertex angle 2/7 that is needed to make exactly seven other heptagrams meet up at the center of each heptagram of the tiling.
Related tilings
It has the same vertex arrangement as the regular order-7 triangular tiling, {3,7}. The full set of edges coincide with the edges of a heptakis heptagonal tiling. The valance 6 vertices in this tiling are false-vertices in the heptagrammic one caused by crossed edges.
It is related to a Kepler-Poinsot polyhedron, the small stellated dodecahedron, {5/2,5}, which is polyhedron and a density-3 regular star-tiling on the sphere:
References
John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
See also
External links
Hyperbolic tilings
Isogonal tilings
Isohedral tilings
Regular tilings
Heptagrammic tilings
Order-7 tilings |
https://en.wikipedia.org/wiki/Heptagrammic-order%20heptagonal%20tiling | In geometry, the heptagrammic-order heptagonal tiling is a regular star-tiling of the hyperbolic plane. It has Schläfli symbol of {7,7/2}. The vertex figure heptagrams are {7/2}, . The heptagonal faces overlap with density 3.
Related tilings
It has the same vertex arrangement as the regular order-7 triangular tiling, {3,7}. The full set of edges coincide with the edges of a heptakis heptagonal tiling.
It is related to a Kepler-Poinsot polyhedron, the great dodecahedron, {5,5/2}, which is polyhedron and a density-3 regular star-tiling on the sphere (resembling a regular icosahedron in this state, similarly to this tessellation resembling the order-7 triangular tiling):
References
John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
External links
Heptagonal tilings
Hyperbolic tilings
Isogonal tilings
Isohedral tilings
Regular tilings
Heptagrammic-order tilings |
https://en.wikipedia.org/wiki/Littlewood%27s%20Tauberian%20theorem | In mathematics, Littlewood's Tauberian theorem is a strengthening of Tauber's theorem introduced by .
Statement
Littlewood showed the following: If an = O(1/n ), and as x ↑ 1 we have
then
Hardy and Littlewood later showed that the hypothesis on an could be weakened to the "one-sided" condition an ≥ –C/n for some constant C. However in some sense the condition is optimal: Littlewood showed that if cn is any unbounded sequence then there is a series with |an| ≤ |cn|/n which is divergent but Abel summable.
History
described his discovery of the proof of his Tauberian theorem. Alfred Tauber's original theorem was similar to Littlewood's, but with the stronger hypothesis that an=o(1/n). Hardy had proved a similar theorem for Cesàro summation with the weaker hypothesis an=O(1/n), and suggested to Littlewood that the same weaker hypothesis might also be enough for Tauber's theorem. In spite of the fact that the hypothesis in Littlewood's theorem seems only slightly weaker than the hypothesis in Tauber's theorem, Littlewood's proof was far harder than Tauber's, though Jovan Karamata later found an easier proof.
Littlewood's theorem follows from the later Hardy–Littlewood Tauberian theorem, which is in turn a special case of Wiener's Tauberian theorem, which itself is a special case of various abstract Tauberian theorems about Banach algebras.
Examples
References
Tauberian theorems |
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