text:
Six of the Best

Six of the Best was a reunion concert between the rock band Genesis, their original lead singer Peter Gabriel and former guitarist Steve Hackett. It took place on a wet Saturday, 2 October 1982, at the National Bowl in Milton Keynes, Buckinghamshire, England. Genesis were introduced on to the stage by Jonathan King, who discovered and christened the band fifteen years earlier. The support bands were John Martyn, The Blues Band and Talk Talk.

Background
The classic Genesis quintet of Peter Gabriel, Mike Rutherford, Tony Banks, Steve Hackett and Phil Collins became a quartet when lead vocalist Gabriel left Genesis at the end of The Lamb Lies Down on Broadway tour in 1975. After a lengthy search for a new lead singer, the band decided that Collins could take on the role while remaining the band's drummer. For touring, they needed an additional drummer to play while Collins sang. Ex-Yes and King Crimson drummer Bill Bruford joined for their 1976 tour before Chester Thompson took on the role for all future live dates. Lead guitarist Hackett's departure in 1977 made Genesis the trio they remained. In 1978, Daryl Stuermer was recruited as a touring guitarist and bassist on live shows.

Peter Gabriel pursued a successful solo career, releasing four albums between 1977 and 1982. Also in 1982, Gabriel and his company planned and staged the first WOMAD concert. It was a commercial failure, put down to lack of suitable transport to the venue and publicity, and left Gabriel facing financial ruin and considerable personal pressure. At the suggestion of his and Genesis' manager, Tony Smith, he and his ex-band mates agreed to play together for a single show under the name 'Six of the Best' along with Chester Thompson and Daryl Stuermer.

Genesis were completing their Three Sides Live Encore tour with three concerts at Hammersmith Odeon on 28–30 September. At least one full band rehearsal took place on 29 September at Hammersmith Odeon.

Gabriel opened the show by rising from a coffin carried to the stage by four pallbearers, a stunt that was not known by the other musicians prior to the show. Hackett appeared on stage during the encores after arriving late from Brazil. Rutherford celebrated his 32nd birthday on the day of the concert and the crowd sang 'Happy Birthday' to him during the show.

The set list was drawn largely from the Gabriel-fronted era of Genesis, featuring songs from four of the band's first five albums, one song from the post-Gabriel iteration of the band, and one song from Gabriel's post-Genesis solo career.

The revenues generated by the concert allowed the WOMAD creditors to be paid, the festival to be established and Gabriel to resume his solo career. To date, Six of the Best is the last time Peter Gabriel played with Genesis for a full-length concert since his departure in 1975.

Set list
Encore
 * 1) "Back in N.Y.C." (from The Lamb Lies Down on Broadway)
 * 2) "Dancing with the Moonlit Knight" (intro and first verse only) (from Selling England by the Pound)
 * 3) "The Carpet Crawlers" (from The Lamb Lies Down on Broadway)
 * 4) "Firth of Fifth" (from Selling England by the Pound)
 * 5) "The Musical Box" (from Nursery Cryme)
 * 6) "Solsbury Hill"£ (from Peter Gabriel)
 * 7) "Turn It On Again" (vocals: Phil Collins; drums: Peter Gabriel ) (from Duke)
 * 8) "The Lamb Lies Down on Broadway" (from The Lamb Lies Down on Broadway)
 * 9) "Fly on a Windshield" (from The Lamb Lies Down on Broadway)
 * 10) "Broadway Melody of 1974" (from The Lamb Lies Down on Broadway)
 * 11) "In the Cage" (from The Lamb Lies Down on Broadway)
 * 12) "Supper's Ready" (from Foxtrot)
 * 1) "I Know What I Like (In Your Wardrobe)" (guitar: Steve Hackett) (from Selling England by the Pound, featuring elements of "Stagnation" from Trespass)
 * 2) "The Knife" (guitar: Steve Hackett) (from Trespass)

 * £ – performed in lower key

Recording
No official recording of the concert has been released but several audience recordings were gathered during 2007 and digitally remastered.

In 2015, Mike Rutherford expressed his regret that the concert had not been filmed.

Personnel

 * Peter Gabriel – lead vocals, drums ("Turn It On Again")
 * Phil Collins – drums, percussion, backing vocals, lead vocals ("Turn It On Again")
 * Tony Banks – keyboards, backing vocals
 * Mike Rutherford – guitars, bass, backing vocals
 * Steve Hackett – guitars ("I Know What I Like (In Your Wardrobe)", "The Knife")
 * Daryl Stuermer – guitars
 * Chester Thompson – drums, percussion

title: Six of the Best


text: User talk:65.96.129.119

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:65.96.129.119


text:
Pyraminx

The Pyraminx is a regular tetrahedron puzzle in the style of Rubik's Cube. It was made and patented by Uwe Mèffert after the original 3 layered Rubik's Cube by Ernő Rubik, and introduced by Tomy Toys of Japan (then the 3rd largest toy company in the world) in 1981.

Description

The Pyraminx was first conceived by Mèffert in 1970. He did nothing with his design until 1981 when he applied for a patent on 27/03 (EP0042695 on 12/30/81) and brought it to Hong Kong for production. Uwe is fond of saying had it not been for Ernő Rubik's invention of the cube, his Pyraminx would have never been produced. Somewhat earlier (for 40 days) in the Soviet Union, the chief technologist of the Kishinev Tractor Plant, Alexander Alexandrovich Ordynets, filed his application for an invention (patent SU980739 dated 12/15/1982, with the filing date 02/18/81), because of that, in Russia many people call the puzzle "Молдавская пирамидка" (Moldavian pyramid).

The Pyraminx is a puzzle in the shape of a regular tetrahedron, divided into 4 axial pieces, 6 edge pieces, and 4 trivial tips. It can be twisted along its cuts to permute its pieces. The axial pieces are octahedral in shape, although this is not immediately obvious, and can only rotate around the axis they are attached to. The 6 edge pieces can be freely permuted. The trivial tips are so called because they can be twisted independently of all other pieces, making them trivial to place in solved position. Meffert also produces a similar puzzle called the Tetraminx, which is the same as the Pyraminx except that the trivial tips are removed, turning the puzzle into a truncated tetrahedron.

The purpose of the Pyraminx is to scramble the colors, and then restore them to their original configuration.

The 4 tips can be easily rotated to line up with the axial piece they are respectively attached to, and the axial pieces are also easily rotated so that their colors line up with each other. This leaves only the 6 edge pieces as a real challenge to the puzzle. They can be solved by repeatedly applying two 4-twist sequences, which are mirror-image versions of each other. These sequences permute 3 edge pieces at a time and change their orientation differently, so that a combination of both sequences is sufficient to solve the puzzle. However, more efficient solutions (requiring a smaller total number of twists) are generally available (see below).

The twist of any axial piece is independent of the other three, as is the case with the tips. The six edges can be placed in 6!/2 positions and flipped in 25 ways, accounting for parity. Multiplying this by the 38 factor for the axial pieces gives 75,582,720 possible positions. However, setting the trivial tips to the right positions reduces the possibilities to 933,120, which is also the number of possible patterns on the Tetraminx. Setting the axial pieces as well reduces the figure to only 11,520, making this a rather simple puzzle to solve.

Optimal solutions
The maximum number of twists required to solve the Pyraminx is 11. There are 933,120 different positions (disregarding the trivial rotation of the tips), a number that is sufficiently small to allow a computer search for optimal solutions. The table below summarizes the result of such a search, stating the number p of positions that require n twists to solve the Pyraminx:

 * {| class="wikitable"

!n !p
 * 0||1||2 ||3 ||4   ||5   ||6    ||7     ||8     ||9     ||10  ||11
 * 1||8||48||288||1728||9896||51808||220111||480467||166276||2457||32
 * }

Records
The world record fastest Pyraminx solve is 0.73 seconds, set by Simon Kellum of United States on 21 December 2023 at Middleton Meetup Thursday 2023. The world record fastest average of five Pyraminx solves (excluding fastest and slowest) is 1.43 seconds, set by Lingkun Jiang of China on 2nd March 2024 at Hangzhou Spring 2024 in Hangzhou, China.

=== Top 5 solvers by single solve ===

=== Top 5 solvers by Olympic average of 5 solves ===

Methods
There are many methods for solving a Pyraminx. They can be split up into two main groups.

1) V First Methods - In these methods, two or three edges are solved first, and a set of algorithms, also called LL (last layer) algorithms, are used to solve the remainder of the puzzle.

2) Top First Methods- In these methods, three edges around a center piece are solved first, and the remainder of the puzzle is solved using a set of algorithms.

Common V first methods-

a) Layer by Layer - In this method, a face with all edges permuted is solved, and then the remaining puzzle is solved by a single algorithm from a set of 5.

b) Algorithmic L4E and Intuitive L4E - L4E or last 4 edges is somewhat similar to Layer by Layer. The only difference is that only two edges are solved around three centers. Both of these methods solve the last four edges in the same step, hence the name. The difference is that Intuitive L4E requires a lot of visualization and "intuition" to solve the last four edges while algorithmic L4E uses algorithms. Algorithmic L4E is generally used more at higher levels, although there are very fast Intuitive L4E users. It is also easy to transition between Intuitive L4E and Algorithmic L4E.

Common top first methods-

a) One Flip - This method uses two edges around one center solved and the third edge flipped. There are a total of six cases after this step, for which algorithms are memorized and executed. The third step involves using a common set of algorithms for all top first methods, also called Keyhole last layer, which involves 5 algorithms, four of them being the mirrors of each other.

b) Keyhole - This method uses two edges in the right place around one center, and the third edge placed elsewhere on the puzzle. The centers of the fourth color are then solved using the slot formed by the non-permuted edge. The last step is solved using Keyhole last layer algorithms.

c) OKA - In this method, one edge is oriented around two edges in the wrong place, but one of the edges that is in the wrong place belongs to the block itself. The last edge is found on the bottom layer, and a very simple algorithm is executed to get it in the right place, followed by keyhole last layer algorithms.

Some other common top first methods are WO and Nutella.

Many Pyraminx speedsolvers learn several methods, particularly top-first methods, and use the method that is best for the given solve.

There is no consensus among pyraminx speedsolvers regarding whether top-first or v-first methods are faster, although v-first is more common in the present day.

Variations
There are several variations of the puzzle. The simplest, Tetraminx, is equivalent to the (3x) Pyraminx but without the tips (see photo), resembling a truncated tetrahedron. There also exist "higher-order" versions, such as the 4x Master Pyraminx (see photos) and the 5x Professor's Pyraminx.

The Master Pyraminx has 4 layers and 16 triangles-per-face (compared to 3 layers and 9 triangles-per-face of the original), and is based on the Skewb Diamond mechanism. This version has about 2.6817 × 1015 combinations. The Master Pyraminx has In summary, the Master Pyraminx has 30 "manipulable" pieces. However, like the original, 8 of the pieces (the tips and middle axials) are fixed in position (relative to each other) and can only be rotated in place. Also, the 4 centers are fixed in position and can only rotate (like the Rubik's Cube). So there are only 18 (30-8-4) "truly movable" pieces; since this is 10% fewer than the 20 "truly movable" pieces of the Rubik's Cube, it should be no surprise that the Master Pyraminx has about 10,000-times fewer combinations than a Rubik's Cube (43 quintilion in the short scale or 43 trilion in the long scale). The Master Pyraminx can be solved in numerous ways: one is layer by layer like the original one or reducing it to a Jing pyraminx.undefined
 * 4 "tips" (same as the original Pyraminx)
 * 4 "middle axials" (same as the original Pyraminx)
 * 4 "centers" (similar to Rubik's Cube, none in the original Pyraminx)
 * 6 "inner edges" (similar to Rubik's Cube, none in the original Pyraminx)
 * 12 "outer edges" (2-times more than the 6 of the original Pyraminx)

Reviews

 * Games

title: Pyraminx


text:
Blanc-Mesnil

Blanc-Mesnil is a village and former commune in the Seine-Maritime department, northwestern France. Since 1822, it is part of Sainte-Marguerite-sur-Mer.

title: Blanc-Mesnil


text:
USS Picuda

USS Picuda (SS-382), a Balao-class submarine, was originally named Obispo, making her the only ship of the United States Navy to be named for the obispo, a spotted sting ray.

Construction and launching
Obispo′s keel was laid down by the Portsmouth Navy Yard in Kittery, Maine, on 15 March 1943. She was launched on 12 July 1943 sponsored by Mrs. Robert H. English. On 24 September 1943, she was renamed Picuda, making her the only ship of the United States Navy to be named for the picuda, a great barracuda, up to 7 ft long, of the Caribbean Sea and the tropical western Atlantic Ocean, known for its ferocious voracity. She was commissioned on 16 October 1943.

Picuda remained in the Portsmouth Navy Yard to complete fitting out until 18 November 1943, when she commenced underway trials. She completed torpedo tube trials off Newport, Rhode Island from 14 December through 16 December 1943, and she shifted to the submarine base at New London, Connecticut, for final training exercises. She put to sea from New London on 1 January 1944, reported for duty with the United States Pacific Fleet at Balboa, Panama Canal Zone, on 13 January 1944, arrived at Pearl Harbor, Hawaii, on 27 January 1944, and joined the Pacific Fleet Submarine Force as a unit of Submarine Division 201, Submarine Squadron 20.

Pacific War
Picuda got underway from Pearl Harbor for her first war patrol on 17 February, setting course for waters off the Caroline Islands, and entering her designated patrol area on 29 February. In an area not far from Truk, she sank 2672-ton ex-gunboat Shinyo Maru on 2 March, going deep to evade a string of 15 depth charges dropped by searching corvettes. On 18 March, Picuda changed course to patrol along the Saipan-Palau shipping lanes. She scored hits on a large enemy tanker that afternoon but was held down by two destroyers while the target escaped. She was off Yap Island a few minutes after midnight of 19 March, and sent 1504-ton freighter Hoko Maru to the bottom with two torpedo hits.

Eleven days later she closed two freighters under escort of two destroyers off the western coast of Yap Island and let go five torpedoes at the largest merchantman. The first hit stopped the target dead in the water and a second torpedo tore off the port quarter capsized the 5873-ton cargo ship Atlantic Maru. Two destroyers came down the torpedo tracks to hover over Picuda and she was shaken by 26 exploding depth charges before she escaped. With only one torpedo worth firing she returned to Midway Island on 5 April. Upon completion of her refit, she took aboard student officers and men for indoctrination training exercises off Midway, from 28 to 30 April. Three days later she formed a wolf-pack with submarines USS Perch (SS-313) and USS Peto (SS-265).

Picuda put to sea from Midway with the wolf-pack 4 May to conduct her second war patrol in waters off Formosa. On 22 May, she sent four bow shots streaking to sink 1200-ton river gunboat Hashidate. She also severely damaged 3172-ton cargo ship Tsukauba Maru with the same salvo. The latter enemy was polished off by land-based aircraft from the United States Army Air Corps the following day. On 2 June, Picuda closed a convoy of twelve ships hugging the coast of Formosa. After sending her contact report to the other submarines of her wolf-pack, she slipped between two of the three leading escorts and pressed home an attack on a large tanker. Three hits were heard as all escorts made for Picuda. She skillfully maneuvered clear and sustained no damage from the many depth charges which exploded on all sides and above from eight enemy vessels during the next hour. She continued to patrol the Formosa coast until 4 June then passed off Batan Island and eastward of the Nansei Shoto to a point northward of Chichi Jima by 14 June. Two days later she pointed her bow for Midway where she arrived 22 June. She put to sea the next day to arrive at Pearl Harbor 27 June. After the end of the second war patrol, Raborn was replaced as skipper of Picuda by Commander Glynn R. Donaho.

Picuda, in wolf-pack with sister ships USS Spadefish (SS-411) and USS Redfish (SS-395), departed Pearl Harbor for her third war patrol 23 July in waters of the Luzon Strait between Formosa and Luzon. On 25 August, Picuda spotted ten ships hugging the coast some 4000 yd off the beach of Luzon. Slipping past five escorts, and with three enemy patrol planes overhead, she sent six torpedoes streaking to sink 1943-ton cargo ship Kotoku Maru, then skillfully maneuvered for a down-the-throat shot that spelled the doom of 1270 ton pursuing JAPANESE DESTROYER Yūnagi. Picuda probed deeper in the interior of Luzon Strait on 16 September, for a bold daylight attack on an eight-ship convoy, guarded by three destroyers and air cover. She sank 5975-ton cargo ship Tokushima Maru and scored hits for unknown damage to two other freighters. Searching the southern border of her assigned patrol area, Picuda found another convoy hugging the north coast of Luzon on 21 September and sent 1948-ton freighter Awaji Maru to the bottom. Picuda made rendezvous with USS Barb (SS-220) and USS Queenfish (SS-393), then set course in company with these two submarines to terminate her third war patrol in the lagoon of Majuro Atoll on 3 October.

At Majuro, Picuda, now under the command of Evan T. Shepard, her final wartime skipper, formed a new wolf-pack with Queenfish and Barb, and departed 27 October. Topping off with fuel at Saipan, 1 November and 2 November, the wolf pack set course to range over the northern waters of the East China Sea, westward of Kyūshū. Picuda sent 9433-ton passenger-cargo vessel Mayasan Maru to the bottom of the sea 17 November in the area southwest of Nagasaki. On 23 November, closing a convoy off the Korean Archipelago and stealing between two lead escorts, Picuda sank 6933-ton freighter Shuyo Maru and 5296-ton passenger-cargo ship Fukuju Maru. She departed her patrol area six days later and returned from her fourth patrol to moor in Apra Harbor, Guam, on 2 December.

On 29 December, Picuda put to sea for her fifth war patrol in the Formosa Straits and the East China Sea off the east coast of China from Shanghai to Kam Kit. On 7 January 1945, Picuda received a contact report from Barb and closed a convoy in the straits of Formosa to inflict severe damage with four torpedo hits on 10,045-ton tanker Munakata Maru. On the afternoon of 8 January, she again received a convoy contact report from Barb and slipped between two escorts of the starboard screen about four hours before midnight to pick out two large passenger-freighters. Three bow tubes fired at each target resulted in one hit on each. She swung and fired stern shots at a tanker, then discovered an escort dead ahead, 700 yd range, and was forced to clear the area. The 2854-ton coastal tanker Hikoshima Maru, hit by both Picuda and Barb, was disabled and ran aground. The freighter Meiho Maru had a similar experience, and severe damage was inflicted on 6600-ton freighter Hisagawa Maru as well as 6516-ton coastal tanker Manju Maru. Picuda having flashed a contact report as she cleared the area, set course for lifeguard station in support of the Third Fleet airstrikes on Formosa. In the early morning darkness of 29 January, Picuda made out at least three large ships in the rain and commenced tracking. The rain slacked as she approached dead ahead of a troop transport, overlapped by a freighter. One hit on the transport and two hits on the freighter were observed by Picuda's officer of the deck. The transport, almost dead in the water, commenced shrill whistle blasts and the mist dropped down to reveal the freighter enveloped in a huge cloud of steam and smoke. An enemy float plane forced Picuda to abandon the attack. The victim sunk in this attack was the 5497-ton passenger-cargo ship Clyde Maru. Picuda reached Tanapag Harbor, Saipan 5–6 February and arrived at Pearl Harbor on 15 February.

Picuda spent much of her sixth war patrol on lifeguard station off the coast of China. She got underway from Pearl Harbor 15 March and cleared the replenishment base of Apra Harbor, Guam on 29 March. She entered her patrol area off Kii Suido on 2 April for uneventful lifeguard duty in support of B-29 Superfortress strikes. On 6 May, Picuda made rendezvous with sister ship USS Scabbardfish (SS-397) off the Nansei Shoto and received five crewmen from an Army B-29 bomber and debarked these survivors at Tanapag Harbor on 10 May, transferring them to the Headquarters of the Twenty-First Bomber Command. After voyage repairs alongside submarine tender USS Orion (AS-18), she departed 11 May for the East Coast of the United States. She stopped at Pearl Harbor, San Francisco, California, and transited the Panama Canal to arrive at the Portsmouth Naval Shipyard, Kittery, Maine, on 22 June.

Picuda received six battle stars for World War II service.

Post-war
Picuda was assigned to Submarine Division 201, Squadron 20, U.S. Atlantic Fleet. She remained in the Portsmouth Naval Shipyard for major overhaul until 18 October. She shifted to the Submarine Base at New London on 31 October for duty as a training ship for the Submarine School. Picuda put to sea from New London 12 November for a training cruise which included visits to Key West, Florida, and Havana, Cuba. Upon her return to New London, 26 November, she was assigned to the New London Group of 16 November (Inactive) Fleet. She shifted to the Portsmouth Naval Shipyard on 12 December to commence preservation incidental to being placed in inactive status. On 15 January 1946, Picuda was ordered to cease inactivation and report to the Second Fleet for duty as a unit of Submarine Division 81, Squadron 8, U.S. Atlantic Fleet.

Picuda prepared for active service in the Portsmouth Naval Shipyard until 18 February and shifted to the Submarine Base at New London the next day. In company with five other submarines of the New London Group, she cleared that base 25 February for a tour of duty out of the Submarine Base at Balboa, Panama, returning by way of St. Thomas, to New London on 27 March. Picuda again entered the Portsmouth Naval Shipyard for inactivation on 27 March and was towed by a fleet tug to New London on 19 September 1946. She was placed out of commission, in reserve 25 September 1946.

Picuda was assigned to the New London Group of the Atlantic Reserve Fleet until late in the year 1952 when she was towed to the Portsmouth Naval Shipyard for snorkel conversion. She recommissioned 19 June 1953, Lieutenant Commander Ted N. Swain. Her conversion was complete by 24 August and she shifted to the Submarine Base at New London. She reported for duty to Submarine Division 122, Squadron 12, U.S. Atlantic Fleet.

Picuda steamed by way of Norfolk, Virginia, and Nassau, Bahamas, to arrive at Key West, Florida, on 17 September. She was assigned to duty as a training ship for Submarine Refit Training Group and based her operations for that command at Key West through September 1959. This duty included almost daily exercises in the Key West operating area, visits to American ports on the Gulf of Mexico, and periodic training cruises to the waters of Cuba, Jamaica and Haiti. This service was intervened by special cruises from Key West and two tours of duty in the Mediterranean Sea. On her first special cruise, she operated off Norfolk from 24 April to 20 May 1954, participating in anti-submarine development exercises. On her second special cruise, she cleared Key West on 3 September and set course for waters of Northern Europe and the Mediterranean. She arrived at Londonderry Port, Northern Ireland, on 24 September for joint maneuvers with ships of the Royal Navy, then arrived at Gibraltar on 29 October to join units of the Sixth Fleet for Operation "Bright Bonfire." She returned to Londonderry Port 14 November to resume hunter-killer and other anti-submarine warfare tactics with units of the British Fleet, and cleared that port 25 November to resume her training duties at Key West, 11 December. She again sailed from Key West 6 January 1958 and arrived at Gibraltar 18 January. Her tour with the Sixth Fleet included participation in operation "ASCENDEX" and visits to the ports of Palma and Barcelona, Spain; Port de Monaco; and Genoa, Italy. She sailed from Gibraltar on 18 August and conducted hunter-killer exercises with destroyers in waters off Cuba and Jamaica before returning to Key West 11 October.

Picuda underwent overhaul in the Charleston Naval Shipyard from 13 October 1958 to 12 March 1959, followed by a brief period of refresher training in the New London, Connecticut–Newport, Rhode Island, area. She resumed her former duties at Key West on 27 March 1959 and put to sea from that port 1 June for her third Mediterranean tour. She touched at Norfolk 4 June and reached Gibraltar on 15 June. Operations in the Mediterranean during this tour included visits to Naples and Genoa, Italy; Marseilles, France; and Lisbon, Portugal. She departed the latter port 26 August to resume training duties at Key West, Florida.

Picuda was brought to Pensacola, Florida during the 50th Anniversary of Naval Aviation and people were allowed to board her to see inside.

In 1961, Picuda visited Guantanamo Bay and underwent a five-month overhaul at Charleston Naval Shipyard. During 1962, Picuda visited Guantanamo Bay twice before making a circumnavigation of the South American continent, conducting joint operations with Brazil, Argentina, Uruguay, Chile and Peru. This operation was terminated due to the Cuban Missile Crisis, and Picuda proceeded to Key West, Florida. Picuda spent most of 1963 operating out of her homeport of Key West making one trip to Guantanamo Bay.

During 1964, Picuda operated out of Key West in the Atlantic and Caribbean, winding up the year with an overhaul in the Philadelphia Naval Shipyard. Picuda made another visit to Guantanamo Bay in 1965. She began 1966 with a three-month Mediterranean tour with the Sixth Fleet, participating in fleet ASW exercises and NATO exercises with French and Italian naval forces. She wound up the year with another visit to Guantanamo Bay.

During the 1967 North Atlantic NATO operation "Quick Pursuit," Picuda lost two men at sea (Lieutenant (junior grade) Jerry R. Alexander and Chief Torpedomans Mate Robert E. Small). She visited Bergen, Norway and Portsmouth, England before returning to Key West.

At the time of her decommissioning, Picuda held the record for being the longest serving submarine in the history of the US Navy. She had served 28 years, 11 months and 15 days. The previous record holder was USS O-4 (SS-65).

Spanish Navy service
Transferred to Spain on 1 October 1972, former Picuda was renamed SPANISH SUBMARINE Narciso Monturiol. The submarine was stricken from the U.S. Navy's Naval Vessel Register on 1 November 1974 and was purchased outright by Spain on 18 November 1974. In 1975, she was laid up with mechanical defects and finally deleted from the Armada Española on 30 April 1977, her name being shifted to former ex-Jallao (SS-368), which the Spanish had acquired.

title: USS Picuda


text:
Category:Broadcast news analysts

Broadcast news analysts analyze, interpret, and broadcast news received from various sources. They may also be called newscasters, news anchors, and news commentators.

See also the related Category: Reporters and correspondents and Category:Commentators.

title: Category:Broadcast news analysts


text:
Category:Reporters and correspondents

They collect and analyze facts about newsworthy events by interview, investigation, or observation. They report and write for newspaper, news magazine, radio, television or internet. See the related category: Broadcast news analysts.

title: Category:Reporters and correspondents


text:
Noriko Sakai

Noriko Sakai (酒井 法子) is a Japanese singer and actress. Under her former stage name Nori-P (のりピー), Sakai released her first single, "Otoko no Ko ni Naritai" (男のコになりたい) on February 5, 1987, nine days short of her seventeenth birthday. Over 40,000 copies of the single were sold. She is particularly popular in Hong Kong and Taiwan. Her best-selling single to date is "Aoi Usagi".

In August 2009, Sakai was arrested on suspicion of possession and abuse of drugs and sentenced to probation for three years. She divorced her husband Yūichi Takasō (高相 祐一) after the incident and temporarily stayed away from the media circle. After her probation ended, she began rehearsals for the theater, and signed on with Office Nigun Niiba, as a first step towards returning to the media community. On May 1, 2021, she left Office Nigun Niiba and joined Smile.

Biography
Noriko Sakai was born in Fukuoka, Fukuoka Prefecture, Japan. She made her debut as an idol singer in 1986.

Sakai released her first single, "Otoko no Ko ni Naritai" (男のコになりたい) on February 5, 1987, nine days short of her sixteenth birthday. Over 40,000 copies of the single were sold. In the early years of her career, she used the nickname Nori-P (のりピー), although around the mid-1990s she started to distance herself from it.

She ventured overseas in the 1990s to Taiwan to shoot VITALON P beverage commercials, as well as holding concerts which received praise.

Sakai returned to the public attention after 1993, where she received recognition for her acting in Hitotsu Yane no Shita as Kashiwagi Koyuki. In 1995, she acted in Hoshi no Kinka (Heaven's Coins) as Aya Kuramoto, also singing the theme song "Aoi Usagi" (碧いうさぎ) which became her best selling album to date.

By the end of 1998 she organized the Asian concert tours throughout Taiwan, mainland China, Singapore, South Korea, Malaysia, Indonesia, Thailand and other countries in the regions.

Personal life
On December 28, 1998, she suddenly held a press conference, announcing her marriage to Yūichi Takasō (高相 祐一). She and Yūichi have one son, born on July 17, 1999.

Return to the entertainment industry
In January 2000, after the birth of her son, Sakai made a comeback to showbiz, and gradually took on roles in movies, drama and advertising. Sakai's popularity in Japan is not outstanding, but she has considerable supporters in Hong Kong, Taiwan and mainland China.

Drug scandal
Sakai re-emerged in the headlines for a drug scandal on August 2, 2009, when Sakai's husband, Yūichi Takasō allegedly inhaled a small amount of stimulant drugs in a public lavatory, at a park in Tokyo's Minato Ward. The next day, Takasō's car, parked on a street in Tokyo's Shibuya Ward, was searched. In the car, 0.817 grams of stimulant drugs were found. On August 4, 2009, Takasō was stopped by Tokyo Metropolitan Police while walking in public in Shibuya. When Takasō was subjected to a body search, stimulant drugs were reportedly found in his underwear. Takasō was immediately placed under arrest. Sakai was summoned to the scene of the arrest. She was asked to go to the police station for further questions and to submit to a urine test. Instead, she told the police she had to pick her 10-year-old son up, and that she would go to the police station later that day. Sakai later disappeared with her son.

While Takasō was being questioned at the police department, he reportedly told the police he and Sakai were involved in drugs. As early as ten days prior to his arrest, the two of them used drugs while on a family trip to Amami Ōshima in Kagoshima Prefecture. At the time of Takasō's arrest, Sakai was living in her own apartment in Tokyo. While Sakai was away, the police searched Sakai's home, and reportedly found 0.008 grams of stimulant drugs, carefully wrapped in aluminum foil. An inhaler among the drugs was discovered to have Sakai's DNA. As a result, a warrant was issued for her arrest. On August 5, 2009, Sakai dropped her son off with an unnamed friend, purchased some underwear and other necessities from a store, and then disappeared.

Attempting to track Sakai down by cell phone, the police reported that her cell phone lost signal within the area of Yamanashi Prefecture, about 60 miles (100 kilometers) west of Tokyo. Sakai later claimed that the cell phone was damaged, and that she threw the phone away. The police believed that the cell phone may have contained information leading to the source of the stimulant drugs.

On August 7, 2009, Sakai turned herself in to the authorities, and then was placed under arrest. The official charge against Sakai was "suspicion of possessing stimulant drugs," according to a Tokyo police official. She admitted to the drugs being in her apartment, but did not admit to taking the drugs herself. She also said she kept the drugs in foil "to use them later."

On August 17, 2009, a beach house in Katsuura, Chiba was also searched. A frequent location for both Sakai and Takasō the past five years, 0.097 grams of amphetamines and paraphernalia were found in the house. On August 21, 2009, after admitting to the drugs found in the beach house, Takasō was served with a second charge for possession of stimulant drugs.

Drug testing and indictment
On August 9, 2009 – two days after Sakai's arrest, a urine test result came up negative. Light use of methamphetamine can only be detected in a urine test within one to four days after use. On August 19, 2009, investigators announced that Sakai's hair tested positive for the stimulant drug, although the results were weak. Before Sakai was caught, she reportedly dyed and cut her hair; both practices would affect the testing results. Because of the positive result in the hair test, Sakai's jail time was extended another nine days – until August 28, 2009.

On the final day of Sakai's detention, prosecutors officially indicted Sakai for alleged amphetamine possession, based on the evidence collected by the police. The fact that the drugs were carefully wrapped for later use was a deciding factor in the verdict. On September 10, 2009, an additional charge of stimulant drug use was added. Sakai allegedly used amphetamines at a hotel during her Kagoshima Prefecture visit with her husband and son.

Sakai was released from jail after posting bail on September 17, 2009. Accompanied by her attorney, and with Sun Music Vice President Masahisa Aizawa in attendance, she apologized to the public during a press conference. "My weakness caused me to give in to illegal drugs and caused grief to many people. I pledge to repent and atone for this crime for the rest of my life," she said. Sakai was checked into a hospital to overcome her drug habit, and asked for restraint from the media during her recovery.

Sakai's first court date was held on October 26, 2009 – drawing a crowd of 6,600 people outside of a Tokyo courthouse. Sakai pleaded guilty to drug use. Prosecutors suggested eighteen months in prison for Sakai, but on November 9, 2009, the court delayed the jail term to November 9, 2012, as long as she stays crime-free. Sakai attended the University of Creation; Art, Music & Social Work in Takasaki, Gunma, where she received her degree in welfare and nursing care in March 2013.

Reactions
The drug scandal cost Sakai billions of yen in canceled contracts and other endeavors she was involved in prior. On August 6, 2009, car manufacturer Toyota reportedly stopped showing a commercial, featuring Sakai, on its web site. Sakai's clothing line "PP rikorino", consisting of over 150 items were pulled from stores throughout Japan.

During the first week of the scandal, Apple Inc's iTunes Store rated Sakai's 1995 song "Aoi Usagi" the number one downloaded song, based on an eleven-day period. Other Sakai songs among the top 100 downloads include Kagami no Doresu (17th) and Sekaijū no Dare Yori Kitto (18th). However, on August 9, 2009, Victor Entertainment, the distributor of Sakai's works, withdrew Sakai's CDs from stores, and suspended downloads of her songs. Online stores such as Amazon Japan still sell Sakai's CDs and DVDs, despite increasing the selling prices as a result of Victor's move.

Immediately after the indictment announcement, Sun Music, the talent agency who has represented Sakai since 1986, suspended her contract and removed her official website from its server. The agency's president Masahisa Aizawa said, "We apologize from the bottom of our hearts for the alleged misdeeds of Ms. Sakai." Soon after Aizawa's announcement, he was demoted to vice-president. Chairman Hideyoshi Aizawa removed himself from the position, and is now an adviser to Sun Music, with no right to represent the firm.

In the aftermath of the scandal, Sakai divorced her husband Takasō on July 31, 2010.

Second return to the entertainment industry
In April 2011, Sakai participated in a tour around Beijing to educate the hazards of drug addiction. She claimed that she would temporarily set aside her entertainment career to partake in charity organizations.

At a news conference on November 24, 2012, Sakai announced her return to the entertainment industry, after finishing her suspended sentence that ended earlier Friday. Sakai also signed on with talent agency Office Nigun Niiba. She returned to the stage in December 2012 as the main character in a story about the Sengoku period, ending December 25, 2012. In all, 7,500 people attended the stage performance during the ten-day period.

In October 2021, Sakai re-recorded "Aoi Usagi" and placed an NFT of it and promo photos on auction to promote the fourth season of the drama series Producer K, which marked her first drama appearance in eight years.

Video

 * Guanbare CDV Special (mini laser disc)

Film

 * Pikachu and Pichu, 2000
 * Ju-on: The Grudge 2, 2003
 * Yogen, 2004
 * SS, 2008
 * Utsusemi no Mori, 2021

Television dramas

 * Tobu ga Gotoku as Saigō Koto, NHK 1990
 * Hitotsu Yane no Shita as Kashiwagi Koyuki, Fuji TV 1993
 * Longing For The Old You, NTV 1994
 * Watashi, Mikata Desu, TBS 1995
 * Hoshi no Kinka (Heaven's Coins) as Aya Kuramoto, NTV 1995
 * Zoku Hoshi no Kinka (Heaven's Coins 2) as Aya Kuramoto, NTV 1996
 * Hitotsu Yane no Shita 2 as Koyuki Kashiwagi, Fuji TV 1997
 * Seija no Koushin, TBS 1999
 * Toi Shinseki Chikaku no Tanin, NHK 1999
 * Tenshi ga Kieta Machi, NTV 2000
 * Honke no Yome, NTV 2001
 * Toshiie and Matsu as One, NHK 2002
 * Mukodono 2003, Fuji TV 2003
 * Fight as Kido Ayako, NHK 2005
 * Marumaru Chibi Maruko-chan as Okaasan, Fuji TV 2007

Photo books

 * Let's Nori-P
 * Shuffle Heart
 * Blue Pearl
 * Aquarius
 * Zephoros
 * In Europe
 * In Greece
 * Comme Le Cinema
 * Shinin Run
 * Orange Hotel
 * Naturelle
 * Fizz

Other

 * Kagami no Kuni no Legend (鏡の国のレジェンド) (video game for the PC Engine CD add-on)

title: Noriko Sakai


text:
User:NeoNSX

I joined to add some major contributions to the Honda NSX/HSC websites and to maintain them. I happen to be very passionate about the Honda NSX. --NeoNSX 15:43, 13 Oct 2004 (UTC)

title: User:NeoNSX


text:
Pott's fracture

Pott's fracture, also known as Pott's syndrome I and Dupuytren fracture, is an archaic term loosely applied to a variety of bimalleolar ankle fractures. The injury is caused by a combined abduction external rotation from an eversion force. This action strains the sturdy medial (deltoid) ligament of the ankle, often tearing off the medial malleolus due to its strong attachment. The talus then moves laterally, shearing off the lateral malleolus or, more commonly, breaking the fibula superior to the tibiofibular syndesmosis. If the tibia is carried anteriorly, the posterior margin of the distal end of the tibia is also sheared off by the talus. A fractured fibula in addition to detaching the medial malleolus will tear the tibiofibular syndesmosis. The combined fracture of the medial malleolus, lateral malleolus, and the posterior margin of the distal end of the tibia is known as a "trimalleolar fracture".

An example of Pott's fracture would be in a sports tackling injury. The player receives a blow to the outside of the ankle, causing the ankle to roll inwards (so that the sole of the foot faces laterally). This damages the ligaments on the inside of the ankle and fractures the fibula at the point of contact (usually just above the tibiofibular syndesmosis). A better way to visualize this is the two hands of a clock, with one hand facing 12 and the other facing 6. The vertical line they form represents the fibula of the person's right leg. The lateral force approaches from 3 o'clock, sending the lower hand snapping outwards to point at 5 o'clock.

Bimalleolar fractures are less likely to result in arthritis than trimalleolar fractures.

History
English physician Percivall Pott experienced this injury in 1765 and described his clinical findings in a paper published in 1769.

The term "Dupuytren fracture" refers to the same mechanism, and it is named for Guillaume Dupuytren. Pott did not describe disruption of the tibio-fibular ligament, whereas Dupuytren did.

title: Pott's fracture


text:
Beck's theorem

Beck's theorem may refer to either of two mathematical results:
 * Beck's monadicity theorem or the Beck tripleability theorem (1964/2003), by Jonathan Mock Beck, on monadic functors in category theory
 * Beck's theorem (geometry) (1983) by József Beck, on finite collections of points in discrete geometry

title: Beck's theorem


text:
Talk:Beck's theorem

I added this page for the incidence geometry result, but realized after some web searching that there is also a category theory result - but this is not my field, someone else will have to flesh it out more! Terry 05:19, 9 Oct 2004 (UTC)

Thanks for that; and your other interesting contributions. I've beefed up the category theory side - I do at least know why this matters, though don't press me on the details.

This page will likely get split up.

Charles Matthews 13:08, 9 Oct 2004 (UTC)

This should be made a disambiguation page. (But it's nowhere near as bad as an article called trunk that has a section on elephants' trunks, a section on tree trunks, and a section on storage lockers.) Michael Hardy 19:54, 9 Jun 2005 (UTC)

title: Talk:Beck's theorem


text:
Talk:Fluorophore

Brightness Index
Would anyone be against me working to add brightness index numbers to the Fluorophores in the list? It would not be easy, but it would provide useful information about the fluorophores as they are used. Brightness Index being (Extinction coeff*QY)/1000). The /1000 makes it easier to read and handle the numbers that are produced. PedroDaGr8 (talk) 19:58, 7 December 2015 (UTC)

Affine
What does it mean? Is there an article in we can link to so that those who do not know the meaning of affine in this context can learn the word without opening a new tab to look it up? Thue Morse (talk) 00:08, 28 February 2017 (PST)

Untitled
a fluorophore is a molecule which absorbs light of uv visible region and emit light of longer wavelength ,the phenomenon called fluorescence ,is the result of it.

A fluorophore does not require UV light, it simply requires the absorption of light of one frequency and the emission of light of another frequency. PedroDaGr8 (talk) 19:54, 7 December 2015 (UTC)

Fluorophor
What is the difference between a Fluorophore and a Fluorophor ? Should these be merged?

Any how can you determine if a given compound is a Fluorophore? See chromophore first. Easiest precise way perhaps would be, presupposed the chemical structure is known, to run simulations in molecular modelling software. (In the end it breaks down to the kinetics possible for a given structure over a certain range of excitation [thermically or by radiation. Huge difference though!])Slicky 14:21, 13 March 2006 (UTC)

 * This article is bioscience oriented so it would quite odd if a definition of "eye-catchy" and the likes were added if you want to add it though please please fell more than free to create a page for dyes used in non-scientific settings. --Squidonius (talk) 16:33, 8 October 2009 (UTC)

Luciferin??
Correct me if I am wrong, but I know luciferin only as a substrate of luciferase in the process of bioluminescence, which is distinct from fluorescence. So why is luciferin listed here? Furthermore, isn't that whole "size" section an odd thing to have in an article this short? Somebody with the requisite chemical knowhow should instead add explanations of the necessary chemical structure for a compound to be fluorophore, etc. --mglg(talk) 02:31, 27 November 2006 (UTC)

>>> Thanks an error so bad, lingered on for 3 years! Squidonius (talk)

I'm also wondering why it says GFP is 26 kDa, when the article it links to says 23 kDa.. --David Munch 13:28, 10 June 2007 (UTC)

What's the smallest known fluorophore?
What's the smallest known fluorophore? Seans Potato Business 10:04, 12 September 2008 (UTC)
 * depends on what you consider useful, say an acetic acid in ethanol is fluorescent due to its carboxy group, but it is unusable (except for 230nm purity tests of DNA/RNA preps), aromatic double-ringed molecules (naphtalene, coumarin etc) are commonly used. --Squidonius (talk) 09:45, 6 August 2009 (UTC)

Fluorophore versus Fluorescent Dye; Categorization Error
The article "Fluorophore" improperly subtends the entire category "Fluorescent Dyes". These terms are not synonymous. Indeed, "fluorophore" has a part-of relationship (it is the photoactive moeity) with "fluorescent dye".

Continued elaboration of either "fluorescent dyes" or "fluorophores" will become more and more difficult until a separate article on fluorescent dyes is created. Contrablue (talk) 22:50, 31 October 2008 (UTC)

Fluorophore (Fluorescent Dyes) -- Scope of Article
This article discusses only applications of fluorescent dyes to microscopy, biology, and biochemistry. These applications, while extremely important and topical, represent only a fraction of the market value of fluorescent dyes. Following a re-classification (see my comment "Fluorophore versus Fluorescent Dye" above), this article should be rewritten with an eye to encompassing the true breadth of impacts of fluorescent dyes on modern life, to wit: multi-ton scale usages in textile dyeing and optical brighteners in laundry detergents; advanced cosmetic formulations; safety equipment and clothing; organic light-emitting diodes (OLED), fine arts and design (posters and paintings), synergists for insecticides and experimental drugs, and others. Contrablue (talk) 22:50, 31 October 2008 (UTC)

 * You're right, there are many non-biomedical applications of flurophores. If you want to write a new stub for the Fluorophore article, I'll handle the page moves and redirects. Click here to start the new stub. -- MarcoTolo (talk) 23:09, 31 October 2008 (UTC)

Advertising and Layout
I know it's really tempting for biotech companies to advertise in wikipedia since scientists tend to be swayed by information over all else. Honestly, I don't think it's a problem to have brief product mentions, or even articles on notable products. When every page related to fluorescence gets spammed with DyLight and Alexa Fluor though, there is a problem. I removed the entire Alexa Fluor section since that chart is on the Alexa Fluor page. I also separated the trademark families from the derivative families. I'm sure similar work needs to be done on most pages related to fluorophores. Ryan Brady (talk) 17:59, 28 July 2010 (UTC)

Cleanup
I've tagged this page for cleanup based on the list of "frequently encountered fluorophores", can we define this list a bit better. Frequently could mean very different things to some readers. Its at risk of becoming a list of everything Aloneinthewild (talk) 22:58, 15 February 2016 (UTC)

External links modified
Hello fellow Wikipedians,

I have just added archive links to 1 one external link on Fluorophore. Please take a moment to review my edit. If necessary, add after the link to keep me from modifying it. Alternatively, you can add to keep me off the page altogether. I made the following changes:
 * Added archive https://web.archive.org/20141020225338/http://pingu.salk.edu:80/flow/fluo.html to http://pingu.salk.edu/flow/fluo.html

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at ).

Cheers.—cyberbot II  Talk to my owner :Online 12:12, 28 February 2016 (UTC)

title: Talk:Fluorophore


text:
Kub

KUB or KUBS or Kub or Kubs may refer to:

 * 2K12 Kub, a Soviet mobile surface-to-air missile system
 * Kubb, a Swedish lawn game with wooden blocks
 * Kidneys, ureters, and bladder, a medical imaging technique
 * Scania K UB, low-entry citybus chassis
 * KUB, a ZALA Aero Group military UAV

title: Kub


text:
Category:Christmas characters

This category is for mythical and/or fictional characters who play a role in Christmas Stories and/or folktales. __NOGALLERY__

title: Category:Christmas characters


text:
Szemerédi–Trotter theorem

The Szemerédi–Trotter theorem is a mathematical result in the field of Discrete geometry. It asserts that given $n$ points and $m$ lines in the Euclidean plane, the number of incidences (i.e., the number of point-line pairs, such that the point lies on the line) is

$$O \left ( n^{2/3} m^{2/3} + n + m \right ).$$

This bound cannot be improved, except in terms of the implicit constants.

As for the implicit constants, it was shown by János Pach, Radoš Radoičić, Gábor Tardos, and Géza Tóth that the upper bound $$ 2.5n^{2/3} m^{2/3} + n + m$$ holds. Since then better constants are known due to better crossing lemma constants; the current best is 2.44. On the other hand, Pach and Tóth showed that the statement does not hold true if one replaces the coefficient 2.5 with 0.42.

An equivalent formulation of the theorem is the following. Given $n$ points and an integer $k ≥ 2$, the number of lines which pass through at least $k$ of the points is

$$O \left( \frac{n^2}{k^3} + \frac{n}{k} \right ).$$

The original proof of Endre Szemerédi and William T. Trotter was somewhat complicated, using a combinatorial technique known as cell decomposition. Later, László Székely discovered a much simpler proof using the crossing number inequality for graphs. (See below.)

The Szemerédi–Trotter theorem has a number of consequences, including Beck's theorem in incidence geometry and the Erdős-Szemerédi sum-product problem in additive combinatorics.

Proof of the first formulation
We may discard the lines which contain two or fewer of the points, as they can contribute at most $2m$ incidences to the total number. Thus we may assume that every line contains at least three of the points.

If a line contains $k$ points, then it will contain $k − 1$ line segments which connect two consecutive points along the line. Because $k ≥ 3$ after discarding the two-point lines, it follows that $k − 1 ≥ k/2$, so the number of these line segments on each line is at least half the number of incidences on that line. Summing over all of the lines, the number of these line segments is again at least half the total number of incidences. Thus if $e$ denotes the number of such line segments, it will suffice to show that

$$e = O \left ( n^{2/3} m^{2/3} + n + m \right).$$

Now consider the graph formed by using the $n$ points as vertices, and the $e$ line segments as edges. Since each line segment lies on one of $m$ lines, and any two lines intersect in at most one point, the crossing number of this graph is at most the number of points where two lines intersect, which is at most $m(m − 1)/2$. The crossing number inequality implies that either $e ≤ 7.5n$, or that $m(m − 1)/2 ≥ e^{3} / 33.75n^{2}$. In either case $e ≤ 3.24(nm)^{2/3} + 7.5n$, giving the desired bound

 * $$e = O \left ( n^{2/3} m^{2/3} + n + m \right ).$$

Proof of the second formulation
Since every pair of points can be connected by at most one line, there can be at most $n(n − 1)/2$ lines which can connect at $k$ or more points, since $k ≥ 2$. This bound will prove the theorem when $k$ is small (e.g. if $k ≤ C$ for some absolute constant $C$). Thus, we need only consider the case when $k$ is large, say $k ≥ C$.

Suppose that there are m lines that each contain at least $k$ points. These lines generate at least $mk$ incidences, and so by the first formulation of the Szemerédi–Trotter theorem, we have

$$mk = O \left ( n^{2/3} m^{2/3} + n + m \right ),$$

and so at least one of the statements $$mk = O( n^{2/3} m^{2/3} ), mk = O(n)$$, or $$mk = O(m)$$ is true. The third possibility is ruled out since $k$ was assumed to be large, so we are left with the first two. But in either of these two cases, some elementary algebra will give the bound $$m = O( n^2 / k^3 + n/k )$$ as desired.

Optimality
Except for its constant, the Szemerédi–Trotter incidence bound cannot be improved. To see this, consider for any positive integer $$N\in \mathbb{N}$$ a set of points on the integer lattice

$$P = \left \{ (a, b) \in \mathbb{Z}^2 \ : \ 1 \leq a \leq N; 1 \leq b \leq 2N^2 \right \},$$

and a set of lines

$$L = \left \{ (x, mx + b) \ : \ m, b \in \mathbb{Z}; 1 \leq m \leq N; 1 \leq b \leq N^2 \right \}.$$

Clearly, $$|P| = 2N^3$$ and $$|L| = N^3$$. Since each line is incident to $N$ points (i.e., once for each $$x \in \{1, \cdots, N\}$$), the number of incidences is $$N^4$$ which matches the upper bound.

Generalization to $$\mathbb{R}^d$$
One generalization of this result to arbitrary dimension, $$\mathbb{R}^d$$, was found by Agarwal and Aronov. Given a set of $n$ points, $S$, and the set of $m$ hyperplanes, $H$, which are each spanned by $S$, the number of incidences between $S$ and $H$ is bounded above by

$$O \left (m^{2/3}n^{d/3}+n^{d-1} \right ),$$

provided $$ n^{d-2} < m < n^{d}$$. Equivalently, the number of hyperplanes in $H$ containing $k$ or more points is bounded above by

$$O\left( \frac{n^d}{k^3} + \frac{n^{d-1}}{k} \right ).$$

A construction due to Edelsbrunner shows this bound to be asymptotically optimal.

József Solymosi and Terence Tao obtained near sharp upper bounds for the number of incidences between points and algebraic varieties in higher dimensions, when the points and varieties satisfy "certain pseudo-line type axioms". Their proof uses the Polynomial Ham Sandwich Theorem.

In $$\mathbb{C}^2$$
Many proofs of the Szemerédi–Trotter theorem over $$\mathbb{R}$$ rely in a crucial way on the topology of Euclidean space, so do not extend easily to other fields. e.g. the original proof of Szemerédi and Trotter; the polynomial partitioning proof and the crossing number proof do not extend to the complex plane.

Tóth successfully generalized the original proof of Szemerédi and Trotter to the complex plane $$\mathbb{C}^2$$ by introducing additional ideas. This result was also obtained independently and through a different method by Zahl. The implicit constant in the bound is not the same in the complex numbers: in Tóth's proof the constant can be taken to be $$10^{60}$$; the constant is not explicit in Zahl's proof.

When the point set is a Cartesian product, Solymosi and Tardos show that the Szemerédi-Trotter bound holds using a much simpler argument.

In finite fields
Let $$\mathbb{F}$$ be a field.

A Szemerédi-Trotter bound is impossible in general due to the following example, stated here in $$\mathbb{F}_p$$: let $$\mathcal{P} = \mathbb{F}_p\times \mathbb{F}_p$$ be the set of all $$p^2$$ points and let $$\mathcal{L}$$ be the set of all $$p^2$$ lines in the plane. Since each line contains $$p$$ points, there are $$p^3$$ incidences. On the other hand, a Szemerédi-Trotter bound would give $$O((p^2)^{2/3} (p^2)^{2/3} + p^2) = O(p^{8/3})$$ incidences. This example shows that the trivial, combinatorial incidence bound is tight.

Bourgain, Katz and Tao show that if this example is excluded, then an incidence bound that is an improvement on the trivial bound can be attained.

Incidence bounds over finite fields are of two types: (i) when at least one of the set of points or lines is `large' in terms of the characteristic of the field; (ii) both the set of points and the set of lines are `small' in terms of the characteristic.

Large set incidence bounds
Let $$q$$ be an odd prime power. Then Vinh showed that the number of incidences between $$n$$ points and $$m$$ lines in $$\mathbb{F}_q^2$$ is at most

$$\frac{nm}{q} + \sqrt{qnm}.$$

Note that there is no implicit constant in this bound.

Small set incidence bounds
Let $$\mathbb{F}$$ be a field of characteristic $$p\neq 2$$. Stevens and de Zeeuw show that the number of incidences between $$n$$ points and $$m$$ lines in $$\mathbb{F}^2$$ is

$$O\left(m^{11/15}n^{11/15}\right)$$

under the condition $$m^{-2}n^{13} \leq p^{15}$$ in positive characteristic. (In a field of characteristic zero, this condition is not necessary.) This bound is better than the trivial incidence estimate when $$m^{7/8} < n < m^{8/7}$$.

If the point set is a Cartesian Product, then they show an improved incidence bound: let $$\mathcal{P} = A\times B \subseteq \mathbb{F}^2$$ be a finite set of points with $$|A|\leq |B|$$ and let $$\mathcal{L} $$ be a set of lines in the plane. Suppose that $$|A||B|^2 \leq |\mathcal{L}|^3$$ and in positive characteristic that $$|A||\mathcal{L}|\leq p^2$$. Then the number of incidences between $$\mathcal{P}$$ and $$\mathcal{L} $$ is

$$O\left(|A|^{3/4}|B|^{1/2} |\mathcal{L}|^{3/4} + |\mathcal{L}| \right).$$

This bound is optimal. Note that by point-line duality in the plane, this incidence bound can be rephrased for an arbitrary point set and a set of lines having a Cartesian product structure.

In both the reals and arbitrary fields, Rudnev and Shkredov show an incidence bound for when both the point set and the line set has a Cartesian product structure. This is sometimes better than the above bounds.

title: Szemerédi–Trotter theorem


text:
Rollerball (video game)

Rollerball (ローラーボール) is a video game produced by HAL Laboratory in 1984 for the MSX. A Nintendo Entertainment System version of the game was released in 1988. It is designed to be played by one to four players, in turn. It is an emulation of a pinball machine.

The pinball machine rendered in Rollerball is composed of four screens, which, by proportion, would be about as long as two standard pinball tables if it were a real table. The graphics on two of the four screens are based on various aspects of the New York City skyline. The topmost screen (hereafter called the bonus screen) merely shows some clouds and a blimp. The second screen (the main screen) shows the top of the Empire State Building, while the third screen (intermediate) shows the lower skyline and the Statue of Liberty. The lowest (final) screen shows only a blue backdrop, representing the Ocean.

Main screen
In the main mode, each player launches the ball directly into the main screen. To the top is a small loop marked SLOT; if the player sends the ball through this loop, a slot machine display in the center of the screen cycles, with various penalties or rewards given when one of the three symbols (an eggplant, a pair of cherries, or a bell) appears three times. The center of the SLOT loop is open, allowing the player to enter the bonus screen.

There is a pair of kickback holes in the upper left of the main screen, with a bumper in proximity to the upper one. The lower one will shoot the ball straight up, relying on the curvature of the wall to direct it into the upper hole if the player is lucky. If the ball falls in the upper hole, one of two things can happen. If the kickback slot in the bonus screen is empty, the ball will be transferred to that slot and another ball will be released to the plunger to enter play. If the kickback slot is already filled, the ball is relaunched from the lower hole.

Intermediate screen
When in the intermediate screen, the most viable way of returning to the main screen is by a kickback hole on the upper left of the screen. It initially fires up to the main screen when entered, but switches directions every time it is used. If the player gets three cherries on the main screen slot, this hole will always shoot the ball upwards. Otherwise, there are some chances to score in this screen, but it is not a desirable place to have the ball.

There are three sets of three drop targets, and a set of three slots. When the game begins, a light (with the letter A) is lit above the first slot, and one set of three drop targets is chosen and marked with a flashing green light. Additionally, a bonus tally on this screen begins at 3,000 points. Completing a set of drop targets increases this bonus tally; sending the ball through a slot when its light is lit (one can move the light by flipping the flippers) adds the current tally to the player's score.

Lower screen
The lower screen, however, is the least desirable place to be. The ball can only be officially drained from this screen. However, some options are still available to the player:

 * The apparatus on the left side of the screen acts as a kind of slot machine to provide bonuses. The button on the lower side of the apparatus enables it, the spinner changes the bonus indicated, and the flashing sensor will (as long as it is flashing when the ball passes over it) award the player the indicated bonus.
 * A smaller right flipper sits near a kickback hole at the upper right of the screen. If enabled through either receiving three cherries on the main screen or the Exit Hole bonus from the lower screen bonus apparatus, this hole sends the ball back to the plunger to be relaunched, with no lost ball penalty.
 * A kickback slot to the left of the left flipper complex can be opened the same way as the Exit Hole, as can a stopper between the two flippers. The kickback can also be opened by lighting the ABC slots in the middle of the screen.
 * A well-aimed hit from the left flipper can send the ball safely back into the intermediate screen.

Bonus screen
While on the bonus screen, the player must shoot the ball over each of seven sensors, with the letters in the phrase "SKY HIGH" written on them, in a random but forced order. (That is, the player must shoot the ball over the flashing letter to light it and activate it; passing over non-flashing or already activated letters has no effect.) After this is done and the ball is placed in the kickback hole at the top of the screen, the letters turn into bumpers which must be hit numerous times to remove and start the bonus game again. Successfully finishing this bonus gives the player a large sum of points, as well as an extra ball (the first time completed) or an increase of the bonus multiplier (any other completion).

Two sets of four targets, similar to drop targets, are in the top corners of the bonus screen. When all activated, the upper left targets, labeled "RAISE THE SAVER", place a stopper at the gap between the left wall and the left flipper apparatus. The upper right targets, labeled "OPEN THE GATE", open a kickback slot in the lower right corner. Locking a ball in the kickback slot will send the ball into play as part of a two-ball multiball event when the bonus game is enabled. If the slot is opened when a ball is already locked, the locked ball will kick the entering ball back into play.

Losing a ball
If the ball passes the flippers on the lower screen, on either side or between the flippers, it is drained and the end-of-ball bonus is calculated. A tally of the current bonus is kept during gameplay and shown on the lower screen; this bonus starts at 1,000 points and is increased in intervals of 1,000 points during play. Upon draining the ball, the bonus is counted down to 0 points and added to the player's score; to represent any increase in the bonus multiplier, this count is repeated. The bonus multiplier can be increased by finishing the bonus game more than once, or by receiving three cherries or three bells on the main screen slot machine.

The game ends after three balls (in addition to any extra balls from the bonus screen) are drained; a typical final score can be around 300,000 points. Scoring 1,000,000 points enables the credits after the final ball is drained.

Match play
The alternate mode is a two-player game called Match Play. In this mode, a much smaller table, only one screen tall, houses a number of buttons and switches that lower the score of the player on that side by various amounts. Four sensors in the middle of the table will switch the scores of the two players whenever they all become lit. A slot machine is spun by the buttons on the outer walls, and its bonus is enacted by hitting the button on the top wall. The first player to lose all his or her points loses.

Two animals in the middle of each player's area show an emotion, from ecstasy to sadness, through neutral indifference, depending on that player's score and the score margin between the two players. In the Japanese version, the left player's animal is an elephant, and the right player's is a giraffe. In the English version, the giraffe was changed to a donkey, likely in reference to the Republican and Democratic U.S. political parties.

title: Rollerball (video game)


text: User talk:4.4.157.23

title: User talk:4.4.157.23


text:
José Vega Santana

José Vega Santana, known by his stage name "Remi" (born February 28, 1958) is a singer and clown from Puerto Rico. His career as a clown, spanning over 35 years, began with the group "Los Dulces Payasos" ("The Sweet Clowns") after developing the character of Remi while a student at the Interamerican University of Puerto Rico. He's one of the most famed clowns in Puerto Rico.

Family life
Vega is married to Bettina Mercado, president of Bettina Cosmetics. He has a daughter from a previous marriage to Marina Berti, Marina Vega Berti who participated in Miss Universe Puerto Rico 2013 as Miss Luquillo.

Early years
Vega was born in San Juan, Puerto Rico, his mother was the lead singer in "Googie Santana" and his grandfather was former baseball player Pepe Santana. Ever since he was young, Vega knew that he wanted to be an entertainer. He started as a radio music programmer and announcer. Later, he joined the dance and theater company of María Teresa Miranda.

In the mid-1970s, Vega was a Psychology student in the Interamerican University of Puerto Rico. During that time he also took painting classes in the School of Plastic Arts in San Juan. It is there that he, together with some other students decided to form an "Artisans Market" at the Luis Muñoz Rivera Park. The purpose of the "Market" was to give painting classes to young children, and on one occasion they dressed up as clowns. This was when Vega developed and created the character of "Remi". They became so popular that they decided to form a group and call themselves Los Dulces Payasos (The Sweet Clowns).

Remi the clown
In 1983, Vega and the group received an offer from local T.V. producer Tommy Muñiz to work in "Channel 7". The channel gave them their own children's show. During this time they also recorded an album with songs composed by Vega. They have the distinction of being the first "cultural clowns" to create new children's songs in Puerto Rico.

During the time that Vega wasn't acting in his clown character, he sang and composed songs for the group Haciendo Punto en Otro Son. Vega composed "Mi Son", a song that summarized the band's journey from the first album until the last studio album Llegaremos. He participated in the group until the live album, Punto Final (1986). He also did a solo of one of his compositions called "Personajes".

In 1985, Vega developed a new concept in children's television, which he called Chiquimundo, and whose main objective was to educate children. This show was also transmitted on "Channel 7" and was produced by Rafo Muñiz (Tommy's son). "Remi" was joined by the clowns "Colorina" and "Cascabel". The show was an instant hit with the children and their parents in Puerto Rico.

In 1986, the three clowns recorded an album for children which became a local hit. Vega joined forces with the musician Pedro Rivera Toledo and produced the theater production of El Soldadito de Plomo (The Little Lead Soldier) in which Vega played the leading role.

Singing career
In the year 2000, Vega was selected to represent Puerto Rico in the international song festival known as the OTI which was celebrated in the city of Acapulco, Mexico. In the festival he sang one of his compositions Con Una Canción (With A Song) and won first place as "Best Singer". He also won a second place prize for "Best Composer". The last time a Puerto Rican had received a distinction in the "OTI" festival was in 1980, when Rafael José won as "Best Singer". Vega received a hero's welcome upon his return to the island and was honored by the Puerto Rico House of Representatives and Senate for his distinguished career of 20 years.

Later years
Vega has traveled to many cities in the United States making presentations as "Remi". He had a comic book which was called Remi, El Clown which presented the adventures of Puerto Rico's Clown, Remi.

title: José Vega Santana


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List of battles of the Imperial Japanese Navy

The following are some of the battles of the Imperial Japanese Navy (IJN):

Boshin War (1868–1869)

 * Naval Battle of Awa, 28 January 1868.
 * Naval Battle of Miyako, March 1869.
 * Naval Battle of Hakodate, May 1869 (Imperial Navy victory over the remnants of the shōgun's Navy of the Republic of Ezo.)

First Sino-Japanese War (1894–1895)

 * Battle of Pungdo (First naval battle of the war)
 * Battle of Yalu River (1894) (Major naval victory over China)
 * Battle of Weihaiwei (Decisive Japanese victory in Land/Naval battle)

Russo-Japanese War (1904–1905)

 * Battle of Port Arthur (February 1904, tactically inconclusive)
 * Battle of Chemulpo Bay (February 1904, Japanese victory over small Russian squadron off present day Inchon)
 * Battle of the Yellow Sea (August 1904, tactically inconclusive, Japanese strategic victory)
 * Battle off Ulsan (August 1904, minor Japanese victory)
 * Battle of Korsakov (August 1904, minor Japanese victory)
 * Battle of Tsushima (May 1905, major Japanese naval victory over Russia)

World War I (1914–1918)

 * Battle of Tsingtao. Naval actions against German interests in the Far-East, in particular the capture of the Tsingtao peninsula.
 * Few ships diverted to Atlantic Ocean and Mediterranean Sea for escort duties cooperating with the British Royal Navy. In the Mediterranean, a fleet consisting of one armoured cruiser, Nisshin, and eight of the Navy's newest destroyers under Admiral Satō Kōzō, was based in Malta and efficiently protected allied shipping between Marseilles, Taranto and ports in Egypt until the end of the War.
 * Seizure of the former possessions of Germany in Micronesia (the Mariana Islands (excluding Guam), Caroline Islands and Marshall Islands).

Second Sino-Japanese War (1937–1945)
Besides support for Imperial Japanese Army operations, the Navy operations involved many landing operations by the Special Naval Landing Forces along the coasts and rivers of the Republic of China, French Indochina and along the Yangtze River and its tributaries. The Navy provided much of the air support for operations in the first few years of the war in central and southern China.

 * Battle of Shanghai
 * Battle of Beiping-Tianjin
 * Battle of Nanking
 * Amoy Operation
 * Battle of Wuhan
 * Canton Operation
 * Hainan Island Operation
 * Battle of Nanchang
 * Swatow Operation
 * 1st Battle of Changsha
 * Battle of South Guangxi
 * 1939-40 Winter Offensive
 * Indochina Expedition
 * 2nd Battle of Changsha
 * 3rd Battle of Changsha

World War II (1941–1945)

 * Attack on Pearl Harbor (7 December 1941, major Japanese tactical victory; destruction of much of the United States Navy (USN) battleship fleet, strategically inconclusive)
 * Battle of Wake Island (8–23 December 1941, Japanese victory against US)
 * Attack on Prince of Wales and Repulse (10 December 1941, decisive Japanese victory; destruction of the British Royal Navy (RN) in Malaya)
 * Battle of Balikpapan (23–24 January 1942, Allied tactical victory, Japanese strategic victory)
 * Battle off Endau (26–27 January 1942, Japanese victory against Allies)
 * Battle of Makassar Strait (4 February, 1942, Japanese victory against Allies)
 * Attack on Darwin (19 February 1942, Japanese victory against Allies)
 * Battle of Badung Strait (18–19 February 1942, Japanese victory against Allies)
 * First Battle of Rabaul (20 February 1942, US tactical victory, Japanese strategic victory)
 * First Battle of the Java Sea (27 February 1942, major Japanese victory against Allies; IJN sinks five warships without loss)
 * Battle of Sunda Strait (28 February–1 March 1942, major Japanese victory against Allies; IJN destroys Allied fleet)
 * Second Battle of the Java Sea (1 March 1942, decisive Japanese victory; destruction of the Allied naval force in Indonesia)
 * Battle of Salamaua-Lae (8-13 March 1942, Allied tactical victory, Japanese strategic victory)
 * Operation C (31 March 1942, Japanese victory against Allies)
 * Battle of the Coral Sea (4-8 May 1942, Japanese tactical victory, Allied strategic victory)
 * Attack on Sydney Harbour (31 May–8 June 1942, Japanese tactical victory, strategically inconclusive)
 * Battle of Midway (5 June 1942, major US victory; IJN loses four carriers, while USN loses one carrier)
 * Battle of Savo Island (9 August 1942, major Japanese tactical victory against Allies; IJN sinks four heavy cruisers without loss, strategically inconclusive)
 * Battle of the Eastern Solomons (24 August 1942, US victory)
 * Battle of Cape Esperance (11-12 October 1942, US tactical victory, strategically inconclusive)
 * Battle of the Santa Cruz Islands (26 October 1942, Japanese tactical victory, US strategic victory)
 * Battle of Guadalcanal (12 November 1942, major US victory; USN repulses major IJN troop convoy)
 * Battle of Tassafaronga (30 November 1942, Japanese tactical victory against US, strategically inconclusive)
 * Battle of Rennell Island (29-30 January 1943, Japanese defensive victory against US)
 * Battle of the Bismarck Sea (2-4 March 1943, major Allied victory; Allied aircraft destroy major IJN troop convoy)
 * Battle of Blackett Strait (6 March 1943, US victory)
 * Battle of the Komandorski Islands (26 March 1943, tactically inconclusive, US strategic victory)
 * Operation I-Go (1-16 April 1943, Japanese tactical victory against Allies, strategically inconclusive)
 * Battle of Kula Gulf (6 July 1943, US tactical victory, strategically inconclusive)
 * Battle of Kolombangara (12–13 July 1943, Japanese tactical victory against Allies, strategically inconclusive)
 * Battle of Vella Gulf (6-7 August 1943, major US victory; USN sinks three destroyers without loss)
 * Battle off Horaniu (17-18 August 1943, Japanese defensive victory against US)
 * Battle of Vella Lavella (6 October 1943, Japanese defensive victory against US)
 * Battle of Empress Augusta Bay (1 November 1943, US victory)
 * Second Battle of Rabaul (2-11 November 1943, Allied victory)
 * Battle of Cape St. George (25 November 1943, major US victory; USN sinks three destroyers without loss)
 * Battle of Truk (17-18 February 1944, major US victory; IJN loses 15 warships and 32 merchant ships)
 * Battle of the Philippine Sea (19 June 1944, decisive US victory; IJN loses three carriers and hundreds of aircraft)
 * Battle of Formosa (12-16 October 1944, major US victory; IJN loses hundreds of aircraft)
 * Battle of Leyte Gulf (23-26 October 1944, decisive Allied victory; IJN loses 28 warships, including four carriers and three battleships)
 * Battle off Samar (25 October 1944, Japanese tactical victory, US strategic victory)
 * Battle of Ormoc Bay (11 November-21 December 1944, US victory)
 * First Battle of Kure (19 March 1945, Japanese defensive victory against US)
 * Battle of the Malacca Strait (15-16 May 1945, RN victory)
 * Operation Kikusui (6 April–22 June 1945, Allied defensive victory)
 * Operation Ten-Go (7 April 1945, major US victory; destruction of the last IJN battle fleet)
 * Battle of Yokosuka (18 July 1945, Allied victory)
 * Battle of Tokyo Bay (22–23 July 1945, US victory)
 * Second Battle of Kure (24-28 July 1945, major Allied victory; most of the remaining IJN warships are sunk)