title: Kidnapping of Carlina White

text: In 2005, when White was pregnant with her daughter, she requested Pettway obtain her birth certificate so she could get health insurance. Pettway acquired a forged Connecticut birth certificate, which White attempted to use as proof of identity so she could obtain the health insurance, but the officials told her the document was forged.


title: Kidnapping of Carlina White

text: Later that evening, in a state of shock, White confronted Pettway, who broke down and confessed that she was not White's biological mother. The revelation was not entirely surprising to White as she had begun to notice that she did not share physical traits with Pettway. Pettway lied and told White that she had been abandoned by a drug addict. At age 23, White used websites such as the National Center for Missing and Exploited Children, where she found that the images of the kidnapped Carlina resembled infant photos of herself as Nejdra and those of her daughter, Samani. She called the center's hotline and was able to contact her birth family. DNA profiling confirmed in January 2011 that she was the missing Carlina White.


title: Kidnapping of Carlina White

text: In 1987, New York City Police Department detectives questioned a woman in Baltimore, who witnesses had identified as having been seen in the hospital, without apparent result.


title: Kidnapping of Carlina White

text: After the confirmation that Nejdra Nance was really Carlina White, the Federal Bureau of Investigation began a search for Ann Pettway. The statute of limitations for the state kidnapping law had expired in New York, but there is no statute of limitations for the federal law on kidnapping. An arrest warrant for Ann Pettway was issued by the North Carolina Department of Correction on January 21, 2011, for violating her probation from a conviction for attempted embezzlement. White stated, "I just hope that the officials be able to get her in their hands, so we can just hear her side of the story now."


title: Kidnapping of Carlina White

text: Pettway turned herself in to the FBI office at Bridgeport on the morning of January 23, 2011. She had driven from North Carolina to Connecticut to arrange care for her biological son. Pettway told federal investigators that she kidnapped White after enduring several miscarriages because of the stress over whether "she would ever be able to be a parent." Pettway did not enter a plea at her arraignment at the U.S. District Court for Southern New York in Manhattan, where she faced between 20 years and life in prison for kidnapping. On February 17, 2011, a federal grand jury indicted Pettway on the kidnapping charge.


title: Kidnapping of Carlina White

text: On February 10, 2012, Pettway pleaded guilty to a federal kidnapping charge. As part of a plea bargain, prosecutors agreed to recommend to the judge a prison sentence of 10 to 12½ years. On July 30, 2012, Judge P. Kevin Castel sentenced Pettway, who was then 50 years old, to 12 years in prison. Her lawyers had asked for leniency, saying Pettway had been severely depressed after suffering from multiple miscarriages and stillbirths. However, the judge said she was selfish and "inflicted a parent's worst nightmare on a couple." Carlina White's father said he thought the sentence was too lenient and that Pettway should've received the amount of time as she'd kept his daughter, 23 years. During the hearing, Pettway apologized, saying "I would like to apologize to the family. It may be rejected, but I am deeply sorry for what I've done. If they don't accept it, it's understandable. I'm here to right my wrong."


title: Kidnapping of Carlina White

text: Pettway served her sentence in the Federal Correctional Institution, Aliceville in Alabama until she was released on April 14, 2021.


title: Kidnapping of Carlina White

text: Upon being reunited with her biological parents, Carlina White's attorney advised her to ask them about the cash settlement from the hospital. Joy White and Carl Tyson both confirmed that most of this money had been spent during the years before their reunion, and that a trust fund that had been established was obtainable only if Carlina had been found before the age of 21. Joy White later stated that there had been a falling out over the issue of the money.


title: Kidnapping of Carlina White

text: In May 2011, public defender Robert Baum said that he met Carlina White during preparations for Ann Pettway's trial and that White agreed to testify on Pettway's behalf. By the following July, White became estranged from her biological parents. However, several months later, she contacted both of her biological parents individually, having had a bit more time to process the situation; she later publicly stated that the issue over settlement funds was "just a misunderstanding." While "Carlina White" is her legal name, as it appears on official documents, she says that she will continue to go by "Netty" in public since it was neither the name her biological parents gave her nor the name given to her by the woman who raised her, but rather is "[the name] I gave myself."


title: Kidnapping of Carlina White

text: In 2014, White spoke at the Crimes Against Children Conference, the leading national training event for law enforcement professionals working to combat child victimization. As of 2014, she continues to have a relationship with her biological parents.


title: USS Wichita (CA-45)

text: USS "Wichita" was a unique heavy cruiser of the United States Navy built in the 1930s. The last American cruiser designed to meet the limits of the London Naval Treaty, she was originally intended to be a heavy cruiser, accordingly with the maximum main armament of three triple gun turrets. These were instead placed on an improved hull derived from the "Brooklyn"-class light cruisers, with increased armoring. This design would go on to form the basis for the later World War II-era heavy cruisers such as the s. The ship was authorized by the 1929 Cruiser Act, laid down at the Philadelphia Naval Shipyard in October 1935, launched in November 1937, and commissioned into the US Navy in February 1939.


title: USS Wichita (CA-45)

text: Following her commissioning, "Wichita" was assigned to neutrality patrols in the Atlantic. After the United States entered World War II, the ship saw heavy service throughout the conflict. She was first assigned to convoy escort duty on the Murmansk Run in early 1942, and supported amphibious landings during Operation Torch in November 1942. During the Naval Battle of Casablanca, "Wichita" engaged several French coastal batteries and warships, including the battleship "Jean Bart". In 1943, "Wichita" was transferred to the Pacific Theater, where she remained for the rest of the war. She frequently provided antiaircraft defense for the Fast Carrier Task Force during operations in the central Pacific, including the Battles of the Philippine Sea and Leyte Gulf in 1944. During the latter engagement, "Wichita" assisted in the sinking of the Japanese aircraft carrier "Chiyoda".


title: USS Wichita (CA-45)

text: "Wichita" was heavily engaged during the invasion of Okinawa, where she provided heavy gunfire support to ground troops ashore. After the Japanese surrender, the ship served as part of the occupation force in Japan and assisted in the repatriation of American military personnel under Operation Magic Carpet. After returning to the United States, she was decommissioned and placed in the mothball fleet in 1947. She remained in reserve until 1959, when she was stricken from the Naval Vessel Register and sold for scrapping in August 1959.


title: USS Wichita (CA-45)

text: In the early 1930s, the Secretary of the Navy, Curtis D. Wilbur, pushed for a new construction program for light and heavy cruisers. Wilbur succeeded in passing the Cruiser Act in 1929, which authorized several new cruisers. Five heavy cruisers, the last of which was "Wichita", were ordered between 1931 and 1934. "Wichita" was the last heavy cruiser permitted under the terms of the London Naval Treaty in 1930, which limited the US to 18 heavy cruisers with a maximum standard displacement of . The ship was originally intended to be built to the design of the , but the design was reworked before construction began. Instead, the design for "Wichita" was based on the of light cruisers. The "Brooklyn" design was modified heavily, to give the new ship higher freeboard and better stability, and an increased cruising radius. The secondary battery of eight guns was identical in number to the light cruisers, but was arranged to give better fields of fire. The main battery of nine guns was mounted in a new gun turret design that rectified problems discovered in earlier cruisers.


title: USS Wichita (CA-45)

text: "Wichita" was laid down at the Philadelphia Naval Shipyard on 28 October 1935, and launched on 16 November 1937. By the time she was completed, in February 1938, "Wichita" was nearly over the 10,000-ton limit; as a result, she was completed with only two of the eight 5-inch guns to keep her under the displacement restriction. When the rest of the 5-inch guns were installed, it was found that the ship was too top-heavy, and so of pig iron had to be added to her bottom to balance the cruiser. "Wichita" was commissioned into the US Navy on 16 February 1939 and was assigned the hull number CA-45. Her first commander was Captain Thaddeus A. Thomson.


title: USS Wichita (CA-45)

text: "Wichita" was long at the waterline and long overall. She had a beam of and a draft of . She displaced at standard displacement and at full combat load. The ship had a crew of 929 officers and enlisted men. She was equipped with four seaplanes and a pair of aircraft catapults and a crane for handling the aircraft which were mounted on the stern. "Wichita" was powered by four Parsons steam turbines and eight Babcock & Wilcox oil-fired water-tube boilers. The propulsion system was rated at and a top speed of . She carried of fuel oil, which gave her a maximum cruising range of at .


title: USS Wichita (CA-45)

text: The hull was protected by a waterline armored belt composed of Class A armor that was thick amidships. It was reduced to thick on either end. The belt was backed with of special treatment steel. The Class A steel was significantly more effective than the Class B armor used in earlier cruisers; 8-inch guns had to be within to penetrate the belt, as opposed to for the earlier armor. "Wichita" had a thick deck, which was immune to 8-inch fire inside . The conning tower had thick sides and a 2.25 in thick roof. The ship's main battery turrets had thick faces, thick sides, thick rears, and thick roofs. The turrets were mounted on armored barbettes protected with of armor plating.


title: USS Wichita (CA-45)

text: "Wichita" was armed with a main battery of nine 8-inch /55 Mark 12 guns mounted in three 3-gun turrets. The guns fired a projectiles at a muzzle velocity of . Maximum elevation of the guns was 41 degrees; this provided a maximum range of . Rate of fire was approximately one salvo every fifteen seconds. The turrets allowed each gun to elevate and fire individually. Her secondary battery consisted of eight 5-inch /38 Mark 12 dual-purpose guns, four in single, enclosed Mark 30 high-angle mounts, and four in open mounts. These guns fired projectiles at a rate of 20 rounds per minute. Muzzle velocity was ; against aerial targets, the guns had a ceiling of at 85 degrees. At 45 degrees, the guns could engage surface targets at a range of . "Wichita" was the first cruiser in the US Navy to be equipped with the new 5-inch /38 gun.


title: USS Wichita (CA-45)

text: By August 1945, the ship had been equipped with numerous smaller guns for close-range anti-aircraft defense. Sixteen Bofors 40 mm guns were placed in quadruple mounts, and another eight were in dual mounts. She also carried eighteen Oerlikon 20 mm guns in single mountings. The 40 mm guns had a ceiling of at 90 degrees elevation and a maximum rate of fire of 160 rounds per minute. The 20 mm gun had a rate of fire of 465–480 rounds per minute; they had a ceiling of . By the end of the war, the ship was armed with a variety of fire control systems for her guns, including Mark 34 fire control gear and Mark 13 and Mark 28 fire control radars.


title: USS Wichita (CA-45)

text: "Wichita" departed Philadelphia after her commissioning, bound for Houston, Texas. She arrived on 20 April 1939 and took part in the dedicatory and memorial service at the San Jacinto Battle Monument and War Relic Museum. The ship left Houston on 1 May for her shakedown cruise, during which she visited the Virgin Islands, Cuba, and the Bahamas before she returned to Philadelphia for post-shakedown repairs. On 25 September, a few weeks after the outbreak of World War II in Europe, "Wichita" was assigned to Cruiser Division 7 in the Atlantic Squadron, based in the Hampton Roads. She conducted her first neutrality patrol on 4–9 October. After returning to port, she went into dock at the Norfolk Navy Yard for maintenance, which lasted until 1 December. On 4 December, "Wichita" steamed to Guantanamo Bay, Cuba, arriving on the 8th. There, Thomson assumed command of the newly formed Caribbean Patrol, which included "Wichita" and the cruiser , and the destroyers , , , , and , and Navy patrol squadrons VP-33 and VP-51. Over the course of the next three months, the force conducted a series of training maneuvers in the Caribbean. At the end of February, "Wichita" returned to Norfolk via Philadelphia, where she participated in further training through May.


title: USS Wichita (CA-45)

text: Starting in June, "Wichita" and conducted a goodwill cruise to South America; "Wichita" carried Rear Admiral Andrew C. Pickens, the commander of Cruiser Division 7. Included in the ports of call were Rio de Janeiro and Santos in Brazil, Buenos Aires, Argentina, and Montevideo, Uruguay. The cruise ended in late September; the two cruisers arrived in Norfolk on the 24th. Over the next three months, "Wichita" served as a training ship for Naval Reserve midshipmen and conducted gunnery practices off the Virginia capes. On 7 January 1941, "Wichita" departed Hampton Roads for Guantanamo, arriving four days later. She participated in fleet maneuvers in the Caribbean through March and took part in practice amphibious landings at Puerto Rico. She returned to the United States, docking at the New York Navy Yard, on 23 March. "Wichita" went to sea again on 6 April, bound for Bermuda; she reached her destination two days later. She then joined the aircraft carrier and the heavy cruiser for a patrol in the North Atlantic, during which the ships sailed to within of Ireland.


title: USS Wichita (CA-45)

text: "Wichita" then returned to the New York Navy Yard on 17 May and went into drydock on 21 June. Repairs were completed on 2 July, after which "Wichita" was transferred to Newport, Rhode Island. She sortied again on 27 July bound for Iceland as part of Task Force 16 under Operation Indigo II, the occupation of Iceland. "Wichita" arrived in Reykjavík on 6 August, along with the carrier and the battleship . The task force landed a contingent of US Army troops and fighter aircraft to provide air support. The cruiser returned to the United States by 20 August. "Wichita" returned to Iceland in September, arriving in Reykjavík on 28 September. Two days prior to "Wichita"s arrival, the US Navy ordered the units of the Atlantic Fleet to protect all ships engaged in commerce in United States defensive waters. The orders authorized the Navy to patrol, escort merchantmen, and attack any German or Italian naval forces encountered. "Wichita" was assigned to Task Group 7.5, which was engaged in patrolling Icelandic waters through the end 1941. On 7 December 1941, the Japanese attacked Pearl Harbor, bringing the United States into World War II; on the day of the attack, "Wichita" lay at anchor at Hvalfjörður, Iceland.


title: USS Wichita (CA-45)

text: "Wichita" left port on 5 January 1942 for training and a patrol in the Denmark Strait; she returned to Hvalfjörður on 10 January. On the 15th, a powerful storm, with sustained winds of and gusts up to , hit Iceland. "Wichita" was damaged by the storm, including a collision with the freighter and the British trawler . She then ran aground off Hrafneyri Light. The following day, the ship's crew evaluated her condition; she had suffered minor damage from the collisions, including some leaks, and damage to the hull from the grounding. Temporary repairs were effected in Iceland to allow "Wichita" to return to the New York Navy Yard for more thorough repairs. She arrived on 9 February, and repairs lasted until 26 February, when she left port for training maneuvers off Maine in early March.


title: USS Wichita (CA-45)

text: On 26 March, "Wichita", assigned to Task Force 39, departed the United States to reinforce the British Home Fleet based in Scapa Flow. Task Force 39, commanded by Rear Admiral John W. Wilcox, Jr., included "Wasp", the battleship , the cruiser "Tuscaloosa", and eight destroyers. While en route, Wilcox was swept overboard in a heavy sea and lost. Rear Admiral Robert C. Giffen, who flew his flag in "Wichita", took command of the task force. After arriving in Scapa Flow, "Wichita" and the other American ships spent several weeks training with their British counterparts. On 28 April, "Wichita" departed on her first major operation with the British. She was assigned to the Allied escort for the Arctic convoys QP 11 and PQ 15. The American component, organized as Task Force 99, comprised "Washington", "Wichita", "Tuscaloosa", and four destroyers. The British assigned the carrier , the battleship , a light cruiser, and five destroyers. After successfully escorting the convoys, "Wichita" returned to Hvalfjörður, arriving on 6 May.


title: USS Wichita (CA-45)

text: "Wichita" sortied on 12 May to relieve "Tuscaloosa", which was patrolling the Denmark Strait. "Wichita" returned to Hvalfjörður a week later, before putting to sea as part of another Allied convoy escort protecting one leg of the movement of Murmansk-bound convoy PQ 16 and eastbound QP 12. She put into Scapa Flow on 29 May after completing the mission. While in Scapa Flow, King George VI inspected "Wichita" on 7 June. "Wichita" left Scapa Flow on 12 June, bound for Hvalfjörður, and arrived 14 June. She then relieved the British cruiser on patrol in the Denmark Strait. While on patrol on 17 June, "Wichita" spotted a German Focke-Wulf Fw 200 reconnaissance bomber and opened fire, though without result. Three days later, she engaged another Fw 200, again without success.


title: USS Wichita (CA-45)

text: After returning to Hvalfjörður, "Wichita" steamed to Seidisfjord at the end of June, where she joined "Tuscaloosa" and three destroyers. They were assigned to the escort for the convoy PQ 17. The convoy escort also included "Washington", "Victorious", and the battleship . The Germans organized a powerful task force, centered on the battleship and three heavy cruisers, to attack the convoy; the operation was codenamed "Rösselsprung" (Knight's Move). Swedish intelligence had meanwhile reported the German departures to the British Admiralty, which ordered the convoy to disperse. Aware that they had been detected, the Germans aborted the operation and turned over the attack to U-boats and the Luftwaffe. The scattered vessels could no longer be protected by the convoy escorts, and the Germans sank 21 of the 34 isolated transports. The next day, while south of Spitzbergen, the ships were spotted and shadowed by a pair of Fw 200s. Both "Wichita" and "Tuscaloosa" opened fire with their antiaircraft guns, but the Fw 200s escaped without damage.


title: USS Wichita (CA-45)

text: In late July, "Wichita" went into drydock at the Royal Navy base in Rosyth, Scotland. Repairs, which included correcting a propeller shaft vibration, lasted from 24 July until 9 August. The repairs to the propeller shaft were ineffective, however, which necessitated a return to the United States. She reached the New York Navy Yard on 22 August for repairs, which lasted until 5 September. She completed a round of post-repair sea trials before conducting gunnery exercises in the Chesapeake Bay. "Wichita" conducted training off the Virginia Capes for the rest of the month, after which she steamed to Casco Bay in Maine for further maneuvers.


title: USS Wichita (CA-45)

text: At the end of October, "Wichita" was assigned to Task Group 34.1, under the command of Rear Admiral H. Kent Hewitt, who flew his flag in . The Task Group also included the battleship and "Tuscaloosa". The ships were assigned to provide gunfire support for Operation Torch, the invasion of French North Africa. "Wichita" participated in the Naval Battle of Casablanca, which began early on the morning of 8 November. The ships were tasked with neutralizing the primary French defenses, which included coastal guns on El Hank, several submarines, and the incomplete battleship which lay at anchor in the harbor. "Wichita" and "Tuscaloosa" initially engaged the French batteries on El Hank and the French submarine pens, while "Massachusetts" attacked "Jean Bart". French naval forces, led by the cruiser , put up a stubborn defense.


title: USS Wichita (CA-45)

text: In response, the French launched a pair of attacks to break up the American landings. During the first French attack, either "Wichita" or "Tuscaloosa" damaged the French destroyer and forced it aground. A second French attack was also defeated; one of the two cruisers sank the destroyer and damaged . "Wichita", "Tuscaloosa", and "Massachusetts" also engaged "Jean Bart". At 11:28, "Wichita" was hit by a shell, fired by a gun on El Hank. The shell penetrated her deck and exploded below, injuring fourteen men. Hewitt broke off the attack temporarily, but by 13:12, several American warships began firing on French vessels exiting the harbor. "Wichita" and "Tuscaloosa" closed on the port to engage the cruisers "Primauguet" and , still in the harbor. Heavy fire from El Hank forced the American cruisers to retreat shortly after 15:00. For the remainder of the operations off North Africa, "Wichita" patrolled between Casablanca and Fedhala. Her part in the amphibious assault complete, "Wichita" departed the area on 12 November, bound for New York for repairs; she arrived on 19 November.


title: USS Wichita (CA-45)

text: Shortly after repairs were completed, "Wichita" was transferred to the Pacific theater. She was assigned to Task Force 18, commanded by Rear Admiral Giffen, and tasked with operations off Guadalcanal. She was joined by the heavy cruisers and , the light cruisers , , and . In addition, the escort carriers and , and eight destroyers were present in the task group. On the night of 29 January 1943, the Task Force was steaming off Rennell Island; wary of the threat from Japanese submarines, which Allied intelligence indicated were likely in the area, Giffen arranged his cruisers and destroyers for anti-submarine defense, not expecting an air attack. The cruisers were aligned in two columns, spaced apart. "Wichita", "Chicago", and "Louisville", in that order, were to starboard, and "Montpelier", "Cleveland", and "Columbia" were to port. The six destroyers were in a semicircle ahead of the cruiser columns. That evening, the ships came under attack from Japanese torpedo bombers. In the ensuing Battle of Rennell Island, "Chicago" was hit by several torpedoes and sunk; "Wichita" was hit by one torpedo, though it failed to explode.


title: USS Wichita (CA-45)

text: "Wichita" then steamed to Efate in the New Hebrides for a training period. She then departed on 7 April, bound for Pearl Harbor and arriving there a week later. On 18 April, she steamed out of Pearl Harbor for Adak, Alaska, again flying Giffen's flag, for Task Group 52.10. In early May, "Wichita" was assigned to the amphibious force tasked with liberating the Aleutian Islands from Japanese control. She served as the flagship of the northern covering force, along with the cruisers "Louisville" and and four destroyers. On 6 July, "Wichita", three other cruisers, and four destroyers bombarded Japanese positions on the island of Kiska. The bombardment convinced the Japanese that the Americans intended to invade the island in the near future; they therefore planned an evacuation by July.


title: USS Wichita (CA-45)

text: On 19 July, a powerful American fleet, including the battleships , , and "Mississippi" joined "Wichita" to conduct another attack on Kiska three days later. Five days later, malfunctioning radar equipment led to a battle with radar phantoms (the "Battle of the Pips"); "Wichita", two battleships, and two other cruisers expended over a thousand rounds of ammunition from their main batteries on the empty sea. That same day, the Japanese successfully evacuated the island, which was invaded by American troops two weeks later. The morning after the assumed engagement, "Wichita" launched a seaplane to reconnoiter the area, but found no evidence of Japanese forces.


title: USS Wichita (CA-45)

text: "Wichita" participated in exercises off Hawaii for the remainder of the year. On 16 January 1944, she departed to take part in the invasion of the Marshall Islands. She was assigned to Task Group 58.3, under the command of Rear Admiral Frederick C. Sherman. The Task Group included the fleet carrier , the light carriers and , the fast battleships , "Massachusetts", , and , and several destroyers. "Wichita" provided anti-aircraft support for the carriers while they conducted air strikes on Kwajalein and Eniwetok on 29–31 January. On 4 February, "Wichita" arrived at Majuro; she was transferred to Task Group 58.2. The force departed Majuro on 12 February and conducted Operation Hailstone, a major air strike on the Japanese base at Truk, four days later.


title: USS Wichita (CA-45)

text: On the night of 16 February, Japanese aircraft launched an attack on the Task Group and torpedoed the carrier . Task Unit 58.2.4, which included "Wichita", was detached to escort "Intrepid" back to safety and repairs. The ships reached Majuro on 20 February, and departed for Hawaii eight days later. The ships arrived in port on 4 March, and on the 9th, "Wichita" became the flagship of Cruiser Division 6. On 15 March, Cruiser Division 6 departed Hawaii to return to Majuro, arriving on 20 March. After arriving, she joined the screen for the Fast Carrier Task Force, which struck Japanese bases on Yap, Woleai, and in the Palaus. "Wichita" supported strikes on Hollandia in New Guinea on 13–22 April. The task force returned to the seas off Truk on 29 April for a second round of airstrikes on the port. While the carriers were striking Truk, "Wichita" and several cruisers and destroyers shelled Japanese targets on Satawan Island in the Nomol group of the Caroline Islands.


title: USS Wichita (CA-45)

text: On 4 May, "Wichita" returned to Majuro for a month of training. In June, she returned to the fleet, which was gathering at Kwajalein in preparations for operations against the Mariana Islands. "Wichita" was assigned to Task Unit 53.10.8, which shelled Saipan on 13 June. The next day, "Wichita" bombarded Japanese gun positions on Guam, before returning to Saipan later that day. On 17 June, she joined Task Group 58.7; the force patrolled to the west of the Marianas over the next three days in an attempt to intercept the large Japanese carrier force known to be approaching. On 19 June, the Japanese carriers struck at the American fleet, starting the Battle of the Philippine Sea. "Wichita" contributed to the antiaircraft screen; her gunners claimed to have assisted in the destruction of two Nakajima B5N torpedo bombers. The ship was detached to cover troop transports and escort carriers off Saipan on 25 June. This duty lasted through the first week of July. Now part of Task Unit 53.18.1, "Wichita" bombarded Japanese positions on Guam on 8–12 July, and again starting on 18 July.


title: USS Wichita (CA-45)

text: "Wichita" departed Guam on 10 August, bound for Eniwetok. She arrived three days later and remained there until 29 July, when she put to sea to join Task Group 38.1. She screened for the fast carrier task group while they launched airstrikes on Japanese targets in Palau, the Carolines, the Philippines, and Dutch East Indies. On 28 August, TG 38.1 raided targets in Palau and Morotai. By mid-September, TG 38.1 provided air support for the assault on Morotai; the operation lasted until 21 September. The following day, the carriers launched an airstrike on Manila in the Philippines. Early on 22 September, Japanese aircraft launched a counterattack. At 07:34, "Wichita" shot down a bomber approximately 50 yards from her. She shot down another bomber at 07:45. She continued to provide antiaircraft defense for the carriers while they struck Japanese installations on Cebu, Negros, and Coron.


title: USS Wichita (CA-45)

text: "Wichita" got underway to support a raid on Okinawa on 2 October. On 10 October, the fleet reached the waters off Okinawa and launched the strike. The following day, the fleet struck Aparri on Luzon. The fleet then raided Formosa, where they targeted Japanese airfields to prepare for the upcoming assault against the Philippines. On 13 October, Japanese bombers attacked the fleet and badly damaged the cruiser . "Wichita" took "Canberra" under tow, though she was relieved by the ocean-going tug on 15 October. "Wichita" joined the screen for "Canberra"; the squadron was joined by the badly damaged cruiser . The ships were attacked again the following day, and "Houston" was torpedoed again. "Wichita" left the damaged ships on 21 October, after they had successfully reached safer waters. "Wichita" then rejoined the fleet off Luzon, assigned to Task Force 34 under Vice Admiral Willis A. Lee.


title: USS Wichita (CA-45)

text: "Wichita" was present during the Battle of Leyte Gulf, which started on 23 October. On 25 October, the Fast Carrier Strike Force had steamed north, to attack the Northern Force commanded by Jisaburō Ozawa. "Wichita" again screened for the carriers, which sank or damaged several Japanese carriers. Task Force 34 was detached to finish off several of the crippled Japanese ships with gunfire; "Wichita" and three other cruisers sank the light carrier and the destroyer . "Wichita" expended twenty-two percent of her armor-piercing rounds at the two ships, which amounted to 148 rounds at "Chiyoda" and 173 against "Hatsuzuki". In the aftermath of the battle, "Wichita" returned to screening for the carriers off Samar. On 28 October, she provided gunfire support to troops ashore on Leyte. Two days later, she defended against a Japanese airstrike on the fleet.


title: USS Wichita (CA-45)

text: On 31 October, "Wichita" left the area, bound for Ulithi, reaching her destination on 2 November. After replenishing her ammunition and stores, she returned to Leyte for several days, until the middle of November. Her crew detected severe vibrations in her No. 4 engine; the propeller shaft had broken and the propeller was trailing. She was therefore detached on 18 November for repairs in California, via Ulithi. While in Ulithi, divers discovered cracks in a strut for No. 3 propeller shaft; now only two screws were operational. She reached San Pedro in California on 15 December. She entered the Terminal Island Navy Yard shortly after reaching port. Repairs lasted until 8 February 1945, and by 28 February, she departed for Pearl Harbor. "Wichita" arrived in Hawaii on 6 March, before departing five days later for Ulithi.


title: USS Wichita (CA-45)

text: "Wichita" arrived in Ulithi on 20 March, and was assigned to Task Force 54 (TF 54) the next day. She put to sea to take part in the invasion of Okinawa. The ship was placed in Task Unit 54.2.3 to cover minesweepers off Okinawa on 25 March. On the afternoon of the following day, "Wichita" bombarded Japanese positions on the island, from 13:50 to 16:30. Japanese aircraft attacked the ships early the next morning; "Wichita"s gunners shot down one of the aircraft. Later that day, the ship resumed bombardment duties in preparation for the amphibious invasion. She continued to shell the island through 28 March. The next day, she retired to Kerama Retto to replenish her ammunition. The ship then returned to Okinawa later that day to cover underwater demolition teams as they cleared beach obstacles. "Wichita" continued to support the demolition teams the next day, as well as shelling targets ashore. On 31 March, "Wichita" bombarded the sea wall to create a breach in preparation for the landings.


title: USS Wichita (CA-45)

text: The invasion began on 1 April, and "Wichita" provided gunfire support to the landing troops on the southern beaches. At around 12:00, she left the firing line to replenish her ammunition. She resumed bombardment the following day and resupplied again on 3 April before covering minesweepers on 4 April. During the night of 4–5 April, "Wichita" shelled the Japanese defenders on Okinawa. The ship was assigned to join Task Group 51.19 the next day to bombard Tsugen Shima in company with "Tuscaloosa" and the battleships and . Japanese aircraft appeared, which forced the cancellation of the mission. Nevertheless, "Wichita" shelled Japanese shore batteries at Chiyama Shima that evening.


title: USS Wichita (CA-45)

text: Late on 6 April, an A6M Zero attempted to attack "Wichita". The fighter came down through a break in the clouds on "Wichita"s port side. The ship's anti-aircraft gunners immediately opened fire; a burst from one of the 20 mm guns shot away the Zero's tail. The plane veered away, out of control, and dropped its bomb, which fell approximately from the ship. The Zero's wing clipped the deck before the plane crashed into the sea. Eleven men were wounded in the attack, though the ship remained undamaged. The following day, "Wichita" steamed into Nakagusuku Bay to shell a coastal battery. Shells from the Japanese guns landed close to the ship, but no hits were scored before "Wichita" neutralized the battery. Over the next two days, the ship continued to bombard Japanese defenses on the island, until she retired to replenish ammunition on 10 April.


title: USS Wichita (CA-45)

text: "Wichita" continued to provide gunfire support throughout the rest of the month. On 27 April, a small caliber shell penetrated a fuel oil tank five feet below the waterline. After temporary repairs while still off Okinawa proved unsuccessful, "Wichita" returned to Kerama Retto where the damage was repaired on 29–30 April. "Wichita" then returned to the gun line. On 12 May, the ship was damaged by friendly fire. A 5-inch round struck the port aircraft catapult; shell fragments hit the shield of an antiaircraft director, killing one man and injuring eleven others. She departed the area to rest and refit at Leyte, returning to Okinawa on 18 June. "Wichita" continued to provide gunfire support to the troops on Okinawa through July, as part of Task Unit 2. On 15 August, the ship's crew received word that the war with Japan was over. "Wichita" was awarded 13 battle stars for her service during World War II.


title: USS Wichita (CA-45)

text: "Wichita" was assigned to the occupying force shortly after the end of the war. She departed Okinawa on 10 September for Nagasaki, arriving the following day as part of Task Group 55.7. "Wichita" was one of the first major warships to reach Japan; she was escorted by a destroyer, a pair of destroyer escorts, two minesweepers, and the hospital ship . "Wichita" was transferred to Sasebo on 25 September for four days before she returned to Nagasaki on 29 September. She returned to Sasebo shortly thereafter, and while she was there, a severe typhoon struck the area on 9–11 October. "Wichita" was not damaged during the storms. While at Sasebo, "Wichita"s crew inspected the Japanese ships and harbor installations to ensure Japanese compliance with the terms of surrender.


title: USS Wichita (CA-45)

text: On 5 November, "Wichita" was assigned to Operation Magic Carpet, the repatriation of American military personnel. She refueled in Tokyo before departing for San Francisco. The ship reached San Francisco on 24 November, where she went into drydock at the Mare Island Naval Shipyard two days later. Repairs and modifications for further Magic Carpet duty were completed by 1 December. "Wichita" departed for Hawaii on 6 December, reaching Pearl Harbor on 12 December before proceeding to the Marianas. There, the ship loaded servicemen from Saipan and steamed back to San Francisco, arriving on 12 January 1946. She left port on 27 January bound for the east coast of the United States; she transited the Panama Canal on 5–9 February and reached Philadelphia on 14 February. There, she was assigned to the Sixteenth Fleet and was placed in reserve on 15 July. "Wichita" was decommissioned on 3 February 1947 and laid up at Philadelphia.


title: USS Wichita (CA-45)

text: In the late 1940s, the Navy considered converting "Wichita" into a guided-missile cruiser, but and "Canberra" were chosen instead. On 1 March 1959, the ship was stricken from the Naval Vessel Register and sold on 14 August to the Union Minerals and Alloys Corp.


title: Adage

text: An adage (; Latin: adagium) is a memorable and usually philosophical aphorism that communicates an important truth derived from experience, custom, or both, and that many people consider true and credible because of its longeval tradition, i.e. being handed down generation to generation, or memetic replication.


title: Adage

text: An adage may warn against a failure to plan, be interesting observations, ethical rules, or skeptical comments on life in general, such as "do not count your chickens before they hatch", "do not burn your bridges", and .


title: Adage

text: Some adages are products of folk wisdom that attempt to summarize a basic truth; these are generally known as "proverbs" or "bywords". An adage that describes a general moral rule is a "maxim". A pithy expression that has not necessarily gained credibility by tradition, but is distinguished by especial depth or excellent style is denominated an "aphorism", while one distinguished by wit or irony is often denominated an "epigram".


title: Adage

text: Through overuse, an adage may become denominated a "cliché", "truism", or "old saw". Adages originating in modernity are often given proper names and denominated "laws", in imitation of the nomenclature of physical laws, or "principles". Some adages, such as Murphy's Law, are first formulated informally and given proper names later, while others, such as the Peter Principle, are given proper names when formulated; it might be argued that the latter do not represent "true" adages, but the two are often difficult to distinguish.


title: Adage

text: Adages that were collected and used by ancient writers inspired Dutch humanist Desiderius Erasmus Roterodamus to publish his own collection. He revised his moderate volume of 800 adages many times until the final edition of "Adagia" published in 1536 included over 4,000. There have been many such collections since, usually in vernacular languages.


title: Adage

text: Adages formulated in popular works of fiction often find their way into popular culture, especially when a subculture devoted to the work or its genre exists, as in the case of novels of science fiction. Many professions and subcultures create their own adages, which are cognizable as a kind of jargon; such adages may find their way into popular use, sometimes being altered in the process. Online communities, such as those that develop in Internet forums or Usenet newsgroups, often generate their own adages.


title: Kutub al-Sittah

text: The Kutub al-Sittah () are six (originally five) books containing collections of "hadith" (sayings or acts of the Islamic prophet Muhammad) compiled by six Sunni Muslim scholars of Persian origin in the ninth century CE, approximately two centuries after the death of Muhammad. They are sometimes referred to as al-Sihah al-Sittah, which translates as "The Authentic Six". They were first formally grouped and defined by Ibn al-Qaisarani in the 11th century, who added Sunan ibn Majah to the list. Since then, they have enjoyed near-universal acceptance as part of the official canon of Sunni Islam.


title: Kutub al-Sittah

text: Not all Sunni Muslim jurisprudence scholars agree on the addition of Ibn Majah. In particular, the Malikis and Ibn al-Athir consider al-Muwatta' to be the sixth book. The reason for the addition of Ibn Majah's Sunan is that it contains many Hadiths which do not figure in the other five, whereas all the Hadiths in the Muwatta' figure in the other Sahih books.


title: Kutub al-Sittah

text: Sunni Muslims view the six major hadith collections as their most important, though the order of authenticity varies between Madhhabs:


title: Kutub al-Sittah

text: The first two, commonly referred to as the "Two Sahihs" as an indication of their authenticity, contain approximately seven thousand hadiths altogether if repetitions are not counted, according to Ibn Hajar.


title: Kutub al-Sittah

text: According to the "Cambridge History of Iran": "After this period commences the age of the authors of the six canonical collections of Sunni hadith, all of whom were Persian, except Imam Malik. The authors of the six collections are as follows:


title: Ubiquitous computing

text: This paradigm is also described as pervasive computing, ambient intelligence, or "everyware". Each term emphasizes slightly different aspects. When primarily concerning the objects involved, it is also known as physical computing, the Internet of Things, haptic computing, and "things that think".


title: Ubiquitous computing

text: Rather than propose a single definition for ubiquitous computing and for these related terms, a taxonomy of properties for ubiquitous computing has been proposed, from which different kinds or flavors of ubiquitous systems and applications can be described.


title: Ubiquitous computing

text: Ubiquitous computing themes include: distributed computing, mobile computing, location computing, mobile networking, sensor networks, human–computer interaction, context-aware smart home technologies, and artificial intelligence.


title: Ubiquitous computing

text: Ubiquitous computing is the concept of using small internet connected and inexpensive computers to help with everyday functions in an automated fashion.


title: Ubiquitous computing

text: For example, a domestic ubiquitous computing environment might interconnect lighting and environmental controls with personal biometric monitors woven into clothing so that illumination and heating conditions in a room might be modulated, continuously and imperceptibly. Another common scenario posits refrigerators "aware" of their suitably tagged contents, able to both plan a variety of menus from the food actually on hand, and warn users of stale or spoiled food.


title: Ubiquitous computing

text: Ubiquitous computing presents challenges across computer science: in systems design and engineering, in systems modelling, and in user interface design. Contemporary human-computer interaction models, whether command-line, menu-driven, or GUI-based, are inappropriate and inadequate to the ubiquitous case. This suggests that the "natural" interaction paradigm appropriate to a fully robust ubiquitous computing has yet to emerge – although there is also recognition in the field that in many ways we are already living in a ubicomp world (see also the main article on natural user interfaces). Contemporary devices that lend some support to this latter idea include mobile phones, digital audio players, radio-frequency identification tags, GPS, and interactive whiteboards.


title: Ubiquitous computing

text: Ubiquitous computing devices proposed by Mark Weiser are all based around flat devices of different sizes with a visual display. Expanding beyond those concepts there is a large array of other ubiquitous computing devices that could exist. Some of the additional forms that have been conceptualized are:


title: Ubiquitous computing

text: In Manuel Castells' book "", Castells puts forth the concept that there is going to be a continuous evolution of computing devices. He states we will progress from stand-alone microcomputers and decentralized mainframes towards pervasive computing. Castells' model of a pervasive computing system, uses the example of the Internet as the start of a pervasive computing system. The logical progression from that paradigm is a system where that networking logic becomes applicable in every realm of daily activity, in every location and every context. Castells envisages a system where billions of miniature, ubiquitous inter-communication devices will be spread worldwide, "like pigment in the wall paint".


title: Ubiquitous computing

text: Ubiquitous computing may be seen to consist of many layers, each with their own roles, which together form a single system:


title: Ubiquitous computing

text: Mark Weiser coined the phrase "ubiquitous computing" around 1988, during his tenure as Chief Technologist of the Xerox Palo Alto Research Center (PARC). Both alone and with PARC Director and Chief Scientist John Seely Brown, Weiser wrote some of the earliest papers on the subject, largely defining it and sketching out its major concerns.


title: Ubiquitous computing

text: Recognizing that the extension of processing power into everyday scenarios would necessitate understandings of social, cultural and psychological phenomena beyond its proper ambit, Weiser was influenced by many fields outside computer science, including "philosophy, phenomenology, anthropology, psychology, post-Modernism, sociology of science and feminist criticism". He was explicit about "the humanistic origins of the 'invisible ideal in post-modernist thought'", referencing as well the ironically dystopian Philip K. Dick novel "Ubik".


title: Ubiquitous computing

text: Andy Hopper from Cambridge University UK proposed and demonstrated the concept of "Teleporting" – where applications follow the user wherever he/she moves.


title: Ubiquitous computing

text: Roy Want, while a researcher and student working under Andy Hopper at Cambridge University, worked on the "Active Badge System", which is an advanced location computing system where personal mobility that is merged with computing.


title: Ubiquitous computing

text: Bill Schilit (now at Google) also did some earlier work in this topic, and participated in the early Mobile Computing workshop held in Santa Cruz in 1996.


title: Ubiquitous computing

text: Ken Sakamura of the University of Tokyo, Japan leads the Ubiquitous Networking Laboratory (UNL), Tokyo as well as the T-Engine Forum. The joint goal of Sakamura's Ubiquitous Networking specification and the T-Engine forum, is to enable any everyday device to broadcast and receive information.


title: Ubiquitous computing

text: MIT has also contributed significant research in this field, notably "Things That Think" consortium (directed by Hiroshi Ishii, Joseph A. Paradiso and Rosalind Picard) at the Media Lab and the CSAIL effort known as Project Oxygen. Other major contributors include University of Washington's Ubicomp Lab (directed by Shwetak Patel), Dartmouth College's DartNets Lab, Georgia Tech's College of Computing, Cornell University's People Aware Computing Lab, NYU's Interactive Telecommunications Program, UC Irvine's Department of Informatics, Microsoft Research, Intel Research and Equator, Ajou University UCRi & CUS.


title: Ubiquitous computing

text: One of the earliest ubiquitous systems was artist Natalie Jeremijenko's "Live Wire", also known as "Dangling String", installed at Xerox PARC during Mark Weiser's time there. This was a piece of string attached to a stepper motor and controlled by a LAN connection; network activity caused the string to twitch, yielding a "peripherally noticeable" indication of traffic. Weiser called this an example of "calm technology".


title: Ubiquitous computing

text: A present manifestation of this trend is the widespread diffusion of mobile phones. Many mobile phones support high speed data transmission, video services, and other services with powerful computational ability. Although these mobile devices are not necessarily manifestations of ubiquitous computing, there are examples, such as Japan's Yaoyorozu ("Eight Million Gods") Project in which mobile devices, coupled with radio frequency identification tags demonstrate that ubiquitous computing is already present in some form.


title: Ubiquitous computing

text: Ambient Devices has produced an "orb", a "dashboard", and a "weather beacon": these decorative devices receive data from a wireless network and report current events, such as stock prices and the weather, like the Nabaztag produced by Violet Snowden.


title: Ubiquitous computing

text: The Australian futurist Mark Pesce has produced a highly configurable 52-LED LAMP enabled lamp which uses Wi-Fi named "MooresCloud" after Gordon Moore.


title: Ubiquitous computing

text: The Unified Computer Intelligence Corporation launched a device called "Ubi – The Ubiquitous Computer" designed to allow voice interaction with the home and provide constant access to information.


title: Ubiquitous computing

text: Ubiquitous computing research has focused on building an environment in which computers allow humans to focus attention on select aspects of the environment and operate in supervisory and policy-making roles. Ubiquitous computing emphasizes the creation of a human computer interface that can interpret and support a user's intentions. For example, MIT's Project Oxygen seeks to create a system in which computation is as pervasive as air:


title: Ubiquitous computing

text: In the future, computation will be human centered. It will be freely available everywhere, like batteries and power sockets, or oxygen in the air we breathe...We will not need to carry our own devices around with us. Instead, configurable generic devices, either handheld or embedded in the environment, will bring computation to us, whenever we need it and wherever we might be. As we interact with these "anonymous" devices, they will adopt our information personalities. They will respect our desires for privacy and security. We won't have to type, click, or learn new computer jargon. Instead, we'll communicate naturally, using speech and gestures that describe our intent...


title: Ubiquitous computing

text: This is a fundamental transition that does not seek to escape the physical world and "enter some metallic, gigabyte-infested cyberspace" but rather brings computers and communications to us, making them "synonymous with the useful tasks they perform".


title: Ubiquitous computing

text: Network robots link ubiquitous networks with robots, contributing to the creation of new lifestyles and solutions to address a variety of social problems including the aging of population and nursing care.


title: Ubiquitous computing

text: Privacy is easily the most often-cited criticism of ubiquitous computing (ubicomp), and may be the greatest barrier to its long-term success.


title: Ubiquitous computing

text: This is a list of notable institutions who claim to have a focus on Ubiquitous computing sorted by country:


title: Deadlock (2021 film)

text: Deadlock is a 2021 American action thriller film directed by Jared Cohn, starring Patrick Muldoon and Bruce Willis. It was released in the United States on December 3, 2021, by Saban Films.


title: Deadlock (2021 film)

text: Wanted criminal Ron Whitlock leads a team of mercenaries on a mission of vengeance. Convinced that the local detectives are responsible for the death of one of his sons and the wrongful imprisonment of the other one for a botched drug bust, the merciless group brutally seizes a hydroelectric dam and holds everyone inside hostage. With a nearby town on the brink of massive flooding and destruction, it's up to a retired Army Green Beret Mack Karr to save thousands of innocent lives before it's too late.


title: Deadlock (2021 film)

text: Bruce Willis was nominated for his performance in this movie, as he was for all movies he appeared in, in 2021, in the category Worst Performance by Bruce Willis in a 2021 Movie at the Golden Raspberry Awards. The category was later rescinded after he announced his retirement due to aphasia.


title: Ashley Parker Angel

text: Ashley Parker Angel is an American musician and actor who rose to prominence as a member of the boyband O-Town. After the band dissolved he had a brief solo music career, and was the only former band member who declined to go on a reunion tour with O-Town in 2011. Parker Angel has acted in several Broadway productions since 2007, and most recently appeared in "Wicked" as the lead male character Fiyero Tigelaar.


title: Ashley Parker Angel

text: Ashley Parker Angel is the child of Darren and Paula Parker. His grandparents are of German and Irish descent. Ashley was named after the fictional character Ashley Wilkes, his mother's favorite character from Margaret Mitchell's 1936 novel "Gone with the Wind", and the classic film of the same title. When Ashley was three years old, his parents divorced. His mother later remarried, and Ashley was legally adopted by his stepfather, Ron Angel, who is of American Indian descent. He then legally assumed the name by which he is also known as, "Ashley Parker-Angel." He has two brothers, Taylor and Justin and two sisters, Annie and Emily.


title: Ashley Parker Angel

text: From a very early age, Ashley studied the piano, as his mother Paula was a successful piano teacher with many students of her own. He was by nature active and adventurous. In one incident, at the age of nine he inadvertently set fire to his elementary school's football and soccer fields due to the explosion of a model rocket he had launched on school property; local police charged him with a misdemeanor.


title: Ashley Parker Angel

text: In 2000 Ashley Parker Angel achieved fame on the hit ABC series "Making the Band", which tracked the formation of a pop music group. The MTV production was the first reality show to be picked up by a major television network. Weekly, viewers saw Angel, after first being plucked from tens of thousands of other auditionees, survive each stage of the selection process to become one of the "final five" members of the new vocal group O-Town.


title: Ashley Parker Angel

text: Ratings were strong, and as a result O-Town quickly achieved success; by the end of the first season, the group had inked a record deal with music legend Clive Davis and became the debut act for Davis' new label J Records. The album "O-Town", boosted by the weekly TV publicity, debuted at No. 5 on "Billboard" and went on to multi-platinum status. "Liquid Dreams," the album's first release, crowned the SoundScan singles chart at No. 1, selling over 42,000 units in one week. The group won the 2001 Teen Choice Award for Breakthrough Artist.


title: Ashley Parker Angel

text: Because of O-Town, J Records made musical history as the first label in SoundScan history (1991 and on) to have its first single release debut at No. 1 on the sales charts. Also, O-Town is the first artist in SoundScan history to have its first single come in at No. 1, an achievement recorded in the 2002 "Guinness Book of World Records".


title: Ashley Parker Angel

text: In late spring 2001, the second single, "All or Nothing," and became the biggest hit of O-Town's career. The song reached No. 1 on the U.S. top 40 chart and was nominated for numerous awards, including Song of the Year during the 2001 Radio Music Awards.


title: Ashley Parker Angel

text: The group toured internationally, and went on to be the first reality show cast to remain unchanged for a second and third season. Near the end of the third season, viewers watched O-Town striving to take their careers to the next level, writing their own music, earning the respect of industry peers, and marketing themselves as more than a "boy band." Unfortunately, by the time of the release of their second album, "O2", the teen-pop genre had begun to fade, and they did not find the acceptance they sought. Despite moderate success, "O2" got nowhere near the market impact of their first album. In November 2003 J Records dropped the band from the label.


title: Ashley Parker Angel

text: In January 2011, O-Town confirmed their reunion plans, four days after confirming the band had gotten back together Ashley released a statement via TMZ.com that he wouldn't be reuniting with the band causing an uproar with the fans and media due to Ashley being a key member during O-Town.


title: Ashley Parker Angel

text: O-Town was one of the greatest chapters of my life, so when the idea of a reunion was brought to me, of course I was intrigued. However I have made the decision not to be a part of an O-Town reunion. It was a difficult decision, but ultimately necessary to move on with the next chapter of my career


title: Ashley Parker Angel

text: In 2004, Ashley had secured a record deal with Blackground/Universal Records, and later that year MTV began filming "There and Back", a reality series tracking his pursuit of solo stardom. The show documented Parker's struggle to transcend his mostly teen idol image, showcasing him as a serious songwriter and musician who co-wrote every track of his album. The series was backlit by the relationship between him and his then-pregnant fiancée (the engagement has since been broken off) and the obstacles of early fatherhood, and also captured the drama and birth of his son Lyric.


title: Ashley Parker Angel

text: In April 2006, Parker was selected to be a contestant on NBC's "Celebrity Cooking Showdown", produced by entertainment mogul/rapper Diddy; Angel placed second, even though he is seen severely lacerating his finger during one of the timed cooking challenges. Shortly thereafter, he competed in the "Kelly Slater Celebrity Surf Invitational", in which he had another severe injury, this time a foot laceration.


title: Ashley Parker Angel

text: In May 2006, his solo album "Soundtrack to Your Life" was released, debuting at No. 5 on "Billboard" and receiving many positive reviews. "Billboard"'s review called it "great melodic rock ... falling somewhere between the earnest balladeering of the Goo Goo Dolls and the driving rock of the All American Rejects." The first single release, "Let U Go," was a hit; its video spent weeks at No. 1 on MTV's TRL and the single had the third-highest-selling debut of 2006. In spring of that year, Parker toured throughout North America with Ashlee Simpson.


title: Ashley Parker Angel

text: Parker was featured as a character in the "Clone High" episode "Gate Expectations". In the episode, he hosts a teen dance show which is set on the sunny beaches of Canada, where it's always "a balmy 32 degrees". Parker is described in the episode as being like "The Beatles and Jesus all rolled into one."


title: Ashley Parker Angel

text: In January 2007, Ashley Parker Angel joined the eight-time Tony Award–winning musical "Hairspray", playing the lead character's love interest, teen heartthrob Link Larkin. The "New York Post" assessed Angel's performance as "an absolute charmer." Angel's presence on Broadway also led the "New York Times" to do a feature on the singer-songwriter turned actor. The "Hairspray" producers asked Angel to extend his contract four times. In early 2008, Parker sustained a back injury onstage, forcing him to leave the show for a few months, but he returned to finish the last few weeks of his latest contract, giving the actor a successful run in the show for more than a year.


title: Ashley Parker Angel

text: During his stay in New York, Parker performed at several other Broadway-related events, including "Broadway in Bryant Park" and "Broadway on Broadway".


title: Ashley Parker Angel

text: In November 2014, Parker Angel joined the globally award-winning touring version of the musical "Wicked", playing the part of the male lead character Fiyero Tigelaar. His debut on the tour was at Chrysler Hall in Norfolk, Virginia for 16 shows, he has since gone on to perform at Detroit, MI, Durham, NC, Greenville, SC, Atlanta, GA and Miami, FL with the current Munchkinland Tour. He reprised the role in January 2016 in Charlotte for 3 weeks. He returned to the role once again on July 31, 2017, in the Broadway production and remained with the show through July 14, 2018.


title: Ashley Parker Angel

text: In 2007 during his run on Broadway Angel began taking acting classes after finding acting during the show fun and challenging. In June 2009, Parker signed for his first major acting role as Carson Wheetly for the movie "" (originally titled, "Wild Things: Criss-Cross") by Sony, filmed in Miami over two months.


title: Ashley Parker Angel

text: On June 20, 2009, Parker guest starred as pop singer Danny Starr in the "Danny Starr / Quinceañera" episode of the children's cartoon "Handy Manny" on the Disney Channel. In this episode, he sang an original song called "Twisty Turn Twist", which he co-wrote for the show.


title: Ashley Parker Angel

text: In late March 2010 Parker was cast in the role of Todd for family movie "Pizza Man" starring Frankie Muniz filmed in Los Angeles. Pizza Man was due for theatrical release in late 2011 but later released on DVD in 2014.


title: Ashley Parker Angel

text: In February 2011 Parker filmed his third movie "Amelia's 25th", he plays the role of Jacob, the movie was first released on Video on Demand then DVD in 2013.


title: Ashley Parker Angel

text: In March 2014 Parker filmed a short in the Mojave Desert "Trona", he plays the role of Tommy, the short incomplete, waiting for film festival releases.


title: Ashley Parker Angel

text: As of 2012 Parker has been working with Xandy Barry on a new joint Band project titled "MOA" standing for "Mansions of Arcadia". He released a 20-second clip in January 2012 of their debut release "Don't Let Me Down".


title: Ashley Parker Angel

text: In 2014, Parker Angel confirmed that he was songwriting whilst being signed to EMI Publishing, he will be releasing a second album in the future, although the status of Mansions of Arcadia is currently unknown due to their official website and social pages no longer being active or online. 2017– he now is acting on Broadway as Fiyero in Wicked at the Gershwin Theater.


title: One Minute (Breaking Bad)

text: "One Minute" is the seventh episode of the third season of American television crime drama series "Breaking Bad", and the 27th overall episode of the series. It was written by Thomas Schnauz and directed by Michelle MacLaren. The episode follows Hank as he deals with a lawsuit against the DEA by Jesse after Hank physically assaults him. Walt tries to pacify Jesse and have him be his cooking partner. Meanwhile, the Cousins plot Hank's assassination and engage in a shootout with him in a parking lot.


title: One Minute (Breaking Bad)

text: "One Minute" originally aired on AMC in the United States and Canada on May 2, 2010. It was watched by an estimated 1.519 million American viewers and received a 0.6 Nielsen rating among adults between the ages of 18 and 49. The episode received universal acclaim from critics, with many considering it to be one of the best in the series.


title: One Minute (Breaking Bad)

text: A flashback in Mexico shows a young Leonel Salamanca complaining to his uncle, Hector, about a toy broken by Leonel's twin brother, Marco, with Leonel proclaiming that he wishes Marco was dead. In response, Hector shoves Marco's head in a tub of icy water despite Leonel's objections, and finally releases him after Leonel punches Hector, while proclaiming, "La familia es todo" (family is everything). In the present, Leonel and Marco light candles at a makeshift Santa Muerte shrine. In the center, the twins place a photo of Hank Schrader.


title: One Minute (Breaking Bad)

text: Furious that he was tricked into believing that his wife was in the hospital, Hank goes to Jesse Pinkman's house and attacks him as he opens the door. He knocks Jesse out cold before realizing that he has gone too far. Paramedics come and wheel Jesse away to the hospital as Hank stands by in shock. Walt and Saul arrive at the hospital and meet Jesse. Walt notes that they would be in jail if they had not tricked Hank after Jesse blames him for his predicament. Jesse also claims that he will make Hank's life miserable, and, despite Saul's objections, threatens to hand Walt to the DEA if he or Saul intervenes. At the DEA, Hank makes a statement about what happened at the junkyard, but pleads the Fifth when it comes to his actions at Jesse's house. He is then informed that Jesse is filing charges for his actions.


title: One Minute (Breaking Bad)

text: Skyler visits Walt at his condo. He initially believes she is mocking him, but she pleads with him to pacify Jesse so that Hank does not face charges. Walt refuses despite Skyler's assertion that Hank is his family and asks her to leave.


title: One Minute (Breaking Bad)

text: Later, at the lab, Gale attempts to be friendly with Walt, but he gives him the cold shoulder. He forces a disagreement with Gale and later convinces a reluctant Gus to make Jesse his partner again. At the hospital, Walt pitches the job to Jesse, who mocks it as a ploy to save Hank. He initially refuses, citing Walter's previous wrongdoings against him and his criticism of Jesse's meth. Walter admits that Jesse's meth is good and leaves. Jesse eventually calls Walt and says he agrees to the partnership.


title: One Minute (Breaking Bad)

text: In the desert, Leonel and Marco meet with a trucker hawking an array of weapons. He gives them a free hollow point bullet and shows off his bulletproof vest, which Leonel and Marco test by shooting him point blank. When he survives, they purchase two vests and leave him on the floor complaining about possible broken ribs.


title: One Minute (Breaking Bad)

text: At the DEA office, Hank admits to assaulting Jesse, resulting in him being suspended without pay and having his gun confiscated. As Hank departs, he learns Jesse is not pressing charges after all. Later, Hank is in an SUV in a parking lot when he gets a phone call and an electronically disguised voice tells Hank that he has one minute to leave before two men show up to kill him. At first, he wonders if it is a prank call, but after one minute Leonel and Marco arrive and ambush Hank. He reverses his car into Leonel, pinning him against another car and maiming him from the waist down, then flees with Leonel's gun. Marco empties his gun at two passers-by and reloads, dropping the hollow point bullet in the process, before eventually knocking Hank down with two shots. Rather than shooting him dead, believing that would be too easy, Marco decides to hack Hank to death with his axe and goes to retrieve it from his car. Hank then loads the hollow point bullet into Leonel's gun and kills Marco with a gunshot to the head. Marco's axe lands right next to Hank, who falls unconscious from massive blood loss.


title: One Minute (Breaking Bad)

text: The episode was written by Thomas Schnauz and directed by Michelle MacLaren; it aired on AMC in the United States and Canada on May 2, 2010.


title: One Minute (Breaking Bad)

text: Schnauz received writing duties for this episode based on seniority. Originally there was a plan to have the Cousins killed as early as episode 2.


title: One Minute (Breaking Bad)

text: "One Minute" originally aired on AMC on Sunday, May 2, 2010. The episode was viewed by an estimated 1.519 million American viewers, and received a 0.6 Nielsen rating among adults between the ages of 18 and 49. This means that it was seen by 0.6% of all 18- to 49-year-olds watching television at the time of the broadcast.


title: One Minute (Breaking Bad)

text: The episode was acclaimed by critics and is considered to be one of the best in the series. Donna Bowman of "The A.V. Club" praised the suspense and tension of the episode, giving it an "A" and writing that "I doubt you needed the threat of imminent natural disaster for this episode to put you on edge". Seth Amitin of "IGN" gave the episode a 10/10 ("Masterpiece") rating, saying that "'One Minute' was this show's finest hour, and maybe one of the best episodes of anything we've seen on TV in the last 20 years." In 2019, The Ringer ranked "One Minute" as the 4th best out of the 62 total "Breaking Bad" episodes.


title: One Minute (Breaking Bad)

text: At the 62nd Primetime Emmy Awards, "One Minute" received a nomination for Outstanding Sound Editing for a Series, while Maclaren received a nomination for Outstanding Directing for a Drama Series. The episode was nominated for Outstanding Achievement in Sound Editing – Sound Effects and Foley for Episodic Short Form Broadcast Media at the 2011 Golden Reel Awards.


title: Jourdan Dunn

text: Jourdan Sherise Dunn (born 3 August 1990) is a British model. She was discovered in Hammersmith Primark in 2006 and signed to The Squad Management in London. She began appearing on international runways in early 2007. In February 2008, she was the first black model to walk a Prada runway in over a decade.


title: Jourdan Dunn

text: In April 2014, it was announced that Dunn was signed as the new face of Maybelline New York. As of July 2014, she was declared an icon by models.com. Dunn is considered to be one of her generation's supermodels.


title: Jourdan Dunn

text: Jourdan Dunn was born in Brent, London, and grew up in nearby Greenford with her mother. She attended Elthorne Park High School in Hanwell. Jourdan is of Jamaican, and Syrian-Lebanese descent. She admitted to being self-conscious as a teenager, due to her height and weight. She stated growing up, people would often tell her she should become a model, but she was apprehensive as she was not really sure what a model did. She commented that shows like "America's Next Top Model" intrigued her, as they gave her a new perspective of the job.


title: Jourdan Dunn

text: In early 2006, at the age of 15, she was scouted by an agent from Storm Management, while accompanying a friend in a London Primark.


title: Jourdan Dunn

text: She has a son born in 2009 named Riley. On 1 February 2020, Dunn became engaged to rapper Dion Hamilton.


title: Jourdan Dunn

text: At the age of 16, Dunn made her runway debut in the New York shows in the autumn of 2007, walking in shows for Marc Jacobs and Polo Ralph Lauren, among others. Soon after, she quickly rose to prominence within the industry. In 2007, she was featured on British "Vogue" as a "new star," and in 2008 Style.com listed her as one of the top 10 newcomers. She also walked 75 shows during the spring/summer 2008 season, including Louis Vuitton and Valentino. Dunn has since become a major fixture on runways, having walked for the industry's biggest designers. She was often distinguished for being the only black model in shows, for which she later condemned designers. She has garnered attention for her legs and for her walk which she says she practises frequently with very tall heels, walking over 60 shows during the spring 2009 season.


title: Jourdan Dunn

text: In July 2008, Steven Meisel selected Dunn to appear on the cover of the "Vogue Italia" issue devoted entirely to black models. She featured as a 'Face of the Moment' in May 2009's US "Vogue". She has also been featured on the cover of "American Vogue", British "Vogue", "Vogue" Turkey, "Vogue" Japan, "Vogue" Brazil and "Teen Vogue", "Miss Vogue", "Vogue Girl Korea", "W Magazine", Glamour Magazine UK, Elle (France, UK, South Africa, Japan, Brazil), "Wonderland", "Manifesto", "Fashion Magazine Canada", "Madame Figaro", "Pop", "Russh", "Muse", "The Sunday Times Style", "Ponystep", "Antidote", "Luella", and covering "i-D" magazine eight times.


title: Jourdan Dunn

text: She has been in campaigns for Ann Taylor, Burberry, Balmain, Calvin Klein, Yves Saint Laurent, DKNY, Michael Kors, John Galliano, Victoria's Secret, Tommy Hilfiger, Topshop, Kate Spade, Express, Jaeger, Rag & Bone, Gap, Aldo, Shiatzy Chen, Benetton, H&M, Banana Republic, Zalando, Free People, Selfridges, Neiman Marcus, Pepe Jeans, Liu Jo and Saks Fifth Avenue, and was the face of Rihanna's collections for River Island.


title: Jourdan Dunn

text: She has appeared in editorials for the American, Italian, French, British, Russian, Spanish, Turkish, Japanese, Brazilian editions of "Vogue", "Elle", "i-D", "Dazed & Confused", "W", "Pop", "Centrefold" and "V", among others. In "Teen Vogue"s November 2009 issue where she appeared alongside Chanel Iman, she discussed her and Chanel's previous competitive relationship, as well as the challenges they faced being black models in the fashion world. The issue sparked controversy as Dunn; who was 18 at the time, announced her pregnancy. "Teen Vogue" faced backlash from the media, who accused them of glorifying teenage pregnancy.


title: Jourdan Dunn

text: She continued to model until she was six months pregnant and couldn't fit into any of the clothes, notably walking the catwalk for the Spring 2010 Jean Paul Gaultier show, with a baby bump. At the age of 19, ten weeks after giving birth, Dunn returned to the runway at London Fashion Week for the Winter 2010 season. For returning to work so quickly, she said her motivation was her son:


title: Jourdan Dunn

text: More than anything, having a son has made me realise I have to make shit work: I'm his voice, I'm his lifeline, I have to be driven. I think he pushed me in the right direction. I've always been ambitious, but now I have more focus. I'm more hardworking.


title: Jourdan Dunn

text: During the 2012 Summer Olympics closing ceremony, Dunn was one of the British models wearing bespoke fashions created by British designers specifically for the event. The other models were Naomi Campbell, Kate Moss, David Gandy, Karen Elson, Lily Donaldson, Lily Cole, Georgia May Jagger and Stella Tennant. She wore a gold and white gown by Jonathan Saunders with feathered headdress by Stephen Jones. She also made her Victoria's Secret Fashion Show debut for the 2012 show.


title: Jourdan Dunn

text: In March 2013, Dunn appeared as the cover story in Net-a-Porter's "The Edit." In it she spoke of encountering discrimination telling the magazine that casting agents would say clients "didn't want any more black girls". In July 2013, she received media attention for tweeting that she had been cancelled from a Dior haute couture show, "for her boobs"; rather than her skin colour – which she noted, "usually happens".


title: Jourdan Dunn

text: In April 2014, it was announced that Maybelline New York had signed her to join the brand. Her first role for the cosmetic company will be fronting the brand's Go Extreme Mascara, accompanied with print and television ads.


title: Jourdan Dunn

text: "Forbes" listed Dunn in their 2014 top-earning models list, estimated to have earned $US4 million in one year. She appeared on the 2015 list having earned $US3.5million.


title: Jourdan Dunn

text: Dunn signed a deal with British multinational retailer Marks & Spencer to design a kidswear clothing collection. The collection; called "Lil' LonDunn by Jourdan Dunn", debuted in April 2016.


title: Jourdan Dunn

text: A collaboration between Jourdan and British fashion retailer Missguided was launched in April 2017, featuring athletic wear. Revenue for the company increased by 75%, with international sales increasing by 130%, whilst the campaign with Dunn was active.


title: Jourdan Dunn

text: She appeared in a music video for Nicki Minaj entitled "Regret In Your Tears", directed by Mert and Marcus in May 2017.


title: Jourdan Dunn

text: In February 2008, Dunn became the first Black model to walk in a Prada fashion show during the 21st Century.


title: Jourdan Dunn

text: As of July 2014, she was declared an icon by models.com after appearing on their "Top 50 Models Women" list for seven consecutive years.


title: Jourdan Dunn

text: As of May 2015, models.com declared her a "New Super", a selection of models who are recognised as modern day supermodels; having transcended the fashion industry and established themselves as brands and celebrities.


title: Jourdan Dunn

text: She won the "Inspiration Award" at the "Glamour" Women of the Year Awards 2015, for her philanthropic work raising awareness for Sickle-cell disease and her consistent activism for diversity within the modeling industry.


title: Jourdan Dunn

text: In 2014, "Forbes" listed Dunn in their top-earning models list, estimated to have earned $US4 million in one year. She was the first Black British model to make the list. She appeared on the February cover of British "Vogue" in 2015, becoming the first solo Black model to grace the cover in 12 years.


title: Jourdan Dunn

text: Dunn appeared in the music videos for "Yoncé" and "XO" from Beyoncé's fifth self-titled studio album which is widely described as a "visual album" due to every song being accompanied by a music video. The videos were shot in Brooklyn and Coney Island, New York, respectively. The "Yoncé" video was directed by Ricky Saiz and features fellow models Joan Smalls and Chanel Iman. The video was inspired by the 1990 David Fincher video for "Freedom" by George Michael, which also featured models, such as Naomi Campbell. The "XO" video was directed by Terry Richardson and features Dunn alongside Jessica White and Diandra Forres.


title: Jourdan Dunn

text: Dunn currently hosts a cooking show entitled "Well Dunn", on Jay Z's Life+Times YouTube channel. The web show has featured celebrity guest co-chefs, such as 2 Chainz, Wale, Karlie Kloss, Chanel Iman, Cara Delevingne and Joan Smalls.


title: Jourdan Dunn

text: She was a guest on "The Jonathan Ross Show" in March 2013 and later again in 2019, to discuss her career.


title: Langlands program

text: In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry. Proposed by , it seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. Widely seen as the single biggest project in modern mathematical research, the Langlands program has been described by Edward Frenkel as "a kind of grand unified theory of mathematics."


title: Langlands program

text: The Langlands program consists of some very complicated theoretical abstractions, which can be difficult even for specialist mathematicians to grasp. To oversimplify, the fundamental lemma of the project posits a direct connection between the generalized fundamental representation of a finite field with its group extension to the automorphic forms under which it is invariant. This is accomplished through abstraction to higher dimensional integration, by an equivalence to a certain analytical group as an absolute extension of its algebra. Consequently, this allows an analytical functional construction of powerful invariance transformations for a number field to its own algebraic structure.


title: Langlands program

text: The meaning of such a construction is nuanced, but its specific solutions and generalizations are very powerful. The consequence for proof of existence to such theoretical objects implies an analytical method in constructing the categoric mapping of fundamental structures for virtually any number field. As an analogue to the possible exact distribution of primes, the Langlands program allows a potential general tool for the resolution of invariance at the level of generalized algebraic structures. This in turn permits a somewhat unified analysis of arithmetic objects through their automorphic functions. Simply put, the Langlands philosophy allows a general analysis of structuring the abstractions of numbers. Naturally, this description is at once a reduction and over-generalization of the program's proper theorems, but these mathematical analogues provide the basis of its conceptualization.


title: Langlands program

text: In a very broad context, the program built on existing ideas: the "philosophy of cusp forms" formulated a few years earlier by Harish-Chandra and , the work and approach of Harish-Chandra on semisimple Lie groups, and in technical terms the trace formula of Selberg and others.


title: Langlands program

text: What initially was very new in Langlands' work, besides technical depth, was the proposed direct connection to number theory, together with the rich organisational structure hypothesised (so-called "functoriality").


title: Langlands program

text: For example, in the work of Harish-Chandra one finds the principle that what can be done for one semisimple (or reductive) Lie group, should be done for all. Therefore, once the role of some low-dimensional Lie groups such as GL(2) in the theory of modular forms had been recognised, and with hindsight GL(1) in class field theory, the way was open at least to speculation about GL("n") for general "n" > 2.


title: Langlands program

text: The "cusp form" idea came out of the cusps on modular curves but also had a meaning visible in spectral theory as "discrete spectrum", contrasted with the "continuous spectrum" from Eisenstein series. It becomes much more technical for bigger Lie groups, because the parabolic subgroups are more numerous.


title: Langlands program

text: In all these approaches there was no shortage of technical methods, often inductive in nature and based on Levi decompositions amongst other matters, but the field wasand isvery demanding.


title: Langlands program

text: And on the side of modular forms, there were examples such as Hilbert modular forms, Siegel modular forms, and theta-series.


title: Langlands program

text: There are a number of related Langlands conjectures. There are many different groups over many different fields for which they can be stated, and for each field there are several different versions of the conjectures. Some versions of the Langlands conjectures are vague, or depend on objects such as the Langlands groups, whose existence is unproven, or on the "L"-group that has several inequivalent definitions. Moreover, the Langlands conjectures have evolved since Langlands first stated them in 1967.


title: Langlands program

text: There are several different ways of stating the Langlands conjectures, which are closely related but not obviously equivalent.


title: Langlands program

text: The starting point of the program may be seen as Emil Artin's reciprocity law, which generalizes quadratic reciprocity. The Artin reciprocity law applies to a Galois extension of an algebraic number field whose Galois group is abelian; it assigns "L"-functions to the one-dimensional representations of this Galois group, and states that these "L"-functions are identical to certain Dirichlet "L"-series or more general series (that is, certain analogues of the Riemann zeta function) constructed from Hecke characters. The precise correspondence between these different kinds of "L"-functions constitutes Artin's reciprocity law.


title: Langlands program

text: For non-abelian Galois groups and higher-dimensional representations of them, one can still define "L"-functions in a natural way: Artin "L"-functions.


title: Langlands program

text: The insight of Langlands was to find the proper generalization of Dirichlet "L"-functions, which would allow the formulation of Artin's statement in this more general setting. Hecke had earlier related Dirichlet "L"-functions with automorphic forms (holomorphic functions on the upper half plane of formula_1 (the complex numbers) that satisfy certain functional equations). Langlands then generalized these to automorphic cuspidal representations, which are certain infinite dimensional irreducible representations of the general linear group GL("n") over the adele ring of formula_2 (the rational numbers). (This ring simultaneously keeps track of all the completions of formula_3 see "p"-adic numbers.)


title: Langlands program

text: Langlands attached automorphic "L"-functions to these automorphic representations, and conjectured that every Artin "L"-function arising from a finite-dimensional representation of the Galois group of a number field is equal to one arising from an automorphic cuspidal representation. This is known as his "reciprocity conjecture".


title: Langlands program

text: Roughly speaking, the reciprocity conjecture gives a correspondence between automorphic representations of a reductive group and homomorphisms from a Langlands group to an "L"-group. There are numerous variations of this, in part because the definitions of Langlands group and "L"-group are not fixed.


title: Langlands program

text: Over local fields this is expected to give a parameterization of "L"-packets of admissible irreducible representations of a reductive group over the local field. For example, over the real numbers, this correspondence is the Langlands classification of representations of real reductive groups. Over global fields, it should give a parameterization of automorphic forms.


title: Langlands program

text: The functoriality conjecture states that a suitable homomorphism of "L"-groups is expected to give a correspondence between automorphic forms (in the global case) or representations (in the local case). Roughly speaking, the Langlands reciprocity conjecture is the special case of the functoriality conjecture when one of the reductive groups is trivial.


title: Langlands program

text: Langlands generalized the idea of functoriality: instead of using the general linear group GL("n"), other connected reductive groups can be used. Furthermore, given such a group "G", Langlands constructs the Langlands dual group "G", and then, for every automorphic cuspidal representation of "G" and every finite-dimensional representation of "G", he defines an "L"-function. One of his conjectures states that these "L"-functions satisfy a certain functional equation generalizing those of other known "L"-functions.


title: Langlands program

text: He then goes on to formulate a very general "Functoriality Principle". Given two reductive groups and a (well behaved) morphism between their corresponding "L"-groups, this conjecture relates their automorphic representations in a way that is compatible with their "L"-functions. This functoriality conjecture implies all the other conjectures presented so far. It is of the nature of an induced representation construction—what in the more traditional theory of automorphic forms had been called a 'lifting', known in special cases, and so is covariant (whereas a restricted representation is contravariant). Attempts to specify a direct construction have only produced some conditional results.


title: Langlands program

text: All these conjectures can be formulated for more general fields in place of formula_2: algebraic number fields (the original and most important case), local fields, and function fields (finite extensions of F("t") where "p" is a prime and F("t") is the field of rational functions over the finite field with "p" elements).


title: Langlands program

text: The so-called geometric Langlands program, suggested by Gérard Laumon following ideas of Vladimir Drinfeld, arises from a geometric reformulation of the usual Langlands program that attempts to relate more than just irreducible representations. In simple cases, it relates -adic representations of the étale fundamental group of an algebraic curve to objects of the derived category of -adic sheaves on the moduli stack of vector bundles over the curve.


title: Langlands program

text: The Langlands conjectures for GL(1, "K") follow from (and are essentially equivalent to) class field theory.


title: Langlands program

text: Langlands proved the Langlands conjectures for groups over the archimedean local fields formula_5 (the real numbers) and formula_1 by giving the Langlands classification of their irreducible representations.


title: Langlands program

text: Lusztig's classification of the irreducible representations of groups of Lie type over finite fields can be considered an analogue of the Langlands conjectures for finite fields.


title: Langlands program

text: Andrew Wiles' proof of modularity of semistable elliptic curves over rationals can be viewed as an instance of the Langlands reciprocity conjecture, since the main idea is to relate the Galois representations arising from elliptic curves to modular forms. Although Wiles' results have been substantially generalized, in many different directions, the full Langlands conjecture for formula_7 remains unproved.


title: Langlands program

text: In 1998, Laurent Lafforgue proved Lafforgue's theorem verifying the Langlands conjectures for the general linear group GL("n", "K") for function fields "K". This work continued earlier investigations by Drinfeld, who proved the case GL(2, "K") in the 1980s.


title: Langlands program

text: In 2018, Vincent Lafforgue established the global Langlands correspondence (the direction from automorphic forms to Galois representations) for connected reductive groups over global function fields.


title: Langlands program

text: In 2008, Ngô Bảo Châu proved the "fundamental lemma", which was originally conjectured by Langlands and Shelstad in 1983 and being required in the proof of some important conjectures in the Langlands program.


title: Langlands program

text: To a lay reader or even nonspecialist mathematician, abstractions within the Langlands program can be somewhat impenetrable. However, there are some strong and clear implications for proof or disproof of the fundamental Langlands conjectures.


title: Langlands program

text: As the program posits a powerful connection between analytic number theory and generalizations of algebraic geometry, the idea of 'functoriality' between abstract algebraic representations of number fields and their analytical prime constructions results in powerful functional tools allowing an exact quantification of prime distributions. This, in turn, yields the capacity for classification of diophantine equations and further abstractions of algebraic functions.


title: Langlands program

text: Furthermore, if the reciprocity of such generalized algebras for the posited objects exists, and if their analytical functions can be shown to be well-defined, some very deep results in mathematics could be within reach of proof. Examples include: rational solutions of elliptic curves, topological construction of algebraic varieties, and the famous Riemann hypothesis. Such proofs would be expected to utilize abstract solutions in objects of generalized analytical series, each of which relates to the invariance within structures of number fields.


title: Langlands program

text: Additionally, some connections between the Langlands program and M theory have been posited, as their dualities connect in nontrivial ways, providing potential exact solutions in superstring theory (as was similarly done in group theory through monstrous moonshine).


title: Langlands program

text: Simply put, the Langlands project implies a deep and powerful framework of solutions, which touches the most fundamental areas of mathematics, through high-order generalizations in exact solutions of algebraic equations, with analytical functions, as embedded in geometric forms. It allows a unification of many distant mathematical fields into a formalism of powerful analytical methods.


title: Bigg Boss (Tamil season 1)

text: Bigg Boss was the first season of the Tamil-language reality TV show "Bigg Boss Tamil" which is the Tamil version of the "Big Brother". The first season aired on Star Vijay from 25 June 2017 to 30 September 2017. The season's presenter was Kamal Haasan and a lavish house set was constructed at EVP theme park, Chennai. This season is the shortest season in the Bigg Boss Tamil series excluding the Ultimate series.


title: Bigg Boss (Tamil season 1)

text: The winner of the season was model/actor Arav, who received a cash prize of 50 lakh. Lyricist Snehan was the runner-up, while the other finalists included Harish Kalyan, Ganesh Venkatraman and Bindu Madhavi.


title: Bigg Boss (Tamil season 1)

text: Snehan, Suja Varunee and Maria Juliana returned as contestants in "Bigg Boss Ultimate (season 1)". While Bindu Madhavi returned as a contestant in "Bigg Boss Non-Stop (season 1)" and eventually she won it.


title: Bigg Boss (Tamil season 1)

text: After the launch of the show, the viewership of the channel increased by 10%. The series garnered a low rating of 5.2 TVR in debut week with 5.6 million impressions and 5.4 million impressions for premiere episode. It improved further the following weeks where it averaged 8.4 TVR for a six weeks average ratings.


title: Bifurcation theory

text: Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. Bifurcations occur in both continuous systems (described by ordinary, delay or partial differential equations) and discrete systems (described by maps).


title: Bifurcation theory

text: The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior. Henri Poincaré also later named various types of stationary points and classified them .


title: Bifurcation theory

text: A local bifurcation occurs when a parameter change causes the stability of an equilibrium (or fixed point) to change. In continuous systems, this corresponds to the real part of an eigenvalue of an equilibrium passing through zero. In discrete systems (described by maps), this corresponds to a fixed point having a Floquet multiplier with modulus equal to one. In both cases, the equilibrium is "non-hyperbolic" at the bifurcation point.


title: Bifurcation theory

text: The topological changes in the phase portrait of the system can be confined to arbitrarily small neighbourhoods of the bifurcating fixed points by moving the bifurcation parameter close to the bifurcation point (hence 'local').


title: Bifurcation theory

text: More technically, consider the continuous dynamical system described by the ordinary differential equation (ODE)


title: Bifurcation theory

text: has an eigenvalue with zero real part. If the eigenvalue is equal to zero, the bifurcation is a steady state bifurcation, but if the eigenvalue is non-zero but purely imaginary, this is a Hopf bifurcation.


title: Bifurcation theory

text: has an eigenvalue with modulus equal to one. If the eigenvalue is equal to one, the bifurcation is either a saddle-node (often called fold bifurcation in maps), transcritical or pitchfork bifurcation. If the eigenvalue is equal to −1, it is a period-doubling (or flip) bifurcation, and otherwise, it is a Hopf bifurcation.


title: Bifurcation theory

text: Global bifurcations occur when 'larger' invariant sets, such as periodic orbits, collide with equilibria. This causes changes in the topology of the trajectories in the phase space which cannot be confined to a small neighbourhood, as is the case with local bifurcations. In fact, the changes in topology extend out to an arbitrarily large distance (hence 'global').


title: Bifurcation theory

text: The codimension of a bifurcation is the number of parameters which must be varied for the bifurcation to occur. This corresponds to the codimension of the parameter set for which the bifurcation occurs within the full space of parameters. Saddle-node bifurcations and Hopf bifurcations are the only generic local bifurcations which are really codimension-one (the others all having higher codimension). However, transcritical and pitchfork bifurcations are also often thought of as codimension-one, because the normal forms can be written with only one parameter.


title: Bifurcation theory

text: Bifurcation theory has been applied to connect quantum systems to the dynamics of their classical analogues in atomic systems, molecular systems, and resonant tunneling diodes. Bifurcation theory has also been applied to the study of laser dynamics and a number of theoretical examples which are difficult to access experimentally such as the kicked top and coupled quantum wells. The dominant reason for the link between quantum systems and bifurcations in the classical equations of motion is that at bifurcations, the signature of classical orbits becomes large, as Martin Gutzwiller points out in his classic work on quantum chaos. Many kinds of bifurcations have been studied with regard to links between classical and quantum dynamics including saddle node bifurcations, Hopf bifurcations, umbilic bifurcations, period doubling bifurcations, reconnection bifurcations, tangent bifurcations, and cusp bifurcations.


title: German military rifles

text: The evolution of German military rifles is a history of common and diverse paths followed by the separate German states, until the mid-19th century when Prussia emerged as the dominant state within Germany and the nation was unified. This article discusses rifled shoulder arms developed in or for the military of the states that later became Germany; it excludes firearms of the Austrian Empire, except where they were used substantially by German troops.


title: German military rifles

text: There was also a period in the late 20th century when Germany was again divided and the two nations had separate armies and weapons, in "Cold War" opposition. The various rifles used during this period are displayed here, identified by either East German or West German usage.


title: German military rifles

text: "Jäger" (German, lit. "hunter") were a type of soldier, a form of light infantry, first named by the Landgrave of Hesse when he formed such a unit from his foresters and huntsmen in 1631. Huntsmen and foresters recruited in certain German states were an established presence in German military units. They were often of middle-class backgrounds or belonged to the lesser nobility. These troops were primarily used for reconnaissance, skirmishing or screening bodies of heavier troops. Since they owned their own weapons there was little standardization, and the early rifles were generally designed for hunting. "Jäger" were not just skilled riflemen; they were also able to handle and maintain delicate, accurate rifles in an age when very few soldiers had mechanical skills.