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Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do break apart recursively. In computer science, if a problem can be solved optimally by breaking it into sub-problems and recursively finding the optimal solutions to the sub-problems it is said to have optimal substructure. If sub-problems can be nested recursively inside larger problems, so that dynamic programming methods are applicable there is a relation between the value of the larger problem and the values of the sub-problems. In the optimization literature this relationship is called the Bellman equation. In terms of mathematical optimization, dynamic programming refers to simplifying a decision by breaking it down into a sequence of decision steps over time.

This is done by defining a sequence of value functions V1, V2... Vn taking y as an argument representing the state of the system at times i from 1 to n; the definition of Vn is the value obtained in state y at the last time n. The values Vi at earlier times i = n −1, n − 2... 2, 1 can be found by working backwards, using a recursive relationship called the Bellman equation. For i = 2... n, Vi−1 at any state y is calculated from Vi by maximizing a simple function of the gain from a decision at time i − 1 and the function Vi at the new state of the system if this decision is made. Since Vi has been calculated for the needed states, the above operation yields Vi−1 for those states. V1 at the initial state of the system is the value of the optimal solution; the optimal values of the decision variables can be recovered, one by one, by tracking back the calculations performed. In control theory, a typical problem is to find an admissible control u ∗ which causes the system x ˙ = g to follow an admissible trajectory x ∗ on a continuous time interval t 0 ≤ t ≤ t 1 that minimizes a cost function J = b + ∫ t 0 t 1 f d t The solution to this problem is an optimal control law or policy u ∗ = h, which produces an optimal trajectory x ∗ and an optimized loss function J ∗.

The latter obeys the fundamental equation of dynamic programming: − J t ∗ = min u a partial differential equation known as the Hamilton–Jacobi–Bellman equation, in which J x ∗ = ∂ J ∗ ∂ x = T {\displaystyle J_^==\left[~~~~~~~~\dots ~~~~{\frac {\par

The 2014 Irwin Tools Night Race was a NASCAR Sprint Cup Series stock car race, held on August 23, 2014, at Bristol Motor Speedway in Bristol, Tennessee. Contested over 500 laps, it was the 24th race of the 2014 NASCAR Sprint Cup Series. Joey Logano of Team Penske took his third win of the season. Logano's teammate Brad Keselowski finished second while Matt Kenseth, Jimmie Johnson, Kurt Busch completed the top five placings; the top rookies of the race were Kyle Larson, Justin Allgaier, Austin Dillon. Jeff Gordon took the lead from Joey Logano at the final restart and went on to win for the 91st time in his career, in the Pure Michigan 400 at Michigan International Speedway. Gordon stated that he had "got a good restart, I got to his quarter panel in Turn 1 and I was able to drag him back and it allowed me to get the momentum and get by him". Logano felt he had Gordon cleared and lamented that he "should have pulled down in front of him". Bristol Motor Speedway is a four-turn short track oval, 0.533 miles long.

The track's turns are banked from twenty-four to thirty degrees, while the front stretch, the location of the finish line, is banked from six to ten degrees. The back stretch has banking from six to ten degrees; the track has a seating capacity of 160,000 people. The race consisted of 500 laps; the defending race winner was Matt Kenseth. Tony Stewart was on the entry list for the weekend's race, but following the events that took place at Canandaigua Motorsports Park, it was unknown if he'd be in the car. On Wednesday, August 20, Stewart-Haas Racing released a statement that Stewart would sit out again and Jeff Burton would drive in his place; the team would continue to evaluate the drive on a week-by-week basis. Ryan Truex was cleared to race at Bristol after missing the previous week's race at Michigan, he suffered a concussion in a single car crash during the second practice session and J. J. Yeley drove in his place. Truex stated; the entry list for the Irwin Tools Night Race was released on Monday, August 18, 2014 at 11:05 a.m.

Eastern time. Forty-three drivers were entered for the race. Kyle Larson was the fastest in the first practice session with a time of 14.638 and a speed of 131.083 mph. David Gilliland hit the wall as a result of a stuck throttle. Ricky Stenhouse, Jr. was the fastest in the final practice session with a time of 14.642 and a speed of 131.048 mph. Kevin Harvick won the pole with a speed of 131.362 mph. Harvick saw his qualifying position as an advantage, as he deemed that "track position is as important as it is anywhere here with the current groove and where you are running" and "felt good about our car during practice and just have to stay in there all night and do the best we can". Jeff Gordon joined Harvick on the front row, stated that he "thought our car was a little bit better in race trim than it was in qualifying trim when we swapped over", stated that the conditions of the track were tricky. Aric Almirola, Kyle Larson and Cole Whitt hit the wall during qualifying, with Almirola lamenting the fact and stating he had "probably the best race car I've had at Bristol and I screwed up and hit the fence".

The race was scheduled to start at 7:46 p.m. Eastern time but started three minutes late when Kevin Harvick led the field to the green. Harvick led the race until lap 38, he led until lap 55 when Kyle Busch assumed the lead of the race, held it to the first caution of the race. Harvick retook the lead during the caution period; the caution came out a lap for a multi-car crash in turn 2, before the race restarted on lap 77. Kenseth maintained the lead of the race, for a good portion of the race; the caution flew for the third time on lap 125 for a multi-car wreck on the backstretch that began when Brian Vickers got into Kyle Larson, spun into Aric Almirola. Clint Bowyer ran into Kyle Busch, sending Busch spinning into the inside wall. Denny Hamlin took the lead during the caution period, held the lead as the race restarted on lap 137. While racing for the lead, Harvick tapped Hamlin, which sent him spinning into the inside wall on the front stretch. Hamlin's car bounced off the wall, back up towards the track where it hit the left-hand side of the car of Dale Earnhardt, Jr. ripping all the protection foam out of it.

This brought out the fourth caution of the race on lap 161. This was the second straight year that the two drivers had a post-crash altercation during the summer Bristol race. Post-race, Harvick described the incident as "I just lost the front end, honestly", apportioning blame on himself. Hamlin was angered at the way which left him with a 40th-place finish. Earnhardt, Jr. tried to avoid a collision with Hamlin's car, but as he described it, "there was a lot of smoke so I couldn't judge the speed of his car to know whether I needed to be going up there and go around him on the top". The damage to his car – the lower control arm was torn off his left-front tire – left him with a 39th-place finish; the race restarted on lap 173 with Harvick leading the way. Harvick held the lead unt

The Ioshima-class escort ship called Yasoshima-class light cruiser were a pair of escort ships reconstructed from former Republic of China Navy Ning Hai class cruisers that were sunk during earlier battles- Ioshima from Ning Hai and Yasoshima from Ping Hai - these ships were salvageable as river water doesn't corrode sunken hulls as badly as sea water would. They were to be transferred to the puppet government of Wang Jing-Wei, but instead of honoring the agreement, the Japanese seized and outfitted them first as barracks hulks and to their final form in 1944. Since they were built on the same design from the start, the reconstruction brought them to a more-or-less common standard: old armaments and fire control platforms were removed, their new armaments, while lighter, were dual-purpose weapons more-suitable against contemporary aircraft. Both Isoshima and Yasoshima were sunk by late 1944. Lacroix, Eric & Wells II, Linton. Japanese Cruisers of the Pacific War. Annapolis, Maryland: Naval Institute Press.

ISBN 0-87021-311-3

Michelle Quilty is, a camogie player. She played in the 2009 All-Ireland Senior Camogie Championship Final and was a member of the Team of the Championship for 2011. With a total of 5-26 she was the fourth highest scoring player in the Championship in 2011, she was an Ashbourne Cup and league medal-winner with Waterford IT in 2009. Michelle's brother, Martin, is Chairman of the Co. Camogie Board, she won two Under-16 and two Minor All-Irelands, along with a National League in 2008 and Leinster honours in Under-16, Minor and Senior. Official Camogie Website Kilkenny Camogie Website of 2009 championship in On The Ball Official Camogie Magazine https://web.archive.org/web/20091228032101/http://www.rte.ie/sport/gaa/championship/gaa_fixtures_camogie_oduffycup.html Fixtures and results] for the 2009 O'Duffy Cup All-Ireland Senior Camogie Championship: Roll of Honour Video highlights of 2009 championship Part One and part two Video Highlights of 2009 All Ireland Senior Final Report of All Ireland final in Irish Times Independent and Examiner

The Horribly Slow Murderer with the Extremely Inefficient Weapon is a 10-minute short film, released in 2008. It was filmed in California over the course of 22 days, it was written and narrated by Richard Gale. The film won the Special Jury Prize at the Fantastic Fest, the Best Short Film award at the Fantasia International Film Festival, the Citizen's Choice Award and the Grand Prize for Short Film at the Puchon International Fantastic Film Festival, was named the Best Short Film of 2009 by Rue Morgue, it was shot on a budget of $600, on a Panasonic HVX200 digital video camera with special effects created in Adobe After Effects, edited on Final Cut Pro. It was not stated if the budget included software costs or salaries for the 30-day shoot; the movie itself is presented as being a trailer for a 9 hour long movie. It starts with a voice-over; the movie portrays the story of a forensic pathologist called Jack Cucchiaio, who finds himself being haunted by a deranged looking man, who is, without any clear reason, hitting him with a spoon. No one seems to believe this though. He is seen stirring his coffee with a fork. Jack attempts to defend himself - stabbing the murderer in the throat with a kitchen knife, but to Jack's surprise his enemy turns out to be immortal, pulling the knife out of his throat and throwing it away continuing to hit Jack with the spoon. However, in this scene Jack notices a strange sign on the arm of his attacker. Jack travels to the far East where he learns that his attacker is known as the Ginosaji, an immortal and unstoppable being. After this, Jack is shown traveling around the world, trying to escape from the Ginosaji or to fight it, he uses various weapons, including dynamite, an RPG. Since the Ginosaji is immortal, however, he will always find Jack again; the last scene shows a weakened, wounded Jack, crawling in the desert, with the Ginosaji still striking him with the spoon. The spoon breaks. However, Jack's final hope is brief as the Ginosaji shows dozens of spoons; the title and credits are shown in typical trailer style. A sequel, Spoon Vs. Spoon was released on YouTube, in which Jack takes on the advice of a viewer to fight back with another spoon, this backfired as the Ginosaji took away Jack's other spoon, mercilessly used the second spoon for double-hitting; the Ginosaji has since used dual weapons with two spoons. Another sequel, Save Jack was released in the form of a game in which the player has to choose what Jack Cucchiaio should do, choices involving wearing protective clothing, using a giant magnet, giving the Ginosaji a hug or kicking it in the crotch. All of these choices backfired horrendously; the only one which succeeded was the magnet one. The Ginosaji had a wooden spoon. A third sequel was featured a duel between Jack and the Ginosaji; the Ginosaji's spoon seemed to be made of an anti-lightsaber alloy. The duel ended in the water when Jack was killed and woke up from the dream. At first he thought that the whole Ginosaji thing was a dream, but he was proven wrong when the Ginosaji attacked him again. A fourth sequel, Ginosaji Vs. Ginosaji, featured Jack attempting to convince the Ginosaji not to attack him since he is another Ginosaji. Wearing make-up and a hoodie, Jack attacks another person with a spoon, but the person hits Jack instead and the Ginosaji is not convinced. An injured Jack tries to commit suicide by jumping in front of a bus, but instead gets attached to it and is dragged by the bus for a while. After getting loose, an insane old woman tries to kill him slowly by hitting him with a cane whilst the Ginosaji hits him with a spoon. Jack is knocked out as a passer-by tries to keep the old woman at bay, finds himself in his'Happy Place', where he meets the'Happy Squirrel' who tries to motivate him. Jack wakes up in a hospital where the nurse turns into the Ginosaji and chases Jack to the top of the hospital, he attempts suicide by throwing himself off of the hospital roof. When he falls, he hits a fat woman; the Happy Squirrel tells Jack, admitted in the hospital that he won't be seeing him anymore. After a year of recovering, Jack tries again to make up himself as the Ginosaji, but far more convincingly. The fight happens in the Gobi Desert, where Jack tries to kill the Happy Squirrel. Angry at Jack's betrayal, the Happy Squirrel runs off. At the end of the last video of Ginosaji vs Ginosaji, Richard Gale announces that there will be a real film of the story, which will be called GINOSAJI - The Horribly Slow Murderer With The Extremely Inefficient Weapon. Richard Gale confirmed he will be directing a feature film based on his original short. On September 10, 2015, a 55-day Kickstarter crowdfunding campaign was launched by Richard Gale to help fund a real feature-length motion picture based on his short; the campaign was cancelled prior to completion. Gale launched a second campaign with a more modest$50,000 goal stating that he would receive partial funding from private investors but needed the additional crowd sourced funds to produce the movie. Richard Gale Films website The Horribly Slow Murderer with the Extre

Thomas de Clare, 1st Lord of Thomond, 1st Lord of Inchiquin and Youghal was a Hiberno-Norman peer and soldier. He was the second son of Richard de Clare, 6th Earl of Gloucester and his wife Maud de Lacy, Countess of Gloucester. In 1272 he served a term as Lieutenant of the Duchy of Aquitaine. On 26 January 1276 he was granted the Lordship of Thomond by Edward I of England. Thomas was born in about 1245 in Tonbridge, England, the second eldest son of Richard de Clare and Maud de Lacy, he and his brother Bogo received gifts from King Henry III when they were studying at Oxford from 1257–59. Thomas was a close friend and intimate advisor of Prince Edward of England, who would in 1272 accede to the throne as King Edward I. Together they took part in the Ninth Crusade, he held many important posts such as Governor of Colchester Castle and Governor of The City of London. He was made Commander of the English forces in Munster and created Lord of Inchiquin and Youghal. On 26 January 1276, he was granted the entire lordship of Thomond by King Edward.

That same year, he jointly commanded a Norman army along with Sir Geoffrey de Geneville, Justiciar of Ireland against the Irish clans of County Wicklow. They were joined by a contingent of men from Connacht led by his father-in-law Maurice FitzGerald, 3rd Lord of Offaly. Thomas and Justiciar de Geneville's forces attacked the Irish at Glenmalure, but they were soundly defeated and suffered severe losses. Civil war raged in Thomond between the rival factions of the O'Brien dynasty. In 1276, Brian Ruad, the deposed King of Thomond appealed to Thomas for support to help him regain his kingdom from his great-nephew Toirrdelbach MacTaidg O' Brien, who had usurped the throne. In return for his aid, Brian Ruad promised that Thomas would be allowed to colonise all the land between Athsollus in Quin and Limerick. Together and Brian Ruad expelled Toirrdelbach MacTaidg O'Brien and recaptured Clonroad which the latter had taken from Brian Ruad. O'Brien escaped to Galway where he elicited the help of his cousin William de Burgh, in 1277 together with the assistance from clans, MacNamara and O'Dea they defeated the combined forces of Thomas and Brian Ruad.

The latter fled to Bunratty Castle. The civil war continued for the next seven years, with Thomas supporting Brian Ruad's son Donnchad against Toirrdelbach. Thereafter until his death in 1306, Toirrdelbach MacTaidg O'Brien ruled as undisputed King of Thomond and Thomas had no choice but to accommodate him. O'Brien rented part of Bunratty Manor at £121 per annum. In 1280, Thomas embarked on a castle-building project at Quin, but was disrupted in his efforts by the O'Briens and MacNamaras. Thomas reconstructed Bunratty Castle in stone, replacing the earlier wooden building. In February 1275, he married Juliana FitzGerald, the 12-year-old daughter of Maurice FitzGerald, 3rd Lord of Offaly and Maud de Prendergast. During their marriage and Juliana lived in Ireland and in England. For instance, on 5 May 1284 the King notified his bailiffs and lieges in Ireland of the attorneys who were to act in Ireland on behalf of the couple as they were in England; this arrangement was to continue except when Thomas and Juliana went to Ireland.

Thomas and Juliana had four children: Maud de Clare, married firstly, Robert de Clifford, 1st Baron de Clifford, by whom she had issue. Gilbert de Clare, Lord of Thomond, Richard de Clare, Steward of Forest of Essex, 1st Lord Clare, Lord of Thomond, married a woman by the name of Joan, by whom he had one son, Thomas, he was killed at the Battle of Dysert O'Dea. Margaret de Clare, married firstly, Gilbert de Umfraville; when evidence was taken in 1302 to prove the age of his son Gilbert, it was established that Thomas had died on 29 August 1287. A mid-18th century compilation known as the Dublin Annals of Inisfallen states that Thomas was killed in battle against Turlough son of Teige and others. However, none of the earlier records of his death indicate; some of the witnesses to Gilbert's age in 1302 referred to the date of Thomas' death in their calculations but all were silent as to its circumstances. This and much other evidence on the subject has been set out and evaluated by Goddard Henry Orpen of Trinity College, Dublin.

Thomas was succeeded as Lord of Thomond by his eldest son, Gilbert, six years old. His widow Juliana, aged 24 years, would go on to marry two more times