title: Finite difference method

text: To use a finite difference method to approximate the solution to a problem, one must first discretize the problem's domain. This is usually done by dividing the domain into a uniform grid (see image to the right). This means that finite-difference methods produce sets of discrete numerical approximations to the derivative, often in a "time-stepping" manner.


title: Finite difference method

text: An expression of general interest is the local truncation error of a method. Typically expressed using Big-O notation, local truncation error refers to the error from a single application of a method. That is, it is the quantity formula_9 if formula_10 refers to the exact value and formula_11 to the numerical approximation. The remainder term of a Taylor polynomial is convenient for analyzing the local truncation error. Using the Lagrange form of the remainder from the Taylor polynomial for formula_12, which is


title: Finite difference method

text: the dominant term of the local truncation error can be discovered. For example, again using the forward-difference formula for the first derivative, knowing that formula_15,


title: Finite difference method

text: and further noting that the quantity on the left is the approximation from the finite difference method and that the quantity on the right is the exact quantity of interest plus a remainder, clearly that remainder is the local truncation error. A final expression of this example and its order is:


title: Finite difference method

text: This means that, in this case, the local truncation error is proportional to the step sizes. The quality and duration of simulated FDM solution depends on the discretization equation selection and the step sizes (time and space steps). The data quality and simulation duration increase significantly with smaller step size. Therefore, a reasonable balance between data quality and simulation duration is necessary for practical usage. Large time steps are useful for increasing simulation speed in practice. However, time steps which are too large may create instabilities and affect the data quality.


title: Finite difference method

text: The von Neumann and Courant-Friedrichs-Lewy criteria are often evaluated to determine the numerical model stability.


title: Finite difference method

text: to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get


title: Finite difference method

text: The last equation is a finite-difference equation, and solving this equation gives an approximate solution to the differential equation.


title: Finite difference method

text: Consider the normalized heat equation in one dimension, with homogeneous Dirichlet boundary conditions


title: Finite difference method

text: One way to numerically solve this equation is to approximate all the derivatives by finite differences. We partition the domain in space using a mesh formula_25 and in time using a mesh formula_26. We assume a uniform partition both in space and in time, so the difference between two consecutive space points will be "h" and between two consecutive time points will be "k". The points


title: Finite difference method

text: Using a forward difference at time formula_29 and a second-order central difference for the space derivative at position formula_30 (FTCS) we get the recurrence equation:


title: Finite difference method

text: So, with this recurrence relation, and knowing the values at time "n", one can obtain the corresponding values at time "n"+1. formula_35 and formula_36 must be replaced by the boundary conditions, in this example they are both 0.


title: Finite difference method

text: This explicit method is known to be numerically stable and convergent whenever formula_37. The numerical errors are proportional to the time step and the square of the space step:


title: Finite difference method

text: If we use the backward difference at time formula_39 and a second-order central difference for the space derivative at position formula_30 (The Backward Time, Centered Space Method "BTCS") we get the recurrence equation:


title: Finite difference method

text: The scheme is always numerically stable and convergent but usually more numerically intensive than the explicit method as it requires solving a system of numerical equations on each time step. The errors are linear over the time step and quadratic over the space step:


title: Finite difference method

text: Finally if we use the central difference at time formula_45 and a second-order central difference for the space derivative at position formula_30 ("CTCS") we get the recurrence equation:


title: Finite difference method

text: The scheme is always numerically stable and convergent but usually more numerically intensive as it requires solving a system of numerical equations on each time step. The errors are quadratic over both the time step and the space step:


title: Finite difference method

text: To summarize, usually the Crank–Nicolson scheme is the most accurate scheme for small time steps. For larger time steps, the implicit scheme works better since it is less computationally demanding. The explicit scheme is the least accurate and can be unstable, but is also the easiest to implement and the least numerically intensive.


title: Finite difference method

text: Here is an example. The figures below present the solutions given by the above methods to approximate the heat equation


title: Finite difference method

text: The 2D case shows all the characteristics of the more general nD case. Each second partial derivative needs to be approximated similar to the 1D case


title: Finite difference method

text: Consistency of the above-mentioned approximation can be shown for highly regular functions, such as formula_62.


title: Finite difference method

text: To prove this, one needs to substitute Taylor Series expansions up to order 3 into the discrete Laplace operator.


title: Finite difference method

text: Similar to continuous subharmonic functions one can define "subharmonic functions" for finite-difference approximations formula_64


title: Finite difference method

text: where the approximation is evaluated on points of the grid, and the stencil is assumed to be of positive type.


title: Finite difference method

text: where formula_71 are discretizations of the continuous domain formula_72, respectively the boundary formula_73.


title: Finite difference method

text: The SBP-SAT ("summation by parts - simultaneous approximation term") method is a stable and accurate technique for discretizing and imposing boundary conditions of a well-posed partial differential equation using high order finite differences.


title: Finite difference method

text: The method is based on finite differences where the differentiation operators exhibit summation-by-parts properties. Typically, these operators consist of differentiation matrices with central difference stencils in the interior with carefully chosen one-sided boundary stencils designed to mimic integration-by-parts in the discrete setting. Using the SAT technique, the boundary conditions of the PDE are imposed weakly, where the boundary values are "pulled" towards the desired conditions rather than exactly fulfilled. If the tuning parameters (inherent to the SAT technique) are chosen properly, the resulting system of ODE's will exhibit similar energy behavior as the continuous PDE, i.e. the system has no non-physical energy growth. This guarantees stability if an integration scheme with a stability region that includes parts of the imaginary axis, such as the fourth order Runge-Kutta method, is used. This makes the SAT technique an attractive method of imposing boundary conditions for higher order finite difference methods, in contrast to for example the injection method, which typically will not be stable if high order differentiation operators are used.


title: Calf (leg)

text: The calf (: calves; Latin: "sura") is the back portion of the lower leg in human anatomy. The muscles within the calf correspond to the posterior compartment of the leg. The two largest muscles within this compartment are known together as the calf muscle and attach to the heel via the Achilles tendon. Several other, smaller muscles attach to the knee, the ankle, and via long tendons to the toes.


title: Calf (leg)

text: From Middle English "calf", "kalf", from Old Norse "kalfi", possibly derived from the same Germanic root as English "calf" ("young cow"). Cognate with Icelandic "kálfi" ("calf of the leg"). "Calf" and "calf of the leg" are documented in use in Middle English circa AD 1350 and AD 1425 respectively.


title: Calf (leg)

text: Historically, the "absence of calf", meaning a lower leg without a prominent calf muscle, was regarded by some authors as a sign of inferiority: "it is well known that monkeys have no calves, and still less do they exist among the lower orders of mammals".


title: Calf (leg)

text: The calf is composed of the muscles of the posterior compartment of the leg: The gastrocnemius and soleus (composing the triceps surae muscle) and the tibialis posterior. The sural nerve provides innervation.


title: Calf (leg)

text: Medical conditions that result in calf swelling among other symptoms include deep vein thrombosis compartment syndrome, Achilles tendon rupture, and varicose veins.


title: Calf (leg)

text: Idiopathic leg cramps are common and typically affect the calf muscles at night. Edema also is common and in many cases idiopathic. In a small study of factory workers in good health, wearing compression garments helped to reduce edema and the pain associated with edema. A small study of runners found that wearing knee-high compression stockings while running significantly improved performance.


title: Calf (leg)

text: The circumference of the calf has been used to estimate selected health risks. In Spain, a study of 22,000 persons 65 or older found that a smaller calf circumference was associated with a higher risk of undernutrition. In France, a study of 6265 persons 65 or older found an inverse correlation between calf circumference and carotid plaques.


title: Calf (leg)

text: Calf augmentation and restoration is available, using a range of prosthesis devices and surgical techniques


title: Calf (leg)

text: The calves can be isolated by performing movements involving plantarflexion (pointing the toes down). The two major categories of calf exercises are those that maintain an extended knee, and those that maintain a flexed knee.


title: Calf (leg)

text: The first category includes movements such as standing calf raises, donkey calf raises and stair calves. The second category includes movements that maintain a bent knee, such as seated calf raises. Movements with a straight knee will target the gastrocnemius muscle more, and movements with a bent-knee will target the soleus muscle more. However, both variations will target both muscles to a large degree.


title: Calf (leg)

text: As the calf muscles are predominantly slow-twitch, they should be trained in a moderate to high repetition range. All repetition ranges offer their own benefits, and as such, calf training should be done in the 5-10 repetition range, the 10-20 repetition range, and the 20-30 repetition range.


title: Calf (leg)

text: It is important to train the calves relatively close to failure, which is 0-4 repetitions away from technical failure. They recover quickly, often requiring rest times of as little as 10 seconds and often no more than 60 seconds. Ensuring a 1-2 second pause at the top and bottom of the movement will put more emphasis on the muscle, and less emphasis on the achilles tendon.


title: Andre De Grasse

text: Andre De Grasse (born November 10, 1994) is a Canadian sprinter. A six-time Olympic medalist, De Grasse is the reigning Olympic champion in the 200 m, and also won the silver in the 200 m in 2016. He won a second silver in the 4×100 relay in 2020. He also has three Olympic bronze medals, placing third in the 100 m at both the 2016 and 2020 Games, and also in the 4×100 m relay in 2016.


title: Andre De Grasse

text: At the World Athletics Championships, De Grasse won a gold medal with the Canadian 4×100 relay team in 2022, as well as a bronze medal in the same event in 2015. He has three individual World medals, winning silver in the 200 m in 2019 in Doha, and two bronzes in the 100 m in 2015 and 2019. He was also the double Pan American champion and the NCAA champion in the 100 m and 200 m. He is the current Canadian record holder in the 200 m, running a 19.62 in Tokyo and making him the eighth fastest man in history in the 200 m.


title: Andre De Grasse

text: De Grasse is the first Canadian sprinter to win three medals in a single Olympics, bettering the two medals in a single Olympics that were won by Canadian sprinters Donovan Bailey and Percy Williams. His gold medal finish at the 2020 Olympics was the first Canadian Olympic gold in track in 25 years and the first in the 200 m in 93 years. A consistent podium finisher, he has won a medal in every Olympic and World Championships in the finals he has competed in.


title: Andre De Grasse

text: Andre De Grasse was born in Scarborough, Ontario. His mother, Beverley De Grasse, was a high school sprinter in Trinidad and Tobago before she moved to Canada at age 26. His father, Alexander Waithe, moved from Barbados to Canada as a teenager.


title: Andre De Grasse

text: De Grasse was raised in Markham, Ontario, and attended St. Marguerite Bourgeoys Catholic Elementary School from kindergarten to grade two and later transferred to Mother Teresa Catholic School in Markham, Ont. to continue until grade eight where he won his first race in 2006. He also attended Father Michael McGivney Catholic Academy and Milliken Mills High School.


title: Andre De Grasse

text: In high school, De Grasse initially played basketball, at one point playing against future NBA player Andrew Wiggins of Vaughan Secondary School. In his first high school track race, the York Region Championships, De Grasse ran wearing basketball shorts and borrowed spikes, he also ignored the starting blocks and did a standing start. Despite his clear inexperience, he finished second in the 100m final with 10.91, third overall in the 200m with 22.64, and 7th overall in the Long Jump with 5.88m. He was spotted by future coach Tony Sharpe who noticed his impressive results compensating for the lack of starting blocks and proper racing attire. Sharpe invited De Grasse to join Pickering's Speed Academy. All 3 events were won by his eventual Olympic teammate Bolade Ajomale of Alexander Mackenzie High School. Having finished in the top 4 in the 100m and 200m, De Grasse qualified for the Ontario Central Championships, where he finished 4th in the 100m and 10th overall in the 200m. Finally, having qualified for the Ontario Championships in the 100m, De Grasse placed 5th in the final. He then began to train under Sharpe at The Speed Academy.


title: Andre De Grasse

text: He attended Coffeyville Community College in 2013 and 2014 before transferring to USC for his junior season in 2015.


title: Andre De Grasse

text: Competing for USC, De Grasse's legal 100 m time of 9.97 won the Pac-12 championship in May 2015 was the first time he ran under 10 seconds, and he became the first Canadian to do so since Bruny Surin. In the 200m, De Grasse broke the Canadian record with 20.03, and closed on it again with 20.05 in the final. De Grasse nabbed global attention at the NCAA Championships by winning both the 100 and 200 metres ahead of favourite Trayvon Bromell of Baylor University with wind-aided times of 9.75 and 19.58, respectively. After the race, with encouragement from his friends to keep going in the pursuit of titles, he said "So I ask myself...world champion? Olympic champion? Why not me? I've come this far, and I've only scratched the surface. I want to keep it going. Track is fun to me, and as long as it stays this way, I expect to keep getting better."


title: Andre De Grasse

text: After winning the national 100m title with a personal best of 9.95, De Grasse's next major event was the 2015 Pan American Games held in his home province of Ontario. There, he won the gold medal in the 100m with a time of 10.05. After the race, De Grasse said of the home crowd that "Aw, it was great. I think they gave me an extra boost of energy, the crowd was amazing, I hear them cheering my name and screaming my name." De Grasse doubled and won gold in the 200m with a new national record of 19.88. De Grasse became the first Canadian in history to run both a sub-10 in the 100 metres and sub-20 in the 200. He appeared to win a third Pan Am Games gold when he ran the second leg of the 4 x 100m relay, in which the Canadian team came first in the race with a Games record of 38.06. However, the team was later disqualified two hours after the race for a lane infringement by Gavin Smellie.


title: Andre De Grasse

text: The 2015 World Championships in Athletics took place in Beijing. At the event, De Grasse cruised through his heat in 9.99, then made headlines when he nearly beat Usain Bolt, who stumbled out of the blocks. The two clocked 9.96, with Bolt just thousandths ahead. In the final, De Grasse tied for the bronze medal with Bromell, running a new personal best of 9.92. He became the first Canadian to win a medal in track's marquee event since Bruny Surin raced to silver in 1999. After the final De Grasse said "I didn't know who had won the race, I didn't know you could actually tie with someone for a bronze medal. So I am very happy for Trayvon and proud of myself to come away with a personal best. To race against these guys and make the final, I couldn't end the season any better than that. I can't let [the lane assignment] distract me. At the end of the day, it's the 100m final. This was the biggest race of my life so I wasn't going to think about no lane assignment. I had a lot of confidence after the semi-finals, being that close to Bolt, and that raised my confidence for the final." De Grasse also participated in the 4 × 100m relay where he won a second bronze medal, running a 38.13 together with Aaron Brown, Brendon Rodney, and Justyn Warner.


title: Andre De Grasse

text: De Grasse got off to a rocky start in the 2016 season, finishing 8th at the Prefontaine Classic. However, he shook off the race rust in June and won the 200m in Birmingham and the 100m in Oslo. He defended his national 100m title in 9.99, his first sub-10 of the season, and qualified for Canada's Olympic team. He also qualified for the 200m, albeit finishing 3rd at the championships behind Rodney and Brown.


title: Andre De Grasse

text: De Grasse entered the Rio Olympics carrying Canada's hopes as a medallist. He advanced to the finals of the 100m with ease after running a time of 10.04 in his heat and then equaling his personal best of 9.92 in the semi-finals. He impressed many by staying level with Usain Bolt during their semifinal and even appeared to mimic the world record holder, the two Puma sponsorees crossing the line together with smiles. De Grasse won the bronze medal in the final in 9.91 seconds, a new personal best, behind Bolt and his main rival Justin Gatlin. He became the first male athlete to win a medal for Canada at the 2016 Summer Olympics. De Grasse's medal sparked talk of him being Bolt's heir apparent in the athletics world, a claim which Bolt supported:


title: Andre De Grasse

text: De Grasse said of his relationship with Bolt after that "We were just having some fun. Me (sic) and Usain met back in January, we did a lot of things together. He feels like I'm the next one, and now I'm just trying to live up to it." Former Canadian Olympic Champion Donovan Bailey was seen jumping up and down in the CBC Sports studio, cheering on De Grasse. After, he said, "I'm shaking. This is great for track and field in Canada."


title: Andre De Grasse

text: In the 200 m, De Grasse had the fastest time in the heats of 20.09. De Grasse and Bolt were lined up beside each other once again in the semi finals. Bolt led at halfway, when De Grasse suddenly rushed to his shoulder appearing to try to beat him. The two exchanged smiles and crossed the line together, one of the most iconic moments of the games. De Grasse claimed his strategy was to tire Bolt out before the final, which Bolt did not appear to appreciate. De Grasse's time of 19.80 was a new Canadian record, and he became the first Canadian to make it to the finals of the 200m since Atlee Mahorn at the 1988 Olympics in Seoul. Despite his tactic, De Grasse finished behind Bolt again, this time with the silver medal in 20.02, the first Canadian to win a medal in the 200m since Percy Williams at the 1928 Olympics in Amsterdam.


title: Andre De Grasse

text: De Grasse ran the anchor for the finals of the 4 x 100 m relay. Initially in 6th place, De Grasse made an incredible close on Japan and the United States by about 4 metres, though he narrowly missed the bronze medal by 0.02 seconds. Despite this, the Canadians set a new national record of 37.64 seconds, breaking the record set in 1996 in Atlanta. However, the American team that placed third was disqualified for a zone violation (handing over the baton outside of the designated zone) at the first baton change, so the Canadians were awarded the bronze medal.


title: Andre De Grasse

text: As in 2016, De Grasse had a rocky start to his season, but quickly picked up again. He took Diamond League wins over the 100m in Oslo and Stockholm, and 200m wins in Rome and Rabat. His time in Stockholm of 9.69w (+4.8 m/s) was over the 2.0 m/s wind limit, but the 4th fastest in history regardless. With Bolt choosing to forego the 200m, De Grasse was considered a strong favourite for the world title in London. His main goal was to beat Bolt in the 100m before his retirement after the championships. After winning both the 100m and 200m national titles, De Grasse was in contention to make the same double in London and defeat the world record holder. However, just days before the world championships, De Grasse strained his hamstring and was forced to pull out of both events, effectively ending his goal of beating Bolt before his retirement. A few weeks earlier, the two were set to face off in Monaco, but De Grasse was reportedly pulled out the race. His coach claimed it was Bolt's doing, likely involving contract clauses with Bolt's team, who were unwilling to see De Grasse potentially defeat him before the championships. A few days later, Bolt also said in an interview that "The last guy I said was going to be great disrespected me", a comment interpreted to be about De Grasse and his unexpected move in the semifinals of the 200 in Rio. Despite the apparent tensions, Bolt admitted he would have liked to race De Grasse in London.


title: Andre De Grasse

text: On January 10, 2018, De Grasse was named to Canada's 2018 Commonwealth Games team. However, he had withdrawn before the games began due to his hamstring injury.


title: Andre De Grasse

text: In the Diamond League, De Grasse finished 6th in the 200m in Doha and 8th in the 100m in Shanghai, clearly affected by his injuries. He was unable to defend his national title in the 100m, settling for third in 10.20. During the 200m heats, he pulled up with a hamstring injury; the crowd cheered De Grasse on as he walked to the finish line, and he ended his season. Following his injuries, De Grasse left ALTIS and coach Stu McMillan in Arizona, moving to Jacksonville to train under Rana Reider.


title: Andre De Grasse

text: Despite initial struggles in the early season, De Grasse appeared to be making a slow return to international competition. He finished second to Aaron Brown in the 200m at the Diamond League in Shanghai. A month later, he won his first Diamond League victory in two years at the Rabat 200m event, beating the reigning World champion Ramil Guliyev. Ultimately, he would finish on the podium in five of seven 100m events and all six 200m in the leadup to the World Championships. The next week, he beat Christian Coleman at the Ostrava Golden Spike in the 200m with 19.91. In July, he broke 10 seconds for the first time in 3 years at the Diamond League in London.


title: Andre De Grasse

text: At the national championships, De Grasse nearly beat Brown in the 100m, the two clocking 10.03 and being separated by thousandths. He was named to the Canadian team for the 2019 World Athletics Championships in Doha in both of his disciplines. Across the season, De Grasse remained consistent at multiple Diamond League races, clocking several sub-20 second races across the 200m. He ended his pre-championship season with a 100m win at the ISTAF Berlin in 9.97.


title: Andre De Grasse

text: At the championships, De Grasse made his contention official by winning his semifinal in the 100m, beating defending champion Justin Gatlin and number 2 all-time Yohan Blake. He won bronze in the final with 9.90, a new personal best once again. Competing next in the 200m, he won the silver medal behind Noah Lyles in 19.95, shy of his season's best of 19.87. De Grasse commented that he tired slightly toward the end of the race, but that "I'm not disappointed. I didn't think I'd be here a year ago." This was the first World Championship medal for a Canadian in the 200m since Atlee Mahorn in 1991. He anchored the Canadian 4 × 100 team once again, but came short of qualifying for the final despite setting a season's best of 37.91 and finishing eighth overall.


title: Andre De Grasse

text: The onset of the COVID-19 pandemic resulted in the cancellation of much of the 2020 international season, and the delay of the 2020 Summer Olympics by a year. De Grasse opened his 2021 season on April 17 at the Tom Jones Memorial Invitational in Gainesville, Florida, running the 100m in 9.99. His subsequent 100 m starts, including two appearances on the 2021 Diamond League circuit, saw times of over ten seconds. He enjoyed more success in the 200m, finishing in the top three in all of his three Diamond League appearances, including winning the Oslo event with a time of 20.09. As well, he participated in the Müller British Grand Prix as part of the Canadian 4 x 100m relay team, which placed second with a time of 38.29.


title: Andre De Grasse

text: De Grasse was named to the 2020 Canadian Olympic team, and was identified as one of Canada's top medal contenders in athletics, notwithstanding some of his early results that year. Former Olympic champion Donovan Bailey dismissed concerns regarding De Grasse's times, stating that in his view he was "more concerned that he's injury-free and been consistent."


title: Andre De Grasse

text: Upon arrival in Tokyo for the 2020 Summer Olympics, De Grasse began by competing in the heats of the men's 100m. He easily won his heat, posting a new season best time of 9.91, just 0.01 shy of his personal best from two years before, and ended up with the fastest time in any of the heats. He was second in his semi-final behind Fred Kerley, running 9.98, and advanced to the final. In the final, De Grasse had the unfavourable ninth lane placement, and was slow off the blocks, but rapidly gained ground over the final forty metres of the race to finish in third place and claim his second bronze medal in the event, with a new personal best time of 9.89. This was Canada's fourteenth medal of the Tokyo Olympics, and the first for a male athlete. The lack of medals for Canadian men had become a point of media and viewer discussion through the first nine days of the Games. He also became the first Canadian man to win multiple Olympic medals in the 100 m.


title: Andre De Grasse

text: De Grasse next competed in the heats of the 200 m, qualifying automatically as the third man in his heat with 20.56. This had him again in the unfavourable ninth lane when in his semi-final, where he set a new personal best and national record of 19.73, the fastest time in the semi-final phase. De Grasse then went on to win the gold medal in the 200m final in a personal best and Canadian record time of 19.62 seconds, making him the 8th fastest of all-time over 200 metres. This was Canada's first track gold medal since 1996, and first gold medal in the 200m since Percy Williams' victory in 1928. De Grasse was the only male sprinter to compete in both the 100 and 200 m races in Tokyo.


title: Andre De Grasse

text: Hours after his gold medal win, De Grasse competed in the heats of the 4x100 m relay alongside Aaron Brown, Jerome Blake and Brendon Rodney. Again taking the anchor leg, at the point De Grasse took the baton from Rodney the Canadian team was judged to be in approximately fifth place, but De Grasse reached the finish line in second, only two thousandths of a second behind Chinese anchor runner Wu Zhiqiang. The Canadian team's qualifying time was third-fastest in the heats, behind Jamaica and China. De Grasse repeated this performance in the event final, taking Canada from fifth to the bronze medal position on the anchor leg, securing his sixth Olympic medal. This bronze was later upgraded to a silver when the team from Great Britain was disqualified. This tied him with Cindy Klassen and Clara Hughes as the second-most decorated Canadian Olympian (behind Penny Oleksiak).


title: Andre De Grasse

text: In his first event subsequent to the Olympics, De Grasse returned to the Diamond League for the Prefontaine Classic in Eugene, Oregon. Running in the 100 metres event, De Grasse recorded a wind-assisted time of 9.74 seconds, winning the event ahead of Tokyo silver medalist Kerley. De Grasse said that following the Olympics he "just went out there to have some fun." Weeks later in the Diamond League Final in Zurich, De Grasse placed second in both the 100 and 200 metres events, running in both on the same night. He equaled his 9.89 time from the Olympics, and then ran 19.72 an hour later, despite later saying "I just had no gas" for the latter. He called it the end of "my greatest season ever."


title: Andre De Grasse

text: The 2022 season began with difficulties for De Grasse, hampered by an injury to his foot. After a ninth-place finish at the Prefontaine Classic in the 100 m, he won gold at the Bislett Games in Oslo with a season best time of 10.05 seconds. Shortly afterward, he contracted COVID-19 for the second time, experiencing a significant setback to his training due to breathing difficulties.


title: Andre De Grasse

text: Despite his health struggles, he opted to compete at the 2022 World Athletics Championships in Eugene, Oregon. In the 100 m, De Grasse was second in his heat with a 10.12 time, qualifying to the semi-finals, despite visible difficulties. He ran a 10.21 in the semi-finals, and did not advance to the final, the first time at an individual World event he had failed to win a medal. In light of his health, De Grasse said "it's alright. It's been a challenging season. I'll take it; I made it to the semifinals." He subsequently chose to withdraw from the 200 m. There were questions raised about his readiness in advance of the 4×100 m relay, but De Grasse indicated that he felt able to compete. The Canadian team qualified for the finals with the third-fastest time in the heats, De Grasse being pipped at the line by Frenchman Jimmy Vicaut by 0.01 seconds. In the final, the Canadians staged a major upset victory over the heavily favoured American team to take the gold medal, aided by smooth baton exchanges while the Americans made multiple fumbles. De Grasse ran the anchor leg for Canada, maintaining the lead over American Marvin Bracy to secure his first ever relay major championship gold, breaking the national record he had previously helped set at the Rio Olympics. This was Canada's third gold in the event, and the others being consecutive Bailey era wins in 1995 and 1997. The result "stunned" the heavily American crowd at Hayward Field, but De Grasse noted "there's a lot of Canadian flags out there, a lot of fans cheering us on -- it definitely feels good. It's not technically on home soil but it kind of felt like it." Reflecting on the historic win with his teammates, he said "we have talked and dreamed about this moment together."


title: Andre De Grasse

text: De Grasse was initially named to the Canadian team for the 2022 Commonwealth Games, but withdrew after the World Championships, with Athletics Canada citing a need "to properly recover and prepare for the rest of the season."


title: Andre De Grasse

text: In 2016, he established Andre De Grasse Holiday Classic Basketball Tournament, a charity event that supports Andre De Grasse Family Foundation. In September 2017, he appeared at WE Day, a WE Charity event in Toronto. De Grasse also created and participates annually in a basketball tournament named "Holiday Classic at Markham" at Pan Am Centre. All proceeds from the tournament go to the Andre De Grasse Family Foundation.


title: Andre De Grasse

text: He and his wife, American hurdler Nia Ali, have a daughter, Yuri, born June 2018 and a second child in May 2021. De Grasse is Catholic, having been influenced by the faith of his parents. He has the word "hope" and a prayer tattooed on his arm.


title: Andre De Grasse

text: De Grasse's success at the Olympics led to him winning the 2016 Lionel Conacher Award as the Canadian Press male athlete of the year, and be presented with the Rising Star Award by the IAAF. In April 2017 De Grasse was a recipient of a Harry Jerome Award.


title: Amazon S3

text: Amazon S3 or Amazon Simple Storage Service is a service offered by Amazon Web Services (AWS) that provides object storage through a web service interface. Amazon S3 uses the same scalable storage infrastructure that Amazon.com uses to run its e-commerce network. Amazon S3 can store any type of object, which allows uses like storage for Internet applications, backups, disaster recovery, data archives, data lakes for analytics, and hybrid cloud storage.


title: Amazon S3

text: Amazon S3 manages data with an object storage architecture which aims to provide scalability, high availability, and low latency with high durability.


title: Amazon S3

text: The basic storage units of Amazon S3 are objects which are organized into buckets. Each object is identified by a unique, user-assigned key. Buckets can be managed using the console provided by Amazon S3, programmatically with the AWS SDK, or the REST application programming interface. Objects can be up to five terabytes in size.


title: Amazon S3

text: Requests are authorized using an access control list associated with each object bucket and support versioning which is disabled by default. Since buckets are typically the size of an entire file system mount in other systems, this access control scheme is very coarse-grained. In other words, unique access controls cannot be associated with individual files.


title: Amazon S3

text: Amazon S3 can be used to replace static web-hosting infrastructure with HTTP client-accessible objects, index document support and error document support.


title: Amazon S3

text: The Amazon AWS authentication mechanism allows the creation of authenticated URLs, valid for a specified amount of time.


title: Amazon S3

text: Every item in a bucket can also be served as a BitTorrent feed. The Amazon S3 store can act as a seed host for a torrent and any BitTorrent client can retrieve the file. This can drastically reduce the bandwidth cost for the download of popular objects. A bucket can be configured to save HTTP log information to a sibling bucket; this can be used in data mining operations.


title: Amazon S3

text: There are various User Mode File System (FUSE)–based file systems for Unix-like operating systems (for example, Linux) that can be used to mount an S3 bucket as a file system. The semantics of the Amazon S3 file system are not that of a POSIX file system, so the file system may not behave entirely as expected.


title: Amazon S3

text: Amazon S3 offers eight different storage classes with different levels of durability, availability, and performance requirements.


title: Amazon S3

text: The Amazon S3 Glacier storage classes above are distinct from Amazon Glacier, which is a separate product with its own APIs.


title: Amazon S3

text: An object in S3 can be between 1 byte and 5TB. If an object is larger than 5TB, it must be divided into chunks prior to uploading.


title: Amazon S3

text: When uploading, Amazon S3 allows a maximum of 5GB in a single upload operation; hence, objects larger than 5GB must be uploaded via the S3 multipart upload API.


title: Amazon S3

text: The broad adoption of Amazon S3 and related tooling has given rise to competing services based on the S3 API. These services use the standard programming interface but are differentiated by their underlying technologies and business models. A standard interface enables better competition from rival providers and allows economies of scale in implementation, among other benefits.


title: Amazon S3

text: Amazon Web Services introduced Amazon S3 in 2006. Amazon reported it stored more than 100 trillion objects , up from 10 billion objects in October 2007, 14 billion objects in January 2008, 29 billion objects in October 2008, 52 billion objects in March 2009, 64 billion objects in August 2009, 102 billion objects in March 2010, and 2 trillion objects in April 2013. In November 2017 AWS added default encryption capabilities at bucket level.


title: Wisden 100

text: The Wisden 100 is a set of lists created by "Wisden" which attempted to objectively rate the 100 best individual innings performances in Test and One Day International cricket in each of the disciplines of batting and bowling. The Test list was released in 2001 and the ODI list was released in 2002.


title: Wisden 100

text: The ratings were calculated by scoring each individual batting and bowling performance in various criteria. Apart from the player's actual score or figures, criteria which were taken into account included the strength of the opposition players, the quality of the pitch, the result of the match, and the player's contribution to this result. The maximum possible rating was 300.


title: Wisden 100

text: Overall in both formats, 13 innings of Vivian Richards were selected by "Wisden" more than anyone in the list.


title: Wisden 100

text: The top-rated batting performance was Donald Bradman's 270 for Australia against England at Melbourne in the 1936–37 Ashes series. 5 of Bradman's innings appeared in the top 100, more than any other batsman.


title: Wisden 100

text: The top-rated bowling performance was Hugh Tayfield's 9/113 for South Africa against England at Johannesburg in the 1956–57 series. Curtly Ambrose and Harbhajan Singh each had 4 performances in the top 100, more than any other bowler.


title: Wisden 100

text: Despite his highly impressive career record, not one of Sachin Tendulkar's innings appeared in the top 100 batting performances. His omission was strongly criticised by fans and many sections of the media in India. Wisden defended the list stating that performances which made a major contribution to victory received a much larger weighting than those in which the match was drawn or lost. Tendulkar's most important innings had usually come in draws and defeats, and therefore received a lower weighting.


title: Wisden 100

text: The list has had no official updated release since its inception. However, shortly after the list's release, Wisden stated that Mark Butcher's match-winning innings of 173* in the 4th Test of the 2001 Ashes series placed him in 48th place on the batting list with a rating of 200.8.


title: Wisden 100

text: Following the success of the list for Test cricket, the Wisden 100 list for ODI cricket was released on 1 February 2002.


title: Wisden 100

text: The top-rated batting performance was Viv Richards' 189* for West Indies against England at Manchester in 1984. 7 of Richards' innings appeared in the top 100, more than any other batsman.


title: Wisden 100

text: The top-rated bowling performance was Gary Gilmour's 6/14 for Australia against England at Leeds in 1975. Waqar Younis appears 9 times in the top 100, more than any other player.


title: Wisden 100

text: As with the Test cricket list, this list has had no official updated release since its inception. However, Wisden stated that Ricky Ponting's 140* against India in the 2003 World Cup final placed him 2nd on the batting list.


title: Wisden 100

text: Following the launch of the top Test and ODI performances lists, Wisden received many requests asking whether it was possible to create a ranking list of all-time great players by using the same formula and examining the average rating each player received per innings. Including a weighting for players with longer careers, Wisden arrived at the lists below. In Tests, Donald Bradman was the clear leader in the batting category and Muttiah Muralitharan was ranked as the top bowler. In the ODI section, Viv Richards and Wasim Akram are the top-ranked players.


title: Wisden 100

text: The same methodology was used to rank each player's overall performance in the 2003 Cricket World Cup. In this list, the top batsman was Sachin Tendulkar and the top bowler was Glenn McGrath.


title: Workers of the world, unite!

text: The political slogan "Workers of the world, unite!" is one of the rallying cries from "The Communist Manifesto" (1848) by Karl Marx and Friedrich Engels (, literally "Proletarians of all countries, unite!", but soon popularised in English as "Workers of the world, unite! You have nothing to lose but your chains!"). A variation of this phrase ("Workers of all lands, unite") is also inscribed on Marx's tombstone. The essence of the slogan is that members of the working classes throughout the world should cooperate to defeat capitalism and achieve victory in the class conflict.


title: Workers of the world, unite!

text: Five years before "The Communist Manifesto", this phrase appeared in the 1843 book "The Workers' Union" by Flora Tristan.


title: Workers of the world, unite!

text: The International Workingmen's Association, described by Engels as "the first international movement of the working class" was persuaded by Engels to change its motto from the League of the Just's "all men are brothers" to "working men of all countries, unite!". It reflected Marx's and Engels' view of proletarian internationalism.


title: Workers of the world, unite!

text: The phrase has overlapping meanings: first, that workers should unite in unions to better push for their demands such as workplace pay and conditions; secondly, that workers should see beyond their various craft unions and unite against the capitalist system; and thirdly, workers of different countries have more in common with each other than workers and employers of the same country.


title: Workers of the world, unite!

text: The phrase was used by the Industrial Workers of the World (IWW) in their publications and songs and was a mainstay on banners in May Day demonstrations. The IWW used it when opposing World War I in both the United States and Australia.


title: Workers of the world, unite!

text: The slogan was the Soviet Union's state motto (Пролетарии всех стран, соединяйтесь!; "Proletarii vsekh stran, soyedinyaytes'!") and it appeared in the State Emblem of the Soviet Union. It also appeared on 1919 Russian SFSR banknotes (in Arabic, Chinese, English, French, German, Italian and Russian), on Soviet ruble coins from 1921 to 1934 and was the slogan of Soviet newspaper "Pravda".


title: Workers of the world, unite!

text: In the first Swedish translation of "The Communist Manifesto", published in 1848, the translator Pehr Götrek substituted the slogan with "Folkets röst, Guds röst!" (i.e. "Vox populi, vox Dei", or "The Voice of the People, the Voice of God"). However, later translations have included the original slogan.


title: Workers of the world, unite!

text: The guiding motto of the 2nd Comintern congress in 1920, under Lenin's directive, was "Workers and oppressed peoples of all countries, unite!". This denoted the anti-colonialist agenda of the Comintern, and was seen as an attempt to unite racially-subjugated black people and the global proletariat in anti-imperialist struggle.


title: Workers of the world, unite!

text: The English phrase and its variants (the variant "All power to the workers" is used by some parties such as the Communist Party of Australia) are used by communist parties in the English-speaking world. The list below does not include the mottos of communist parties of the above countries or in languages listed above.


title: Star Ocean: The Divine Force

text: Star Ocean: The Divine Force is a 2022 action role-playing game developed by tri-Ace and published by Square Enix. It is the sixth major installment in the "Star Ocean" series and was released for PlayStation 4, PlayStation 5, Windows, Xbox One, and Xbox Series X/S on October 27. The game's score was composed by series regular Motoi Sakuraba, with character art designed by Akira Yasuda.


title: Star Ocean: The Divine Force

text: The game received mix to good reception from critics with some praising the combat, characters, and narrative but many felt it was a step-down from a graphical standpoint and some performance inconsistency.


title: Star Ocean: The Divine Force

text: The PlayStation 4 version of "Star Ocean: The Divine Force" sold 27,001 physical copies within its first week of release in Japan, making it the third bestselling retail game of the week in the country. The PlayStation 5 version sold 17,177 physical copies in Japan throughout the same week, making it the country's seventh bestselling retail game.


title: Reinheitsgebot

text: The Reinheitsgebot (, literally "purity order") is a series of regulations limiting the ingredients in beer in Germany and the states of the former Holy Roman Empire. The best known version of the law was adopted in Bavaria in 1516 (by William IV), but similar regulations predate the Bavarian order, and modern regulations also significantly differ from the 1516 Bavarian version. Although today, the Reinheitsgebot is mentioned in various texts about the history of beer, historically it was only applied in the duchy of Bavaria and from 1906 in Germany as a whole, and it had little or no effect in other countries or regions.


title: Reinheitsgebot

text: The most influential predecessor of the modern "Reinheitsgebot" was a law first adopted in the duchy of Munich in 1487. After Bavaria was reunited, the Munich law was adopted across the entirety of Bavaria on 23 April 1516. As Germany unified, Bavaria pushed for adoption of this law on a national basis (see "Broader adoption").


title: Reinheitsgebot

text: According to the 1516 Bavarian law, the only ingredients that could be used in the production of beer were water, barley and hops. The text does not mention yeast as an ingredient, although yeast was at the time knowingly used in the brewing process. It is likely that brewers of the time preferred to see yeast as a fixture of the brewing process. Yeast produced in one batch was commonly transferred to a subsequent batch, thus giving yeast a more permanent character in the brewing process. A full understanding of chemical basis of yeast and the fermentation process did not come until much later.


title: Reinheitsgebot

text: The 1516 Bavarian law set the price of beer (depending on the time of year and type of beer), limited the profits made by innkeepers, and made confiscation the penalty for making impure beer.


title: Reinheitsgebot

text: The Bavarian order of 1516 was introduced in part to prevent price competition with bakers for wheat and rye. The restriction of grains to barley was meant to ensure the availability of affordable bread, as wheat and rye were reserved for use by bakers. The rule may have also had a protectionist role, as beers from Northern Germany often contained additives that could not be grown in Bavaria.


title: Reinheitsgebot

text: Religious conservatism may have also played a role in adoption of the rule in Bavaria, to suppress the use of plants that were allegedly used in pagan rituals, such as gruit, henbane, belladonna, or wormwood. The rule also excluded problematic methods of preserving beer, such as soot, stinging nettle and henbane.


title: Reinheitsgebot

text: While some sources refer to the Bavarian law of 1516 as the first law regulating food safety, this is inaccurate, as earlier food safety regulations can be traced back as far as ancient Rome. Similarly, some sources claim that the law has been essentially unchanged since its adoption, but as early as the mid-1500s Bavaria began to allow ingredients such as coriander, bay leaf, and wheat. Yeast was also added to modern versions of the law after the discovery of its role in fermentation.


title: Reinheitsgebot

text: The "Reinheitsgebot" remains the most famous law that regulates the brewing of beer, and continues to influence brewing not only in Germany, but around the world.


title: Reinheitsgebot

text: Modern versions of the law have contained significant exceptions for different types of beer (such as top-fermented beers), for export beers, and for different regions. The basic law now declares that only malted grains, hops, water and yeast are permitted.


title: Reinheitsgebot

text: In response to the growth of craft breweries globally, some commentators, German brewers, and even German politicians have argued that the "Reinheitsgebot" has slowed Germany's adoption of beer trends popular in the rest of the world, such as Belgian lambics and American craft styles. In late 2015, Bavarian brewers voted in favor of a revision to the beer laws to allow other natural ingredients.


title: Reinheitsgebot

text: The earliest documented mention of beer by a German nobleman is the granting of a brewing licence by Emperor Otto II to the church at Liege (now Belgium), awarded in 974. A variety of other beer regulations also existed in Germany during the late Middle Ages, including in Nuremberg in 1293, Erfurt in 1351, and Weißensee in 1434.


title: Reinheitsgebot

text: The Bavarian order of 1516 formed the basis of rules that spread slowly throughout Germany. Bavaria insisted on its application throughout Germany as a precondition of German unification in 1871. The move encountered strong resistance from brewers outside Bavaria, and imperial law of 1873 taxed the use of other ingredients (rather than banning them) when used by Northern German brewers. It was not until 1906 that the law was applied consistently across all of Germany, and it was not formally referred to as "Reinheitsgebot" until the Weimar Republic.


title: Reinheitsgebot

text: In 1952, the basic regulation of the "Reinheitsgebot" were incorporated into the West German "Biersteuergesetz" (Beer Taxation Law). Bavarian law remained stricter than that of the rest of the country, leading to legal conflict during the 1950s and early 1960s. The law initially applied only to bottom-fermented ("lager") beers, but brewers of other types of beer soon accepted the law as well.


title: Reinheitsgebot

text: Outside of Germany, the "Reinheitsgebot" was formally incorporated in Greek law by the first Greek king, Otto (originally a Bavarian prince). German brewers at the Tsingtao Brewery in the German colony in Qingdao, China also followed the law voluntarily.


title: Reinheitsgebot

text: In March 1987 French brewers sued and, in the case of "Commission v Germany (C-178/84)", the European Court of Justice found that the "Reinheitsgebot" was protectionist, and therefore in violation of Article 30 of the Treaty of Rome.<ref name="Judgment of the Court of 12 March 1987. - Commission of the European Communities v Federal Republic of Germany. - Failure of a State to fulfil its obligations - Purity requirement for beer. - Case 178/84."></ref> This ruling concerned only imported beer, so Germany chose to continue to apply the law to beer brewed in Germany. (Greece's version of the "Reinheitsgebot" was struck down around the same time.) General food safety and labeling laws may also apply.


title: Reinheitsgebot

text: After German reunification in 1990 the Neuzeller Kloster Brewery, a former monastery brewery in the East German town of Neuzelle, Brandenburg, was warned to stop selling its black beer as it contained sugar. After some negotiations the brewery was allowed to sell it under the name "Schwarzer Abt" ("Black Abbot") but could not label it "Bier". This decision was repealed by the Federal Administrative Court of Germany through a special permit, and after legal disputes lasting ten years (known as the "Brandenburg Beer War") Neuzeller Kloster Brewery gained the right to call "Schwarzer Abt" "Bier" again.


title: Reinheitsgebot

text: The revised "Vorläufiges Biergesetz" (Provisional Beer Law) of 1993, which replaced the earlier regulations, is a slightly expanded version of the "Reinheitsgebot", stipulating that only water, malted barley, hops and yeast be used for any bottom-fermented beer brewed in Germany. In addition, the law allows the use of powdered or ground hops and hop extracts, as well as stabilization and fining agents such as PVPP. Top-fermented beer is subject to the same rules, with the addition that a wider variety of malted grains can be used, as well as pure sugars for flavor and coloring.


title: Reinheitsgebot

text: The law's applicability was further limited by a court ruling in 2005, which allowed the sale of beer with different ingredients as long as it was not labeled "beer". The law thus became a labeling standard.


title: Reinheitsgebot

text: Exceptions to the current rules can be sought, and have been granted to allow gluten-free beer to be labeled as beer despite the use of different ingredients.


title: Reinheitsgebot

text: Because of strong German consumer preferences, labeling beer as being compliant with "Reinheitsgebot" is believed to be a valuable marketing tool in Germany. German brewers have used the law to market German beer internationally, including a failed attempt to have the law added to the UNESCO list of intangible cultural heritages. Breweries in Norway often follow the same rules as in the Reinheitsgebot. Some breweries outside Germany also claim to be compliant to the "Reinheitsgebot" as part of their marketing, such as:


title: Reinheitsgebot

text: For some vegans the "Reinheitsgebot" can be seen as a strong indication that the beer marked as such is vegan. This is in absence of legislation in the UK and elsewhere which require beers to be labelled with all their ingredients and nutritional information.


title: Titans (season 2)

text: The second season of the American superhero streaming television series "Titans" premiered on DC Universe on September 6, 2019, and concluded on November 29, 2019, consisting of 13 episodes. It was executive produced by Akiva Goldsman, Geoff Johns, Greg Berlanti, Sarah Schechter, and Greg Walker, with Walker serving as showrunner for the second consecutive season. Created by Goldsman, Johns, and Berlanti, the series is based on the DC Comics team Teen Titans. Brenton Thwaites, Anna Diop, Teagan Croft, and Ryan Potter return to the main cast from the previous season, joined by season 1 guest stars Curran Walters, Conor Leslie, Minka Kelly, and Alan Ritchson and series newcomers Chelsea Zhang, Joshua Orpin, and Esai Morales. The season also introduces Damaris Lewis, who would join the main cast in the following season. It is currently the only season to feature Zhang and Morales.


title: Titans (season 2)

text: The season sees Dick Grayson (Thwaites) form a new Titans team comprising Rachel Roth (Croft), Gar Logan (Potter), and Jason Todd (Walters) in his original San Francisco base. Concurrent with the Titans' return, an old enemy resurfaces in the form of Deathstroke (Morales), whose past conflict with the original Titans team of Dick, Donna Troy (Leslie), Dawn Granger (Kelly), and Hank Hall (Ritchson) caused them to disband. As Deathstroke looks to eliminate the Titans, with his daughter Rose Wilson (Zhang) also taking part in the fight, the heroes face another threat from Cadmus Laboratories when they encounter runaway test subject Conner (Orpin). Meanwhile, Kory Anders (Diop) discovers she is being hunted by her sister Blackfire (Lewis).


title: Titans (season 2)

text: A second season of "Titans" was confirmed in 2018 prior to the premiere of the first season. Filming began the following year and 13 episodes were announced, two more than the 11 episodes of its predecessor. The season was originally planned to feature H.I.V.E. as the Titans' enemies, while Dick would operate under his new mantle of Nightwing after assuming the identity in the initially intended season 1 finale. Before the start of filming, however, the original season 1 finale would be removed and reworked into the second season, which provided a new resolution to the previous season's story in its premiere episode. The second season was subsequently re-envisioned to depict Dick's gradual transformation into Nightwing, with Deathstroke replacing H.I.V.E. Its story was influenced by the 1984 comic arc "The Judas Contract" from Marv Wolfman and George Pérez's "The New Teen Titans" and the 2003 "Teen Titans" comics by Johns.


title: Titans (season 2)

text: Critical reception to the second season was generally positive. While episodes in the first half and the early 2nd half of the season received positive reviews, the premiere and later episodes were met with a more negative response for the plot, writing, character arcs, and story resolutions. The second season was the last to release on DC Universe following the repurposing of the service into comic distributor DC Universe Infinite and HBO Max's acquisition of its original programming.


title: Titans (season 2)

text: Dog actors Digby, Lacey, and Wrigley portray Krypto, a dog possessing Kryptonian powers who accompanies Conner.


title: Titans (season 2)

text: Ahead of the series' premiere at New York Comic Con in October 2018, "Titans" was renewed for a second season. At the 2019 San Diego Comic-Con, the second season's premiere was announced for September 6, 2019, on DC Universe and would consist of 13 episodes. Greg Walker returned as showrunner from the first season, who also served as an executive producer alongside Akiva Goldsman, Geoff Johns, Greg Berlanti, and Sarah Schechter.


title: Titans (season 2)

text: The season was the last to release on DC Universe due to its original programming moving to HBO Max in 2021 and the repurposing of the service into comic distributor DC Universe Infinite.


title: Titans (season 2)

text: The second season was initially planned to follow the events of the original season 1 finale, which would have seen Dick Grayson assume the identity of Nightwing and establish H.I.V.E. as the Titans' next adversaries. After the original season 1 finale was pulled, elements of the episode were given to the season 2 premiere, which became the resolution of season 1's Trigon story. H.I.V.E. was replaced by Deathstroke, while Dick's arc into Nightwing was re-envisoned to conclude in the season 2 finale.


title: Titans (season 2)

text: Series regulars Brenton Thwaites, Anna Diop, Teagan Croft, and Ryan Potter reprise their roles from the first season as Dick Grayson, Kory Anders, Rachel Roth, and Gar Logan. Season 1 guest stars Curran Walters, Conor Leslie, Minka Kelly, and Alan Ritchson also return as Jason Todd, Donna Troy, Dawn Granger, and Hank Hall, after being promoted to series regular status.


title: Titans (season 2)

text: In February 2019, it was announced that Joshua Orpin had been cast as Conner for season two, taking over for body double Brooker Muir in the first season. After the character was teased by co-creator Geoff Johns, Esai Morales was cast as Deathstroke in March 2019, with Chella Man and Chelsea Zhang announced as his children Jericho and Rose. Iain Glen was cast as Bruce Wayne in April 2019, marking the character's first physical appearance after being portrayed by stunt doubles in the first season finale. In June 2019, Natalie Gumede and Drew Van Acker were cast as Mercy Graves and Garth, respectively. Genevieve Angelson was announced as Cadmus Laboratories scientist Dr. Eve Watson the following month. In August 2019, Michael Mosley was revealed to be portraying Dr. Light. Also in August, Oluniké Adeliyi announced on her Instagram she had joined the cast in an undisclosed role that was later revealed as burlesque dancer Mati Matisse and Hanneke Talbot was revealed to be Shimmer. In September 2019, Demore Barnes was revealed to be portraying Wintergreen. Following the character's appearance in an October 2019 trailer, Diop confirmed on her Instagram that Damaris Lewis would be portraying Kory's sister Blackfire, which was also confirmed by Lewis.


title: Titans (season 2)

text: Filming for the second season began on April 2, 2019, and concluded on September 20, 2019. Production was temporarily put on hold in July due to accidental death of special effects coordinator Warren Appleby; the season 2 premiere is dedicated in his memory.


title: Titans (season 2)

text: The second season premiered in the United States through DC Universe on September 6, 2019, and concluded on November 29, 2019. Outside the United States, the second season became available for streaming via Netflix on January 10, 2020.


title: Titans (season 2)

text: On Rotten Tomatoes, the second season holds an 81% approval rating based on 21 reviews, with an average rating of 7 out of 10. The critical consensus reads, "Though "Titans"s sophomore season suffers from a slight slump at the start, it quickly resets itself, building on the momentum from its first season while laying fascinating framework for where the show could go."


title: Titans (season 2)

text: The premiere episode "Trigon" was criticized for having story elements originally intended for the season 1 finale. Kevin Yeoman of "Screen Rant" wrote that the premiere "feels like two distinct episodes roughly stitched together, rather than a proper start to a new season" and "the show's simply carrying too much baggage at the start and is reaching for a conclusion too long after the ostensible end of season 1 to deliver much in the way of a fulfilling resolution or a promising new beginning". Giving the episode a 5.8/10, Jesse Schedeen of IGN called it "an extremely messy episode, with one half tasked with wrapping up Season 1's Trigon storyline and the other laying the groundwork for a new status quo and new villain" and "delivers a very anticlimactic finish to Season 1's story", although he found promise for future episodes. Den of Geek reviewer Aaron Sagers said the premiere "would have served as an excellent season 1 finale", but concluded that "it feels quite a bit like a much-needed course correction for this series" and gave it a 3.5/5.


title: Titans (season 2)

text: Following the premiere, early episodes of the season earned a positive reception. In a review for the second episode "Rose", "Forbes" contributor Linda Maleh called it "the real season premiere" and wrote, "season 2 has taken the best things about season 1, and elevated them". Praising the sixth episode "Conner" and Joshua Orpin's performance in the title role, Sagers said, "it is a strong introduction of the anticipated character, and "Titans" makes up for the fact we've waited so long in the season for it". Schedeen gave the eighth episode "Jericho" a 9.3/10, which he described as "easily the strongest installment of "Titans: Season 2", and a clear contender for the series' best episode overall".


title: Titans (season 2)

text: However, the later episodes were received more negatively. In a review for the 11th episode "E.L._.O.", Charles Pulliam-Moore of Gizmodo wrote, ""Titans" seemingly lost its focus" after the eighth episode and "with just two episodes to go, it doesn't seem possible that the writers are going to be able to wrap things up in satisfying or interesting ways". For the finale "Nightwing", Pulliam-Moore called it "a travesty of epic proportions", criticizing how the episode concluded the season's storylines. The death of Donna Troy in the finale was widely panned as illogical and unnecessary, with several reviewers questioning if electrical discharge from a transmission tower would have been sufficient to kill the character. Although giving the overall episode a 3.5/5, Sagers commented, "Even if I were to accept that Donna couldn't withstand that electrical charge, and even if I could explain why the super-boy [Conner] didn't rush to stop the falling tower, the death played out in cheap fashion, like yet another box that had to be ticked for the finale." "Entertainment Weekly"<nowiki>'</nowiki>s Christian Holub said, "Donna Troy's last-minute death felt so stupidly unnecessary that I can't help but throw up my hands at this whole season finale", describing the scene as "such a stupid death I honestly thought it was a joke at first". Donna's actress Conor Leslie agreed with the criticism during a 2021 interview, noting the episode aired shortly before a "Wonder Woman 1984" trailer that depicted Diana Prince unaffected by lightning.


title: Fox squirrel

text: The fox squirrel (Sciurus niger), also known as the eastern fox squirrel or Bryant's fox squirrel, is the largest species of tree squirrel native to North America. Despite the differences in size and coloration, it is sometimes mistaken for American red squirrels or eastern gray squirrels in areas where the species co-exist.


title: Fox squirrel

text: The squirrel's total length measures , with a body length of and a similar tail length. They range in weight from . There is no sexual dimorphism in size or appearance. Individuals tend to be smaller in the west. There are three distinct geographical phases in coloration: In most areas the animal's upper body is brown-grey to brown-yellow with a typically brownish-orange underside, while in eastern regions such as the Appalachians there are more strikingly-patterned dark brown and black squirrels with white bands on the face and tail. In the south are isolated communities with uniform black coats. To help with climbing, the squirrels have sharp claws, developed extensors of digits and flexors of forearms, and abdominal musculature. Fox squirrels have excellent vision and well-developed senses of hearing and smell. They use scent marking to communicate with other fox squirrels. "Fox squirrels also have several sets of vibrissae, hairs or whiskers that are used as touch receptors to sense the environment. These are found above and below their eyes, on their chin and nose, and on each forearm." The dental formula of "S. niger" is .


title: Fox squirrel

text: The fox squirrel's natural range extends through most of the eastern United States, north into the southern prairie provinces of Canada, and west to the Dakotas, Colorado, and Texas. They are absent (except for vagrants) in New England, New Jersey, most of New York, northern and eastern Pennsylvania, Ontario, Quebec, and the Atlantic provinces of Canada. They have been introduced to both northern and southern California, Oregon, Idaho, Montana, Washington, and New Mexico, as well as Ontario and British Columbia in Canada. While very versatile in their habitat choices, fox squirrels are most often found in forest patches of 40 hectares or less with an open understory, or in urban neighborhoods with trees. They thrive best among oak, hickory, walnut, pecan and pine trees, storing their nuts for winter. Western range extensions in Great Plains regions such as Kansas are associated with riverine corridors of cottonwood. A subspecies native to several eastern US states is the Delmarva fox squirrel ("S. n. cinereus").


title: Fox squirrel

text: In Europe, "Sciurus niger" is included since 2016 in the list of Invasive Alien Species of Union concern (the Union list). This implies that this species cannot be imported, bred, transported, commercialized, or intentionally released into the environment in the whole of the European Union.


title: Fox squirrel

text: Fox squirrels are most abundant in open forest stands with little understory vegetation; they are not found in stands with dense undergrowth. Ideal habitat is small stands of large trees interspersed with agricultural land. The size and spacing of pines and oaks are among the important features of fox squirrel habitat. The actual species of pines and oaks themselves may not always be a major consideration in defining fox squirrel habitat. Fox squirrels are often observed foraging on the ground several hundred meters from the nearest woodlot. Fox squirrels also commonly occupy forest edge habitat.


title: Fox squirrel

text: Fox squirrels have two types of shelters: leaf nests (dreys) and tree dens. They may have two tree cavity homes or a tree cavity and a leaf nest. Tree dens are preferred over leaf nests during the winter and for raising young. When den trees are scarce, leaf nests are used year-round. Leaf nests are built during the summer months in forks of deciduous trees about 30 feet (9 m) above the ground. Fox squirrels use natural cavities and crotches (forked branches of a tree) as tree dens. Den trees in Ohio had an average diameter at breast height (d.b.h.) of and were an average of from the nearest woodland border. About 88% of den trees in eastern Texas had an average d.b.h. (diameter at breast height) of or more. Dens are usually wide and inches deep. Den openings are generally circular and about . Fox squirrels may make their own den in a hollow tree by cutting through the interior; however, they generally use natural cavities or cavities created by northern flickers ("Colaptes auratus") or red-headed woodpeckers ("Melanerpes erythrocephalus"). Crow nests have also been used by fox squirrels.


title: Fox squirrel

text: Fox squirrels use leaf nests or tree cavities for shelter and litter rearing. Forest stands dominated by mature to over mature trees provide cavities and a sufficient number of sites for leaf nests to meet the cover requirements. Overstory trees with an average d.b.h. of or more generally provide adequate cover and reproductive habitat. Optimum tree canopy closure for fox squirrels is from 20% to 60%. Optimum conditions of understory closure occur when the shrub-crown closure is 30% or less.


title: Fox squirrel

text: Fox squirrels are tolerant of human proximity, and even thrive in crowded urban and suburban environments. They exploit human habitations for sources of food and nesting sites, being as happy nesting in an attic as they are in a hollow tree.


title: Fox squirrel

text: Food habits of fox squirrels depend largely on geographic location. In general, fox squirrel foods include mast, tree buds, insects, tubers, bulbs, roots, bird eggs, pine seeds and spring-fruiting trees, and fungi. Agricultural crops such as corn, soybeans, oats, wheat, and fruit are also eaten. Mast eaten by fox squirrels commonly includes turkey oak ("Quercus laevis"), southern red oak ("Quercus falcata"), blackjack oak ("Quercus marilandica"), bluejack oak ("Quercus incana"), post oak ("Quercus stellata"), and live oak ("Quercus virginiana").


title: Fox squirrel

text: In Illinois, fox squirrels rely heavily on hickories from late August through September. Pecans, black walnuts ("Juglans nigra"), osage orange ("Maclura pomifera") fruits, and corn are also important fall foods. In early spring, elm buds and seeds are the most important food. In May and June, mulberries ("Morus" spp.) are heavily used. By early summer, corn in the milk stage becomes a primary food.


title: Fox squirrel

text: During the winter in Kansas, osage orange is a staple item supplemented with seeds of the Kentucky coffee tree ("Gymnocladus dioicus") and honey locust ("Gleditsia triacanthos"), corn, wheat, eastern cottonwood ("Populus deltoides" var. "deltoides") bark, ash seeds, and eastern red cedar ("Juniperus virginiana") berries. In the spring, fox squirrels feed primarily on buds of elm, maple, and oaks but also on newly sprouting leaves and insect larvae.


title: Fox squirrel

text: Fox squirrels in Ohio prefer hickory nuts, acorns, corn, and black walnuts. The squirrels are absent where two or more of these mast trees are missing. Fox squirrels also eat buckeyes, seeds and buds of maple and elm, hazelnuts ("Corylus" spp.), blackberries ("Rubus" spp.), and tree bark. In March, they feed mainly on buds and seeds of elm, maple, and willow. In Ohio, eastern fox squirrels have the following order of food preference: white oak ("Quercus alba") acorns, black oak ("Quercus velutina") acorns, red oak ("Quercus rubra") acorns, walnuts, and corn.


title: Fox squirrel

text: In eastern Texas, fox squirrels prefer the acorns of bluejack oak, pecans, southern red oak ("Q. falcata"), and overcup oak ("Q. lyrata"). The least preferred foods are acorns of swamp chestnut oak ("Q. michauxii") and overcup oak. In California, fox squirrels feed on English walnuts ("J. regia"), oranges, avocados, strawberries, and tomatoes. In midwinter, they feed on eucalyptus seeds.


title: Fox squirrel

text: In Michigan, fox squirrels feed on a variety of foods throughout the year. Spring foods are mainly tree buds and flowers, insects, bird eggs, and seeds of red maple ("Acer rubrum"), silver maple ("Acer saccharinum"), and elms. Summer foods include a variety of berries, plum and cherry pits, fruits of basswood ("Tilia americana"), fruits of box elder ("Acer negundo"), black oak acorns, hickory nuts, seeds of sugar ("Acer saccharum") and black maple ("Acer nigrum"), grains, insects, and unripe corn. Fall foods consist mainly of acorns, hickory nuts, beechnuts, walnuts, butternuts ("Juglans cinerea"), and hazelnuts. Caches of acorns and hickory nuts are heavily used in winter.


title: Fox squirrel

text: Fox squirrels are strictly diurnal, non-territorial, and spend more of their time on the ground than most other tree squirrels. They are still, however, agile climbers. They construct two types of homes called "dreys", depending on the season. Summer dreys are often little more than platforms of sticks high in the branches of trees, while winter dens are usually hollowed out of tree trunks by a succession of occupants over as many as 30 years. Cohabitation of these dens is not uncommon, particularly among breeding pairs.


title: Fox squirrel

text: Fox squirrels will form caches by burying food items for later consumption. They like to store foods that are shelled and high in fat, such as acorns and nuts. Shelled foods are favored because they are less likely to spoil than non-shelled foods, and fatty foods are valued for their high energy density.


title: Fox squirrel

text: They are not particularly gregarious or playful, in fact they have been described as solitary and asocial creatures, coming together only in breeding season. They have a large vocabulary, consisting most notably of an assortment of clucking and chucking sounds, not unlike some "game" birds, and they warn of approaching threats with distress screams. In the spring and fall, groups of fox squirrels clucking and chucking together can make a small ruckus. They also make high-pitched whines during mating. When threatening another fox squirrel, they will stand upright with their tail over their back and flick it.


title: Fox squirrel

text: They are impressive jumpers, easily spanning fifteen feet in horizontal leaps and free-falling twenty feet or more to a soft landing on a limb or trunk.


title: Fox squirrel

text: Female fox squirrels come into estrus in mid-December or early January, then again in June. They normally produce two litters a year; however, yearling females may only produce one. Females become sexually mature at 10 to 11 months of age and usually produce their first litter when they are a year old.


title: Fox squirrel

text: Gestation occurs over a period of 44 to 45 days. Earliest litters appear in late January; most births occur in mid-March and July. The average litter size is three, but can vary according to season and food conditions.


title: Fox squirrel

text: Tree cavities, usually those formed by woodpeckers, are remodeled to winter dens and often serve as nurseries for late winter litters. If existing trees lack cavities, leaf nests known as dreys are built by cutting twigs with leaves and weaving them into warm, waterproof shelters. Similar leafy platforms are built for summer litters and are often referred to as "cooling beds."


title: Fox squirrel

text: Tree squirrels develop slowly compared to other rodents. At birth, the young are blind, without fur and helpless. Eyes open at 4 to 5 weeks of age and ears open at 6 weeks. Eastern fox squirrels are weaned between 12 and 14 weeks but may not be self-supporting until 16 weeks. Juveniles usually disperse in September or October, but may den either together or with their mother during their first winter.


title: Fox squirrel

text: In captivity, fox squirrels have been known to live 18 years, but in the wild most fox squirrels die before they become adults. Their maximum life expectancy is typically 12.6 years for females and 8.6 years for males. Because of overhunting and the destruction of mature forests, many subspecies of fox squirrel (the Delmarva fox squirrel for example) are endangered. Another major cause of fox squirrel population decline is mange mite ("Cnemidoptes" sp.) along with severe winter weather.


title: Fox squirrel

text: Relatively few natural predators can regularly capture adult fox squirrels. Of these predators, most only take fox squirrels opportunistically. Predators include: bobcats ("Lynx rufus"), Canada lynx ("Lynx canadensis"), foxes ("Vulpes vulpes" and "Urocyon cinereoargenteus"), red-tailed hawks ("Buteo jamaicensis"), red-shouldered hawks ("Buteo lineatus"), great horned owls ("Bubo virginianus"), barred owls ("Strix varia"), and coyotes ("Canis latrans"). Former predators extirpated from most of the fox squirrel's range included cougars ("Puma concolor") and gray wolves ("Canis lupus"). Nestlings and young fox squirrels are particularly vulnerable to climbing predators such as raccoons ("Procyon lotor"), opossums ("Didelphis virginiana"), rat snakes ("Pantherophis spp."), and pine snakes ("Pituophis melanoleucus"). In those states where fox squirrels are not protected, they are considered a game animal. Fox squirrels were an important source of meat for European settlers in the 17th and 18th centuries. They are still hunted over most of their range.


title: Auxiliary power unit

text: An auxiliary power unit (APU) is a device on a vehicle that provides energy for functions other than propulsion. They are commonly found on large aircraft and naval ships as well as some large land vehicles. Aircraft APUs generally produce 115 V AC voltage at 400 Hz (rather than 50/60 Hz in mains supply), to run the electrical systems of the aircraft; others can produce 28 V DC voltage. APUs can provide power through single or three-phase systems.


title: Auxiliary power unit

text: During World War I, the British Coastal class blimps, one of several types of airship operated by the Royal Navy, carried a ABC auxiliary engine. These powered a generator for the craft's radio transmitter and, in an emergency, could power an auxiliary air blower. One of the first military fixed-wing aircraft to use an APU was the British, World War 1, Supermarine Nighthawk, an anti-Zeppelin night fighter.


title: Auxiliary power unit

text: During World War II, a number of large American military aircraft were fitted with APUs. These were typically known as "putt–putts", even in official training documents. The putt-putt on the B-29 Superfortress bomber was fitted in the unpressurised section at the rear of the aircraft. Various models of four-stroke, Flat-twin or V-twin engines were used. The engine drove a "P2", DC generator, rated 28.5 Volts and 200 Amps (several of the same "P2" generators, driven by the main engines, were the B-29's DC power source in flight). The putt-putt provided power for starting the main engines and was used after take-off to a height of . The putt-putt was restarted when the B-29 was descending to land.


title: Auxiliary power unit

text: Some models of the B-24 Liberator had a putt–putt fitted at the front of the aircraft, inside the nose-wheel compartment. Some models of the Douglas C-47 Skytrain transport aircraft carried a putt-putt under the cockpit floor.


title: Auxiliary power unit

text: The first German jet engines built during the Second World War used a mechanical APU starting system designed by the German engineer Norbert Riedel. It consisted of a two-stroke flat engine, which for the Junkers Jumo 004 design was hidden in the intake diverter, essentially functioning as a pioneering example of an auxiliary power unit for starting a jet engine. A hole in the extreme nose of the diverter contained a manual pull-handle which started the piston engine, which in turn rotated the compressor. Two spark plug access ports existed in the Jumo 004's intake diverter to service the Riedel unit's cylinders in situ, for maintenance purposes. Two small "premix" tanks for the Riedel's petrol/oil fuel were fitted in the annular intake. The engine was considered an extreme short stroke (bore / stroke: 70 mm / 35 mm = 2:1) design so it could fit within the intake diverter of jet engines like the Jumo 004. For reduction it had an integrated planetary gear. It was produced by Victoria in Nuremberg and served as a mechanical APU-style starter for all three German jet engine designs to have made it to at least the prototype stage before May 1945 – the Junkers Jumo 004, the BMW 003 (which uniquely appears to use an electric starter for the Riedel APU), and the prototypes (19 built) of the more advanced Heinkel HeS 011 engine, which mounted it just above the intake passage in the Heinkel-crafted sheetmetal of the engine nacelle nose.


title: Auxiliary power unit

text: The Boeing 727 in 1963 was the first jetliner to feature a gas turbine APU, allowing it to operate at smaller airports, independent from ground facilities. The APU can be identified on many modern airliners by an exhaust pipe at the aircraft's tail.


title: Auxiliary power unit

text: The power section is the gas-generator portion of the engine and produces all the shaft power for the APU. In this section of the engine, air and fuel are mixed, compressed and ignited to create hot and expanding gases. This gas is highly energetic and is used to spin the turbine, which in turn powers other sections of the engine, such as auxiliary gearboxes, pumps, electrical generators, and in the case of a turbo fan engine, the main fan


title: Auxiliary power unit

text: The load compressor is generally a shaft-mounted compressor that provides pneumatic power for the aircraft, though some APUs extract bleed air from the power section compressor. There are two actuated devices to help control the flow of air: the inlet guide vanes that regulate airflow to the load compressor and the surge control valve that maintains stable or surge-free operation of the turbo machine.


title: Auxiliary power unit

text: The gearbox transfers power from the main shaft of the engine to an oil-cooled generator for electrical power. Within the gearbox, power is also transferred to engine accessories such as the fuel control unit, the lubrication module, and cooling fan. There is also a starter motor connected through the gear train to perform the starting function of the APU. Some APU designs use a combination starter/generator for APU starting and electrical power generation to reduce complexity.


title: Auxiliary power unit

text: On the Boeing 787, an aircraft which has greater reliance on its electrical systems, the APU delivers only electricity to the aircraft. The absence of a pneumatic system simplifies the design, but high demand for electricity requires heavier generators.


title: Auxiliary power unit

text: The market of Auxiliary power units is dominated by Honeywell, followed by Pratt & Whitney, Motorsich and other manufacturers such as PBS Velká Bíteš, Safran Power Units, Aerosila and Klimov. Local manufacturers include Bet Shemesh Engines and Hanwha Aerospace. The 2018 market share varied according to the application platforms:


title: Auxiliary power unit

text: On June 4, 2018, Boeing and Safran announced their 50–50 partnership to design, build and service APUs after regulatory and antitrust clearance in the second half of 2018.


title: Auxiliary power unit

text: Boeing produced several hundred T50/T60 small turboshafts and their derivatives in the early 1960s.Safran produces helicopters and business jets APUs but stopped the large APUs since Labinal exited the APIC joint venture with Sundstrand in 1996.


title: Auxiliary power unit

text: This could threaten the dominance of Honeywell and United Technologies. Honeywell has a 65% share of the mainliner APU market and is the sole supplier for the Airbus A350, the Boeing 777 and all single-aisles: the Boeing 737 MAX, Airbus A220 (formerly Bombardier CSeries), Comac C919, Irkut MC-21 and Airbus A320neo since Airbus eliminated the P&WC APS3200 option.P&WC claims the remaining 35% with the Airbus A380, Boeing 787 and Boeing 747-8.


title: Auxiliary power unit

text: It should take at least a decade for the Boeing/Safran JV to reach $100 million in service revenue.The 2017 market for production was worth $800 million (88% civil and 12% military), while the MRO market was worth $2.4 billion, spread equally between civil and military.


title: Auxiliary power unit

text: The Space Shuttle APUs provided hydraulic pressure. The Space Shuttle had three redundant APUs, powered by hydrazine fuel. They were only powered up for ascent, re-entry, and landing. During ascent, the APUs provided hydraulic power for gimballing of the Shuttle's three engines and control of their large valves, and for movement of the control surfaces. During landing, they moved the control surfaces, lowered the wheels, and powered the brakes and nose-wheel steering. Landing could be accomplished with only one APU working. In the early years of the Shuttle there were problems with APU reliability, with malfunctions on three of the first nine Shuttle missions.


title: Auxiliary power unit

text: APUs are fitted to some tanks to provide electrical power without the high fuel consumption and large infrared signature of the main engine. As early as World War II, the American M4 Sherman had a small, piston-engine powered APU for charging the tank's batteries, a feature the Soviet-produced T-34 tank did not have.


title: Auxiliary power unit

text: A refrigerated or frozen food semi trailer or train car may be equipped with an independent APU and fuel tank to maintain low temperatures while in transit, without the need for an external transport-supplied power source.


title: Auxiliary power unit

text: On some older diesel engined-equipment, a small gasoline engine (often called a "pony engine") was used instead of an electric motor to start the main engine. The exhaust path of the pony engine was typically arranged so as to warm the intake manifold of the diesel, to ease starting in colder weather. These were primarily used on large pieces of construction equipment.


title: Auxiliary power unit

text: In recent years, truck and fuel cell manufacturers have teamed up to create, test and demonstrate a fuel cell APU that eliminates nearly all emissions and uses diesel fuel more efficiently. In 2008, a DOE sponsored partnership between Delphi Electronics and Peterbilt demonstrated that a fuel cell could provide power to the electronics and air conditioning of a Peterbilt Model 386 under simulated "idling" conditions for ten hours. Delphi has said the 5 kW system for Class 8 trucks will be released in 2012, at an $8000–9000 price tag that would be competitive with other "midrange" two-cylinder diesel APUs, should they be able to meet those deadlines and cost estimates.


title: Shankar Dayal Sharma

text: Shankar Dayal Sharma (; 19 August 1918 – 26 December 1999) was an Indian lawyer and politician from the state of Madhya Pradesh who served as the ninth President of India, from 1992 to 1997.


title: Shankar Dayal Sharma

text: Born in Bhopal, Sharma studied at Agra, Allahabad and Lucknow and received a doctorate in constitutional law from the University of Cambridge and was a bar-at-law from Lincoln's Inn and a Brandeis Fellow at Harvard University. In 1948-49, Sharma was one of the leaders of the movement for the merger of Bhopal State with India, a cause for which he served eight months' imprisonment.


title: Shankar Dayal Sharma

text: A member of the Indian National Congress party, Sharma was Chief Minister (1952–1956) of Bhopal State and served as a Cabinet Minister (1956–1971) in the government of Madhya Pradesh holding several portfolios. Sharma was president of the Bhopal State Congress Committee (1950-1952), Madhya Pradesh Congress Committee (1966-1968) and of the All India Congress Committee (1972-1974). He served as Union Minister for Communications from 1974 to 1977 under Prime Minister Indira Gandhi. Twice elected to the Lok Sabha, Sharma served as Governor of Andhra Pradesh (1984-1985), Punjab (1985-1986) and Maharashtra (1986-1987) before being elected unopposed as the eighth Vice President of India in 1987.


title: Shankar Dayal Sharma

text: Sharma was elected President of India in 1992 and served till 1997 during which period he dealt with four Prime Ministers, three of whom he appointed in the last year of his presidency. He was assertive with the P. V. Narasimha Rao ministry, forcing his government to sack a governor, instigating a strong response to the demolition of the Babri Masjid and refusing to sign ordinances presented to him on the eve of elections. His appointment of Atal Bihari Vajpayee as Prime Minister on the grounds of him being the leader of the largest party in Parliament attracted widespread criticism especially as Vajpayee was forced to resign in only thirteen days without facing a vote of confidence. Sharma's appointment of H. D. Deve Gowda and I. K. Gujral as Prime Minsters followed the assurance of support to their candidature by the Congress party but neither government lasted more than a year. Sharma chose not to seek a second term in office and was succeeded to the presidency by K. R. Narayanan.


title: Shankar Dayal Sharma

text: Shankar Dayal Sharma was born on 19 August 1918 in Bhopal, then the capital of the princely state of Bhopal, in a Hindu Brahmin family. Sharma completed his schooling in Bhopal and then studied at St. John's College, Agra and at the Allahabad and Lucknow universities obtaining a master’s degree in English literature, Hindi and Sanskrit and an L.L.M. He topped both the courses, was awarded the Chakravarty Gold Medal for social service and was a thrice swimming champion at Lucknow University and Cross country running champion at Allahabad. He obtained a doctorate in constitutional law from Cambridge University for his thesis on "Interpretation of Legislative Powers under Federal Constitutions" and received a Diploma in Public Administration from the University of London. During his years in Cambridge he was associated with the Tagore Society and the Cambridge Majlis. Sharma began practicing law at Lucknow from 1940 where he taught law at the University and soon joined the Indian National Congress. In 1946, he was admitted to the Lincoln’s Inn and taught at Cambridge University during 1946-47. The following year, he was Brandeis Fellow at Harvard University.


title: Shankar Dayal Sharma

text: During 1948-49, Sharma underwent eight months’ imprisonment for his leadership of the popular movement for merging the princely state of Bhopal with India. Although the Nawab of Bhopal had acceded his state to the Dominion of India, he had held out against signing the Instrument of Merger. The popular movement had the support of the Praja Mandal and an interim government with Chatur Narain Malviya as its head was constituted by the Nawab in 1948. However, as the movement gained support, the Nawab dismissed this government. Public pressure and the intervention of V. P. Menon led the Nawab to merge his state with the Indian Union in 1949 with the princely state reconstituted as Bhopal State.


title: Shankar Dayal Sharma

text: Sharma was president of the Bhopal State Congress during 1950 to 1952. He was elected to the Legislative Assembly of Bhopal from Berasia in the elections of 1952 and became Chief Minister of Bhopal State in 1952. In 1956, following the reorganization of states, Bhopal State was merged with the new state of Madhya Pradesh. Sharma played an important role in retaining Bhopal as the capital of this new state. In the elections of 1957, 1962 and 1967 Sharma was elected to the Assembly from Udaipura as a candidate of the Congress party. During this time he was a cabinet minister in the Madhya Pradesh government and variously held portfolios of education, law, public works, industry and commerce and Revenue. As minister for education, he emphasized secular pedagogy in schools and textbooks were revised to avoid religious bias.


title: Shankar Dayal Sharma

text: During 1967-68, he was president of the Madhya Pradesh Congress Committee and served as general secretary of the party from 1968 to 1972. During the split in 1969, Sharma sided with Indira Gandhi and was removed from party posts by the president S. Nijalingappa but reappointed by Gandhi in her faction of the party.


title: Shankar Dayal Sharma

text: Sharma was elected to the Lok Sabha from Bhopal in the general elections of 1971. The following year he was made the president of the Indian National Congress by Prime Minister Indira Gandhi. Prior to his appointment as president, Sharma had been a member of the Congress Working Committee since 1967 and general secretary of the Congress party from 1968. As president, Sharma launched a public campaign against the CIA accusing it of being actively involved in fomenting violence in India. In October 1974, Sharma was appointed Minister of Communications in the Indira Gandhi ministry and was succeeded as president of the Congress by D. K. Barooah. He remained in that post until his defeat in the general election of 1977 by Arif Baig. Sharma was reelected from Bhopal in the general election of 1980.


title: Shankar Dayal Sharma

text: On 15 August 1984, N. T. Rama Rao, the Chief Minister of Andhra Pradesh who had led the Telugu Desam Party to victory in the state assembly election of 1983, was dismissed from that post by the Governor of Andhra Pradesh, Thakur Ram Lal. He appointed N. Bhaskara Rao, who had been finance minister under N. T. Rama Rao, as the new chief minister and gave him a month’s time to prove his majority in the assembly despite the ousted chief minister’s claim of being able to prove his own majority in two days’ time and evidence that he had the support of the majority of legislators in the assembly. Following widespread protests, Ram Lal resigned on 24 August 1984 and was replaced by Sharma.


title: Shankar Dayal Sharma

text: Sharma convened a session of the assembly on 11 September 1984 but as Bhaskara Rao failed to prove his majority within the period of one month stipulated by Thakur Ram Lal, Sharma suggested that he resign with effect from 16 September. Bhaskar Rao refused to do so seeking the reconvening of the assembly a few days later. Sharma then dismissed him and reappointed N. T. Rama Rao as Chief Minister. Rama Rao won the vote of confidence when the assembly reconvened on 20 September 1984. Soon after, the Rama Rao government called for fresh elections and Sharma dissolved the assembly in November 1984.


title: Shankar Dayal Sharma

text: In the assembly election of 1985, Rama Rao's party was returned to power with a two-thirds majority. A few months later, Sharma refused to repromulgate three ordinances sent to him by the state government stating that ordinances are required to be ratified by the legislature and that their repromulgation would be a constitutional impropriety. His refusal to repromulgate these ordinances, pertaining to the abolition of offices of part-time village officers, formation of districts and payment of salaries and removal of disqualifications of government employees, a fourth time soured his relation with the state government.


title: Shankar Dayal Sharma

text: On 31 July 1985, Sharma's daughter Gitanjali and his son-in-law, the Congress politician Lalit Maken, were killed by Sikh militants in retaliation for Maken's alleged role in the anti-Sikh riots of 1984. Sharma was thereafter transferred to Punjab as governor and was succeeded in Andhra Pradesh by Kumudben Joshi.


title: Shankar Dayal Sharma

text: Sharma succeeded Hokishe Sema as governor of Punjab in November 1985. His appointment came after the assembly elections in that state and in the backdrop of the Rajiv–Longowal Accord which sought to resolve the insurgency in Punjab. Sharma's tenure was characterized by continued violence and he was replaced in April 1986 by Siddhartha Shankar Ray.


title: Shankar Dayal Sharma

text: Sharma was sworn in as Governor of Maharashtra in April 1986 and served until September 1987 when he was elected Vice-President of India.


title: Shankar Dayal Sharma

text: Sharma was nominated by the Congress party for the vice-presidential election of 1987. Although 27 candidates had filed nominations, only the nomination filed by Sharma was found valid by the returning officer. After the last date of withdrawal of candidates was over, Sharma was declared elected unanimously on 21 August 1987. Sharma was sworn in as Vice-President of India on 3 September 1987. He was only the third person to be elected unopposed to the vice-presidency.


title: Shankar Dayal Sharma

text: Sharma, who was also the ex-officio Chairman of the Rajya Sabha, offered to quit in February 1988 after his ruling admitting a discussion in the house of the purported extravagance of the then Governor of Andhra Pradesh was vociferously objected to by members of the government. Several ministers of the council of ministers led the protests against the Chairman's ruling even as Prime Minister Rajiv Gandhi, who was present in the house, chose not to intervene or restrain the members of his party. Sharma's response chastened the protesting members but their request to have the proceedings expunged from parliament records was turned down by Sharma.


title: Shankar Dayal Sharma

text: In 1991, following the assassination of Rajiv Gandhi, Sharma was first offered the presidentship of the Congress party and the post of Prime Minister by Sonia Gandhi. He however refused citing ill health and advanced age. Thereafter, P. V. Narasimha Rao was chosen to lead the Congress party.