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15,900 | Fleming, Florey, and Chain shared the 1945 Nobel Prize in Physiology or Medicine for the development of penicillin. | https://en.wikipedia.org/wiki?curid=23312 |
15,901 | The chemical structure of penicillin was first proposed by Edward Abraham in 1942 and was later confirmed in 1945 using X-ray crystallography by Dorothy Crowfoot Hodgkin, who was also working at Oxford. She later in 1964 received the Nobel Prize for Chemistry for this and other structure determinations. | https://en.wikipedia.org/wiki?curid=23312 |
15,902 | Chemist John C. Sheehan at the Massachusetts Institute of Technology (MIT) completed the first chemical synthesis of penicillin in 1957. Sheehan had started his studies into penicillin synthesis in 1948, and during these investigations developed new methods for the synthesis of peptides, as well as new protecting group... | https://en.wikipedia.org/wiki?curid=23312 |
15,903 | 6-APA was discovered by researchers at the Beecham Research Laboratories (later the Beecham Group) in Surrey in 1957 (published in 1959). Attaching different groups to the 6-APA 'nucleus' of penicillin allowed the creation of new forms of penicillins which are more versatile and better in activity. | https://en.wikipedia.org/wiki?curid=23312 |
15,904 | The narrow range of treatable diseases or "spectrum of activity" of the penicillins, along with the poor activity of the orally active phenoxymethylpenicillin, led to the search for derivatives of penicillin that could treat a wider range of infections. The isolation of 6-APA, the nucleus of penicillin, allowed for the... | https://en.wikipedia.org/wiki?curid=23312 |
15,905 | The first major development was ampicillin in 1961. It offered a broader spectrum of activity than either of the original penicillins. Further development yielded β-lactamase-resistant penicillins, including flucloxacillin, dicloxacillin, and methicillin. These were significant for their activity against β-lactamase-pr... | https://en.wikipedia.org/wiki?curid=23312 |
15,906 | Another development of the line of true penicillins was the antipseudomonal penicillins, such as carbenicillin, ticarcillin, and piperacillin, useful for their activity against Gram-negative bacteria. However, the usefulness of the β-lactam ring was such that related antibiotics, including the mecillinams, the carbapen... | https://en.wikipedia.org/wiki?curid=23312 |
15,907 | Penicillin is produced by the fermentation of various types of sugar by the fungus "Penicillium rubens". The fermentation process produces penicillin as a secondary metabolite when the growth of the fungus is inhibited by stress. The biosynthetic pathway outlined below experiences feedback inhibition involving the by-p... | https://en.wikipedia.org/wiki?curid=23312 |
15,908 | The "Penicillium" cells are grown using a technique called fed-batch culture, in which the cells are constantly subjected to stress, which is required for induction of penicillin production. While the usage of glucose as a carbon source represses penicillin biosynthesis enzymes, lactose does not exert any effect and al... | https://en.wikipedia.org/wiki?curid=23312 |
15,909 | The biotechnological method of directed evolution has been applied to produce by mutation a large number of "Penicillium" strains. These techniques include error-prone PCR, DNA shuffling, ITCHY, and strand-overlap PCR. | https://en.wikipedia.org/wiki?curid=23312 |
15,910 | Overall, there are three main and important steps to the biosynthesis of penicillin G (benzylpenicillin). | https://en.wikipedia.org/wiki?curid=23312 |
15,911 | Buzz Aldrin (; born Edwin Eugene Aldrin Jr.; January 20, 1930) is an American former astronaut, engineer and fighter pilot. He made three spacewalks as pilot of the 1966 Gemini 12 mission. As the Lunar Module "Eagle" pilot on the 1969 Apollo 11 mission, he and mission commander Neil Armstrong were the first two people ... | https://en.wikipedia.org/wiki?curid=65777 |
15,912 | Born in Glen Ridge, New Jersey, Aldrin graduated third in the class of 1951 from the United States Military Academy at West Point, with a degree in mechanical engineering. He was commissioned into the United States Air Force, and served as a jet fighter pilot during the Korean War. He flew 66 combat missions and shot d... | https://en.wikipedia.org/wiki?curid=65777 |
15,913 | After earning a Doctor of Science degree in astronautics from the Massachusetts Institute of Technology, Aldrin was selected as a member of NASA's Astronaut Group 3, making him the first astronaut with a doctoral degree. His doctoral thesis, "Line-of-Sight Guidance Techniques for Manned Orbital Rendezvous", earned him ... | https://en.wikipedia.org/wiki?curid=65777 |
15,914 | After leaving NASA in 1971, Aldrin became Commandant of the U.S. Air Force Test Pilot School. He retired from the Air Force in 1972, after 21 years of service. His autobiographies "Return to Earth" (1973) and "Magnificent Desolation" (2009) recount his struggles with clinical depression and alcoholism in the years afte... | https://en.wikipedia.org/wiki?curid=65777 |
15,915 | Aldrin was born Edwin Eugene Aldrin Jr. on January 20, 1930, at Mountainside Hospital in Glen Ridge, New Jersey. His parents, Edwin Eugene Aldrin Sr. and Marion Aldrin ( Moon), lived in neighboring Montclair. His father was an Army aviator during World War I and the assistant commandant of the Army's test pilot school ... | https://en.wikipedia.org/wiki?curid=65777 |
15,916 | Aldrin did well in school, maintaining an A average. He played football and was the starting center for Montclair High School's undefeated 1946 state champion team. His father wanted him to go to the United States Naval Academy in Annapolis, Maryland and enrolled him at nearby Severn School, a preparatory school for An... | https://en.wikipedia.org/wiki?curid=65777 |
15,917 | Aldrin entered West Point in 1947. He did well academically, finishing first in his class his plebe (first) year. Aldrin was also an excellent athlete, competing in pole vault for the academy track and field team. In 1950, he traveled with a group of West Point cadets to Japan and the Philippines to study the military ... | https://en.wikipedia.org/wiki?curid=65777 |
15,918 | Among the top of his class, Aldrin had his choice of assignments. He chose the United States Air Force, which had become a separate service in 1947 while Aldrin was still at West Point and did not yet have its own academy. He was commissioned as a second lieutenant, and underwent basic flight training in T-6 Texans at ... | https://en.wikipedia.org/wiki?curid=65777 |
15,919 | When Aldrin was deciding what sort of aircraft he should fly, his father advised him to choose bombers, because command of a bomber crew gave an opportunity to learn and hone leadership skills, which could open up better prospects for career advancement. Aldrin chose instead to fly fighters. He moved to Nellis Air Forc... | https://en.wikipedia.org/wiki?curid=65777 |
15,920 | In December 1952, Aldrin was assigned to the 16th Fighter-Interceptor Squadron, which was part of the 51st Fighter-Interceptor Wing. At the time it was based at Suwon Air Base, about south of Seoul, and was engaged in combat operations as part of the Korean War. During an acclimatization flight, his main fuel system fr... | https://en.wikipedia.org/wiki?curid=65777 |
15,921 | The first MiG-15 he shot down was on May 14, 1953. Aldrin was flying about south of the Yalu River, when he saw two MiG-15 fighters below him. Aldrin opened fire on one of the MiGs, whose pilot may never have seen him coming. The June 8, 1953, issue of "Life" magazine featured gun camera footage taken by Aldrin of the ... | https://en.wikipedia.org/wiki?curid=65777 |
15,922 | Aldrin's second aerial victory came on June 4, 1953, when he accompanied aircraft from the 39th Fighter-Interceptor Squadron in an attack on an airbase in North Korea. Their newer aircraft were faster than his and he had trouble keeping up. He then spotted a MiG approaching from above. This time, Aldrin and his opponen... | https://en.wikipedia.org/wiki?curid=65777 |
15,923 | Aldrin's year-long tour ended in December 1953, by which time the fighting in Korea had ended. Aldrin was assigned as an aerial gunnery instructor at Nellis. In December 1954 he became an aide-de-camp to Brigadier General Don Z. Zimmerman, the Dean of Faculty at the nascent United States Air Force Academy, which opened... | https://en.wikipedia.org/wiki?curid=65777 |
15,924 | Through the Air Force Institute of Technology, Aldrin enrolled as a graduate student at the Massachusetts Institute of Technology (MIT) in 1959 intending to earn a master's degree. Richard Battin was the professor for his astrodynamics class. Two other USAF officers who later became astronauts, David Scott and Edgar Mi... | https://en.wikipedia.org/wiki?curid=65777 |
15,925 | Aldrin enjoyed the classwork and soon decided to pursue a doctorate instead. In January 1963, he earned a Sc.D. degree in astronautics. His doctoral thesis was "Line-of-Sight Guidance Techniques for Manned Orbital Rendezvous", the dedication of which read: "In the hopes that this work may in some way contribute to thei... | https://en.wikipedia.org/wiki?curid=65777 |
15,926 | After completing his doctorate Aldrin was assigned to the Gemini Target Office of the Air Force Space Systems Division in Los Angeles, working with the Lockheed Aircraft Corporation on enhancing the maneuver capabilities of the Agena target vehicle which was to be used by NASA's Project Gemini. He was then posted to th... | https://en.wikipedia.org/wiki?curid=65777 |
15,927 | Aldrin initially applied to join the astronaut corps when NASA's Astronaut Group 2 was selected in 1962. His application was rejected on the grounds that he was not a test pilot. Aldrin was aware of the requirement and asked for a waiver but the request was turned down. On May 15, 1963, NASA announced another round of ... | https://en.wikipedia.org/wiki?curid=65777 |
15,928 | Jim Lovell and Aldrin were selected as the backup crew of Gemini 10, commander and pilot respectively. Backup crews usually became the prime crew of the third following mission, but the last scheduled mission in the program was Gemini 12. The February 28, 1966, deaths of the Gemini 9 prime crew, Elliot See and Charles ... | https://en.wikipedia.org/wiki?curid=65777 |
15,929 | Initially, Gemini 12's mission objectives were uncertain. As the last scheduled mission, it was primarily intended to complete tasks that had not been successfully or fully carried out on earlier missions. While NASA had successfully performed rendezvous during Project Gemini, the gravity-gradient stabilization test on... | https://en.wikipedia.org/wiki?curid=65777 |
15,930 | It therefore fell to Aldrin to complete Gemini's EVA goals. NASA formed a committee to give him a better chance of success. It dropped the test of the Air Force's astronaut maneuvering unit (AMU) that had given Gordon trouble on Gemini11 so Aldrin could focus on EVA. NASA revamped the training program, opting for under... | https://en.wikipedia.org/wiki?curid=65777 |
15,931 | Gemini 12's main objectives were to rendezvous with a target vehicle, and fly the spacecraft and target vehicle together using gravity-gradient stabilization, perform docked maneuvers using the Agena propulsion system to change orbit, conduct a tethered stationkeeping exercise and three EVAs, and demonstrate an automat... | https://en.wikipedia.org/wiki?curid=65777 |
15,932 | Gemini12 was launched from Launch Complex 19 at Cape Canaveral on 20:46 UTC on November 11, 1966. The Gemini Agena Target Vehicle had been launched about an hour and a half before. The mission's first major objective was to rendezvous with this target vehicle. As the target and Gemini12 capsule drew closer together, ra... | https://en.wikipedia.org/wiki?curid=65777 |
15,933 | The next task was to practice undocking and docking again. On undocking, one of the three latches caught, and Lovell had to use the Gemini's thrusters to free the spacecraft. Aldrin then docked again successfully a few minutes later. The flight plan then called for the Agena main engine to be fired to take the docked s... | https://en.wikipedia.org/wiki?curid=65777 |
15,934 | Aldrin performed three EVAs. The first was a standup EVA on November 12, in which the spacecraft door was opened and he stood up, but did not leave the spacecraft. The standup EVA mimicked some of the actions he would do during his free-flight EVA, so he could compare the effort expended between the two. It set an EVA ... | https://en.wikipedia.org/wiki?curid=65777 |
15,935 | On November 15, the crew initiated the automatic reentry system and splashed down in the Atlantic Ocean, where they were picked up by a helicopter, which took them to the awaiting aircraft carrier . After the mission, his wife realized he had fallen into a depression, something she had not seen before. | https://en.wikipedia.org/wiki?curid=65777 |
15,936 | Lovell and Aldrin were assigned to an Apollo crew with Neil Armstrong as Commander, Lovell as Command Module Pilot (CMP), and Aldrin as Lunar Module Pilot (LMP). Their assignment as the backup crew of Apollo 9 was announced on November 20, 1967. Due to design and manufacturing delays in the lunar module (LM), Apollo 8 ... | https://en.wikipedia.org/wiki?curid=65777 |
15,937 | Michael Collins, the CMP on the Apollo8 prime crew, required surgery to remove a bone spur on his spine. Lovell took his place on the Apollo8 crew. When Collins recovered he joined Armstrong's crew as CMP. In the meantime, Fred Haise filled in as backup LMP, and Aldrin as backup CMP for Apollo 8. While the CMP usually ... | https://en.wikipedia.org/wiki?curid=65777 |
15,938 | Apollo11 was the second American space mission made up entirely of astronauts who had already flown in space, the first being Apollo 10. The next would not be flown until STS-26 in 1988. Deke Slayton, who was responsible for astronaut flight assignments, gave Armstrong the option to replace Aldrin with Lovell, since so... | https://en.wikipedia.org/wiki?curid=65777 |
15,939 | Early versions of the EVA checklist had the Lunar Module Pilot as the first to step onto the lunar surface. However, when Aldrin learned that this might be amended, he lobbied within NASA for the original procedure to be followed. Multiple factors contributed to the final decision, including the physical positioning of... | https://en.wikipedia.org/wiki?curid=65777 |
15,940 | Aldrin and Armstrong did not have time to perform much geological training. The first lunar landing focused more on landing on the Moon and making it safely back to Earth than the scientific aspects of the mission. The duo was briefed by NASA and USGS geologists. They made one geological field trip to West Texas. The p... | https://en.wikipedia.org/wiki?curid=65777 |
15,941 | On the morning of July 16, 1969, an estimated one million spectators watched the launch of Apollo11 from the highways and beaches in the vicinity of Cape Canaveral, Florida. The launch was televised live in 33 countries, with an estimated 25 million viewers in the United States alone. Millions more listened to radio br... | https://en.wikipedia.org/wiki?curid=65777 |
15,942 | On July 19 at 17:21:50 UTC, Apollo11 passed behind the Moon and fired its service propulsion engine to enter lunar orbit. In the thirty orbits that followed, the crew saw passing views of their landing site in the southern Sea of Tranquillity about southwest of the crater Sabine D. At 12:52:00 UTC on July 20, Aldrin an... | https://en.wikipedia.org/wiki?curid=65777 |
15,943 | Throughout the descent, Aldrin called out navigation data to Armstrong, who was busy piloting the "Eagle". Five minutes into the descent burn, and above the surface of the Moon, the LM guidance computer (LGC) distracted the crew with the first of several unexpected alarms that indicated that it could not complete all i... | https://en.wikipedia.org/wiki?curid=65777 |
15,944 | As a Presbyterian elder, Aldrin was the first and only person to hold a religious ceremony on the Moon. He radioed Earth: "I'd like to take this opportunity to ask every person listening in, whoever and wherever they may be, to pause for a moment and contemplate the events of the past few hours, and to give thanks in h... | https://en.wikipedia.org/wiki?curid=65777 |
15,945 | On reflection in his 2009 book, Aldrin said, "Perhaps, if I had it to do over again, I would not choose to celebrate communion. Although it was a deeply meaningful experience for me, it was a Christian sacrament, and we had come to the moon in the name of all mankind – be they Christians, Jews, Muslims, animists, agnos... | https://en.wikipedia.org/wiki?curid=65777 |
15,946 | Preparations for the EVA began at 23:43. Once Armstrong and Aldrin were ready to go outside, "Eagle" was depressurized, and the hatch was opened at 02:39:33 on July 21. Aldrin set foot on the Moon at 03:15:16 on July 21, 1969 (UTC), nineteen minutes after Armstrong first touched the surface. Armstrong and Aldrin became... | https://en.wikipedia.org/wiki?curid=65777 |
15,947 | After the call, Aldrin began photographing and inspecting the spacecraft to document and verify its condition before their flight. Aldrin and Armstrong then set up a seismometer, to detect moonquakes, and a laser beam reflector. While Armstrong inspected a crater, Aldrin began the difficult task of hammering a metal tu... | https://en.wikipedia.org/wiki?curid=65777 |
15,948 | Aldrin reentered "Eagle" first but, as he tells it, before ascending the module's ladder he became the first person to urinate on the Moon. With some difficulty they lifted film and two sample boxes containing of lunar surface material to the hatch using a flat cable pulley device. Armstrong reminded Aldrin of a bag of... | https://en.wikipedia.org/wiki?curid=65777 |
15,949 | At 17:54 UTC, they lifted off in "Eagle" ascent stage to rejoin Collins aboard "Columbia" in lunar orbit. After rendezvous with "Columbia", the ascent stage was jettisoned into lunar orbit, and "Columbia" made its way back to Earth. It splashed down in the Pacific east of Wake Island at 16:50 UTC (05:50 local time) on ... | https://en.wikipedia.org/wiki?curid=65777 |
15,950 | Bringing back pathogens from the lunar surface was considered a possibility, albeit remote, so divers passed biological isolation garments (BIGs) to the astronauts, and assisted them into the life raft. The astronauts were winched on board the recovery helicopter, and flown to the aircraft carrier , where they spent th... | https://en.wikipedia.org/wiki?curid=65777 |
15,951 | On September 16, 1969, the astronauts addressed a joint session of Congress where they thanked the representatives for their past support and implored them to continue funding the space effort. The astronauts embarked on a 38-day world tour on September 29 that brought the astronauts to 22 foreign countries and include... | https://en.wikipedia.org/wiki?curid=65777 |
15,952 | After Apollo 11, Aldrin was kept busy giving speeches and making public appearances. In October 1970, he joined Soviet cosmonauts Andriyan Nikolayev and Vitaly Sevastyanov on their tour of the NASA space centers. He was also involved in the design of the Space Shuttle. With the Apollo program coming to an end, Aldrin, ... | https://en.wikipedia.org/wiki?curid=65777 |
15,953 | Aldrin hoped to become Commandant of Cadets at the United States Air Force Academy, but the job went to his West Point classmate Hoyt S. Vandenberg Jr. Aldrin was made Commandant of the USAF Aerospace Research Pilot School at Edwards Air Force Base, California. Aldrin had neither managerial nor test pilot experience, b... | https://en.wikipedia.org/wiki?curid=65777 |
15,954 | Aldrin did not get along well with his superior, Brigadier General Robert M. White, who had earned his USAF astronaut wings flying the X-15. Aldrin's celebrity status led people to defer to him more than the higher-ranking general. There were two crashes at Edwards, of an A-7 Corsair II and a T-33. No people died, but ... | https://en.wikipedia.org/wiki?curid=65777 |
15,955 | Aldrin went to see the base surgeon. In addition to signs of depression, he experienced neck and shoulder pains, and hoped that the latter might explain the former. He was hospitalized for depression at Wilford Hall Medical Center for four weeks. His mother had committed suicide in May 1968, and he was plagued with gui... | https://en.wikipedia.org/wiki?curid=65777 |
15,956 | In February 1972, General George S. Brown paid a visit to Edwards and informed Aldrin that the USAF Aerospace Research Pilot School was being renamed the USAF Test Pilot School and the astronaut training was being dropped. With the Apollo program winding down, and Air Force budgets being cut, the Air Force's interest i... | https://en.wikipedia.org/wiki?curid=65777 |
15,957 | Aldrin's father died on December 28, 1974, from complications following a heart attack. Aldrin's autobiographies "Return to Earth," (1973) and "Magnificent Desolation" (2009), recounted his struggles with clinical depression and alcoholism in the years after leaving NASA. Encouraged by a therapist to take a regular job... | https://en.wikipedia.org/wiki?curid=65777 |
15,958 | On September 9, 2002, Aldrin was lured to a Beverly Hills hotel on the pretext of being interviewed for a Japanese children's television show on the subject of space. When he arrived, Moon landing conspiracy theorist Bart Sibrel accosted him with a film crew and demanded he swear on a Bible that the Moon landings were ... | https://en.wikipedia.org/wiki?curid=65777 |
15,959 | In 2005, while being interviewed for a Science Channel documentary titled "First on the Moon: The Untold Story", Aldrin told an interviewer they had seen an unidentified flying object (UFO). The documentary makers omitted the crew's conclusion that they probably saw one of the four detached spacecraft adapter panels fr... | https://en.wikipedia.org/wiki?curid=65777 |
15,960 | In December 2016, Aldrin was part of a tourist group visiting the Amundsen–Scott South Pole Station in Antarctica when he fell ill and was evacuated, first to McMurdo Station and from there to Christchurch, New Zealand. At 86 years of age, Aldrin's visit made him the oldest person to reach the South Pole. He had travel... | https://en.wikipedia.org/wiki?curid=65777 |
15,961 | After leaving NASA, Aldrin continued to advocate for space exploration. In 1985 he joined the University of North Dakota (UND)'s College of Aerospace Sciences at the invitation of John D. Odegard, the dean of the college. Aldrin helped to develop UND's Space Studies program and brought Dr. David Webb from NASA to serve... | https://en.wikipedia.org/wiki?curid=65777 |
15,962 | In 1985, Aldrin proposed a special spacecraft trajectory now known as the Aldrin cycler. Cycler trajectories offer reduced cost of repeated travel to Mars by using less propellant. The Aldrin cycler provided a five and a half month journey from the Earth to Mars, with a return trip to Earth of the same duration on a tw... | https://en.wikipedia.org/wiki?curid=65777 |
15,963 | In December 2003, Aldrin published an opinion piece in "The New York Times" criticizing NASA's objectives. In it, he voiced concern about NASA's development of a spacecraft "limited to transporting four astronauts at a time with little or no cargo carrying capability" and declared the goal of sending astronauts back to... | https://en.wikipedia.org/wiki?curid=65777 |
15,964 | In a June 2013 opinion piece in "The New York Times", Aldrin supported a human mission to Mars and which viewed the Moon "not as a destination but more a point of departure, one that places humankind on a trajectory to homestead Mars and become a two-planet species." In August 2015, Aldrin, in association with the Flor... | https://en.wikipedia.org/wiki?curid=65777 |
15,965 | Aldrin was awarded the Air Force Distinguished Service Medal (DSM) in 1969 for his role as lunar module pilot on Apollo 11. He was awarded an oak leaf cluster in 1972 in lieu of a second DSM for his role in both the Korean War and in the space program, and the Legion of Merit for his role in the Gemini and Apollo progr... | https://en.wikipedia.org/wiki?curid=65777 |
15,966 | In 1999, while celebrating the 30th anniversary of the lunar landing, Vice President Al Gore, who was also the vice-chancellor of the Smithsonian Institution's Board of Regents, presented the Apollo11 crew with the Smithsonian Institution's Langley Gold Medal for aviation. After the ceremony, the crew went to the White... | https://en.wikipedia.org/wiki?curid=65777 |
15,967 | The Apollo11 crew were awarded the Collier Trophy in 1969. The National Aeronautic Association president awarded a duplicate trophy to Collins and Aldrin at a ceremony. The crew was awarded the 1969 General Thomas D. White USAF Space Trophy. The National Space Club named the crew the winners of the 1970 Dr. Robert H. G... | https://en.wikipedia.org/wiki?curid=65777 |
15,968 | In 2001, President George W. Bush appointed Aldrin to the Commission on the Future of the United States Aerospace Industry. Aldrin received the 2003 Humanitarian Award from Variety, the Children's Charity, which, according to the organization, "is given to an individual who has shown unusual understanding, empathy, and... | https://en.wikipedia.org/wiki?curid=65777 |
15,969 | Aldrin received honorary degrees from six colleges and universities, and was named as the Chancellor of the International Space University in 2015. He was a member of the National Space Society's Board of Governors, and has served as the organization's chairman. In 2016, his hometown middle school in Montclair, New Jer... | https://en.wikipedia.org/wiki?curid=65777 |
15,970 | In 2019, Aldrin was awarded the Starmus Festival's Stephen Hawking Medal for Science Communication for Lifetime Achievement. | https://en.wikipedia.org/wiki?curid=65777 |
15,971 | Aldrin has been married three times. His first marriage was on December 29, 1954, to Joan Archer, a Rutgers University and Columbia University alumna with a master's degree. They had three children, James, Janice and Andrew. They filed for divorce in 1974. His second was to Beverly Van Zile, whom he married on December... | https://en.wikipedia.org/wiki?curid=65777 |
15,972 | In 2018, Aldrin was involved in a legal dispute with his children Andrew and Janice and former business manager Christina Korp over their claims that he was mentally impaired through dementia and Alzheimer's disease. His children alleged that he made new friends who were alienating him from the family and encouraging h... | https://en.wikipedia.org/wiki?curid=65777 |
15,973 | Aldrin is an active supporter of the Republican Party, headlining fundraisers for its members of Congress and endorsing its candidates. He appeared at a rally for George W. Bush in 2004 and campaigned for Paul Rancatore in Florida in 2008, Mead Treadwell in Alaska in 2014 and Dan Crenshaw in Texas in 2018. He appeared ... | https://en.wikipedia.org/wiki?curid=65777 |
15,974 | In 2007, Aldrin confirmed to "Time" magazine that he had recently had a face-lift, joking that the g-forces he was exposed to in space "caused a sagging jowl that needed some attention." He primarily resided in the Los Angeles area, including Beverly Hills and Laguna Beach and Emerald Bay. Following his third divorce, ... | https://en.wikipedia.org/wiki?curid=65777 |
15,975 | A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial fre... | https://en.wikipedia.org/wiki?curid=52247 |
15,976 | The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that frequency, and the argument of the complex... | https://en.wikipedia.org/wiki?curid=52247 |
15,977 | Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statistics as well a... | https://en.wikipedia.org/wiki?curid=52247 |
15,978 | The Fourier transform can be formally defined as an improper Riemann integral, making it an integral transform, although this definition is not suitable for many applications requiring a more sophisticated integration theory. For example, many relatively simple applications use the Dirac delta function, which can be tr... | https://en.wikipedia.org/wiki?curid=52247 |
15,979 | The Fourier transform can also be generalized to functions of several variables on Euclidean space, sending a function of 'position space' to a function of momentum (or a function of space and time to a function of 4-momentum). This idea makes the spatial Fourier transform very natural in the study of waves, as well as... | https://en.wikipedia.org/wiki?curid=52247 |
15,980 | The Fourier transform is an extension of the Fourier series, which in its most general form introduces the use of complex exponential functions. For example, for a function formula_1, the amplitude and phase of a frequency component at frequency formula_2, is given by this complex number: | https://en.wikipedia.org/wiki?curid=52247 |
15,981 | The extension provides a frequency continuum of components formula_4 using an infinite integral of integration: | https://en.wikipedia.org/wiki?curid=52247 |
15,982 | Here, the transform of function formula_1 at frequency formula_6 is denoted by the complex number formula_7, which is just one of several common conventions. Evaluating for all values of formula_6 produces the "frequency-domain" function. When the independent variable (formula_9) represents "time" (often denoted by for... | https://en.wikipedia.org/wiki?curid=52247 |
15,983 | A key to interpreting is that the effect of multiplying formula_1 by formula_14 is to subtract formula_6 from every frequency component of function formula_16 (also see Negative frequency) So the component that was at formula_6 ends up at zero hertz, and the integral produces its amplitude, because all the other compon... | https://en.wikipedia.org/wiki?curid=52247 |
15,984 | The functions formula_12 and formula_19 are often referred to as a "Fourier transform pair". A common notation for designating transform pairs is: | https://en.wikipedia.org/wiki?curid=52247 |
15,985 | And the Fourier transform extension is:The complex number, formula_7, conveys both amplitude and phase of frequency formula_6. So is a representation of formula_1 as a weighted summation of complex exponential functions. This is known as the Fourier inversion theorem, and was first introduced in Fourier's "Analytical T... | https://en.wikipedia.org/wiki?curid=52247 |
15,986 | For other common conventions and notations, including using the angular frequency instead of the ordinary frequency , see Other conventions and Other notations below. The Fourier transform on Euclidean space is treated separately, in which the variable often represents position and momentum. The conventions chosen in t... | https://en.wikipedia.org/wiki?curid=52247 |
15,987 | Many other characterizations of the Fourier transform exist. For example, one uses the Stone–von Neumann theorem: the Fourier transform is the unique unitary intertwiner for the symplectic and Euclidean Schrödinger representations of the Heisenberg group. | https://en.wikipedia.org/wiki?curid=52247 |
15,988 | In 1822, Fourier claimed (see ) that any function, whether continuous or discontinuous, can be expanded into a series of sines. That important work was corrected and expanded upon by others to provide the foundation for the various forms of the Fourier transform used since. | https://en.wikipedia.org/wiki?curid=52247 |
15,989 | Although Fourier series can represent periodic waveforms as the sum of harmonically-related sinusoids, Fourier series can't represent "non-periodic" waveforms. However, the Fourier transform is able to represent "non-periodic" waveforms as well. It achieves this by applying a limiting process to lengthen the period of ... | https://en.wikipedia.org/wiki?curid=52247 |
15,990 | In the study of Fourier series, the Fourier coefficients represent the amplitude of each "harmonically-related" sinusoid present in the Fourier series of a periodic function . Similarly, the Fourier transform represents the amplitude and phase of every sinusoid present in a (possibly non-periodic) function . | https://en.wikipedia.org/wiki?curid=52247 |
15,991 | The Fourier transform uses an integral (or "continuous sum") that exploits properties of sine and cosine to recover the amplitude and phase of each sinusoid in a Fourier series. The inverse Fourier transform recombines these waves using a similar integral to reproduce the original function. | https://en.wikipedia.org/wiki?curid=52247 |
15,992 | To simplify the math, it is desirable to write the Fourier series as a sum of complex exponentials (see ). Each complex exponential or "complex sinusoid" of frequency can be expressed using Euler's formula as the sum of a cosine wave of frequency for the real component plus a sine wave also of frequency for the imagina... | https://en.wikipedia.org/wiki?curid=52247 |
15,993 | Expressing real sinusoids as complex sinusoids makes it necessary for the Fourier coefficients formula_26to be complex valued, but has the benefit of compactly representing all necessary information about each frequency. The usual interpretation of this complex number is that formula_27 (its magnitude) gives the amplit... | https://en.wikipedia.org/wiki?curid=52247 |
15,994 | These complex exponentials may have negative frequency. For example, both complex sinusoids and complete one cycle per unit of , but the first represents a positive frequency while the second represents a negative frequency. Positive frequency can be understood as rotating counter-clockwise about the complex plane whil... | https://en.wikipedia.org/wiki?curid=52247 |
15,995 | Real sine and cosine waves can be recovered from the complex exponential representation of sinusoids. For example, a corollary to Euler's formula allows expressing cosine and sine waves as either the real or imaginary part of a complex sinusoid or as a weighted sum of two complex sinusoids of opposite frequency: | https://en.wikipedia.org/wiki?curid=52247 |
15,996 | Consequently, a general form of any real sinusoid (with frequency , phase shift , and amplitude ) can be expressed as the sum of two complex sinusoids of opposite frequency ( and -) but equal magnitude () and with the phase shift embedded in both their complex coefficients: | https://en.wikipedia.org/wiki?curid=52247 |
15,997 | Hence, every real sinusoid (and real signal) can be considered to consist of a positive and negative frequency, whose imaginary components cancel but whose real components contribute equally to form the real signal. | https://en.wikipedia.org/wiki?curid=52247 |
15,998 | To avoid the use of complex numbers and negative frequencies, the sine and cosine transforms together can be used as an equivalent alternative form of the Fourier transform. | https://en.wikipedia.org/wiki?curid=52247 |
15,999 | There is a close connection between the definition of Fourier series and the Fourier transform for functions that are zero outside an interval. For such a function, we can calculate its Fourier series on any interval that includes the points where is not zero. The Fourier transform is also defined for such a function. ... | https://en.wikipedia.org/wiki?curid=52247 |
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