title: Lost River (film)

text: Billy meets with a banker, Dave, regarding a loan the previous bank manager talked her into so that she could stay in her house, which originally belonged to her grandmother. Since Billy is unemployed, she is unable to repay the bank and must find a way to pay for the house. After their meeting, Dave offers Billy a job, leaving out the details of what it is.


title: Lost River (film)

text: A construction crew begins tearing down the vacant houses in the neighborhood. Along with Bones, Billy, and Franky, three of the few remaining residents are Rat, her grandmother, and her pet rat, Nick. Rat's grandmother repeatedly watches her old wedding video out of grief for her husband, who died while constructing a dam. Bones discovers an old road that is overgrown and leads under a lake. While hanging out with Rat, Bones learns there is an abandoned town under the lake that was flooded when a reservoir was built. Rat says the only way to break the "curse" that is plaguing their neighborhood is to capture a "beast" from the underwater town and bring it to the surface.


title: Lost River (film)

text: Dave's job offer leads Billy to a cabaret downtown, driven there by a friendly taxi driver. She enters to see a show put on by the main performer, Cat. The appeal of the show is a realistically gory "murder" where Cat ostensibly gets stabbed multiple times and has her "blood" spray all over the delighted audience. Billy goes backstage and meets with Cat, who shows her where the real money is made: in the basement. Down there, women stand in locked plastic "shells" while men do whatever they want in their presence.


title: Lost River (film)

text: Rat invites Bones out for "a night on the town." They go dancing at an abandoned high school and imply they would leave town together if it ever came to that. Later, they go to a convenience store and run into Bully and Face, whose lips were cut off by Bully after he let Bones get away. Bones hides from Bully, and to protect Bones, Rat accepts Bully's offer to give her a ride home. Bully walks Rat to her front door and asks her if he can see Nick. He then grabs Nick and brutally kills him in front of her.


title: Lost River (film)

text: Billy has to take Franky to work with her since Bones is out with Rat. For her performance, Billy makes it look like she is cutting off her face, which excites the audience. She later sits with Dave, who hosts the place and performs a song. He takes Billy and Franky home and makes a pass at Billy, but stops when he sees Bones standing outside the car.


title: Lost River (film)

text: Bones drops Billy off at work one night and sees what she has been doing to make money to keep the house. Unable to help their financial situation anymore by stealing copper piping, Bones decides he is going to break the aforementioned "curse." He leaves Franky with Rat and goes into the river to cut the head off a dinosaur statue in an old children's park. Meanwhile, Face enters Rat's house and sets it on fire. He dies in the flames as Rat goes to rescue her grandmother, but she is unable to rouse her from her catatonia and leaves with Franky. Having succeeded in cutting off the dinosaur's head, Bones comes ashore to find his car has been set on fire. Bully tries to run Bones over with his car, but at the last moment, Bones steps out of the way and throws the dinosaur head through Bully's windshield, causing him to crash against the burning car. Bully is thrown from his car, ends up stuck head first in the lake, and drowns.


title: Lost River (film)

text: At work, Billy is sealed in a "shell" while Dave performs a sexual dance routine around her. Despite having a button that locks the shell from the inside, Dave has a remote that releases the lock. Billy finally steps out of the chamber and stabs Dave in the ear then flees. Billy returns to find her sons and Rat sitting on the steps of their house while Rat's home continues to burn. With the help of the taxi driver, the four of them leave the neighbourhood with the dinosaur head strapped to the top of the taxi.


title: Lost River (film)

text: The film was originally titled "How to Catch a Monster". In May 2013, scenes were shot at the Masonic Temple in Detroit, Michigan.


title: Lost River (film)

text: The first official tease of the film's music came on February 3, 2015, when Chromatics issued a single for their song, "Yes (Love Theme from Lost River)", which is featured in the film. Jewel released the soundtrack album on his own label, Italians Do It Better, on March 30, 2015. The soundtrack features music from the score, as well as songs from the film by Glass Candy, Chromatics, Desire, and Symmetry, as well as songs sung by Saoirse Ronan and Ben Mendelsohn, who star in the film. The song "Tell Me", sung by Ronan, was featured in the first episode of the 2017 television series "Riverdale" and in the eighth episode for the third season of "Killing Eve". The soundtrack was released on CD, digitally, and as a limited 3xLP on purple vinyl.


title: Lost River (film)

text: The film premiered on May 20, 2014, at the Cannes Film Festival, where it was met with a mixed reception from the audience. Warner Bros. Pictures, the U.S. distributor of the film, was subsequently reported to be considering selling its distribution rights to another studio. The film was released simultaneously in select theaters in the United States and through video on demand platforms on April 10, 2015.


title: Lost River (film)

text: An airing of the film by the Asian FX network on February 13, 2017, led to Indonesia's Broadcasting Commission giving the network a five-day sanction from April 10–14 where it was prohibited for broadcasting due to unapproved sensitive content.


title: Lost River (film)

text: "Lost River" received mixed reviews at the time of its release. On Rotten Tomatoes, the film has a rating of 31%, based on 74 reviews, with an average rating of 4.60/10. The site's critics consensus reads, ""Lost River" suggests that debuting writer-director Ryan Gosling may have a bright future as a filmmaker, but it doesn't hold together well enough to recommend on its own merit." On Metacritic, the film has a score of 42 out of 100, based on 21 critics, indicating "mixed or average reviews".


title: Lost River (film)

text: Peter Bradshaw of "The Guardian" stated that the film is "colossally indulgent, shapeless, often fantastically and unthinkingly offensive and at all times insufferably conceited". Kate Muir of "The Sunday Times" described the film as "a lurid mash up of Lynch, Refn and Edward Hopper. In a bad way." Robbie Collin of "The Telegraph" called the film "dumbfoundingly poor" and stated that Gosling "confuses 'making film' with 'assembling Tumblr of David Lynch & Mario Bava gifs'".


title: Lost River (film)

text: By 2016, the film had begun to receive a more positive opinion from fans of the surreal fantasy genre.


title: Sign function

text: In mathematics, the sign function or signum function (from "signum", Latin for "sign") is an odd mathematical function that extracts the sign of a real number. In mathematical expressions the sign function is often represented as . To avoid confusion with the sine function, this function is usually called the signum function.


title: Sign function

text: The signum function is the derivative of the absolute value function, up to (but not including) the indeterminacy at zero. More formally, in integration theory it is a weak derivative, and in convex function theory the subdifferential of the absolute value at 0 is the interval , "filling in" the sign function (the subdifferential of the absolute value is not single-valued at 0). Note, the resultant power of is 0, similar to the ordinary derivative of . The numbers cancel and all we are left with is the sign of .


title: Sign function

text: The signum function is differentiable with derivative 0 everywhere except at 0. It is not differentiable at 0 in the ordinary sense, but under the generalised notion of differentiation in distribution theory,


title: Sign function

text: the derivative of the signum function is two times the Dirac delta function, which can be demonstrated using the identity


title: Sign function

text: for any complex number except . The signum of a given complex number is the point on the unit circle of the complex plane that is nearest to . Then, for ,


title: Sign function

text: For reasons of symmetry, and to keep this a proper generalization of the signum function on the reals, also in the complex domain one usually defines, for :


title: Sign function

text: Another generalization of the sign function for real and complex expressions is , which is defined as:


title: Sign function

text: At real values of , it is possible to define a generalized function–version of the signum function, such that everywhere, including at the point , unlike , for which . This generalized signum allows construction of the algebra of generalized functions, but the price of such generalization is the loss of commutativity. In particular, the generalized signum anticommutes with the Dirac delta function


title: Sign function

text: in addition, cannot be evaluated at ; and the special name, is necessary to distinguish it from the function . ( is not defined, but .)


title: Sign function

text: Thanks to the Polar decomposition theorem, a matrix formula_17 (formula_18 and formula_19) can be decomposed as a product formula_20 where formula_21 is a unitary matrix and formula_22 is a self-adjoint, or Hermitian, positive definite matrix, both in formula_23. If formula_24 is invertible then such a decomposition is unique and formula_21 plays the role of formula_24's signum. A dual construction is given by the decomposition formula_27 where formula_28 is unitary, but generally different than formula_21. This leads to each invertible matrix having a unique left-signum formula_21 and right-signum formula_28.


title: Sign function

text: In the special case where formula_32 and the (invertible) matrix formula_33, which identifies with the (nonzero) complex number formula_34, then the signum matrices satisfy formula_35 and identify with the complex signum of formula_36, formula_37. In this sense, polar decomposition generalizes to matrices the signum-modulus decomposition of complex numbers.


title: Abbas (actor)

text: Abbas (born 21 May 1975 as Mirza Abbas Ali) is a former Indian actor and model from Kolkata, who has predominantly appeared in Tamil and Telugu films, and a few films in Malayalam, Hindi and Kannada. He made his debut with Kadhir's "Kadhal Desam" in 1996.


title: Abbas (actor)

text: Abbas grew up watching Hindi films. His maternal grandfather being an actor Farrukh Mirza acted in Neel Darpan (Bengali) and his paternal family being related to actor Feroz Khan. He partook in modelling assignments since his college days won "Face of 94" in Bangalore. Initially, after hearing that director Kadhir was looking for a new actor for his latest venture, Abbas had recommended his friends who knew Tamil to audition and took part in a speculative audition at the insistence of his friend. Kadhir was impressed with Abbas' performance and invited him to a screen test for "Kadhal Desam" (1996), before eventually signing him on to play a leading role. Unfamiliar with the Tamil language, Abbas memorised his lines on the set of the film and Kadhir began the shoot with easier portions, in order to ease Abbas into his role. Featuring alongside Vineeth and Tabu, "Kadhal Desam" became a critical and commercial success and Abbas was dubbed by the media as a "heart-throb" and garnered several more acting offers. His busy schedule meant that he missed out on various successful films including "Kadhalukku Mariyadhai" (1997) and "Jeans" (1998), and the Tamil films he appeared in such as "Jolly" (1998) "Ini Ellam Sugame" (1998), "Aasai Thambi" (1998) were predominantly box office failures. Meanwhile, the success of "Kaadhal Desam"<nowiki>'</nowiki>s dubbed Telugu version, allowed him to make a breakthrough in Telugu films and his next ventures "Priya O Priya" (1997) and "Rajahamsa" (1998) were profitable. He also appeared in the youth-centric Kannada film, "Shanti Shanti Shanti" (1999), featuring alongside debutant Madhavan for the first time.


title: Abbas (actor)

text: Following a spell of commercially disappointing Tamil films as the lead actor, Abbas worked on several prestigious films in the early 2000s as a second hero. He appeared as Rajinikanth's son-in-law in "Padayappa" (1999), before portraying the role of a doctor in Kamal Haasan's historical film, "Hey Ram" (2000). Abbas then appeared in Rajiv Menon's multi-starrer "Kandukondain Kandukondain" (2000), in which he was paired with Aishwarya Rai, and the film went on to win positive reviews from critics. In 2001, he made further supporting appearances in the commercially successful films, "Minnale" by Gautham Vasudev Menon and "Aanandham" by N. Linguswamy, with Mammootty as well in "Pammal K. Sambandam" (2002) with Kamal Haasan again, and critics labelled the period as a "career high". He appeared in a music video for Rajshri Pictures and was subsequently given the opportunity from producers to appear in Hindi films, then made his debut with "Ansh" (2002). The failure of the film prompted two further films, including "Aur Phir" with Bipasha Basu to be shelved, and he continued to appear in Tamil films in supporting roles through the mid-2000s.


title: Abbas (actor)

text: With multi-starrers diminishing in Tamil cinema, Abbas appeared in some low-budget ventures such as "Unarchigal" (2005) and "47A Besant Nagar Varai" (2006), before opting to pursue anti-hero roles. He starred as a womaniser in the horror film "Shock" (2004) and "Thiruttu Payale" (2006), and then also played a comic villain in "Sadhu Miranda" (2008) and "Guru En Aalu" (2009). In 2010, he made a return to Kannada films with the family drama "Appu and Pappu", portraying the father of young boy. In recent years, Abbas has appeared in television serials, while he also portrayed scientist Prasanta Chandra Mahalanobis in "Ramanujan" (2014).


title: Abbas (actor)

text: As his acting career started to decline, He settled down in New Zealand with his family and is currently working as a Business Analyst. He also became a motivational speaker to teenagers who have suicidal thoughts.


title: Abbas (actor)

text: Abbas was born on 21 May 1975. He married Erum Hussain Khan, in 1997. Erum after marriage launched her own label known as Erum ALi & EA Bridal Lounge. The couple have two kids a daughter Emira & a son Aymaan. Erum designed costumes for movies' notably "Aayirathil Oruvan" and "Guru En Aalu" where his co-star Madhavan's wife, Saritha, too worked as designer.He left actor career on year 2015 and currently he is working as software engineer settled in <nowiki>Auckland</nowiki>,<nowiki>New Zealand</nowiki>.


title: Motion sickness

text: Motion sickness occurs due to a difference between actual and expected motion. Symptoms commonly include nausea, vomiting, cold sweat, headache, dizziness, tiredness, loss of appetite, and increased salivation. Complications may rarely include dehydration, electrolyte problems, or a lower esophageal tear.


title: Motion sickness

text: The cause of motion sickness is either real or perceived motion. This may include from car travel, air travel, sea travel, space travel, or reality simulation. Risk factors include pregnancy, migraines, and Ménière's disease. The diagnosis is based on symptoms.


title: Motion sickness

text: Treatment may include behavioral measures or medications. Behavioral measures include keeping the head still and focusing on the horizon. Three types of medications are useful: antimuscarinics such as scopolamine, H antihistamines such as dimenhydrinate, and amphetamines such as dexamphetamine. Side effects, however, may limit the use of medications. A number of medications used for nausea such as ondansetron are not effective for motion sickness.


title: Motion sickness

text: Nearly all people are affected with sufficient motion and most people will experience motion sickness at least once in their lifetime. Susceptibility, however, is variable, with about one-third of the population being highly susceptible while most other people are affected under extreme conditions. Women are more easily affected than men. Motion sickness has been described since at least the time of Homer ( eighth century BC).


title: Motion sickness

text: Symptoms commonly include nausea, vomiting, cold sweat, headache, dizziness, tiredness, loss of appetite, and increased salivation. Occasionally, tiredness can last for hours to days after an episode of motion sickness, known as "sopite syndrome". Rarely severe symptoms such as the inability to walk, ongoing vomiting, or social isolation may occur while rare complications may include dehydration, electrolyte problems, or a lower esophageal tear from severe vomiting.


title: Motion sickness

text: In these cases, motion is sensed by the vestibular system and hence the motion is felt, but no motion or little motion is detected by the visual system, as in terrestrial motion sickness.


title: Motion sickness

text: A specific form of terrestrial motion sickness, being carsick is quite common and evidenced by disorientation while reading a map, a book, or a small screen during travel. Carsickness results from the sensory conflict arising in the brain from differing sensory inputs. Motion sickness is caused by a conflict between signals arriving in the brain from the inner ear, which forms the base of the vestibular system, the sensory apparatus that deals with movement and balance, and which detects motion mechanically. If someone is looking at a stationary object within a vehicle, such as a magazine, their eyes will inform their brain that what they are viewing is not moving. Their inner ears, however, will contradict this by sensing the motion of the vehicle.


title: Motion sickness

text: Varying theories exist as to cause. The sensory conflict theory notes that the eyes view motion while riding in the moving vehicle while other body sensors sense stillness, creating conflict between the eyes and inner ear. Another suggests the eyes mostly see the interior of the car which is motionless while the vestibular system of the inner ear senses motion as the vehicle goes around corners or over hills and even small bumps. Therefore, the effect is worse when looking down but may be lessened by looking outside of the vehicle.


title: Motion sickness

text: In the early 20th century, Austro-Hungarian scientist Róbert Bárány observed the back and forth movement of the eyes of railroad passengers as they looked out the side windows at the scenery whipping by. He called it "railway nystagmus". Also called "optokinetic nystagmus". It causes nausea and vomiting. His findings were published in the journal "Laeger", 83:1516, Nov.17, 1921.


title: Motion sickness

text: Air sickness is a kind of terrestrial motion sickness induced by certain sensations of air travel. It is a specific form of motion sickness and is considered a normal response in healthy individuals. It is essentially the same as carsickness but occurs in an airplane. An airplane may bank and tilt sharply, and unless passengers are sitting by a window, they are likely to see only the stationary interior of the plane due to the small window sizes and during flights at night. Another factor is that while in flight, the view out of windows may be blocked by clouds, preventing passengers from seeing the moving ground or passing clouds.


title: Motion sickness

text: Seasickness is a form of terrestrial motion sickness characterized by a feeling of nausea and, in extreme cases, vertigo experienced after spending time on a boat. It is essentially the same as carsickness, though the motion of a watercraft tends to be more regular. It is typically brought on by the rocking motion of the craft or movement while the craft is immersed in water. As with airsickness, it can be difficult to visually detect motion even if one looks outside the boat since water does not offer fixed points with which to visually judge motion. Poor visibility conditions, such as fog, may worsen seasickness. The greatest contributor to seasickness is the tendency for people being affected by the rolling or surging motions of the craft to seek refuge below decks, where they are unable to relate themselves to the boat's surroundings and consequent motion. Some people with carsickness are resistant to seasickness and vice versa. Adjusting to the craft's motion at sea is called "gaining one's sea legs"; it can take a significant portion of the time spent at sea after disembarking to regain a sense of stability "post-sea legs".


title: Motion sickness

text: Rotating devices such as centrifuges used in astronaut training and amusement park rides such as the Rotor, and the Gravitron can cause motion sickness in many people. While the interior of the centrifuge does not appear to move, one will experience a sense of motion. In addition, centrifugal force can cause the vestibular system to give one the sense that downward is in the direction away from the center of the centrifuge rather than the true downward direction.


title: Motion sickness

text: When one spins and stops suddenly, fluid in the inner ear continues to rotate causing a sense of continued spinning while one's visual system no longer detects motion.


title: Motion sickness

text: Usually, VR programs would detect the motion of the user's head and adjust the rotation of vision to avoid dizziness. However, some cases such as system lagging or software crashing could cause lags in the screen updates. In such cases, even some small head motions could trigger the motion sickness by the defense mechanism mentioned below: the inner ear transmits to the brain that it senses motion, but the eyes tell the brain that everything is still.


title: Motion sickness

text: In these cases, motion is detected by the visual system and hence the motion is seen, but no motion or little motion is sensed by the vestibular system. Motion sickness arising from such situations has been referred to as "visually induced motion sickness" (VIMS).


title: Motion sickness

text: Zero gravity interferes with the vestibular system's gravity-dependent operations, so that the two systems, vestibular and visual, no longer provide a unified and coherent sensory representation. This causes unpleasant disorientation sensations often quite distinct from terrestrial motion sickness, but with similar symptoms. The symptoms may be more intense because a condition caused by prolonged weightlessness is usually quite unfamiliar.


title: Motion sickness

text: Space motion sickness was effectively unknown during the earliest spaceflights because the very cramped conditions of the spacecraft allowed for only minimal bodily motion, especially head motion. Space motion sickness seems to be aggravated by being able to freely move around, and so is more common in larger spacecraft. Around 60% of Space Shuttle astronauts experienced it on their first flight; the first case of space motion sickness is now thought to be the Soviet cosmonaut Gherman Titov, in August 1961 onboard "Vostok 2", who reported dizziness, nausea, and vomiting. The first severe cases were in early Apollo flights; Frank Borman on "Apollo 8" and Rusty Schweickart on "Apollo 9". Both experienced identifiable and quite unpleasant symptoms—in the latter case causing the mission plan to be modified.


title: Motion sickness

text: This type of terrestrial motion sickness is particularly prevalent when susceptible people are watching films presented on very large screens such as IMAX, but may also occur in regular format theaters or even when watching TV or playing games. For the sake of novelty, IMAX and other panoramic type theaters often show dramatic motions such as flying over a landscape or riding a roller coaster. This type of motion sickness can be prevented by closing one's eyes during such scenes.


title: Motion sickness

text: In regular-format theaters, an example of a movie that caused motion sickness in many people is "The Blair Witch Project". Theaters warned patrons of its possible nauseating effects, cautioning pregnant women in particular. "Blair Witch" was filmed with a handheld camcorder, which was subjected to considerably more motion than the average movie camera, and lacks the stabilization mechanisms of steadicams.


title: Motion sickness

text: Home movies, often filmed with a cell phone camera, also tend to cause motion sickness in those who view them. The person holding the cell phone or other camera usually is unaware of this as the recording is being made since the sense of motion seems to match the motion seen through the camera's viewfinder. Those who view the film afterward only see the movement, which may be considerable, without any sense of motion. Using the zoom function seems to contribute to motion sickness as well since zooming is not a normal function of the eye. The use of a tripod or a camera or cell phone with image stabilization while filming can reduce this effect.


title: Motion sickness

text: Motion sickness due to virtual reality is very similar to simulation sickness and motion sickness due to films. In virtual reality the effect is made more acute as all external reference points are blocked from vision, the simulated images are three-dimensional and in some cases stereo sound that may also give a sense of motion. The NADS-1, a simulator located at the National Advanced Driving Simulator, is capable of accurately stimulating the vestibular system with a 360-degree horizontal field of view and 13 degrees of freedom motion base. Studies have shown that exposure to rotational motions in a virtual environment can cause significant increases in nausea and other symptoms of motion sickness.


title: Motion sickness

text: In a study conducted by the U.S. Army Research Institute for the Behavioral and Social Sciences in a report published May 1995 titled "Technical Report 1027 – Simulator Sickness in Virtual Environments", out of 742 pilot exposures from 11 military flight simulators, "approximately half of the pilots (334) reported post-effects of some kind: 250 (34%) reported that symptoms dissipated in less than one hour, 44 (6%) reported that symptoms lasted longer than four hours, and 28 (4%) reported that symptoms lasted longer than six hours. There were also four (1%) reported cases of spontaneously occurring flashbacks."


title: Motion sickness

text: When moving within a rotating reference frame such as in a centrifuge or environment where gravity is simulated with centrifugal force, the coriolis effect causes a sense of motion in the vestibular system that does not match the motion that is seen.


title: Motion sickness

text: Contemporary sensory conflict theory, referring to "a discontinuity between either visual, proprioceptive, and somatosensory input, or semicircular canal and otolith input", is probably the most thoroughly studied. According to this theory, when the brain presents the mind with two incongruous states of motion; the result is often nausea and other symptoms of disorientation known as motion sickness. Such conditions happen when the vestibular system and the visual system do not present a synchronized and unified representation of one's body and surroundings.


title: Motion sickness

text: According to sensory conflict theory, the cause of terrestrial motion sickness is the opposite of the cause of space motion sickness. The former occurs when one perceives visually that one's surroundings are relatively immobile while the vestibular system reports that one's body is in motion relative to its surroundings. The latter can occur when the visual system perceives that one's surroundings are in motion while the vestibular system reports relative bodily immobility (as in zero gravity.)


title: Motion sickness

text: A variation of the sensory conflict theory is known as neural mismatch, implying a mismatch occurring between ongoing sensory experience and long-term memory rather than between components of the vestibular and visual systems. This theory emphasizes "the limbic system in the integration of sensory information and long-term memory, in the expression of the symptoms of motion sickness, and the impact of anti-motion-sickness drugs and stress hormones on limbic system function. The limbic system may be the neural mismatch center of the brain."


title: Motion sickness

text: It has also been proposed that motion sickness could function as a defense mechanism against neurotoxins. The area postrema in the brain is responsible for inducing vomiting when poisons are detected, and for resolving conflicts between vision and balance. When feeling motion but not seeing it (for example, in the cabin of a ship with no portholes), the inner ear transmits to the brain that it senses motion, but the eyes tell the brain that everything is still. As a result of the incongruity, the brain concludes that the individual is hallucinating and further concludes that the hallucination is due to poison ingestion. The brain responds by inducing vomiting, to clear the supposed toxin. Treisman's indirect argument has recently been questioned via an alternative direct evolutionary hypothesis, as well as modified and extended via a direct poison hypothesis. The direct evolutionary hypothesis essentially argues that there are plausible means by which ancient real or apparent motion could have contributed directly to the evolution of aversive reactions, without the need for the co-opting of a poison response as posited by Treisman. Nevertheless, the direct poison hypothesis argues that there still are plausible ways in which the body's poison response system may have played a role in shaping the evolution of some of the signature symptoms that characterize motion sickness.


title: Motion sickness

text: Yet another theory, known as the nystagmus hypothesis, has been proposed based on stimulation of the vagus nerve resulting from the stretching or traction of extra-ocular muscles co-occurring with eye movements caused by vestibular stimulation. There are three critical aspects to the theory: first is the close linkage between activity in the vestibular system, i.e., semicircular canals and otolith organs, and a change in tonus among various of each eye's six extra-ocular muscles. Thus, with the exception of voluntary eye movements, the vestibular and oculomotor systems are thoroughly linked. Second is the operation of Sherrington's Law describing reciprocal inhibition between agonist-antagonist muscle pairs, and by implication the stretching of extraocular muscle that must occur whenever Sherrington's Law is made to fail, thereby causing an unrelaxed (contracted) muscle to be stretched. Finally, there is the critical presence of afferent output to the Vagus nerves as a direct result of eye muscle stretch or traction. Thus, tenth nerve stimulation resulting from eye muscle stretch is proposed as the cause of motion sickness. The theory explains why labyrinthine-defective individuals are immune to motion sickness; why symptoms emerge when undergoing various body-head accelerations; why combinations of voluntary and reflexive eye movements may challenge the proper operation of Sherrington's Law, and why many drugs that suppress eye movements also serve to suppress motion sickness symptoms.


title: Motion sickness

text: A recent theory argues that the main reason motion sickness occurs is due to an imbalance in vestibular outputs favoring the semicircular canals (nauseogenic) vs. otolith organs (anti-nauseogenic). This theory attempts to integrate previous theories of motion sickness. For example, there are many sensory conflicts that are associated with motion sickness and many that are not, but those in which canal stimulation occurs in the absence of normal otolith function (e.g., in free fall) are the most provocative. The vestibular imbalance theory is also tied to the different roles of the otoliths and canals in autonomic arousal (otolith output more sympathetic).


title: Motion sickness

text: The diagnosis is based on symptoms. Other conditions that may present similarly include vestibular disorders such as benign paroxysmal positional vertigo and vestibular migraine and stroke.


title: Motion sickness

text: Behavioral measures to decrease motion sickness include holding the head still and lying on the back. Focusing on the horizon may also be useful. Listening to music, mindful breathing, being the driver, and not reading while moving are other techniques.


title: Motion sickness

text: Habituation is the most effective technique but requires significant time. It is often used by the military for pilots. These techniques must be carried out at least every week to retain effectiveness.


title: Motion sickness

text: A head-worn, computer device with a transparent display can be used to mitigate the effects of motion sickness (and spatial disorientation) if visual indicators of the wearer's head position are shown. Such a device functions by providing the wearer with digital reference lines in their field of vision that indicate the horizon's position relative to the user's head. This is accomplished by combining readings from accelerometers and gyroscopes mounted in the device. This technology has been implemented in both standalone devices and Google Glass. One promising looking treatment is to wear LCD shutter glasses that create a stroboscopic vision of 4 Hz with a dwell of 10 milliseconds.


title: Motion sickness

text: Three types of medications are useful: antimuscarinics such as scopolamine, H antihistamines such as dimenhydrinate, and amphetamines such as dexamphetamine. Benefits are greater if used before the onset of symptoms or shortly after symptoms begin. Side effects, however, may limit the use of medications. A number of medications used for nausea such as ondansetron and metoclopramide are not effective in motion sickness.


title: Motion sickness

text: Scopolamine is the most effective medication. Evidence is best for when it is used preventatively. It is available as a skin patch. Side effects may include blurry vision.


title: Motion sickness

text: Other effective first generation antihistamines include doxylamine, diphenhydramine, promethazine, meclizine, cyclizine, and cinnarizine. In pregnancy meclizine, dimenhydrinate and doxylamine are generally felt to be safe. Side effects include sleepiness. Second generation antihistamines have not been found to be useful.


title: Motion sickness

text: Dextroamphetamine may be used together with an antihistamine or an antimuscarinic. Concerns include their addictive potential.


title: Motion sickness

text: Those involved in high-risk activities, such as SCUBA diving, should evaluate the risks versus the benefits of medications. Promethazine combined with ephedrine to counteract the sedation is known as "the Coast Guard cocktail".


title: Motion sickness

text: Alternative treatments include acupuncture and ginger although their effectiveness against motion sickness is variable. Providing smells does not appear to have a significant effect on the rate of motion sickness.


title: Motion sickness

text: Roughly one-third of people are highly susceptible to motion sickness, and most of the rest get motion sick under extreme conditions. Around 80% of the general population is susceptible to cases of medium to high motion sickness. The rates of space motion sickness have been estimated at between forty and eighty percent of those who enter weightless orbit. Several factors influence susceptibility to motion sickness, including sleep deprivation and the cubic footage allocated to each space traveler. Studies indicate that women are more likely to be affected than men, and that the risk decreases with advancing age. There is some evidence that people with Asian ancestry may develop motion sickness more frequently than people of European ancestry, and there are situational and behavioral factors, such as whether a passenger has a view of the road ahead, and diet and eating behaviors.


title: 2015 Copa América

text: The 2015 Copa América was the 44th edition of the Copa América, the main international football tournament for national teams in South America, and took place in Chile between 11 June and 4 July 2015. The competition was organized by CONMEBOL, South America's football governing body.


title: 2015 Copa América

text: Twelve teams competed: the ten members of CONMEBOL and two guests from CONCACAF – Mexico and Jamaica, the latter of which competed in the Copa América for the first time.


title: 2015 Copa América

text: Uruguay were the defending champions, but were eliminated by the host nation Chile in the quarter-finals. Chile won their first title, defeating Argentina in the final on penalties after a goalless draw. As winners, they qualified for the 2017 FIFA Confederations Cup in Russia.


title: 2015 Copa América

text: Originally, it was to be hosted by Brazil, as suggested by the Brazilian Football Confederation (CBF) in February 2011 due to CONMEBOL's rotation policy of tournaments being held in alphabetical order. However, due to the organization of the 2013 FIFA Confederations Cup, 2014 FIFA World Cup and the 2016 Summer Olympics in that country, Brazil decided against also hosting the Copa América. CONMEBOL's president Nicolas Leoz had mentioned the possibility of the tournament being organized in Mexico (despite this country not being a member of CONMEBOL) as part of the federation's centenary celebrations. Brazil and Chile's Football Federations discussed the idea of swapping around the order of being hosts of the 2015 and 2019 tournaments. The swap was made official in May 2012.


title: 2015 Copa América

text: There were nine different stadiums in eight cities used for the tournament. Most stadiums were renovated or rebuilt for the contest.


title: 2015 Copa América

text: Mexico and Japan were initially invited to join the 10 CONMEBOL nations in the tournament. Japan declined the invitation, and China was invited instead, but later withdrew due to the Asian sector of qualification for the 2018 World Cup being held at the same time. In May 2014, it was announced that the Jamaica Football Federation had accepted an invitation to participate, thus making Jamaica the first Caribbean nation to compete in Copa America.


title: 2015 Copa América

text: The draw of the tournament was originally to be held on 27 October 2014 in Viña del Mar, but was postponed to 24 November. The 12 teams were drawn into three groups of four.


title: 2015 Copa América

text: CONMEBOL announced the composition of the four pots on 10 November 2014. Pot 1 contained the hosts Chile (which has been automatically assigned to position A1), together with Argentina and Brazil. The remaining nine teams were allocated to the other three pots according to their FIFA World Rankings as of 23 October 2014 (shown in brackets), even though Colombia was rated higher than Brazil. On 23 November 2014, it was announced by CONMEBOL that Argentina and Brazil had been assigned to positions B1 and C1, respectively.


title: 2015 Copa América

text: Each country had a final squad of 23 players (three of whom had to be goalkeepers) which had to be submitted before the deadline of 1 June 2015.


title: 2015 Copa América

text: The 2015 UEFA Champions League Final date of 6 June caused problems for South American players for Barcelona and Juventus. FIFA international rules require clubs to release players 14 days prior to the start of an international tournament, but the players featured in the final, leaving them at most five days to acclimate. For example, Arturo Vidal arrived two days before Chile's first match against Ecuador, and played with little training with his national team.


title: 2015 Copa América

text: Mexico manager Miguel Herrera decided to prioritize the upcoming 2015 CONCACAF Gold Cup, saying, "We have to win at all costs in order to face the United States in the playoffs that guarantee a spot in the 2017 Confederations Cup." The Mexican squad was a team composed mostly from the local league with little international experience.


title: 2015 Copa América

text: Uruguayan forward Luis Suárez was suspended for the whole tournament, as he served a nine-match ban in international football for biting Italian defender Giorgio Chiellini during Uruguay's final group stage match against Italy in the 2014 FIFA World Cup.


title: 2015 Copa América

text: The first round, or group stage, saw the twelve teams divided into three groups of four teams. Each group was a round-robin of six games, where each team played one match against each of the other teams in the same group. Teams were awarded three points for a win, one point for a draw and none for a defeat. The teams finishing first, second and two best-placed third teams in each group qualified for the quarter-finals.


title: 2015 Copa América

text: Chile's Eduardo Vargas and Peru's Paolo Guerrero scored the most goals, with 4 each. In total, 59 goals were scored by 39 different players, with two of them credited as own goals.


title: 2015 Copa América

text: On 2 April 2014, the official logo was unveiled, along with the slogan "El Corazón del Fútbol" ("The Heart of Football").


title: 2015 Copa América

text: On 16 November 2014, the official match ball (OMB) was unveiled at the Estadio Nacional. The name of the ball is Nike Cachaña, which is a Chilean slang term for a successful feint or dribble. During its launch, the Chilean international Arturo Vidal was present. The ball is mainly designed with white as main appearance featured with blue and red applications, representing host nation Chile. The colors of Chilean flag make a statement in the design of this ball: the red representing the people, the blue symbolizing the Chilean sky, and the white for the Andes that so strongly define the geography of this country.


title: 2015 Copa América

text: The official mascot of the tournament, a young culpeo fox, was unveiled on 17 November 2014. The name of the mascot, "Zincha" (from "Zorro" (fox) and "hINCHA" (fan)), was chosen by the public over two other options, "Andi" and "Kul".


title: 2015 Copa América

text: "Al Sur del Mundo" by Chilean group Noche de Brujas served as the official song of the tournament. It was performed during the opening ceremony of the competition on 11 June. It features the different cultures of the twelve competing nations.


title: 2015 Copa América

text: The day after Chile's 3–3 draw against Mexico in their second group match, Jorge Sampaoli gave the players a day off from training. They had to return to the training ground by 9pm, but Arturo Vidal did not arrive. He had been involved in a traffic accident on his way back to the ground, and arrested for driving under the influence. He spent the night in jail, and appeared in court the morning after. His driving license was revoked, and he was sentenced to pay for the damage done. Although there was speculation that he would be dropped, Sampaoli opted to keep him on the team.


title: 2015 Copa América

text: An on-pitch brawl broke out following Colombia's 1–0 win over Brazil in their second group match; Brazilian captain Neymar deliberately kicked the ball at opponent Pablo Armero and attempted to headbutt Colombian matchwinner Jeison Murillo, earning a red card. As a result, Colombian forward Carlos Bacca retaliated by pushing Neymar over, and was himself sent off. CONMEBOL fined Neymar $10,000 and suspended him for four matches, ruling him out for the remainder of the tournament, while Bacca was suspended for two matches.


title: 2015 Copa América

text: In Chile's quarter-final victory over Uruguay, full-back Gonzalo Jara poked Uruguayan forward Edinson Cavani in the anus, and then fell when Cavani slapped him in retaliation. Both Cavani and Jara received a yellow card for the incident, which resulted in Cavani being sent off because he had previously received another yellow card for insulting one of the referees' assistants. Jara was later suspended for two games, which made him miss the rest of the tournament. His club, Mainz 05 of Germany, criticized Jara for the incident and stated that he would be sold. However he would remain with the club until 16 January 2016 when he agreed to terminate his contract with them.


title: Perturbation theory (quantum mechanics)

text: In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates) can be expressed as "corrections" to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. In effect, it is describing a complicated unsolved system using a simple, solvable system.


title: Perturbation theory (quantum mechanics)

text: Perturbation theory is an important tool for describing real quantum systems, as it turns out to be very difficult to find exact solutions to the Schrödinger equation for Hamiltonians of even moderate complexity. The Hamiltonians to which we know exact solutions, such as the hydrogen atom, the quantum harmonic oscillator and the particle in a box, are too idealized to adequately describe most systems. Using perturbation theory, we can use the known solutions of these simple Hamiltonians to generate solutions for a range of more complicated systems.


title: Perturbation theory (quantum mechanics)

text: Perturbation theory is applicable if the problem at hand cannot be solved exactly, but can be formulated by adding a "small" term to the mathematical description of the exactly solvable problem.


title: Perturbation theory (quantum mechanics)

text: For example, by adding a perturbative electric potential to the quantum mechanical model of the hydrogen atom, tiny shifts in the spectral lines of hydrogen caused by the presence of an electric field (the Stark effect) can be calculated. This is only approximate because the sum of a Coulomb potential with a linear potential is unstable (has no true bound states) although the tunneling time (decay rate) is very long. This instability shows up as a broadening of the energy spectrum lines, which perturbation theory fails to reproduce entirely.


title: Perturbation theory (quantum mechanics)

text: The expressions produced by perturbation theory are not exact, but they can lead to accurate results as long as the expansion parameter, say , is very small. Typically, the results are expressed in terms of finite power series in that seem to converge to the exact values when summed to higher order. After a certain order however, the results become increasingly worse since the series are usually divergent (being asymptotic series). There exist ways to convert them into convergent series, which can be evaluated for large-expansion parameters, most efficiently by the variational method. Even convergent perturbations can converge to the wrong answer and divergent perturbations expansions can sometimes give good results at lower order.


title: Perturbation theory (quantum mechanics)

text: In the theory of quantum electrodynamics (QED), in which the electron–photon interaction is treated perturbatively, the calculation of the electron's magnetic moment has been found to agree with experiment to eleven decimal places. In QED and other quantum field theories, special calculation techniques known as Feynman diagrams are used to systematically sum the power series terms.


title: Perturbation theory (quantum mechanics)

text: Under some circumstances, perturbation theory is an invalid approach to take. This happens when the system we wish to describe cannot be described by a small perturbation imposed on some simple system. In quantum chromodynamics, for instance, the interaction of quarks with the gluon field cannot be treated perturbatively at low energies because the coupling constant (the expansion parameter) becomes too large, violating the requirement that corrections must be small.


title: Perturbation theory (quantum mechanics)

text: Perturbation theory also fails to describe states that are not generated adiabatically from the "free model", including bound states and various collective phenomena such as solitons. Imagine, for example, that we have a system of free (i.e. non-interacting) particles, to which an attractive interaction is introduced. Depending on the form of the interaction, this may create an entirely new set of eigenstates corresponding to groups of particles bound to one another. An example of this phenomenon may be found in conventional superconductivity, in which the phonon-mediated attraction between conduction electrons leads to the formation of correlated electron pairs known as Cooper pairs. When faced with such systems, one usually turns to other approximation schemes, such as the variational method and the WKB approximation. This is because there is no analogue of a bound particle in the unperturbed model and the energy of a soliton typically goes as the "inverse" of the expansion parameter. However, if we "integrate" over the solitonic phenomena, the nonperturbative corrections in this case will be tiny; of the order of or in the perturbation parameter . Perturbation theory can only detect solutions "close" to the unperturbed solution, even if there are other solutions for which the perturbative expansion is not valid.


title: Perturbation theory (quantum mechanics)

text: The problem of non-perturbative systems has been somewhat alleviated by the advent of modern computers. It has become practical to obtain numerical non-perturbative solutions for certain problems, using methods such as density functional theory. These advances have been of particular benefit to the field of quantum chemistry. Computers have also been used to carry out perturbation theory calculations to extraordinarily high levels of precision, which has proven important in particle physics for generating theoretical results that can be compared with experiment.


title: Perturbation theory (quantum mechanics)

text: Time-independent perturbation theory is one of two categories of perturbation theory, the other being time-dependent perturbation (see next section). In time-independent perturbation theory, the perturbation Hamiltonian is static (i.e., possesses no time dependence). Time-independent perturbation theory was presented by Erwin Schrödinger in a 1926 paper, shortly after he produced his theories in wave mechanics. In this paper Schrödinger referred to earlier work of Lord Rayleigh, who investigated harmonic vibrations of a string perturbed by small inhomogeneities. This is why this perturbation theory is often referred to as Rayleigh–Schrödinger perturbation theory.


title: Perturbation theory (quantum mechanics)

text: The process begins with an unperturbed Hamiltonian , which is assumed to have no time dependence. It has known energy levels and eigenstates, arising from the time-independent Schrödinger equation:


title: Perturbation theory (quantum mechanics)

text: For simplicity, it is assumed that the energies are discrete. The superscripts denote that these quantities are associated with the unperturbed system. Note the use of bra–ket notation.


title: Perturbation theory (quantum mechanics)

text: A perturbation is then introduced to the Hamiltonian. Let be a Hamiltonian representing a weak physical disturbance, such as a potential energy produced by an external field. Thus, is formally a Hermitian operator. Let be a dimensionless parameter that can take on values ranging continuously from 0 (no perturbation) to 1 (the full perturbation). The perturbed Hamiltonian is:


title: Perturbation theory (quantum mechanics)

text: The energy levels and eigenstates of the perturbed Hamiltonian are again given by the time-independent Schrödinger equation,


title: Perturbation theory (quantum mechanics)

text: The objective is to express and formula_4 in terms of the energy levels and eigenstates of the old Hamiltonian. If the perturbation is sufficiently weak, they can be written as a (Maclaurin) power series in ,


title: Perturbation theory (quantum mechanics)

text: When , these reduce to the unperturbed values, which are the first term in each series. Since the perturbation is weak, the energy levels and eigenstates should not deviate too much from their unperturbed values, and the terms should rapidly become smaller as the order is increased.


title: Perturbation theory (quantum mechanics)

text: Expanding this equation and comparing coefficients of each power of results in an infinite series of simultaneous equations. The zeroth-order equation is simply the Schrödinger equation for the unperturbed system,


title: Perturbation theory (quantum mechanics)

text: Operating through by formula_9, the first term on the left-hand side cancels the first term on the right-hand side. (Recall, the unperturbed Hamiltonian is Hermitian). This leads to the first-order energy shift,


title: Perturbation theory (quantum mechanics)

text: This is simply the expectation value of the perturbation Hamiltonian while the system is in the unperturbed eigenstate.


title: Perturbation theory (quantum mechanics)

text: This result can be interpreted in the following way: supposing that the perturbation is applied, but the system is kept in the quantum state formula_11, which is a valid quantum state though no longer an energy eigenstate. The perturbation causes the average energy of this state to increase by formula_12. However, the true energy shift is slightly different, because the perturbed eigenstate is not exactly the same as "formula_11". These further shifts are given by the second and higher order corrections to the energy.


title: Perturbation theory (quantum mechanics)

text: Before corrections to the energy eigenstate are computed, the issue of normalization must be addressed. Supposing that


title: Perturbation theory (quantum mechanics)

text: Since the overall phase is not determined in quantum mechanics, without loss of generality, in time-independent theory it can be assumed that formula_19 is purely real. Therefore,


title: Perturbation theory (quantum mechanics)

text: To obtain the first-order correction to the energy eigenstate, the expression for the first-order energy correction is inserted back into the result shown above, equating the first-order coefficients of . Then by using the resolution of the identity:


title: Perturbation theory (quantum mechanics)

text: Supposing that the zeroth-order energy level is not degenerate, i.e. that there is no eigenstate of in the orthogonal complement of formula_24 with the energy formula_27. After renaming the summation dummy index above as formula_28, any formula_29 can be chosen and multiplying the first-order equation through by formula_30 gives


title: Perturbation theory (quantum mechanics)

text: The first-order change in the -th energy eigenket has a contribution from each of the energy eigenstates . Each term is proportional to the matrix element formula_35, which is a measure of how much the perturbation mixes eigenstate with eigenstate ; it is also inversely proportional to the energy difference between eigenstates and , which means that the perturbation deforms the eigenstate to a greater extent if there are more eigenstates at nearby energies. The expression is singular if any of these states have the same energy as state , which is why it was assumed that there is no degeneracy. The above formula for the perturbed eigenstates also implies that the perturbation theory can be legitimately used only when the absolute magnitude of the matrix elements of the perturbation is small compared with the corresponding differences in the unperturbed energy levels, i.e., formula_36


title: Perturbation theory (quantum mechanics)

text: We can find the higher-order deviations by a similar procedure, though the calculations become quite tedious with our current formulation. Our normalization prescription gives that


title: Perturbation theory (quantum mechanics)

text: If an intermediate normalization is taken (it means, if we require that formula_40), we obtain the same expression for the second-order correction to the wave function, except for the last term.


title: Perturbation theory (quantum mechanics)

text: E_n^{(3)} &= \frac{V_{nk_3}V_{k_3k_2}V_{k_2n}}{E_{nk_2}E_{nk_3}}-V_{nn}\frac{|V_{nk_3}|^2}{E_{nk_3}^2} \\


Perturbation theory (quantum mechanics)


title: Perturbation theory (quantum mechanics)

text: It is possible to relate the "k"-th order correction to the energy "E" to the "k"-point connected correlation function of the perturbation "V" in the state formula_24. For formula_44, one has to consider the inverse Laplace transform formula_45 of the two-point correlator:


title: Perturbation theory (quantum mechanics)

text: where formula_47 is the perturbing operator "V" in the interaction picture, evolving in Euclidean time. Then


title: Perturbation theory (quantum mechanics)

text: Similar formulas exist to all orders in perturbation theory, allowing one to express formula_49 in terms of the inverse Laplace transform formula_50 of the connected correlation function


title: Perturbation theory (quantum mechanics)

text: Suppose that two or more energy eigenstates of the unperturbed Hamiltonian are degenerate. The first-order energy shift is not well defined, since there is no unique way to choose a basis of eigenstates for the unperturbed system. The various eigenstates for a given energy will perturb with different energies, or may well possess no continuous family of perturbations at all.


title: Perturbation theory (quantum mechanics)

text: Let denote the subspace spanned by these degenerate eigenstates. No matter how small the perturbation is, in the degenerate subspace the energy differences between the eigenstates of are non-zero, so complete mixing of at least some of these states is assured. Typically, the eigenvalues will split, and the eigenspaces will become simple (one-dimensional), or at least of smaller dimension than "D".


title: Perturbation theory (quantum mechanics)

text: The successful perturbations will not be "small" relative to a poorly chosen basis of "D". Instead, we consider the perturbation "small" if the new eigenstate is close to the subspace . The new Hamiltonian must be diagonalized in , or a slight variation of "D", so to speak. These perturbed eigenstates in are now the basis for the perturbation expansion,


title: Perturbation theory (quantum mechanics)

text: For the first-order perturbation, we need solve the perturbed Hamiltonian restricted to the degenerate subspace ,


title: Perturbation theory (quantum mechanics)

text: simultaneously for all the degenerate eigenstates, where formula_57 are first-order corrections to the degenerate energy levels, and "small" is a vector of formula_58 orthogonal to "D". This amounts to diagonalizing the matrix


title: Perturbation theory (quantum mechanics)

text: This procedure is approximate, since we neglected states outside the subspace ("small"). The splitting of degenerate energies formula_57 is generally observed. Although the splitting may be small, formula_58, compared to the range of energies found in the system, it is crucial in understanding certain details, such as spectral lines in Electron Spin Resonance experiments.


title: Perturbation theory (quantum mechanics)

text: Higher-order corrections due to other eigenstates outside can be found in the same way as for the non-degenerate case,


title: Perturbation theory (quantum mechanics)

text: The operator on the left-hand side is not singular when applied to eigenstates outside , so we can write


title: Perturbation theory (quantum mechanics)

text: Near-degenerate states should also be treated similarly, when the original Hamiltonian splits aren't larger than the perturbation in the near-degenerate subspace. An application is found in the nearly free electron model, where near-degeneracy, treated properly, gives rise to an energy gap even for small perturbations. Other eigenstates will only shift the absolute energy of all near-degenerate states simultaneously.


title: Perturbation theory (quantum mechanics)

text: Let us consider degenerate energy eigenstates and a perturbation that completely lifts the degeneracy to first order of correction.


title: Perturbation theory (quantum mechanics)

text: where formula_66 is the unperturbed Hamiltonian, formula_67 is the perturbation operator, and formula_68 is the parameter of the perturbation.


title: Perturbation theory (quantum mechanics)

text: Let us focus on the degeneracy of the formula_69-th unperturbed energy formula_27. We will denote the unperturbed states in this degenerate subspace as formula_71 and the other unperturbed states as formula_72, where formula_73 is the index of the unperturbed state in the degenerate subspace and formula_74 represents all other energy eigenstates with energies different from formula_27. The eventual degeneracy among the other states with formula_76 does not change our arguments. All states formula_71 with various values of formula_73 share the same energy formula_27 when there is no perturbation, i.e., when formula_80. The energies formula_81 of the other states formula_72 with formula_74 are all different from formula_27, but not necessarily unique, i.e. not necessarily always different among themselves.


title: Perturbation theory (quantum mechanics)

text: By formula_85 and formula_86, we denote the matrix elements of the perturbation operator formula_67 in the basis of the unperturbed eigenstates. We assume that the basis vectors formula_71 in the degenerate subspace are chosen such that the matrix elements formula_89 are diagonal. Assuming also that the degeneracy is completely lifted to the first order, i.e. that formula_90 if formula_91, we have the following formulae for the energy correction to the second order in formula_92


title: Perturbation theory (quantum mechanics)

text: The generalization of time-independent perturbation theory to the case where there are multiple small parameters formula_97 in place of λ can be formulated more systematically using the language of differential geometry, which basically defines the derivatives of the quantum states and calculates the perturbative corrections by taking derivatives iteratively at the unperturbed point.


title: Perturbation theory (quantum mechanics)

text: From the differential geometric point of view, a parameterized Hamiltonian is considered as a function defined on the parameter manifold that maps each particular set of parameters formula_98 to an Hermitian operator that acts on the Hilbert space. The parameters here can be external field, interaction strength, or driving parameters in the quantum phase transition. Let and formula_99 be the -th eigenenergy and eigenstate of respectively. In the language of differential geometry, the states formula_99 form a vector bundle over the parameter manifold, on which derivatives of these states can be defined. The perturbation theory is to answer the following question: given formula_101 and formula_102 at an unperturbed reference point formula_103, how to estimate the and formula_99 at close to that reference point.


title: Perturbation theory (quantum mechanics)

text: Without loss of generality, the coordinate system can be shifted, such that the reference point formula_105 is set to be the origin. The following linearly parameterized Hamiltonian is frequently used


title: Perturbation theory (quantum mechanics)

text: If the parameters are considered as generalized coordinates, then should be identified as the generalized force operators related to those coordinates. Different indices label the different forces along different directions in the parameter manifold. For example, if denotes the external magnetic field in the -direction, then should be the magnetization in the same direction.


title: Perturbation theory (quantum mechanics)

text: The validity of perturbation theory lies on the adiabatic assumption, which assumes the eigenenergies and eigenstates of the Hamiltonian are smooth functions of parameters such that their values in the vicinity region can be calculated in power series (like Taylor expansion) of the parameters:


title: Perturbation theory (quantum mechanics)

text: Here denotes the derivative with respect to . When applying to the state formula_108, it should be understood as the covariant derivative if the vector bundle is equipped with non-vanishing connection. All the terms on the right-hand-side of the series are evaluated at , e.g. and formula_109. This convention will be adopted throughout this subsection, that all functions without the parameter dependence explicitly stated are assumed to be evaluated at the origin. The power series may converge slowly or even not converge when the energy levels are close to each other. The adiabatic assumption breaks down when there is energy level degeneracy, and hence the perturbation theory is not applicable in that case.


title: Perturbation theory (quantum mechanics)

text: The above power series expansion can be readily evaluated if there is a systematic approach to calculate the derivates to any order. Using the chain rule, the derivatives can be broken down to the single derivative on either the energy or the state. The Hellmann–Feynman theorems are used to calculate these single derivatives. The first Hellmann–Feynman theorem gives the derivative of the energy,


title: Perturbation theory (quantum mechanics)

text: The second Hellmann–Feynman theorem gives the derivative of the state (resolved by the complete basis with m ≠ n),


title: Perturbation theory (quantum mechanics)

text: The theorems can be simply derived by applying the differential operator to both sides of the Schrödinger equation formula_112 which reads


title: Perturbation theory (quantum mechanics)

text: Then overlap with the state formula_114 from left and make use of the Schrödinger equation formula_115 again,


title: Perturbation theory (quantum mechanics)

text: Given that the eigenstates of the Hamiltonian always form an orthonormal basis formula_117, the cases of and can be discussed separately. The first case will lead to the first theorem and the second case to the second theorem, which can be shown immediately by rearranging the terms. With the differential rules given by the Hellmann–Feynman theorems, the perturbative correction to the energies and states can be calculated systematically.


title: Perturbation theory (quantum mechanics)

text: The first order derivative is given by the first Hellmann–Feynman theorem directly. To obtain the second order derivative , simply applying the differential operator to the result of the first order derivative formula_120, which reads


title: Perturbation theory (quantum mechanics)

text: Note that for linearly parameterized Hamiltonian, there is no second derivative on the operator level. Resolve the derivative of state by inserting the complete set of basis,


title: Perturbation theory (quantum mechanics)

text: then all parts can be calculated using the Hellmann–Feynman theorems. In terms of Lie derivatives, formula_123 according to the definition of the connection for the vector bundle. Therefore, the case can be excluded from the summation, which avoids the singularity of the energy denominator. The same procedure can be carried on for higher order derivatives, from which higher order corrections are obtained.


title: Perturbation theory (quantum mechanics)

text: The same computational scheme is applicable for the correction of states. The result to the second order is as follows


title: Perturbation theory (quantum mechanics)

text: Both energy derivatives and state derivatives will be involved in deduction. Whenever a state derivative is encountered, resolve it by inserting the complete set of basis, then the Hellmann-Feynman theorem is applicable. Because differentiation can be calculated systematically, the series expansion approach to the perturbative corrections can be coded on computers with symbolic processing software like Mathematica.


title: Perturbation theory (quantum mechanics)

text: Let be the Hamiltonian completely restricted either in the low-energy subspace formula_125 or in the high-energy subspace formula_126, such that there is no matrix element in connecting the low- and the high-energy subspaces, i.e. formula_127 if formula_128. Let be the coupling terms connecting the subspaces. Then when the high energy degrees of freedoms are integrated out, the effective Hamiltonian in the low energy subspace reads


title: Perturbation theory (quantum mechanics)

text: Here formula_130 are restricted in the low energy subspace. The above result can be derived by power series expansion of formula_131.


title: Perturbation theory (quantum mechanics)

text: In a formal way it is possible to define an effective Hamiltonian that gives exactly the low-lying energy states and wavefunctions. In practice, some kind of approximation (perturbation theory) is generally required.


title: Perturbation theory (quantum mechanics)

text: Time-dependent perturbation theory, developed by Paul Dirac, studies the effect of a time-dependent perturbation applied to a time-independent Hamiltonian .


title: Perturbation theory (quantum mechanics)

text: Since the perturbed Hamiltonian is time-dependent, so are its energy levels and eigenstates. Thus, the goals of time-dependent perturbation theory are slightly different from time-independent perturbation theory. One is interested in the following quantities:


title: Perturbation theory (quantum mechanics)

text: The first quantity is important because it gives rise to the classical result of an measurement performed on a macroscopic number of copies of the perturbed system. For example, we could take to be the displacement in the -direction of the electron in a hydrogen atom, in which case the expected value, when multiplied by an appropriate coefficient, gives the time-dependent dielectric polarization of a hydrogen gas. With an appropriate choice of perturbation (i.e. an oscillating electric potential), this allows one to calculate the AC permittivity of the gas.


title: Perturbation theory (quantum mechanics)

text: The second quantity looks at the time-dependent probability of occupation for each eigenstate. This is particularly useful in laser physics, where one is interested in the populations of different atomic states in a gas when a time-dependent electric field is applied. These probabilities are also useful for calculating the "quantum broadening" of spectral lines (see line broadening) and particle decay in particle physics and nuclear physics.


title: Perturbation theory (quantum mechanics)

text: We will briefly examine the method behind Dirac's formulation of time-dependent perturbation theory. Choose an energy basis formula_132 for the unperturbed system. (We drop the (0) superscripts for the eigenstates, because it is not useful to speak of energy levels and eigenstates for the perturbed system.)


title: Perturbation theory (quantum mechanics)

text: If the unperturbed system is an eigenstate (of the Hamiltonian) formula_133 at time = 0, its state at subsequent times varies only by a phase (in the Schrödinger picture, where state vectors evolve in time and operators are constant),


title: Perturbation theory (quantum mechanics)

text: Let formula_136 denote the quantum state of the perturbed system at time . It obeys the time-dependent Schrödinger equation,


title: Perturbation theory (quantum mechanics)

text: The quantum state at each instant can be expressed as a linear combination of the complete eigenbasis of formula_4:


title: Perturbation theory (quantum mechanics)

text: where the s are to be determined complex functions of which we will refer to as amplitudes (strictly speaking, they are the amplitudes in the Dirac picture).


title: Perturbation theory (quantum mechanics)

text: We have explicitly extracted the exponential phase factors formula_139 on the right hand side. This is only a matter of convention, and may be done without loss of generality. The reason we go to this trouble is that when the system starts in the state formula_140 and no perturbation is present, the amplitudes have the convenient property that, for all ,


title: Perturbation theory (quantum mechanics)

text: Plugging into the Schrödinger equation and using the fact that ∂/∂"t" acts by a product rule, one obtains


title: Perturbation theory (quantum mechanics)

text: By resolving the identity in front of and multiplying through by the bra formula_143 on the left, this can be reduced to a set of coupled differential equations for the amplitudes,


title: Perturbation theory (quantum mechanics)

text: where we have used equation () to evaluate the sum on in the second term, then used the fact that formula_145.


title: Perturbation theory (quantum mechanics)

text: The matrix elements of play a similar role as in time-independent perturbation theory, being proportional to the rate at which amplitudes are shifted between states. Note, however, that the direction of the shift is modified by the exponential phase factor. Over times much longer than the energy difference , the phase winds around 0 several times. If the time-dependence of is sufficiently slow, this may cause the state amplitudes to oscillate. ( E.g., such oscillations are useful for managing radiative transitions in a laser.)


title: Perturbation theory (quantum mechanics)

text: Up to this point, we have made no approximations, so this set of differential equations is exact. By supplying appropriate initial values , we could in principle find an exact (i.e., non-perturbative) solution. This is easily done when there are only two energy levels ( = 1, 2), and this solution is useful for modelling systems like the ammonia molecule.


title: Perturbation theory (quantum mechanics)

text: However, exact solutions are difficult to find when there are many energy levels, and one instead looks for perturbative solutions. These may be obtained by expressing the equations in an integral form,


title: Perturbation theory (quantum mechanics)

text: To the same approximation, the summation in the above expression can be removed since in the unperturbed state formula_149 so that we have


title: Perturbation theory (quantum mechanics)

text: Several further results follow from this, such as Fermi's golden rule, which relates the rate of transitions between quantum states to the density of states at particular energies; or the Dyson series, obtained by applying the iterative method to the time evolution operator, which is one of the starting points for the method of Feynman diagrams.


title: Perturbation theory (quantum mechanics)

text: Time-dependent perturbations can be reorganized through the technique of the Dyson series. The Schrödinger equation


title: Perturbation theory (quantum mechanics)

text: Note that in the second term, the 1/2! factor exactly cancels the double contribution due to the time-ordering operator, etc.


title: Perturbation theory (quantum mechanics)

text: Using the solution of the unperturbed problem formula_160 and formula_161 (for the sake of simplicity assume a pure discrete spectrum), yields, to first order,


title: Perturbation theory (quantum mechanics)

text: Thus, the system, initially in the unperturbed state formula_163, by dint of the perturbation can go into the state formula_164. The corresponding transition probability amplitude to first order is


title: Perturbation theory (quantum mechanics)

text: as detailed in the previous section——while the corresponding transition probability to a continuum is furnished by Fermi's golden rule.


title: Perturbation theory (quantum mechanics)

text: As an aside, note that time-independent perturbation theory is also organized inside this time-dependent perturbation theory Dyson series. To see this, write the unitary evolution operator, obtained from the above Dyson series, as


title: Perturbation theory (quantum mechanics)

text: It is evident that, at second order, one must sum on all the intermediate states. Assume formula_170 and the asymptotic limit of larger times. This means that, at each contribution of the perturbation series, one has to add a multiplicative factor formula_171 in the integrands for arbitrarily small. Thus the limit gives back the final state of the system by eliminating all oscillating terms, but keeping the secular ones. The integrals are thus computable, and, separating the diagonal terms from the others yields


title: Perturbation theory (quantum mechanics)

text: where the time secular series yields the eigenvalues of the perturbed problem specified above, recursively; whereas the remaining time-constant part yields the corrections to the stationary eigenfunctions also given above (formula_173.)


title: Perturbation theory (quantum mechanics)

text: The unitary evolution operator is applicable to arbitrary eigenstates of the unperturbed problem and, in this case, yields a secular series that holds at small times.


title: Perturbation theory (quantum mechanics)

text: In a similar way as for small perturbations, it is possible to develop a strong perturbation theory. Consider as usual the Schrödinger equation


title: Perturbation theory (quantum mechanics)

text: and we consider the question if a dual Dyson series exists that applies in the limit of a perturbation increasingly large. This question can be answered in an affirmative way and the series is the well-known adiabatic series. This approach is quite general and can be shown in the following way. Consider the perturbation problem


title: Perturbation theory (quantum mechanics)

text: but a direct substitution into the above equation fails to produce useful results. This situation can be adjusted making a rescaling of the time variable as formula_177 producing the following meaningful equations


title: Perturbation theory (quantum mechanics)

text: that can be solved once we know the solution of the leading order equation. But we know that in this case we can use the adiabatic approximation. When formula_181 does not depend on time one gets the Wigner-Kirkwood series that is often used in statistical mechanics. Indeed, in this case we introduce the unitary transformation


title: Perturbation theory (quantum mechanics)

text: that defines a free picture as we are trying to eliminate the interaction term. Now, in dual way with respect to the small perturbations, we have to solve the Schrödinger equation


title: Perturbation theory (quantum mechanics)

text: and we see that the expansion parameter appears only into the exponential and so, the corresponding Dyson series, a dual Dyson series, is meaningful at large s and is


title: Perturbation theory (quantum mechanics)

text: After the rescaling in time formula_177 we can see that this is indeed a series in formula_186 justifying in this way the name of dual Dyson series. The reason is that we have obtained this series simply interchanging and and we can go from one to another applying this exchange. This is called duality principle in perturbation theory. The choice formula_187 yields, as already said, a Wigner-Kirkwood series that is a gradient expansion. The Wigner-Kirkwood series is a semiclassical series with eigenvalues given exactly as for WKB approximation.


title: Perturbation theory (quantum mechanics)

text: When the unperturbed state is a free motion of a particle with kinetic energy formula_203, the solution of the Schrödinger equation


title: Perturbation theory (quantum mechanics)

text: corresponds to plane waves with wavenumber formula_205. If there is a weak potential energy formula_206 present in the space, in the first approximation, the perturbed state is described by the equation


title: Perturbation theory (quantum mechanics)

text: where formula_211 and formula_212 is the Hankel function of the first kind. In the one-dimensional case, the solution is


title: Cerina Vincent

text: Cerina Vincent (born February 7, 1979) is an American actress. She had her breakthrough role starring as Maya in the television series "Power Rangers Lost Galaxy," followed by a part in the comedy film "Not Another Teen Movie", before going on to star in the horror film "Cabin Fever", which established her as a "scream queen" and led to further roles in horror movies. More recently, she appeared as Suzy Diaz in the Disney Channel series "Stuck in the Middle". She has also written three books with Jodi Lipper, wrote a regular column for "The Huffington Post", and co-hosts the podcast "Raising Amazing" with Dr. Joel Gator.


title: Cerina Vincent

text: Vincent was born on February 7, 1979, in Las Vegas, Nevada, to parents of Italian descent. Vincent loved to perform from an early age, encouraged by her mother, who was a dance instructor. She performed in a Christmas production at Diskin Elementary School, learning the lines for all the characters. She also appeared in productions at the Rainbow Company Youth Theater, which was sponsored by the Cultural Affairs division of Las Vegas. In 1996, at the age of sixteen, Vincent won the Miss Nevada Teen USA title and competed at Miss Teen USA. Though she made it to the top 15, she failed to place at the pageant (televised live), which was held in Las Cruces, New Mexico.


title: Cerina Vincent

text: Vincent graduated from Durango High School in 1997, and moved to Los Angeles, where she attended Marymount College on a scholarship. Between classes, she went on auditions and eventually landed several commercials and a role on "USA High" for the USA Network.


title: Cerina Vincent

text: In 1999, Vincent made her film debut in the direct-to-video thriller "Fear Runs Silent", starring Billy Dee Williams. Her first significant role as an actress, however, was as the Yellow Galaxy Ranger, Maya, in the television series "Power Rangers Lost Galaxy", the seventh season of the program's franchise that aired from February 6, 1999 to December 18, 1999. Vincent later recalled, "It was a great way to learn a lot and get a taste for this business on a small show like that, but for kids. It was cool to be a role model for kids."


title: Cerina Vincent

text: Following the success of "Power Rangers Lost Galaxy", Vincent appeared on MTV's "Undressed", "Son of the Beach", "Malcolm in the Middle", "Felicity" and "Ally McBeal". She also returned as Maya in the two-part "Power Rangers Lightspeed Rescue" episode, “Trakeena’s Revenge”, which saw the two teams of Rangers team up.


title: Cerina Vincent

text: In 2001, Vincent landed her first role in a major motion picture, spoof film "Not Another Teen Movie," playing foreign exchange student Areola. The part notably required her to be nude whenever she appeared throughout the movie: as a satirical take on the gratuitous nudity that was prevalent in teen films of the time, and specifically as a parody of Shannon Elizabeth's character Nadia in "American Pie", the character never wears clothes, even in public. Vincent is naked in all of her scenes, with her body serving as a sight gag of sorts: subtitles for her ever-changing accent are spaced to avoid obscuring her breasts, as she interacts with fully clothed characters, none of whom seem to notice her out-of-place nudity.


title: Cerina Vincent

text: Vincent described taking the part as a "huge decision" for her, having never previously done any nude scenes. She initially turned down the role several times, ultimately deciding to do it because she thought it was funny; however, she still had reservations about performing in the nude for the first time and so extensively. In a 2011 interview, Vincent explained:


title: Cerina Vincent

text: In 2003, Vincent starred in the R-rated horror film "Cabin Fever", which featured some of her most memorable film moments, including her "leg-shaving" scene and the "plane-crash" seduction and sex scene. The film included topless scenes and two sex scenes with two different characters. Fearing that she would be typecast into nude roles, Vincent was cautious about over-exposing herself in the film, which became a point of contention between her and director Eli Roth.


title: Cerina Vincent

text: Starting in 2004, Vincent appeared in a series of theatrical and television films, including "Murder-Set-Pieces" (2004) as the L.A. Girl, "Intermedio" (2005) as Gen, and "Conversations with Other Women" (2005) as Sarah the Dancer. In 2005, she appeared in her first starring role in the film "It Waits" (2005) as forest ranger Danielle "Danny" St. Claire. Vincent made several television appearances beginning in 2005, with appearances on "", "Palmetto Pointe" and "Sex, Love & Secrets". Since then, she has also worked on the series "Bones", "Two and a Half Men", "Gary Unmarried", "Zombie Family", "Mike & Molly", and "The Walking Dead". In 2006, she appeared in "The Surfer King" as Tiffany, "Seven Mummies" as Lacy, and the Sci-Fi Channel original movie "Sasquatch Mountain" as Erin Price, alongside Lance Henriksen. In 2007, she appeared in the television films "Manchild" and "Wifey", as well as "Return to House on Haunted Hill" as Michelle, and "Everybody Wants to Be Italian" as Marisa Costa. In 2008, she appeared in "Toxic" as Malvi, the independent film, "Just Add Water" as The Mrs., and in "Fashion Victim".


title: Cerina Vincent

text: Vincent returned to films in 2012, appearing in "Complacent" as Myah Sanderson and "Chasing Happiness" as Andrea, and playing the title role in "MoniKa", for which she was also the executive producer. In 2013, Vincent appeared in the Hallmark Channel original movie "The Thanksgiving House" in the role of Ashleigh, and produced and starred in the acclaimed horror short "Skypemare," which also starred Annika Marks and featured Ryan Dillon and Adam J. Yeend; the film screened at Telluride Horror Show and ScreamFest 2013 in Los Angeles. In 2017, Vincent had a small role in the indie movie "Broken Memories".


title: Cerina Vincent

text: From 2016 to 2018, Vincent played Suzy Diaz, mother to seven children, on the Disney Channel series "Stuck in the Middle". The series ran for three seasons.


title: Cerina Vincent

text: Vincent's most recent performances include the lead role of Jen in the 2018 feature film thriller "The Work Wife", a 2019 guest starring appearance on "", and a part in the 2020 Lifetime TV movie "My Daughter's Psycho Friend".


title: Cerina Vincent

text: In November 2018, Vincent announced her pregnancy with her first child, a boy with her long-time partner Mike Estes. Her son was born in February 2019.


title: Cerina Vincent

text: Vincent and her co-writer Jodi Lipper wrote a regular column for "HuffPost" from 2007 to 2016. The pair have also authored three books:


title: Solntsevskaya Bratva

text: The Solntsevskaya Organized Crime Group (), also known as the Solntsevskaya Bratva (), is a Russian crime syndicate group.


title: Solntsevskaya Bratva

text: Other simplified versions of the name are Solntsevskaya Brotherhood and Solntsevskaya gang. The group is not a common gang, but a well organized criminal organization.


title: Solntsevskaya Bratva

text: The Solntsevskaya gang was founded in the late 1980s by Sergei Mikhailov, a former waiter who had served a prison term for fraud. Based in the Solntsevo District of Moscow, the gang recruited local unemployed, aggressive young men as foot soldiers and also made use of thief in law Dzhemal Khachidze to enhance their reputation amongst established criminals. The Solntsevo District was also strategically located near the M3 highway leading to Ukraine, the MKAD, Moscow's ring road, as well as the Vnukovo International Airport. Controlling these transport hubs allowed the Solntsevo group to muscle in on the car import business. But by the early 1990s, the Solntsevo's dominance was challenged by the Chechen mafia. Together with the Orekhovskaya gang and other Slavic mobs, the Solntsevo made an alliance to drive the Chechens out. The gang war claimed many casualties, such as a gun battle at the Kazakhstan Cinema where six Chechens and four Russians were killed. After the Soviet Union collapsed, the gang utilized the chaos to empower themselves by establishing relationships with politicians. They were now able to influence the Russian state for their own benefit. They also bought several legitimate businesses to launder their money including banks, casinos, and even the Vnukovo airport.


title: Solntsevskaya Bratva

text: The gang was at one point linked to criminal mastermind Semion Mogilevich, through whom they laundered money. But a 1995 party at a Prague hotel, attended by Mikhailov as well as Uzbek drug trafficker Gafur Rakhimov, was raided by Czech police who received information that they were planning to kill Mogilevich there following a dispute. Mogilevich himself was nowhere to be found, having received advance information about both groups' intentions.


title: Solntsevskaya Bratva

text: By the end of the 1990s, the Solntsevskaya gang started moving into the banking sector, a move which enabled them to launder their money as well as get closer to the oligarchs.


title: Solntsevskaya Bratva

text: In the 1990s, the Solntsevskaya dispatched Vyacheslav Ivankov to Brighton Beach, New York City, and Mikhail Odenussa to Atlanta, Georgia, to take control of the Russian mob activities there. The FBI was alerted to Ivankov's presence, however, and after a long investigation he was arrested and convicted of extortion, becoming the first thief-in-law to be convicted in the United States. While Ivankov was not as successful, his counterpart Odenussa has been controlling Russian organized crime in Atlanta for over 20 years, while avoiding prosecution. Odenussa has had a firm grip on the city, with an army of killers to back him up. Although not as large as the drug cartels of Mexico that have sent men to try and set up shop in Atlanta, Odenussa and his cohorts have out-gunned the Mexican drug cartels and the African American gangs in Atlanta. The Solntsevskaya have also been active in Israel, primarily using it as a base for money laundering. But attempts to infiltrate Israeli politics were countered by vigilant law enforcement.


title: Solntsevskaya Bratva

text: "Doktor's Bratvavor" Is a subdivision of the Solntsevskaya Bratva, being independently operated and headed by the notorious "Doktor Spatz", after his refusal to submit to Odenussa's order, and an agreement was reached to form an alliance between the groups. Spatz singlehandedly controls a large portion of upstate New York, encompassing large cities such as Rochester and Syracuse, outnumbering the African American and Mexican street gangs of the area.


title: Solntsevskaya Bratva

text: The organization is also involved in the international cocaine trade, with its links to Colombian drug cartels brokered by the Cuntrera-Caruana Mafia clan.


title: Solntsevskaya Bratva

text: According to the US, as published during the 2010 Wikileaks scandal, the Solntsevo gang continues racketeering operations under the protection of the FSB, a Russian state security agency. In September 2017, Arnold Tamm was arrested in Marbella, Spain, during the Spanish operation "Oligarch" () under suspicion of tax evasion, money laundering, and involvement in the activities of the Solntsevskaya group.


title: Vincent Astor

text: William Vincent Astor (November 15, 1891 – February 3, 1959) was an American businessman, philanthropist, and member of the prominent Astor family.


title: Vincent Astor

text: Called Vincent, he was born in New York City on November 15, 1891. Astor was the elder child of John Jacob Astor IV, a wealthy businessman and inventor, and his first wife, Ava Lowle Willing, an heiress from Philadelphia.


title: Vincent Astor

text: He graduated in 1910 from St. George's School in Middletown, Rhode Island, and attended Harvard College from 1911 to 1912, leaving school without graduating. In 1912 Vincent Astor's father, John Jacob Astor IV died on the Titanic and left him the biggest fortune at that time and made Vincent Astor one of the richest people in the world.


title: Vincent Astor

text: Like his father, Astor belonged to the New York Society of Colonial Wars. He served as commodore of the New York Yacht Club from 1928 to 1930.


title: Vincent Astor

text: Astor was interested in trains. In the early 1930s, he established an estate in Bermuda which included a private narrow-gauge railway and union station with the Bermuda Railway. The estate is now divided among several private owners, none of whom are part of the Astor family. As recently as 1992, the remains of some of his rolling stock were visible.


title: Vincent Astor

text: Vincent Astor was, according to family biographer Derek Wilson, "a hitherto unknown phenomenon in America: an Astor with a highly developed social conscience." He was 20 when his father died in the sinking of the ocean liner "Titanic" and, having inherited a massive fortune, he dropped out of Harvard University. He set out to change the family's image from that of miserly, aloof slum landlords who enjoyed the good life at the expense of others.


title: Vincent Astor

text: Over time, he sold off the family's New York City slum housing and reinvested in reputable enterprises, while spending a great deal of time and energy helping others. He was responsible for the construction of a large housing complex in the Bronx that included sufficient land for a large children's playground, and in Harlem, he transformed a valuable piece of real estate into another playground for children.


title: Vincent Astor

text: Astor appeared at No. 12 on the first list of America's richest people, compiled by "Forbes" magazine. His net worth at the time was estimated at $75 million. Among his holdings was "Newsweek" magazine, and he was its chairman. The magazine had for a time its headquarters in the former Knickerbocker Hotel, which had been built by his father.


title: Vincent Astor

text: He also inherited Ferncliff, the Astor family's estate in Rhinebeck, New York, where his father had been born. However, Vincent Astor would be the last Astor family member to own the estate as well as the final Astor to occupy the "Ferncliff Casino", a Stanford White-designed 1904 Beaux-Arts style building, which was inspired by the Grand Trianon at Versailles.


title: Vincent Astor

text: On his death in 1959, Astor bequeathed a main house at Ferncliff to the Benedictine Hospital in Kingston, New York. His widow, Brooke, later donated the "Ferncliff Casino" to the Catholic Archdiocese of New York and sold off many parcels of the estate. In 1963, Homer Staley, a retired businessman in the area, asked Brooke Astor to preserve the remaining natural acreage of woodlands from development. She donated the woodlands to the Rotary Club of Rhinebeck, and the land became the Ferncliff Forest Game Refuge and Forest Preserve.


title: Vincent Astor

text: Upton Sinclair, author of The Jungle, wrote Astor an open letter, which he describes in The Brass Check and he also sent to over half a dozen newspapers, requesting that he support the Socialist cause and help the poor, at a time when Sinclair claims Astor was erecting a million dollar estate, without benefiting the rest of society; the only newspaper to publish his letter was a Socialist newspaper, the New York Call. Vincent Astor replied to this letter, and also sent a copy out to over half a dozen newspapers, and according to Sinclair, all of them published his reply in full, including The New York Call. Sinclair claimed this was what he considered a scientific demonstration of bias of the media in favor of the wealthy because they gave Astor complete coverage, often on the front page, and, except for The Call, they declined to publish his first letter, and only three of the traditional newspapers published a small portion of his reply to Astor's letter, without featuring it as prominently.


title: Vincent Astor

text: Astor married Helen Dinsmore Huntington on April 30, 1914. At the ceremony, he was stricken with the mumps, a disease that made him sterile; as for the bride, her friend Glenway Wescott, the novelist, admiringly described her in his unpublished diaries as "a grand, old-fashioned lesbian." The couple divorced in 1940. A year later, Helen became the second wife of Lytle Hull (1882–1958), a real-estate broker who was a friend and business associate of her former husband.


title: Vincent Astor

text: Shortly after his divorce, Astor married Mary Benedict Cushing, the eldest daughter of Dr. Harvey Williams Cushing and Katharine Stone Crowell. Mary's sisters were Betsey Maria Cushing and Barbara "Babe" Cushing. They divorced in September 1953, and the following month, Mary wed James Whitney Fosburgh, a painter who worked as an art lecturer at the Frick Museum.


title: Vincent Astor

text: On October 8, 1953, several weeks after divorcing his second wife, Astor married the once-divorced, once-widowed Roberta Brooke Russell. According to an often-told story in society circles, Astor agreed to divorce his second wife only after she had found him a replacement spouse. Her first suggestion was Janet Newbold Ryan Stewart Bush, the newly divorced wife of James Smith Bush II (brother of Prescott Bush), who turned Astor down with startling candor, saying, "I don't even like you." Astor proceeded to tell her that he was not well and, though only in his early 60s, he could not be expected to live for very long, whereupon she would inherit his millions. At that, Janet Bush reportedly replied, "What if you do live?" Mary Cushing then proposed Brooke. Together, Vincent and Brooke developed the Vincent Astor Foundation, a foundation that was designed to give back to New York City. Brooke died in 2007 at the age of 105.


title: Vincent Astor

text: Astor joined the Naval Reserve shortly after it was founded and was commissioned as an ensign on December 28, 1915. He was called to active duty as part of the New York Naval Militia in February 1917 by order of Governor Charles S. Whitman to help guard bridges and aqueducts against possible German sabotage. Astor was assigned to help guard the Brooklyn and Manhattan bridges.