title: Boeing X-20 Dyna-Soar

text: The original intention for Dyna-Soar, outlined in the Weapons System 464L proposal, called for a project combining aeronautical research with weapons system development. Many questioned whether the USAF should have a crewed space program, when that was the primary domain of NASA. It was frequently emphasized by the Air Force that, unlike the NASA programs, Dyna-Soar allowed for controlled re-entry, and this was where the main effort in the X-20 program was placed. On January 19, 1963, the Secretary of Defense, Robert McNamara, directed the U.S. Air Force to undertake a study to determine whether Gemini or Dyna-Soar was the more feasible approach to a space-based weapon system. In the middle of March 1963, after receiving the study, Secretary McNamara "stated that the Air Force had been placing too much emphasis on controlled re-entry when it did not have any real objectives for orbital flight". This was seen as a reversal of the Secretary's earlier position on the Dyna-Soar program. Dyna-Soar was also an expensive program that would not launch a crewed mission until the mid-1960s at the earliest. This high cost and questionable utility made it difficult for the U.S. Air Force to justify the program. Eventually, the X-20 Dyna-Soar program was canceled on December 10, 1963.


title: Boeing X-20 Dyna-Soar

text: On the day that X-20 was canceled, the U.S. Air Force announced another program, the Manned Orbiting Laboratory, a spin-off of Gemini. This program was also eventually canceled.


title: Boeing X-20 Dyna-Soar

text: Another black program, ISINGLASS, which was to be air-launched from a B-52 bomber, was evaluated and some engine work done, but was eventually cancelled as well.


title: Boeing X-20 Dyna-Soar

text: Despite cancellation of the X-20, the affiliated research on spaceplanes influenced the much larger Space Shuttle. The final design also used delta wings for controlled landings. The later, and much smaller Soviet BOR-4 was closer in design philosophy to the Dyna-Soar, while NASA's Martin X-23 PRIME and Martin Marietta X-24A/HL-10 research aircraft also explored aspects of sub-orbital and space flight. The ESA's proposed Hermes crewed space craft was superficially similar to but not derived from the X-20.


title: Hotep

text: Hotep (; also rendered "hetep") is an Egyptian word that roughly translates as "to be satisfied, at peace". The word also refers to an "offering" ritually presented to a deity or a dead person, hence "be pleased, be gracious, be at peace". It is rendered in hieroglyphs as an altar/offering table (Gardiner sign R4). The noun "ḥtp.w" means "peace, contentment". Davies (2018) interprets the concept of as "the result of action in accord with "maat" [the proper order of the universe]".


title: Hotep

text: Hotep as part of ancient Egyptian names, such as Hotepsekhemwy ( "the two powers are at peace"), the first ruler of Egypt's Second Dynasty.


title: PVT Chat

text: PVT Chat is a 2020 erotic drama film, written and directed by Ben Hozie. It stars Peter Vack as an online gambler who becomes obsessed with a cam girl played by Julia Fox. "PVT Chat" premiered at the Fantasia International Film Festival on August 21, 2020.


title: PVT Chat

text: Jack is an internet gambler who lives in New York and becomes obsessed with Scarlet, a cam girl from San Francisco. His obsession reaches a boiling point when fantasy materializes into reality after Jack spots Scarlet on a rainy street in Chinatown.


title: PVT Chat

text: The film was shot the last week of January through mid-February 2018 in New York City (Brooklyn, Queens, and Manhattan).


title: PVT Chat

text: The film had its world premiere at the 2020 Fantasia International Film Festival. Distribution rights for United Kingdom and Ireland were acquired by Vertigo Releasing in November 17, 2020. Dark Star Pictures released the film in available theaters on February 5, 2021, followed by a VOD and Digital HD release on February 9, 2021.


title: PVT Chat

text: The review aggregator Rotten Tomatoes gives the film a 63% approval rating based on 41 reviews, with an average rating of 6.10/10. The website's critics consensus reads: "Its intelligent and nuanced approach to potentially salacious material is refreshing, but "PVT Chat" struggles to use it in service of a meaningful story." According to Metacritic, which sampled nine critics and calculated a weighted average score of 61 out of 100, the film received "generally favorable reviews".


title: Sarah-Jane Potts

text: Sarah-Jane Potts (born 30 August 1976) is an English actress, best known for her roles as Saint (Sarah) in "Sugar Rush", Ellie, Abs' on/off girlfriend in "Casualty" and Jo Lipsett in "Waterloo Road". Potts is the sister of actor Andrew-Lee Potts. From 2011 to 2012, she appeared in "Holby City" as Senior Nurse Eddi McKee on AAU, playing a different character to the one she played in "Casualty". Potts left "Holby City" in the second episode of Series 15; her departure was kept a secret by the production team and was not reported at all by the media, resulting in a shock exit for her character.


title: Sarah-Jane Potts

text: Early in her career she noted that, "In the three years I have been acting I have spent most of the time looking dirty, scruffy, ill or tarty."


title: Sarah-Jane Potts

text: Potts attended Bradford's Scala Kids stage school with her brother Andrew. As a teenager she worked in a greasy spoon cafe in Bradford. She left school during her A-levels to star in "Meat". From 1999 to 2001, she dated Erik Palladino. They met at a film festival in Sweden during the summer of 1999 and at the end of the year she moved to Los Angeles to live with him. She met her former husband, Tony Denman, when filming "National Lampoon's Barely Legal" and they were married in June 2002. She has a son, named Buster Alan Denman, born 2004. She met her second husband, Joseph Millson, while working together on the medical drama "Holby City" and married him on 31 December 2013.


title: Washington Square Arch

text: The Washington Square Arch, officially the Washington Arch, is a marble memorial arch in Washington Square Park, in the Greenwich Village neighborhood of Lower Manhattan, New York City. Designed by architect Stanford White in 1891, it commemorates the centennial of George Washington's 1789 inauguration as President of the United States, and forms the southern terminus of Fifth Avenue.


title: Washington Square Arch

text: Washington Arch, constructed of white Tuckahoe marble, was conceived by Stanford White, who imitated a Roman triumphal arch, namely the Arch of Titus, iconic monuments which Roman emperors built throughout the empire to celebrate a victory or event. The monument's total height is 77 feet (23 m). The piers stand apart and the arch opening is high. The iconography of the Arch centers on images of war and peace. On the frieze are 13 large stars and 42 small stars, interspersed with capital "W"s. The spandrels contain figures of Victory.


title: Washington Square Arch

text: The north side of the eastern pier bears the sculpture "George Washington as Commander-in-Chief, Accompanied by Fame and Valor" (1914–1916) by Hermon A. MacNeil; the President is flanked by Fame (left) and Valor (right). The western pier has "George Washington as President, Accompanied by Wisdom and Justice" (1917–18) by Alexander Stirling Calder (father of Alexander Calder), with flanking Justice (right) and Wisdom (left) figures. In the latter sculpture, a hand holds a book bearing the Latin phrase "Exitus Acta Probat" ("the end justifies the deed"). These sculptures are commonly referred to as "Washington at War" and "Washington at Peace", respectively. These figures and most of the rest of the carving on the arch was performed by the Piccirilli Brothers.


title: Washington Square Arch

text: In 1889, a large plaster and wood memorial arch was erected over Fifth Avenue just north of Washington Square Park by local businessman and philanthropist William Rhinelander Stewart (1852–1929). Stewart lived at 17 Washington Square North, and his friends contributed $2,765 toward the work. The temporary arch was so popular that more money was raised and, three years later, the permanent stone arch, designed by architect Stanford White, was erected.


title: Washington Square Arch

text: During the excavations for the eastern pier, human remains, a coffin, and a gravestone dated 1803 were uncovered below ground level. The Arch was dedicated in 1895. In 1918, two statues of Washington were added to the north side.


title: Washington Square Arch

text: By the late 20th century, the Washington Arch had become extensively defaced with spray-painted graffiti. It was cleaned and restored in 2003-04.


title: Washington Square Arch

text: Upon the last stone is carved a huge "P" in honor of Ignacy Jan Paderewski, the famous Polish pianist and 3rd Prime Minister of Poland, who donated $4,500 collected from one of his concerts in New York.


title: Screw (TV series)

text: Screw is a British prison drama series starring Nina Sosanya and Jamie-Lee O'Donnell. The series was produced by STV Studios and first broadcast on Channel 4 on 6 January 2022. It has been renewed for a second series.


title: Screw (TV series)

text: The series follows two prison officers and their colleagues, working in C-Wing of men's prison, Long Marsh.


title: Screw (TV series)

text: The series was inspired by Williams' work with prisons. Kelvin Hall film studio, Glasgow and Peterhead Prison in Scotland were used as the filming location.


title: Screw (TV series)

text: Rebecca Nicholson for "The Guardian" gave it four stars and said: '("Screw") settles somewhere between soap and Sunday night blockbuster, and I mean that as a compliment. This is broad and warm and welcoming, with enough of a sharp side to make it worth sticking with.' "The Times" gave it four stars and praised the use of humour.


title: Skinny Love

text: "Skinny Love" is a song written by American musician and songwriter Justin Vernon. It was originally released by indie folk band Bon Iver, of which Vernon is a member, in 2007. A cover version by the British vocalist Birdy was released in 2011. Both versions charted internationally and have been featured in multiple television and film soundtracks. The song has since become a popular tune for various singing competition shows around the English-speaking world.


title: Skinny Love

text: "Skinny Love" was the first single released from Bon Iver's 2007 debut album, "For Emma, Forever Ago", in the United States. The song was released as a single in the United Kingdom on April 28, 2008. While "Skinny Love" has been considered a reference to singer Justin Vernon's relationship with former girlfriend Christy Smith, Vernon countered this as "not entirely accurate [...] it's about that time in a relationship that I was going through; you're in a relationship because you need help, but that's not necessarily why you should be in a relationship. And that's skinny."


title: Skinny Love

text: The song was used in the second episode of "Grey's Anatomy"s fifth season. The digital download track "Skinny Love" was selected to be iTunes (UK) single of the week and was available for free during that time, as well as being featured as the track of the day on National Public Radio. On October 6, 2008, "Skinny Love" was featured in the NBC series "Chuck" (season 2, episode 3). On December 11, 2008, Bon Iver performed "Skinny Love" on the "Late Show with David Letterman". On January 26, 2009, "Skinny Love" was announced at #21 by the Australian national radio station Triple J in the annual Hottest 100 countdown of the previous year's best songs. In July 2009, "Skinny Love" was announced at #92 in Triple J's Hottest 100 of All Time countdown. In June 2013, "Skinny Love" was announced at #16 in Triple J's Hottest 100 of the Last 20 Years countdown.


title: Skinny Love

text: British musician Birdy released a cover version of the song in 2011 as her debut single. The single has been B-listed on Xfm and is a particular favourite with listeners of Shak's overnight show. The song was also chosen as "Record of The Week" by UK radio DJ Fearne Cotton. This version was used in Season 2 Episode 21 of "The Vampire Diaries" and in Season 1 Episode 1 of "Prisoners' Wives".


title: Skinny Love

text: The song also skyrocketed in Australian popularity within the ARIA Charts' top ten, partly because of Bella Ferraro, an "X Factor" 2012 Top Four contestant who performed the song at the "X Factor" auditions aired in Australia in August 2012. The song reached number two on the ARIA Singles Chart in September, kept off the number-one spot by Guy Sebastian's song "Battle Scars" for three weeks. A similar event took place in New Zealand in May 2013 after "X Factor" winner Jackie Thomas performed the song at her audition. The song entered the top 40 for the first time and reached number two on the RIANZ chart following the broadcast, behind Robin Thicke's "Blurred Lines".


title: Skinny Love

text: In 2011, "Skinny Love" sold 259,000 copies in the UK, becoming the third biggest selling rock single of that year. As of August 2016, the song had sold 744,502 copies in the UK.


title: Skinny Love

text: There are three music videos for this single. The first music video for the song was uploaded to YouTube on April 1, 2011. It features Birdy playing the piano of walking in a dark house. The second music video was shot in one take and framed on Birdy's face. The camera changes focus as she sings. It was uploaded on October 14, 2011. The third music video was uploaded on January 15, 2014.


title: Friedman test

text: The Friedman test is a non-parametric statistical test developed by Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to detect differences in treatments across multiple test attempts. The procedure involves ranking each row (or "block") together, then considering the values of ranks by columns. Applicable to complete block designs, it is thus a special case of the Durbin test.


title: Friedman test

text: The Friedman test is used for one-way repeated measures analysis of variance by ranks. In its use of ranks it is similar to the Kruskal–Wallis one-way analysis of variance by ranks.


title: Friedman test

text: Post-hoc tests were proposed by Schaich and Hamerle (1984) as well as Conover (1971, 1980) in order to decide which groups are significantly different from each other, based upon the mean rank differences of the groups. These procedures are detailed in Bortz, Lienert and Boehnke (2000, p. 275). Eisinga, Heskes, Pelzer and Te Grotenhuis (2017) provide an exact test for pairwise comparison of Friedman rank sums, implemented in R. The Eisinga c.s. exact test offers a substantial improvement over available approximate tests, especially if the number of groups (formula_3) is large and the number of blocks (formula_2) is small.


title: Friedman test

text: Not all statistical packages support post-hoc analysis for Friedman's test, but user-contributed code exists that provides these facilities (for example in SPSS, and in R.). Also, there is a specialized package available in R containing numerous non-parametric methods for post-hoc analysis after Friedman.


title: Constantine VI

text: Constantine VI (, "Kōnstantinos"; 14 January 771 – before 805) was Byzantine emperor from 780 to 797. The only child of Emperor Leo IV, Constantine was named co-emperor with him at the age of five in 776 and succeeded him as sole Emperor in 780, aged nine. His mother Irene exercised control over him as regent until 790, assisted by her chief minister Staurakios. The regency ended when Constantine reached maturity, but Irene sought to remain an active participant in the government. After a brief interval of sole rule Constantine named his mother empress in 792, making her his official colleague.


title: Constantine VI

text: Constantine suffered military defeats and made controversial decisions, such as blinding his loyal general Alexios Mosele and illicitly marrying his mistress, Theodote. Taking advantage of her son's unpopularity, Irene had Constantine deposed, blinded and imprisoned in 797 and seized power for herself alone, becoming the first Empress regnant of the Empire. Constantine likely died shortly thereafter.


title: Constantine VI

text: Constantine VI was the final ruler to be universally recognized as Roman emperor, being recognized as such by both the Empire which he ruled in the east, the papacy and the Western European powers over which the pope held suzerainty. The Byzantines' ability to protect the Papacy had waned following the Arab Conquests, leading to the Papacy to increasingly seek protection from the Franks. This culminated in 800 when Pope Leo III, who owed his power and position to the Franks, crowned Charlemagne as 'Emperor of the Romans'. Based on the assertion that a woman could not be Empress in her own right, this laid the foundations of a new polity, independent of the East, that would evolve into the Holy Roman Empire.


title: Constantine VI

text: Constantine VI was the only child of Emperor Leo IV and Irene. Constantine was crowned co-emperor by his father in 776, and succeeded as sole emperor in 780, at the age of nine. Due to his minority, Irene and her chief minister Staurakios exercised the regency for him.


title: Constantine VI

text: In 787 Constantine had signed the decrees of the Second Council of Nicaea, but he appears to have had iconoclast sympathies. By then Constantine had turned 16 years old, but his mother did not relinquish executive authority to him.


title: Constantine VI

text: In 788, Irene herself broke off the engagement of Constantine with Rotrude, a daughter of Charlemagne. Turning against Charlemagne, the Eastern Romans now supported Lombard pretender Adalgis, who had been forced into exile after the Frankish invasion of Italy. Adalgis was given command of a Roman expeditionary corps, landing in Calabria towards the end of 788 but was defeated by the united armies of the Lombard dukes Hildeprand of Spoleto and Grimoald III of Benevento as well as Frankish troops under Winiges.


title: Constantine VI

text: After a conspiracy against Irene was suppressed in the spring of 790 she attempted to get official recognition as empress. This backfired and with military support Constantine finally came to actual power in 790, after the Armeniacs rebelled against Irene. Nevertheless, after campaigning unsuccessfully in the Balkans, Constantine restored his mother in 792 after just two years out of power and made her co-ruler.


title: Constantine VI

text: Once in control of the state, Constantine proved incapable of sound governance. His army was defeated by the Muslims, and Constantine himself suffered a humiliating defeat at the hands of Kardam of Bulgaria in the 792 Battle of Marcellae. A movement developed in favor of his uncle, the "Caesar" Nikephoros. Constantine had his uncle's eyes put out and the tongues of his father's four other half-brothers cut off. His former Armenian supporters revolted after he had blinded their general Alexios Mosele. He crushed this revolt with extreme cruelty in 793.


title: Constantine VI

text: He then divorced his wife Maria of Amnia, who had failed to provide him with a male heir, and married his mistress Theodote, an unpopular and canonically illegal act which sparked off the so-called "Moechian Controversy". Although the Patriarch Tarasios did not publicly speak against it, he did refuse to officiate the marriage. Popular disapproval was expressed by Theodote's uncle, Plato of Sakkoudion, who even broke communion with Tarasios for his passive stance. Plato's intransigence led to his own imprisonment, while his monastic supporters were persecuted and exiled to Thessalonica. The "Moechian Controversy" cost Constantine what popularity he had left, especially in the church establishment, which Irene took care to vocally support against her own son.


title: Constantine VI

text: On 19 August 797 Constantine was captured, blinded, and imprisoned by the supporters of his mother, who had organized a conspiracy, leaving Irene to be crowned as first Empress regnant of Constantinople. It is unknown when exactly Constantine died; it was certainly before 805, though he may have died of his wounds shortly after being blinded. He was buried in the Monastery of St. Euphrosyne, which Irene had founded.


title: Constantine VI

text: In the early 820s, the rebel Thomas the Slav claimed to be Constantine VI in an effort to gain support against Michael II.


title: Constantine VI

text: By his mistress and then second wife Theodote (m. 795), Constantine VI had two sons, both of whom died young:


title: Russell Morash

text: Russell Morash (born February 11, 1936) is an American television producer and director. Morash's many television programs are produced through WGBH and airing on PBS.


title: Russell Morash

text: Morash started his entertainment career as a cameraman for Boston public-television WGBH. In 1961, as a cameraman, Morash met Julia Child when she appeared on a WGBH program called "I've Been Reading," while promoting her cookbook "Mastering the Art of French Cooking." Viewers flooded the station with calls and letters asking to see more. "The French Chef" premiered on WGBH in 1962 and then was distributed nationally by American Public Television. Morash began directing "The French Chef" in 1963. They worked together on other cooking shows for more than thirty years.


title: Russell Morash

text: Morash's theater-inspired directorial style, and the technology of the day, required that the staff and host — all collected in a makeshift studio cobbled together with equipment that had escaped a massive station fire — would shoot each episode in one take. It established an in-the-moment template for a new kind of public television show that Morash took with him to launch other series, such as "This Old House" and "The Victory Garden".


title: Russell Morash

text: "The Victory Garden" and "This Old House" spinoff series "The New Yankee Workshop" were filmed in Morash's own backyard in Massachusetts.


title: Russell Morash

text: Morash's wife is Marian Morash, a James Beard Award-winning chef who also appeared on Julia Child's cooking show, appeared on "The Victory Garden" and edited "The Victory Garden Cookbook".


title: Guinea Pig: Devil's Experiment

text: The film depicts a group of three men who graphically abuse a woman in a number of ways. It is presented in a found-footage style, with on-screen text claiming that the film features real footage of torture—supposedly intended as an experiment on the human body's tolerance to pain—that was purportedly sent to Ogura. However, the scenes of violence featured in the film are not authentic, extensively utilising practical effects.


title: Guinea Pig: Devil's Experiment

text: "Guinea Pig: Devil's Experiment" has been called a "faux snuff film", and has been noted for its depiction of violence.


title: Guinea Pig: Devil's Experiment

text: The film is presented under the guise of being a video sent to director Satoru Ogura, with opening text claiming the following:


title: Guinea Pig: Devil's Experiment

text: Several years ago, I obtained a private video under the title "Guinea Pig". Its commentary said that 'this is a report of an experiment on the breaking point of bearable pain and the corrosion of people's senses'... but it was, in fact, an exhibition of devilish cruelty as three perpetrators severely abused a woman. Note: 'Guinea Pig' is defined as any experimental material.


title: Guinea Pig: Devil's Experiment

text: A woman is seen hanging motionless outdoors in a net. Throughout the film, she is tortured by three men in a variety of ways. The film is divided into ten segments, each depicting a different method of torture. The first segment, titled "hit" (殴), shows the men taking turns striking the woman in her face numerous times. The next segment, "kick" (蹴), depicts the woman, blindfolded with her hands behind her back, being repeatedly kicked and berated by the three men. In the third segment, "claw" (抓), the woman's right hand and forearm are pinched with pliers. The fourth segment, "spin" (回), shows the men spinning the woman in a chair over 100 times. The fifth segment, "sound" (音), depicts the woman being forced to endure hours of sound torture, wherein headphones playing loud white noise are secured to her head.


title: Guinea Pig: Devil's Experiment

text: In the sixth segment, "skin" (剥), one of the woman's fingernails is ripped off, and she is shown hanging outside in a net once again. The seventh segment, "burn" (焼), depicts the woman laid out on a table, and scalding oil of varying degrees is poured on her skin, burning her. The eighth segment, "worm" (虫), shows maggots being dumped on her. In the ninth segment, "guts" (臓), the men throw organs and entrails on the woman. An incision is made along the back of one of her hands with a blade, and the hand is then smashed with a hammer. In the tenth and final segment, "needle" (針), the men insert a needle into the woman's temple, poking it through her left eye. She is then shown hanging outdoors in the net once again, unmoving.


title: Guinea Pig: Devil's Experiment

text: The details of this experiment were missing when I received this video but the name, age and other information of the woman and the three men in this video are under investigation.


title: Guinea Pig: Devil's Experiment

text: In 1984, Satoru Ogura set out to portray a series of highly grotesque films. The first draft of "Devil's Experiment" was passed to manga artist and writer Hideshi Hino and was met with positive feedback. Hino began simultaneously working on the script for the second installment. Thinking that it would be highly difficult to find actors for this series, Ogura ran advertisements requesting volunteers. Much to his surprise, he received a plethora of responses. Both "Devil's Experiment" and "Flower of Flesh and Blood" were shot consecutively in 1985 and was released publicly in 1986. Upon release, "Devil's Experiment" impacted the Japanese rental market. Family friendly shops that were opposed of the idea of carrying the title later gave in to keep up with the number of requests from their customer base.


title: Guinea Pig: Devil's Experiment

text: Writing about the presentation of "Devil's Experiment" as being a genuine snuff film, J. Doyle Wallis of DVD Talk wrote that "it didn't strike me as the slightest bit true", but noted that, "despite spotting the stumbles that betray its reality, it is quite disturbing". He called it "hard to watch" and "bold but also utterly deplorable", and asserted that its "perversity is there merely to exploit a part of the human psyche that is totally without merit."


title: Guinea Pig: Devil's Experiment

text: In his book "Eros in Hell: Sex, Blood and Madness in Japanese Cinema", Jack Hunter wrote that the filming and editing techniques implemented in the film lend to it being "an effective and surprisingly low-key meditation on the cumulative dehumanization that violence causes in both aggressor and victim alike." In "Nightmare Japan: Contemporary Japanese Horror Cinema", author Jay McRoy similarly notes such techniques, writing that while the film "[blurs] audience distinctions between fact and fiction, thus heightening the visceral impact generated by the 'experiment's' verisimilitude", its "technical sophistication and artistry" exposes its fictional nature.


title: Guinea Pig: Devil's Experiment

text: "Guinea Pig: Devil's Experiment" was released on VHS by Midnight 25 Video. In the early 2000s, distributor Unearthed Films released the film on DVD as a double feature with another entry in the "Guinea Pig" series, "Android of Notre Dame".


title: Insurance broker

text: An insurance broker is an intermediary who sells, solicits, or negotiates insurance on behalf of a client for compensation. An insurance broker is distinct from an insurance agent in that a broker typically acts on behalf of a client by negotiating with multiple insurers, while an agent represents one or more specific insurers under a contract.


title: Insurance broker

text: As of 2019, the largest insurance brokers in the world by revenue are Marsh & McLennan, Aon plc, Willis Towers Watson, Arthur J. Gallagher and Hub International.


title: Insurance broker

text: In Australia, all insurance brokers are required under the Financial Services Reform Act 2001 to be licensed by the federal government's Australian Securities and Investments Commission (ASIC). Reputable and experienced insurance brokers in Australia will generally also hold additional qualifications such as a certificate or diploma in financial services which requires the completion of in depth studies in a specific area, the most common being general insurance or insurance brokering.


title: Insurance broker

text: Within Australia there are also a number of industry bodies that issue professional accreditations to members that comply with best standards of professional practice and integrity and maintain up to date skills and knowledge. The two main accreditations are the Australian and New Zealand Institute of Insurance and Finance (ANZIIF) Certified Insurance Professional (CIP) and National Insurance Brokers Association (NIBA) Qualified Practicing Insurance Broker (QPIB) qualifications.


title: Insurance broker

text: Dealing with an insurance broker as opposed to directly with an insurer is something many customers (particularly businesses) choose to do in Australia for reasons including: the ease of having the "shopping around done for them"; having the opportunity for premium funding which allows for larger insurance policies to be paid in installments rather than all at once; dealing with one broker for all policies from the car insurance to professional indemnity insurance rather than dealing directly with several insurers; and, the ease of having claims managed by the broker who deals directly with the insurer on the client's behalf.


title: Insurance broker

text: In Canada, insurance brokers are regulated on a provincial and territorial basis. Insurance brokers and insurance agents are licensed and regulated by the same entity in most of Canada; either an arms-length organization, such as the General Insurance Council of Saskatchewan, or directly by a government body. In some provinces, such as Ontario, insurance brokers have self-governing bodies responsible for licensing and regulation.


title: Insurance broker

text: "Insurance broker" became a regulated term under the Insurance Brokers (Registration) Act 1977, which was designed to prevent firms holding themselves as brokers but in fact acting as representative of one or more favoured insurance companies. The term has no legal definition following the repeal of the 1977 Act. The sale of general insurance was regulated by the Financial Services Authority from 14 January 2005 until 31 March 2013 and by the Financial Conduct Authority since 1 April 2013. Any person or firm authorized by the Authority can now call themselves an insurance broker.


title: Insurance broker

text: Insurance brokerage is largely associated with general insurance (car, house etc.) rather than life insurance, although some brokers continued to provide investment and life insurance brokerage until the onset of new regulation in 2001. This drove a more transparent regime, based predominantly on upfront negotiation of a fee for the provision of advice and/or services. This saw the splitting of intermediaries into two groups: general insurance intermediaries/brokers and independent financial advisers (IFAs) for life insurance, investments and pensions.


title: Insurance broker

text: General insurance brokering is carried out today by many types of authorized organisations including traditional high street brokers and telephone or web-based firms.


title: Insurance broker

text: The British Insurance Brokers' Association is a representative organisation for brokers in the UK. It has over 1800 members.


title: Insurance broker

text: In the United States, insurance brokers are regulated by individual states. Most states require anyone who sells, solicits, or negotiates insurance in that state to obtain an insurance broker license, with certain limited exceptions. This includes a business entity, the business entity's officers or directors (the "sublicensees" through whom the business entity operates), and individual employees. In order to obtain a broker's license, a person typically must take pre-licensing courses and pass an examination. An insurance broker also must submit an application (with an application fee) to the state insurance regulator in the state in which the applicant wishes to do business, who will determine whether the insurance broker has met all the state requirements and will typically do a background check to determine whether the applicant is considered trustworthy and competent. A criminal conviction, for example, may result in a state determining that the applicant is untrustworthy or incompetent. Some states also require applicants to submit fingerprints.


title: Insurance broker

text: Once licensed, an insurance broker generally must take continuing education courses when their licenses reach a renewal date. For example, the state of California requires license renewals every 2 years, which is accomplished by completing continuing education courses. Most states have reciprocity agreements whereby brokers from one state can become easily licensed in another state. As a result of the federal Gramm-Leach-Bliley Act, most states have adopted uniform licensing laws, with 47 states being deemed reciprocal by the National Association of Insurance Commissioners. A state may revoke, suspend, or refuse to renew an insurance broker's license if at any time the state determines (typically after notice and a hearing) that the broker has engaged in any activity that makes him untrustworthy or incompetent.


title: Insurance broker

text: Because of industry regulation, smaller brokerage firms can easily compete with larger ones, and in most states, all insurance brokers generally are forbidden by law from providing their customers with rebates or inducements.


title: Insurance broker

text: Insurance brokers play a significant role in helping companies and individuals procure property and casualty (liability) insurance, life insurance and annuities, and accident and health insurance. For example, research shows that brokers play a significant role in helping small employers find health insurance, particularly in more competitive markets. Average small group commissions range from two percent to eight percent of premiums. Brokers provide services beyond procuring insurance, such as providing risk assessments, insurance consulting services, insurance-related regulatory and legislative updates, claims assistance services, assisting with employee enrollment, and helping to resolve benefit issues. However, some states consider the provision of services that are unrelated to the insurance procured through the broker to be an impermissible rebate or inducement.


title: Insurance broker

text: Negligence on the part of insurance brokers can have severe effects upon clients when they discover their insurance coverage is worthless. In one case, Near North Entertainment Insurance Services provided alternative rock band Third Eye Blind with a commercial general liability (CGL) insurance policy that excluded coverage for the "entertainment business". After insurance coverage for a lawsuit was denied because Third Eye Blind was and is, after all, in the entertainment business, the California Court of Appeal ruled in a published opinion that a subsequent court ruling establishing that the insurer had wrongfully denied coverage—that the insurer had a duty to defend the band and had breached that duty—did not absolve the broker of its duty to advise the band it needed something more than a basic CGL policy (namely, errors and omissions insurance).


title: Insurance broker

text: In 2004, Eliot Spitzer found apparent cases of bid-rigging by the major brokers, where the brokers arranged with insurers to provide "fake" quotes in exchange for providing favorable risks amidst contingent commission arrangements. In 2008, AIG paid $125 million to settle with 9 states.


title: Insurance broker

text: In most states there is no requirement to disclose the commission of the broker to the customer, but in New York, a regulation ("Regulation 194") was adopted in 2011 which required disclosure. Brokers or agents may decide to reveal their commission upon request.


title: Insurance broker

text: In most states, agents cannot charge a fee in addition to their commission, although Texas is one of the exceptions.


title: Insurance broker

text: Though not an absolute separation; an insurance agent is an insurance company's representative by way of "agent-principal" legal custom. The agent's primary alliance is with the insurance carrier, not the insurance buyer. In contrast, an insurance broker represents the insured, generally has no contractual agreements with insurance carriers, and relies on common or direct methods of perfecting business transactions with insurance carriers. This can have a significant beneficial impact on insurance negotiations obtained through a broker (vs. those obtained from an agent).


title: Insurance broker

text: Any person acting as an insurance agent or broker must be licensed to do so by the state or jurisdiction that the person is operating in. Whereas states previously would issue separate licenses for agents and brokers, most states now issue a single producer license regardless if the person is acting on behalf of the insured or insurer. The term insurance producers is used to reference both insurance agents and brokers.


title: Insurance broker

text: As in many industries, there is a trend toward disintermediation where consumers buy directly from the insurer without an intermediary. However, the $46 billion online vehicle, home, and life insurance markets for retail consumers have accelerated since 2012, with the rise of insurance comparison websites.  Publicly traded companies Amazon, Walmart, and Google continue to disrupt how consumers purchase insurance with varying success. Google, later exited the online insurance comparison market in 2016, and Allstate threatened to shutter their online consumer brand Esurance after disappointing profits.


title: Marion County, Indiana

text: Marion County is located in the U.S. state of Indiana. The 2020 United States Census reported a population of 977,203, making it the largest county in the state and 51st most populated county in the country. Indianapolis is the county seat, the state capital, and largest city. Marion County is consolidated with Indianapolis through an arrangement known as Unigov.


title: Marion County, Indiana

text: The low rolling hills of Marion County have been cleared of trees, and the area is completely devoted to municipal development or to agriculture, except for wooded drainages. The highest point (920 feet/279 meters ASL) is a small ridge at the county's northwest corner.


title: Marion County, Indiana

text: According to the 2010 census, the county has an area of , of which (or 98.34%) is land and (or 1.66%) is water.


title: Marion County, Indiana

text: The White River flows southwestward through the central part of the county; it is joined by Eagle Creek and Fall Creek, both of which have dams in the county forming Eagle Creek Reservoir and Geist Reservoir, respectively.


title: Marion County, Indiana

text: Marion County has two Indiana State Parks, Fort Harrison State Park and White River State Park, as well as many municipal parks.


title: Marion County, Indiana

text: <nowiki>*</nowiki> I-69 currently ends in Indianapolis at the I-465 interchange in the northeast section of the county. The extension connecting Indianapolis and Evansville is expected to be completed in 2024.


title: Marion County, Indiana

text: Marion County was created on April 1, 1822, from part of the "New Purchase" lands that had been obtained from its inhabitants, the Lenape, by the Treaty of St. Mary's. It is named for Francis Marion, a brigadier general from South Carolina in the American Revolutionary War.


title: Marion County, Indiana

text: The state capital was moved to Indianapolis in Marion County from Corydon on January 10, 1825. This began a period of rapid growth in population.


title: Marion County, Indiana

text: In recent years, average temperatures in Indianapolis have ranged from a low of in January to a high of in July, although a record low of was recorded in January 1985 and a record high of was recorded in June 1988. Average monthly precipitation ranged from in January to in July.


title: Marion County, Indiana

text: As of the 2010 United States Census, there were 903,393 people, 366,176 households, and 218,338 families in the county. The population density was . There were 417,862 housing units at an average density of . The racial makeup of the county was 62.7% white, 26.7% black or African American, 2.0% Asian, 0.3% American Indian, 0.1% Pacific islander, 5.4% from other races, and 2.8% from two or more races. Those of Hispanic or Latino origin made up 9.3% of the population. In terms of ancestry, 18.9% were German, 11.8% were Irish, 8.4% were English, 6.6% were American, and 5.2% were Subsaharan African.


title: Marion County, Indiana

text: Of the 366,176 households, 32.3% had children under the age of 18 living with them, 36.9% were married couples living together, 17.1% had a female householder with no husband present, 40.4% were non-families, and 32.0% of all households were made up of individuals. The average household size was 2.42 and the average family size was 3.08. The median age was 33.9 years.


title: Marion County, Indiana

text: The median income for a household in the county was $47,697 and the median income for a family was $54,142. Males had a median income of $42,215 versus $34,169 for females. The per capita income for the county was $24,498. About 13.5% of families and 17.3% of the population were below the poverty line, including 25.7% of those under age 18 and 9.0% of those age 65 or over.


title: Marion County, Indiana

text: Marion County has a consolidated city-county government, known as Unigov, in which only four municipalities retain full government autonomy (including a mayor and city council) as "excluded cities". The remaining municipalities within the county are "included towns" and exercise very limited authority, mainly in zoning and appointing their own police departments and maintaining some of their own municipal services and town identities. They retain the ability to levy taxes for these purposes.


title: Marion County, Indiana

text: Marion County has nine townships roughly organized into a grid-like, three-by-three pattern. This arrangement can be seen below, with the top being north.


title: Marion County, Indiana

text: Most of Marion County is in Indiana's 7th congressional district, which is held by Democrat André Carson. Indiana's 5th congressional district, which runs along the northern edge of the county, is held by Republican Victoria Spartz. The county is represented by 15 seats in the Indiana House of Representatives, 86th through 100th districts, with ten seats held by Democrats and five by Republicans. In the State Senate Marion County is divided among nine districts, which are held by two Democrats and seven Republicans. The Senate districts are numbered 28 through 36.


title: Marion County, Indiana

text: The Indianapolis City-County Council is the combined legislative body of Indianapolis and Marion County. The consolidated government, known as Unigov, was formally established in 1970 upon the merger of the city government with the county government. The council passes ordinances for the city and county, and makes appointments to certain boards and commissions.


title: Marion County, Indiana

text: For most of the 20th century, Marion County was considered one of the most conservative urban counties in the nation. Between 1896 and 2000, it went Democratic only four times, in the national landslides of 1932, 1936 and 1964 as well as 1912 when Woodrow Wilson won a plurality in the county. The Republican edge began to lessen considerably in the 1990s, and in 2004 John Kerry became the first Democrat since Lyndon B. Johnson in 1964 to carry the county. The trend continued in 2008 and 2012 with Barack Obama showing strongly in Marion County, winning 63% and 60% of the vote respectively. Hillary Clinton won it with 58 percent in 2016, and Joe Biden took 63 percent in 2020. Biden’s 247,772 votes is the highest number of votes a candidate has ever received in the county. It is now one of the few Democratic bastions in traditionally heavily Republican central Indiana.


title: Marion County, Indiana

text: The six northern and central townships lean more Democratic, especially Center township containing Downtown Indianapolis, and Pike Township in the northwestern corner with an African-American majority. In contrast, the three less-populated southern townships with a higher Caucasian population (Decatur, Perry and Franklin) lean more Republican.


title: Riesz representation theorem

text: The Riesz representation theorem, sometimes called the Riesz–Fréchet representation theorem after Frigyes Riesz and Maurice René Fréchet, establishes an important connection between a Hilbert space and its continuous dual space. If the underlying field is the real numbers, the two are isometrically isomorphic; if the underlying field is the complex numbers, the two are isometrically anti-isomorphic. The (anti-) isomorphism is a particular natural isomorphism.


title: Riesz representation theorem

text: Let formula_1 be a Hilbert space over a field formula_2 where formula_3 is either the real numbers formula_4 or the complex numbers formula_5 If formula_6 (resp. if formula_7) then formula_1 is called a (resp. a ). Every real Hilbert space can be extended to be a dense subset of a unique (up to bijective isometry) complex Hilbert space, called its complexification, which is why Hilbert spaces are often automatically assumed to be complex. Real and complex Hilbert spaces have in common many, but by no means all, properties and results/theorems.


title: Riesz representation theorem

text: This article is intended for both mathematicians and physicists and will describe the theorem for both.


title: Riesz representation theorem

text: In both mathematics and physics, if a Hilbert space is assumed to be real (that is, if formula_7) then this will usually be made clear. Often in mathematics, and especially in physics, unless indicated otherwise, "Hilbert space" is usually automatically assumed to mean "complex Hilbert space." Depending on the author, in mathematics, "Hilbert space" usually means either (1) a complex Hilbert space, or (2) a real complex Hilbert space.


title: Riesz representation theorem

text: Every constant formula_15 map is always both linear and antilinear. If formula_7 then the definitions of linear maps and antilinear maps are completely identical. A linear map from a Hilbert space into a Banach space (or more generally, from any Banach space into any topological vector space) is continuous if and only if it is bounded; the same is true of antilinear maps. The inverse of any antilinear (resp. linear) bijection is again an antilinear (resp. linear) bijection. The composition of two linear maps is a map.


title: Riesz representation theorem

text: Denote by formula_20 (resp. by formula_21 the set of all continuous linear (resp. continuous antilinear) functionals on formula_22 which is called the (resp. the ) of formula_23


title: Riesz representation theorem

text: If formula_7 then linear functionals on formula_1 are the same as antilinear functionals and consequently, the same is true for such continuous maps: that is, formula_26


title: Riesz representation theorem

text: This assignment is most useful when formula_6 because if formula_7 then formula_31 and the assignment formula_32 reduces down to the identity map.


title: Riesz representation theorem

text: The Hilbert space formula_1 has an associated inner product formula_39 valued in formula_1's underlying scalar field formula_3 that is linear in one coordinate and antilinear in the other (as described in detail below).


title: Riesz representation theorem

text: If formula_1 is a complex Hilbert space (meaning, if formula_6), which is very often the case, then which coordinate is antilinear and which is linear becomes a important technicality.


title: Riesz representation theorem

text: However, if formula_7 then the inner product is a symmetric map that is simultaneously linear in each coordinate (that is, bilinear) and antilinear in each coordinate. Consequently, the question of which coordinate is linear and which is antilinear is irrelevant for real Hilbert spaces.


title: Riesz representation theorem

text: In mathematics, the inner product on a Hilbert space formula_1 is often denoted by formula_46 or formula_47 while in physics, the bra–ket notation formula_48 or formula_49 is typically used instead. In this article, these two notations will be related by the equality:


title: Riesz representation theorem

text: In mathematics, the prevailing convention (i.e. the definition of an inner product) is that the inner product is coordinate and antilinear in the other coordinate. In physics, the convention/definition is unfortunately the , meaning that the inner product is coordinate and antilinear in the other coordinate.


title: Riesz representation theorem

text: Instead, the assumptions made above make it so that the mathematics notation formula_46 satisfies the mathematical convention/definition for the inner product (that is, linear in the first coordinate and antilinear in the other), while the physics bra–ket notation formula_54 satisfies the physics convention/definition for the inner product (that is, linear in the second coordinate and antilinear in the other). Consequently, the above two assumptions makes the notation used in each field consistent with that field's convention/definition for which coordinate is linear and which is antilinear.


title: Riesz representation theorem

text: As with all normed spaces, the (continuous) dual space formula_20 carries a canonical norm, called the , that is defined by


title: Riesz representation theorem

text: The canonical norm on the (continuous) anti-dual space formula_62 denoted by formula_63 is defined by using this same equation:


title: Riesz representation theorem

text: This canonical norm on formula_20 satisfies the parallelogram law, which means that the polarization identity can be used to define a which this article will denote by the notations


title: Riesz representation theorem

text: where this inner product turns formula_20 into a Hilbert space. There are now two ways of defining a norm on formula_68 the norm induced by this inner product (that is, the norm defined by formula_69) and the usual dual norm (defined as the supremum over the closed unit ball). These norms are the same; explicitly, this means that the following holds for every formula_70


title: Riesz representation theorem

text: As will be described later, the Riesz representation theorem can be used to give an equivalent definition of the canonical norm and the canonical inner product on formula_72


title: Riesz representation theorem

text: The same equations that were used above can also be used to define a norm and inner product on formula_1's anti-dual space formula_74


title: Riesz representation theorem

text: The inner products on the dual space formula_20 and the anti-dual space formula_62 denoted respectively by formula_84 and formula_85 are related by


title: Riesz representation theorem

text: Two vectors formula_91 and formula_92 are if formula_93 which happens if and only if formula_94 for all scalars formula_95 The orthogonal complement of a subset formula_96 is


title: Riesz representation theorem

text: The Hilbert projection theorem guarantees that for any nonempty closed convex subset formula_99 of a Hilbert space there exists a unique vector formula_100 such that formula_101 that is, formula_100 is the (unique) global minimum point of the function formula_103 defined by formula_104


title: Riesz representation theorem

text: Historically, the theorem is often attributed simultaneously to Riesz and Fréchet in 1907 (see references).


title: Riesz representation theorem

text: Define formula_108 by formula_109 which is a linear functional on formula_1 since formula_111 is in the linear argument.


title: Riesz representation theorem

text: The proof above did not use the fact that formula_1 is complete, which shows that the formula for the norm formula_124 holds more generally for all inner product spaces.


title: Riesz representation theorem

text: If formula_136 (or equivalently, if formula_137) then taking formula_138 completes the proof so assume that formula_139 and formula_140


title: Riesz representation theorem

text: The continuity of formula_141 implies that formula_142 is a closed subspace of formula_1 (because formula_144 and formula_145 is a closed subset of formula_3).


title: Riesz representation theorem

text: Because formula_142 is closed and formula_1 is a Hilbert space, formula_1 can be written as the direct sum formula_153 (a proof of this is given in the article on the Hilbert projection theorem).


title: Riesz representation theorem

text: Let formula_174 be any non-zero vector. Replacing formula_175 with formula_176 in the proof above shows that the vector formula_177 satisfies formula_178 for every formula_179 The uniqueness of the (non-zero) vector formula_180 representing formula_141 implies that formula_182 which in turn implies that formula_183 and formula_184 Thus every vector in formula_171 is a scalar multiple of formula_186 formula_122


title: Riesz representation theorem

text: So in particular, formula_190 is always real and furthermore, formula_191 if and only if formula_192 if and only if formula_193


title: Riesz representation theorem

text: A non-trivial continuous linear functional formula_141 is often interpreted geometrically by identifying it with the affine hyperplane formula_195 (the kernel formula_196 is also often visualized alongside formula_195 although knowing formula_198 is enough to reconstruct formula_199 because if formula_200 then formula_201 and otherwise formula_202). In particular, the norm of formula_141 should somehow be interpretable as the "norm of the hyperplane formula_198". When formula_205 then the Riesz representation theorem provides such an interpretation of formula_206 in terms of the affine hyperplane


title: Riesz representation theorem

text: formula_195 as follows: using the notation from the theorem's statement, from formula_208 it follows that formula_209 and so formula_210 implies formula_211 and thus formula_212


title: Riesz representation theorem

text: This can also be seen by applying the Hilbert projection theorem to formula_198 and concluding that the global minimum point of the map formula_214 defined by formula_215 is formula_216


title: Riesz representation theorem

text: provide the promised interpretation of the linear functional's norm formula_206 entirely in terms of its associated affine hyperplane formula_219 (because with this formula, knowing only the formula_198 is enough to describe the norm of its associated linear ). Defining formula_221 the infimum formula


title: Riesz representation theorem

text: When the supremum is taken in formula_4 (as is typically assumed), then the supremum of the empty set is formula_225 but if the supremum is taken the non-negative reals formula_226 (which is the image/range of the norm formula_227 when formula_228) then this supremum is instead formula_229 in which case the supremum formula formula_230 will also hold when formula_137 (although the atypical equality formula_232 is usually unexpected and so risks causing confusion).


title: Riesz representation theorem

text: Using the notation from the theorem above, several ways of constructing formula_180 from formula_188 are now described.


title: Riesz representation theorem

text: This special case of formula_137 is henceforth assumed to be known, which is why some of the constructions given below start by assuming formula_140


title: Riesz representation theorem

text: If formula_248 is a unit vector satisfying the above condition then the same is true of formula_249 which is also a unit vector in formula_250 However, formula_251 so both these vectors result in the same formula_186


title: Riesz representation theorem

text: If formula_253 is such that formula_254 and if formula_255 is the orthogonal projection of formula_91 onto formula_257 then


title: Riesz representation theorem

text: Given an orthonormal basis formula_259 of formula_1 and a continuous linear functional formula_261 the vector formula_262 can be constructed uniquely by


title: Riesz representation theorem

text: where all but at most countably many formula_264 will be equal to formula_15 and where the value of formula_180 does not actually depend on choice of orthonormal basis (that is, using any other orthonormal basis for formula_1 will result in the same vector).


title: Riesz representation theorem

text: Consider the special case of formula_277 (where formula_278 is an integer) with the standard inner product


title: Riesz representation theorem

text: where formula_280 are represented as column matrices formula_281 and formula_282 with respect to the standard orthonormal basis formula_283 on formula_1 (here, formula_285 is formula_172 at its formula_287 coordinate and formula_15 everywhere else; as usual, formula_20 will now be associated with the dual basis) and where formula_290 denotes the conjugate transpose of formula_291


title: Riesz representation theorem

text: As usual, also identify the linear functional formula_141 with its transformation matrix, which is the row matrix formula_305 so that formula_306 and the function formula_141 is the assignment formula_308 where the right hand side is matrix multiplication. Then for all formula_309


title: Riesz representation theorem

text: which shows that formula_180 satisfies the defining condition of the Riesz representation of formula_312


title: Riesz representation theorem

text: The bijective antilinear isometry formula_313 defined in the corollary to the Riesz representation theorem is the assignment that sends formula_314 to the linear functional formula_315 on formula_1 defined by


title: Riesz representation theorem

text: where under the identification of vectors in formula_1 with column matrices and vector in formula_20 with row matrices, formula_320 is just the assignment


title: Riesz representation theorem

text: As described in the corollary, formula_320's inverse formula_323 is the antilinear isometry formula_324 which was just shown above to be:


title: Riesz representation theorem

text: Thus in terms of matrices, each of formula_313 and formula_323 is just the operation of conjugate transposition formula_330 (although between different spaces of matrices: if formula_1 is identified with the space of all column (respectively, row) matrices then formula_20 is identified with the space of all row (respectively, column) matrices).


title: Riesz representation theorem

text: This example used the standard inner product, which is the map formula_333 but if a different inner product is used, such as formula_334 where formula_335 is any Hermitian positive-definite matrix, or if a different orthonormal basis is used then the transformation matrices, and thus also the above formulas, will be different.


title: Riesz representation theorem

text: When the Hilbert space formula_1 is reinterpreted as a real Hilbert space then it will be denoted by formula_339 where the (real) inner-product on formula_340 is the real part of formula_1's inner product; that is:


title: Riesz representation theorem

text: The norm on formula_340 induced by formula_344 is equal to the original norm on formula_1 and the continuous dual space of formula_340 is the set of all -valued bounded formula_4-linear functionals on formula_340 (see the article about the polarization identity for additional details about this relationship).


title: Riesz representation theorem

text: Let formula_349 and formula_350 denote the real and imaginary parts of a linear functional formula_351 so that formula_352


title: Riesz representation theorem

text: It can also be shown that formula_359 where formula_360 and formula_361 are the usual operator norms.


title: Riesz representation theorem

text: In particular, a linear functional formula_362 is bounded if and only if its real part formula_363 is bounded.


title: Riesz representation theorem

text: The Riesz representation of a continuous linear function formula_141 on a complex Hilbert space is equal to the Riesz representation of its real part formula_365 on its associated real Hilbert space.


title: Riesz representation theorem

text: Explicitly, let formula_188 and as above, let formula_367 be the Riesz representation of formula_141 obtained in formula_369 so it is the unique vector that satisfies formula_370 for all formula_371


title: Riesz representation theorem

text: The real part of formula_141 is a continuous real linear functional on formula_340 and so the Riesz representation theorem may be applied to formula_374 and the associated real Hilbert space formula_375 to produce its Riesz representation, which will be denoted by formula_376


title: Riesz representation theorem

text: That is, formula_377 is the unique vector in formula_340 that satisfies formula_379 for all formula_371


title: Riesz representation theorem

text: In other words, in the theorem and constructions above, if formula_1 is replaced with its real Hilbert space counterpart formula_340 and if formula_141 is replaced with formula_365 then formula_394 This means that vector formula_180 obtained by using formula_375 and the real linear functional formula_365 is the equal to the vector obtained by using the origin complex Hilbert space formula_398 and original complex linear functional formula_141 (with identical norm values as well).


title: Riesz representation theorem

text: Furthermore, if formula_205 then formula_180 is perpendicular to formula_402 with respect to formula_403 where the kernel of formula_141 is be a "proper" subspace of the kernel of its real part formula_405 Assume now that formula_140


title: Riesz representation theorem

text: Then formula_407 because formula_408 and formula_257 is a proper subset of formula_410 The vector subspace formula_199 has real codimension formula_172 in formula_413 while formula_402 has codimension formula_172 in formula_339 and formula_417 That is, formula_180 is perpendicular to formula_402 with respect to formula_420


title: Riesz representation theorem

text: The map defined by placing formula_92 into the coordinate of the inner product and letting the variable formula_422 vary over the coordinate results in an functional:


title: Riesz representation theorem

text: The Fundamental theorem of Hilbert spaces, which is related to Riesz representation theorem, states that this map is surjective (and thus bijective). Consequently, every antilinear functional on formula_1 can be written (uniquely) in this form.


title: Riesz representation theorem

text: If formula_90 is the canonical linear bijective isometry formula_32 that was defined above, then the following equality holds:


title: Riesz representation theorem

text: Given a vector formula_156 let formula_437 denote the continuous linear functional formula_438; that is,


title: Riesz representation theorem

text: so that this functional formula_437 is defined by formula_441 This map was denoted by formula_442 earlier in this article.


title: Riesz representation theorem

text: The assignment formula_443 is just the isometric antilinear isomorphism formula_444 which is why formula_445 holds for all formula_446 and all scalars formula_447


title: Riesz representation theorem

text: The result of plugging some given formula_448 into the functional formula_437 is the scalar formula_450 which may be denoted by formula_451


title: Riesz representation theorem

text: Given a continuous linear functional formula_452 let formula_453 denote the vector formula_454; that is,


title: Riesz representation theorem

text: The assignment formula_456 is just the isometric antilinear isomorphism formula_457 which is why formula_458 holds for all formula_459 and all scalars formula_447


title: Riesz representation theorem

text: which is why the notation formula_463 is used in place of formula_464 With this notation, the defining condition becomes


title: Riesz representation theorem

text: The assignment formula_470 is just the identity map formula_471 which is why formula_472 holds for all formula_446 and all scalars formula_447


title: Riesz representation theorem

text: The notation formula_475 and formula_476 is used in place of formula_477 and formula_478 respectively. As expected, formula_479 and formula_480 really is just the scalar formula_481


title: Riesz representation theorem

text: Let formula_482 be a continuous linear operator between Hilbert spaces formula_483 and formula_484 As before, let formula_485 and formula_486


title: Riesz representation theorem

text: is a continuous linear functional on formula_1 and so by the Riesz representation theorem, there exists a unique vector in formula_22 denoted by formula_495 such that formula_496 or equivalently, such that


title: Riesz representation theorem

text: The assignment formula_498 thus induces a function formula_499 called the of formula_482 whose defining condition is


title: Riesz representation theorem

text: If formula_1 is finite dimensional with the standard inner product and if formula_335 is the transformation matrix of formula_198 with respect to the standard orthonormal basis then formula_335's conjugate transpose formula_507 is the transformation matrix of the adjoint formula_508


title: Riesz representation theorem

text: It is also possible to define the or of formula_509 which is the map formula_510 defined by sending a continuous linear functionals formula_511 to


title: Riesz representation theorem

text: where the composition formula_513 is always a continuous linear functional on formula_1 and it satisfies formula_515 (this is true more generally, when formula_1 and formula_517 are merely normed spaces).


title: Riesz representation theorem

text: So for example, if formula_518 then formula_519 sends the continuous linear functional formula_520 (defined on formula_517 by formula_522) to the continuous linear functional formula_523 (defined on formula_1 by formula_525);


title: Riesz representation theorem

text: using bra-ket notation, this can be written as formula_526 where the juxtaposition of formula_527 with formula_198 on the right hand side denotes function composition: formula_529


title: Riesz representation theorem

text: The adjoint formula_499 is actually just to the transpose formula_510 when the Riesz representation theorem is used to identify formula_517 with formula_533 and formula_1 with formula_72


title: Riesz representation theorem

text: Alternatively, the value of the left and right hand sides of () at any given formula_518 can be rewritten in terms of the inner products as:


title: Riesz representation theorem

text: so that formula_539 holds if and only if formula_540 holds; but the equality on the right holds by definition of formula_541


title: Riesz representation theorem

text: Whether or not formula_546 is self-adjoint, normal, or unitary depends entirely on whether or not formula_198 satisfies certain defining conditions related to its adjoint, which was shown by () to essentially be just the transpose formula_549


title: Riesz representation theorem

text: Because the transpose of formula_198 is a map between continuous linear functionals, these defining conditions can consequently be re-expressed entirely in terms of linear functionals, as the remainder of subsection will now describe in detail.


title: Riesz representation theorem

text: The linear functionals that are involved are the simplest possible continuous linear functionals on formula_1 that can be defined entirely in terms of formula_552 the inner product formula_553 on formula_22 and some given vector formula_179


title: Riesz representation theorem

text: A continuous linear operator formula_546 is called self-adjoint it is equal to its own adjoint; that is, if formula_560 Using (), this happens if and only if:


title: Riesz representation theorem

text: Unraveling notation and definitions produces the following characterization of self-adjoint operators in terms of the aforementioned continuous linear functionals: formula_198 is self-adjoint if and only if for all formula_564 the linear functional formula_565 is equal to the linear functional formula_566; that is, if and only if


title: Riesz representation theorem

text: A continuous linear operator formula_546 is called normal if formula_569 which happens if and only if for all formula_570


title: Riesz representation theorem

text: Using () and unraveling notation and definitions produces the following characterization of normal operators in terms of inner products of continuous linear functionals: formula_198 is a normal operator if and only if


title: Riesz representation theorem

text: The left hand side of this characterization involves "only" linear functionals of the form formula_574 while the right hand side involves "only" linear functions of the form formula_575 (defined as above).


title: Riesz representation theorem

text: So in plain English, characterization () says that an operator is "normal" when the inner product of any two linear functions of the first form is equal to the inner product of their second form (using the same vectors formula_576 for both forms).


title: Riesz representation theorem

text: In other words, if it happens to be the case (and when formula_198 is injective, it is) that the assignment of linear functionals formula_578 is well-defined (or alternatively, if formula_579 is well-defined) where formula_580 ranges over formula_22 then formula_198 is a normal operator if and only if this assignment preserves the inner product on formula_72


title: Riesz representation theorem

text: The fact that every self-adjoint bounded linear operator is normal follows readily by direct substitution of formula_584 into either side of formula_585


title: Riesz representation theorem

text: This same fact also follows immediately from the direct substitution of the equalities () into either side of ().


title: Riesz representation theorem

text: Alternatively, for a complex Hilbert space, the continuous linear operator formula_198 is a normal operator if and only if formula_587 for every formula_564 which happens if and only if


title: Riesz representation theorem

text: An invertible bounded linear operator formula_546 is said to be unitary if its inverse is its adjoint: formula_591


title: Riesz representation theorem

text: The fact that a bounded invertible linear operator formula_546 is unitary if and only if formula_596 (or equivalently, formula_597) produces another (well-known) characterization: an invertible bounded linear map formula_198 is unitary if and only if


title: Riesz representation theorem

text: Because formula_546 is invertible (and so in particular a bijection), this is also true of the transpose formula_549 This fact also allows the vector formula_602 in the above characterizations to be replaced with formula_603 or formula_604 thereby producing many more equalities. Similarly, formula_605 can be replaced with formula_606 or formula_607


title: Wright Flyer III

text: The Wright Flyer III was the third powered aircraft by the Wright Brothers, built during the winter of 1904–05. Orville Wright made the first flight with it on June 23, 1905. The Flyer III had an airframe of spruce construction with a wing camber of 1-in-20 as used in 1903, rather than the less effective 1-in-25 used in 1904. The new machine was equipped with the engine and other hardware from the scrapped Flyer II and, after major modifications, achieved much greater performance than Flyers I and II.


title: Wright Flyer III

text: The 1905 flyer was made stronger, more durable, and with a longer tail to provide better directional stability and control. A larger cylinder bore engine provided more power, while a more effective leading edge, and efficient propellers, improved performance. The propeller blades were made wider and thinner, while according to Harry Combs, "...adding a backward sweep to the blades, calculated precisely to avoid the pressures of flight and to keep the blades free from distortion." Other modifications included vertical rather than horizontal cylinders for its 35-horsepower engine.


title: Wright Flyer III

text: As initially built, the Flyer III looked almost the same as its predecessors, and offered equally marginal performance. Orville suffered minor injuries in a serious nose-dive crash in the machine on July 14, 1905. When rebuilding the airplane, the Wrights made important design changes that solved the stability problems of the earlier models. They almost doubled the size of the elevator and rudder, and moved them about twice the distance from the wings. They added two fixed half-moon shaped vertical vanes (called "blinkers") between the elevators (but later removed), and widened the skid-undercarriage which helped give the wings a very slight dihedral.


title: Wright Flyer III

text: They disconnected the rear rudder of the rebuilt Flyer III from the wing-warping control, and as in most future aircraft, placed it on a separate control handle. They also installed a larger fuel tank, and mounted two radiators on front and back struts for extra coolant to the engine for the anticipated lengthy duration flights.


title: Wright Flyer III

text: When testing of Flyer III resumed in September, improvement was obvious. The pitch instability that had hampered Flyers I and II was brought under control. Crashes, some of which had been severe, no longer occurred. Flights with the redesigned aircraft started lasting over 20 minutes. The Flyer III became practical and dependable, flying reliably for significant durations, and bringing its pilot back to the starting point safely, and landing without damage.


title: Wright Flyer III

text: On 5 October 1905 Wilbur made a circling flight of in 39 minutes and 23 seconds, over Huffman Prairie, longer than the total duration of all the flights of 1903 and 1904. On 19 October 1905, the brothers wrote in a third letter to the U.S. War Department, "We propose to sell the results of experiments finished at our own expense."


title: Wright Flyer III

text: To keep their knowledge from falling into competitors' hands, the Wrights stopped flying, and disassembled the airplane on November 7, 1905.


title: Wright Flyer III

text: They returned to Kitty Hawk in May of 1908 to flight test their modified 1905 flyer, which they equipped with upright hand controls and seats for the pilot and passenger. They were required by the Signal Corps to produce an airplane "capable of carrying two men and sufficient fuel supplies for a flight of 125 miles, with a speed of at least 40 miles an hour." They started flying on 6 May, were first witnessed flying by correspondents on 11 May, and flew their first passenger on 14 May.


title: Wright Flyer III

text: On May 14, 1908, Wilbur flew mechanic Charles Furnas (1880–1941) in 29 seconds, making him the first airplane passenger. The same day, Orville also flew with Furnas, this time in 4 minutes 2 seconds. Orville's flight with Furnas was seen by newspaper reporters hiding among the sand dunes; they mistakenly thought Wilbur and Orville were flying together. He is one of the few people to fly with both Wright brothers (their sister Katharine being another).


title: Wright Flyer III

text: Later that day, Wilbur was flying solo when he moved one of the new control levers the wrong way and crashed into the sand, suffering bruises. The Flyer's front elevator was wrecked, and the practice flights ended. Due to deadlines for their upcoming public demonstration flights in France and Virginia, the Wrights did not repair the airplane, and it never flew again.


title: Wright Flyer III

text: The Wright Flyer III was left in its damaged condition in the North Carolina hangar. In 1911, the Berkshire Museum of Pittsfield, Massachusetts, through one Zenas Crane, obtained most of the components from both the abandoned Flyer and the 1911 Wright glider, but never assembled or exhibited them. The parts of the 1905 aircraft remained in Massachusetts for almost forty years, until Orville requested their return in 1946 for the Flyer's restoration as a central exhibit at Edward A. Deeds' Carillon Park in Dayton, Ohio.


title: Wright Flyer III

text: Some Kitty Hawk residents also possessed pieces of the 1905 airplane. Deeds and Orville also obtained many of these for the restoration. At the end of the 1947–1950 restoration process, craftsmen estimated that the 1905 aircraft retained between 60 and 85% of its original material. The 1905 airplane is now displayed in the Wright Brothers Aviation Center at Carillon Historical Park. The aircraft and display are part of the Dayton Aviation Heritage National Historical Park. The restored 1905 Wright Flyer III is the only fixed-wing aircraft to be designated a National Historic Landmark.


title: Wright Flyer III

text: A historic missing piece of the Flyer III, thought to be a piece of the original "Wright Flyer", turned up in 2010 in the hands of Palmer Wood, whose uncle, Thomas, had given him the piece in the 1960s. Wood took the piece to Brian Coughlin, an aircraft collector, who, not knowing what the piece was, took it to Peter Jakab of the Smithsonian Institution.


title: Wright Flyer III

text: The missing piece is the actuator, which connects the moment chain or arm (the Wrights still used chain link in 1905) to the front elevator. In the 1940s, Orville gathered all of the stray pieces of the Flyer that were not in Massachusetts from Kitty Hawk locals who, as children, raided the Wrights' 1908 hangar for souvenirs. The actuator piece, which more than likely broke away in Wilbur's sand dune crash of May 14, 1908, somehow missed Orville's gathering efforts, and was replaced with a solid or flanged piece, which the Wrights did not start using until 1908.


title: Wright Flyer III

text: According to Peter Jakab, the flanged piece is not accurate to the 1905 configuration of the Flyer III. The Wrights in 1905 used a wood assembly joined together by small flat plates and screws. The solid flat piece now on the Flyer was substituted in the 1947–1950 restoration for the missing actuator.


title: Incest pornography

text: Incest pornography is a genre of pornography involving the depiction of incest between relatives. Incest pornography can feature actual relatives, but the main type of this pornography is fauxcest, which features non-related actors of similar looks to suggest family relationship. This genre includes characters with various levels of kinship, including first cousins, aunts, uncles, parent(s), offspring, nieces and nephews. In many countries, incest pornography amounts to illegal pornography.


title: Incest pornography

text: Arguably the most famous example of the genre is the "Taboo" film series of the 1980s. The first film in this series, which starred Kay Parker, was released in 1980. It spawned numerous sequels, several of which won adult film awards.


title: Incest pornography

text: There is a substantial amount of incest pornography on the Internet, leading some to argue it may legitimize or encourage real-life incest. Jeffrey Masson has even argued that incest porn is "the very nucleus of pornography — its prototypical form."


title: Incest pornography

text: Going back at least as far as the Christy twins in the 1970s, depictions of incest, and particularly incest between twins, have been a feature of gay pornography. Though the Christy twins may have been unrelated but similar-looking men and some twins have appeared together in scenes without substantial contact between them, some genuine twins have performed sexual acts on each other. It is illegal in many jurisdictions. For example, in Australia it is rated "Refused Classification" (RC).


title: Incest pornography

text: The 1999 William Higgins production "Double Czech" included actual sex between the Bartok twins, as did the 2009 sequel between the Richter twins, though the Bartok brothers were described as "looking utterly mortified" in their scene. Not so for another pair of Czech twins, Elijah and Milo Peters, who work together condomless for both oral and anal sex for studio Bel Ami. As of 2010, they were reported to live together as a monogamous couple outside of their porn careers and want to continue working together for another 50 years. Some scenes with the Peters twins together have needed to be re-edited in order to gain approval from film classification censors for distribution in markets including the United Kingdom and the United States.


title: Incest pornography

text: Fauxcest refers to pornographic or erotic depictions of incest by actors who are merely pretending to be related but in actuality have no biological relation. The term "fauxcest" is a portmanteau of "faux" and "incest", sometimes transcribed as "faux-incest" and sometimes used interchangeably with "family roleplay" or "fictional incest". Besides women, its primary consumers are couples and millennials. According to one pornographic film director, part of the appeal of the fauxcest genre is a desire by porn consumers to view taboo and controversial content. As of 2016, the genre had been growing in popularity at a rate of 1000% since 2011 and 178% since 2014, a spike that some industry professionals have attributed to female porn consumers who largely seek a content that is accompanied by a narrative. Variations of pretend relationships include siblings, mom–son, dad–daughter, step-relatives and various others.


title: Incest pornography

text: One of the reasons behind a trend towards pseudoincest over actual blood-relation incest within fiction is the bannable nature of consanguineal forms since some publishers will refuse to publish such content.


title: Incest pornography

text: On GameLink, one in ten purchases had a fauxcestual theme, and one sociologist has said the theme has become more mainstream as evidenced by its depiction on fantasy novel and television series such as "Game of Thrones". Pseudo-incest fictional books began to increase in popularity in the year 2011. However, some self-publishing companies are welcoming towards content that has pseudo-incestual themes.


title: William Walker Atkinson

text: was an attorney, merchant, publisher, and author, as well as an occultist and an American pioneer of the New Thought movement. He is the author of the pseudonymous works attributed to Theron Q. Dumont and Yogi Ramacharaka.


title: William Walker Atkinson

text: He wrote an estimated 100 books, all in the last 30 years of his life. He was mentioned in past editions of "Who's Who in America", in "Religious Leaders of America", and in similar publications. His works have remained in print more or less continuously since 1900.


title: William Walker Atkinson

text: William Walker Atkinson was born in Baltimore, Maryland on December 5, 1862, to Emma and William Atkinson. He began his working life as a grocer at 15 years old. He married Margret Foster Black of Beverly, New Jersey, in October 1889, and they had two children. Their first child died young. The second later married and had two daughters.


title: William Walker Atkinson

text: Atkinson pursued a business career from 1882 onwards and in 1894 he was admitted as an attorney to the Bar of Pennsylvania. While he gained much material success in his profession as a lawyer, the stress and over-strain eventually took its toll, and during this time he experienced a complete physical and mental breakdown, and financial disaster. He looked for healing and in the late 1880s he found it with New Thought, later attributing the restoration of his health, mental vigor and material prosperity to the application of the principles of New Thought.


title: William Walker Atkinson

text: Some time after his healing, Atkinson began to write articles on the truths he felt he had discovered, which were then known as Mental Science. In 1889, an article by him entitled "A Mental Science Catechism," appeared in Charles Fillmore's new periodical, "Modern Thought."


title: William Walker Atkinson

text: By the early 1890s Chicago had become a major centre for New Thought, mainly through the work of Emma Curtis Hopkins, and Atkinson decided to move there. Once in the city, he became an active promoter of the movement as an editor and author. He was responsible for publishing the magazines "Suggestion" (1900–1901), "New Thought" (1901–1905) and "Advanced Thought" (1906–1916).


title: William Walker Atkinson

text: In 1900 Atkinson worked as an associate editor of "Suggestion, a New Thought Journal", and wrote his first book, "Thought-Force in Business and Everyday Life", being a series of lessons in personal magnetism, psychic influence, thought-force, concentration, will-power, and practical mental science.


title: William Walker Atkinson

text: He then met Sydney Flower, a well-known New Thought publisher and businessman, and teamed up with him. In December, 1901 he assumed editorship of Flower's popular "New Thought" magazine, a post which he held until 1905. During these years he built for himself an enduring place in the hearts of its readers. Article after article flowed from his pen. Meanwhile, he also founded his own Psychic Club and the Atkinson School of Mental Science. Both were located in the same building as Flower's Psychic Research and New Thought Publishing Company.


title: William Walker Atkinson

text: Throughout his subsequent career, Atkinson was thought to have written under many pseudonyms. It is not known whether he ever confirmed or denied authorship of these pseudonymous works, but all of the supposedly independent authors whose writings are now credited to Atkinson were linked to one another by virtue of the fact that their works were released by a series of publishing houses with shared addresses and they also wrote for a series of magazines with a shared roster of authors. Atkinson was the editor of all of those magazines and his pseudonymous authors acted first as contributors to the periodicals, and were then spun off into their own book-writing careers—with most of their books being released by Atkinson's own publishing houses.


title: William Walker Atkinson

text: One key to unravelling this tangled web of pseudonyms is found in "Advanced Thought" magazine, billed as "A Journal of The New Thought, Practical Psychology, Yogi Philosophy, Constructive Occultism, Metaphysical Healing, Etc."


title: William Walker Atkinson

text: This magazine, edited by Atkinson, advertised articles by Atkinson and Theron Q. Dumont—the latter two were later credited to Atkinson—and it had the same address as The Yogi Publishing Society, which published the works attributed to Yogi Ramacharaka.


title: William Walker Atkinson

text: "Advanced Thought" magazine also carried articles by Swami Bhakta Vishita, but when it came time for Vishita's writings to be collected in book form, they were not published by the Yogi Publishing Society. Instead they were published by The Advanced Thought Publishing Co., the same house that brought out the Theron Q. Dumont books—and published "Advanced Thought."


title: William Walker Atkinson

text: In the 1890s, Atkinson had become interested in Hinduism and after 1900 he devoted a great deal of effort to the diffusion of yoga and Oriental occultism in the West. It is unclear at this late date whether he actually ever subscribed to any form of Hindu religion, or merely wished to write on the subject.


title: William Walker Atkinson

text: According to unverifiable sources, while Atkinson was in Chicago at the World's Columbian Exposition in 1893, he met one Baba Bharata, a pupil of the late Indian mystic Yogi Ramacharaka (1799 - c.1893). As the story goes, Bharata had become acquainted with Atkinson's writings after arriving in America, the two men shared similar ideas, and so they decided to collaborate. While editing "New Thought" magazine, it is claimed, Atkinson co-wrote with Bharata a series of books which they attributed to Bharata's teacher, Yogi Ramacharaka. This story cannot be verified and—like the "official" biography that falsely claimed Atkinson was an "English author"—it may be a fabrication.


title: William Walker Atkinson

text: No record exists in India of a Yogi Ramacharaka, nor is there evidence in America of the immigration of a Baba Bharata. Furthermore, although Atkinson may have travelled to Chicago to visit the 1892 - 1893 World's Columbian Exposition, where the authentic Indian yogi Swami Vivekananda attracted enthusiastic audiences, he is only known to have taken up residence in Chicago around 1900 and to have passed the Illinois Bar Examination in 1903.


title: William Walker Atkinson

text: Atkinson's claim to have an Indian co-author was actually not unusual among the New Thought and New Age writers of his era. As Carl T. Jackson made clear in his 1975 article "The New Thought Movement and the Nineteenth Century Discovery of Oriental Philosophy", Atkinson was not alone in embracing a vaguely exotic "orientalism" as a running theme in his writing, nor in crediting Hindus, Buddhists, or Sikhs with the possession of special knowledge and secret techniques of clairvoyance, spiritual development, sexual energy, health, or longevity.


title: William Walker Atkinson

text: The way had been paved in the mid to late 19th century by Paschal Beverly Randolph, who wrote in his books "Eulis" and "Seership" that he had been taught the mysteries of mirror scrying by the deposed Indian Maharajah Dalip Singh. Randolph was known for embroidering the truth when it came to his own autobiography (he claimed that his mother Flora Randolph, an African American woman from Virginia, who died when he was eleven years old, had been a foreign princess) but he was actually telling the truth—or something very close to it, according to his biographer John Patrick Deveney—when he said that he had met the Maharajah in Europe and had learned from him the proper way to use both polished gemstones and Indian "bhattah mirrors" in divination.


title: William Walker Atkinson

text: In 1875, the year of Randolph's death, the Ukrainian-born Helena Petrovna Blavatsky founded the Theosophical Society, by means of which she spread the teachings of mysterious Himalayan enlightened yogis, the Masters of the Ancient Wisdom, and the doctrines of the Eastern philosophy in general. After this pioneer work, some representatives from known lineages of Indian and Asian spiritual and philosophical tradition like Vivekananda, Anagarika Dharmapala, Paramahansa Yogananda, and others, started coming to the West.


title: William Walker Atkinson

text: In any case, with or without a co-author, Atkinson started writing a series of books under the name Yogi Ramacharaka in 1903, ultimately releasing more than a dozen titles under this pseudonym. The Ramacharaka books were published by the Yogi Publication Society in Chicago and reached more people than Atkinson's New Thought works did. In fact, all of his books on yoga are still in print today.


title: William Walker Atkinson

text: Atkinson apparently enjoyed the idea of writing as a Hindu so much that he created two more Indian personas, Swami Bhakta Vishita and Swami Panchadasi. Strangely, neither of these identities wrote on Hinduism. Their material was for the most part concerned with the arts of divination and mediumship, including "oriental" forms of clairvoyance and seership. Of the two, Swami Bhakta Vishita was by far the more popular, and with more than 30 titles to his credit, he eventually outsold even Yogi Ramacharaka.


title: William Walker Atkinson

text: During the 1910s, Atkinson put his attention into another pseudonym, that of Theron Q. Dumont. This entity was supposed to be French, and his works, written in English and published in Chicago, combined an interest in New Thought with ideas about the training of the will, memory enhancement, and personal magnetism.


title: William Walker Atkinson

text: In 1903, the same year that he began his writing career as Yogi Ramacharaka, Atkinson was admitted to the Bar of Illinois. Perhaps it was a desire to protect his ongoing career as a lawyer that led him to adopt so many pseudonyms—but if so, he left no written account documenting such a motivation.


title: William Walker Atkinson

text: How much time Atkinson devoted to his law practice after moving to Chicago is unknown, but it is unlikely to have been a full-time career, given his amazing output during the next 15 years as a writer, editor, and publisher in the fields of New Thought, yoga, occultism, mediumship, divination, and personal success.


title: William Walker Atkinson

text: The high point of his prodigious capacity for production was reached in the late 1910s. In addition to writing and publishing a steady stream of books and pamphlets, Atkinson started writing articles for Elizabeth Towne's New Thought magazine "Nautilus", as early as November 1912, while from 1916 to 1919, he simultaneously edited his own journal "Advanced Thought". During this same period he also found time to assume the role of the honorary president of the International New Thought Alliance.


title: William Walker Atkinson

text: Among the last collaborators with whom Atkinson may have been associated was the mentalist C. Alexander, "The Crystal Seer," whose New Thought booklet of affirmative prayer, "Personal Lessons, Codes, and Instructions for Members of the Crystal Silence League", published in Los Angeles during the 1920s, contained on its last page an advertisement for an extensive list of books by Atkinson, Dumont, Ramacharaka, Vishita, and Atkinson's collaborator, the occultist L. W. de Laurence.


title: William Walker Atkinson

text: Atkinson was a prolific writer, and his many books achieved wide circulation among New Thought devotees and occult practitioners. He published under several pen names, including Magus Incognito, Theodore Sheldon, Theron Q. Dumont, Swami Panchadasi, Yogi Ramacharaka, Swami Bhakta Vishita, and probably other names not identified at present. He is also popularly held to be one (if not all) of the Three Initiates who anonymously authored "The Kybalion", which certainly resembles Atkinson's other writings in style and subject matter. Atkinson's two co-authors in the latter venture, if they even existed, are unknown, but speculation often includes names like Mabel Collins, Michael Whitty, Paul Foster Case, and Harriett Case.


title: William Walker Atkinson

text: A major collection of Atkinson's works is among the holdings of a Brazilian organization called Circulo de Estudos Ramacháraca. According to this group, Atkinson has been identified as the author or co-author (with individuals such as Edward E. Beals and Lauron William de Laurence) of 105 separate titles. These can be broken down roughly into the following groups:


title: William Walker Atkinson

text: These works treat themes related to the mental world, occultism, divination, psychic reality, and mankind's nature. They constitute a basis for what Atkinson called "New Psychology" or "New Thought". Titles include "Thought Vibration or the Law of Attraction in the Thought World," and "Practical Psychomancy and Crystal Gazing: A Course of Lessons on the Psychic Phenomena of Distant Sensing, Clairvoyance, Psychometry, Crystal Gazing, etc."


title: William Walker Atkinson

text: Although most of the Atkinson titles were published by Atkinson's own Advanced Thought Publishing Company in Chicago, with English distribution by L. N. Fowler of London, England, at least a few of his books in the "New Psychology" series were published by Elizabeth Towne in Mount Holyoke, Massachusetts, and offered for sale in her New Thought magazine "The Nautilus." One such title, for which Atkinson is credited as the author, with the copyright internally assigned to Towne, is "The Psychology of Salesmanship," published in 1912. The probable reason that Atkinson made an assignment of copyright to Towne is that his "New Psychology" books had initially been serialized in Towne's magazine, where he was a freelance writer from 1912 at least through 1914.


title: William Walker Atkinson

text: These include Atkinson's teachings on Yoga and Oriental philosophy, as well as New Thought and occult titles. They were written in such a way as to form a course of practical instruction.


title: William Walker Atkinson

text: When Atkinson wrote under the pseudonym Yogi Ramacharaka, he claimed to be a Hindu. As Ramacharaka, he helped to popularize Eastern concepts in America, with Yoga and a broadly-interpreted Hinduism being particular areas of focus. The works of Yogi Ramacharaka were published over the course of nearly ten years beginning in 1903. Some were originally issued as a series of lectures delivered at the frequency of one lesson per month. Additional material was issued at each interval in the form of supplementary text books.


title: William Walker Atkinson

text: Ramacharaka's "Advanced Course in Yoga Philosophy and Oriental Occultism" remains popular in some circles.


title: William Walker Atkinson

text: According to Atkinson's publisher, the Yogi Publication Society, some of these titles were inspired by a student of the "real" Yogi Ramacharaka, Baba Bharata, although there is no historical record that either of these individuals ever existed.


title: William Walker Atkinson

text: In reply to inquiries about Yogi Ramacharaka, this official information was provided by the Yogi Publication Society:


title: William Walker Atkinson

text: Note that in at least one point, this "official" account is false: William Walker Atkinson was an American, not "an English author" and L. N. Fowler, an occult publishing house, was the British publisher of books that Atkinson had published under various of his own imprints in Chicago.