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# Mere Christianity ## Background ### The Case for Christianity (Broadcast Talks in UK) {#the_case_for_christianity_broadcast_talks_in_uk} The core of the first section centres on an argument from morality, the basis of which is the \"law of human nature\", a \"rule about right and wrong,\" which, Lewis maintained, i...
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# Mere Christianity ## Critical reception {#critical_reception} Initial reviews of *Mere Christianity* generally show enthusiasm, and most of them were from Christian publications. However, combining them with the reviews published decades later indicated a more mixed reception. The historian Stephanie L. Derrick obs...
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# Mere Christianity ## Legacy *Mere Christianity* has been referred to as a classic of Lewis\'s career, as well as of religious literature, particularly in the category of Christian apologetics. Commentators have also seen it as a guide to the basics of the Christian faith and to his theology. The book, along with hi...
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# Mathematical game A **mathematical game** is a game whose rules, strategies, and outcomes are defined by clear mathematical parameters.`{{Verify source|date=August 2021}}`{=mediawiki}`{{clarify|reason=What's a mathematical parameter?|date=February 2024}}`{=mediawiki} Often, such games have simple rules and match pro...
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# MIDI timecode **MIDI time code** (**MTC**) embeds the same timing information as standard SMPTE timecode as a series of small \'quarter-frame\' MIDI messages. There is no provision for the user bits in the standard MIDI time code messages, and SysEx messages are used to carry this information instead. The quarter-fr...
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# MIDI timecode ## Time code format {#time_code_format} The MIDI time code is 32 bits long, of which 24 are used, while 8 bits are unused and always zero. Because the full-time code messages require that the most significant bits of each byte are zero (valid MIDI data bytes), there are really only 28 available bits a...
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# Mass transfer **Mass transfer** is the net movement of mass from one location (usually meaning stream, phase, fraction, or component) to another. Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtration, and distillation. Mass transfer is used by different s...
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# Meconium aspiration syndrome **Meconium aspiration syndrome** (**MAS**), also known as **neonatal aspiration of meconium**, is a medical condition affecting newborn infants. It describes the spectrum of disorders and pathophysiology of newborns born in meconium-stained amniotic fluid (MSAF) and have meconium within ...
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# Meconium aspiration syndrome ## Pathophysiology As MAS describes a spectrum of disorders of newborns born through MSAF, without any congenital respiratory disorders or other underlying pathology, there are numerous hypothesised mechanisms and causes for the onset of this syndrome. Long-term consequences may arise f...
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# Meconium aspiration syndrome ## Pathophysiology ### Apoptosis Apoptosis is an important mechanism in the clearance of injured cells and in tissue repair, however too much apoptosis may cause harm, such as acute lung injury. Meconium induces apoptosis and DNA cleavage of lung airway epithelial cells, this is detecte...
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# Meconium aspiration syndrome ## Diagnosis Respiratory distress in an infant born through the darkly coloured MSAF as well as meconium obstructing the airways is usually sufficient to diagnose MAS. Additionally, newborns with MAS can have other types of respiratory distress such as tachypnea and hypercapnia. Sometim...
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# Meconium aspiration syndrome ## Treatment ### Antiinflammatories As inflammation is such a huge issue in MAS, treatment has consisted of anti-inflammatories. #### Glucocorticoids Glucocorticoids have a strong anti-inflammatory activity and works to reduce the migration and activation of neutrophils, eosinophils, ...
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# Meconium aspiration syndrome ## Treatment ### Previous treatments {#previous_treatments} Originally, it was believed that MAS developed as a result of the meconium being a physical blockage of the airways. Thus, to prevent newborns, who were born through MSAF, from developing MAS, suctioning of the oropharyngeal an...
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# Meconium aspiration syndrome ## Future research {#future_research} Research is being focused on developing both a successful method for preventing MAS as well as an effective treatment. For example, investigations are being made in the efficiency of anti-inflammatory agents, surfactant replacement therapy and antib...
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# Meconium **Meconium** is the earliest stool of a mammalian infant resulting from defecation. Unlike later feces, meconium is composed of materials ingested during the time the infant spends in the uterus: intestinal epithelial cells, lanugo, mucus, amniotic fluid, bile, and water. Meconium, unlike later feces, is vi...
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# Meconium ## Etymology The Latin term *meconium* derives from Greek *μηκώνιον*, *mēkōnion*, a diminutive of *μήκων*, *mēkōn* \'poppy\', in reference either to its tar-like appearance that may resemble some raw opium preparations or to Aristotle\'s belief that it induces sleep in the fetus. ## Other uses {#other_use...
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# Film promotion **Film promotion** is the practice of promotion specifically in the film industry, and usually occurs in coordination with the process of film distribution. Sometimes this is called the **press junket** or **film junket**. Film promotion generally includes press releases, advertising campaigns, mercha...
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# Film promotion ## Techniques ### Merchandising - Paid co-branding (*Eragon* in *American Chopper*-two episodes), or co-advertising (Aston Martin and James Bond films) of a product with the film - Promotional giveaways: branded drink cups, toys, or food combinations at fast food chains - Building a life-sized ...
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# Maggie Out \"**Maggie Out**\" was a chant popular during the miners\' strike, student grant protests, poll tax protests and other public demonstrations that fell within the time when Margaret Thatcher was the Prime Minister of the United Kingdom. ## Lyrics The chant called for her to be removed from that role. It ...
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# Magnetopause The **magnetopause** is the abrupt boundary between a magnetosphere and the surrounding plasma. For planetary science, the magnetopause is the boundary between the planet\'s magnetic field and the solar wind. The location of the magnetopause is determined by the balance between the pressure of the dynam...
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# Magnetopause ## Solar System magnetopauses {#solar_system_magnetopauses} Planet Number Magnetic moment Magnetopause distance Observed size of the magnetosphere variance of magnetosphere -------- -------- ------------------ ------------------------ ------------------------------------ ---------------...
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# Magnus **Magnus**, meaning \"Great\" in Latin, was used as cognomen of Gnaeus Pompeius Magnus in the first century BC. The best-known use of the name during the Roman Empire is for the fourth-century Western Roman Emperor Magnus Maximus. The name gained wider popularity in the Middle Ages among various European peop...
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# Magnus ## Fictional characters {#fictional_characters} - Magnus Bane, in *The Mortal Instruments* series by Cassandra Clare, and character in the TV Series Shadowhunters - Magnus Burnsides, one of the main protagonists in The Adventure Zone Dungeons & Dragons podcast - Magnus Chase, the main protagonist in th...
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# Magnetic tape **Magnetic tape** is a medium for magnetic storage made of a thin, magnetizable coating on a long, narrow strip of plastic film. It was developed in Germany in 1928, based on the earlier magnetic wire recording from Denmark. Devices that use magnetic tape can with relative ease record and play back aud...
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# Magnetic tape ## Uses ### Audio *Main article: Audiotape* Magnetic tape was invented for recording sound by Fritz Pfleumer in 1928 in Germany. Because of escalating political tensions and the outbreak of World War II, these developments in Germany were largely kept secret. Although the Allies knew from their moni...
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# MeatballWiki **MeatballWiki** is a wiki dedicated to online communities, network culture, and hypermedia. Containing a record of experience on running wikis, it is intended for \"discussion about wiki philosophy, wiki culture, instructions and observations.\" According to founder Sunir Shah, it ran on \"a hacked-up...
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# Matilda of Ringelheim **Matilda of Ringelheim** (`{{c.|892}}`{=mediawiki} -- 14 March 968), also known as **Saint Matilda**, was a Saxon noblewoman who became queen of Germany. Her husband, Henry the Fowler, was the first king from the Ottonian dynasty, and their eldest son, Otto the Great, restored the Holy Roman E...
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# Matilda of Ringelheim ## Life as a widow {#life_as_a_widow} Henry died in 936 in Memleben and was buried in Quedlinburg. It was here that Queen Matilda founded a convent in the same year. She lived there during the following years and took care of the family\'s legacy. Thus, Quedlinburg Abbey became not only the mo...
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# Monometer In poetry, a **monometer** is a line of verse with just one metrical foot. ## Example Monometer can be exemplified by this portion of Robert Herrick\'s poem \"Upon His Departure Hence\": Thus I Passe by, And die: As one, Unknown, And gone
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# Maasai Mara **Maasai Mara**, sometimes also spelt **Masai Mara** and locally known simply as **The Mara**, is a large national game reserve in Narok County, Kenya, contiguous with the Serengeti National Park in Tanzania. It is named in honour of the Maasai people, the ancestral inhabitants of the area, who migrated ...
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# Maasai Mara ## Wildlife Blue wildebeest are the dominant inhabitants of the Maasai Mara. Around July of each year, these animals migrate north from the Serengeti plains in search of fresh pasture, and return to the south around October. The Great Migration is one of the most impressive natural events worldwide. It ...
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# Maasai Mara ## Administration As of 2023, Mara Conservancy manages the Mara Triangle on behalf of the county, while the County Government of Narok manages the Narok Sector. The more visited eastern part of the park, known as the Maasai Mara National Reserve, is managed by the Narok County Council. The Mara Triangle...
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# Maasai Mara ## Threats Between 1989 and 2003, ungulates were monitored in the Maasai Mara on a monthly basis; the survey revealed a decline of giraffes by 75%, of common warthogs by 80%, of hartebeest by 76%, and of impala by 67%, attributed to the increased number of livestock grazing in the park and an increase i...
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# Medieval fortification **Medieval fortification** refers to medieval military methods that cover the development of fortification construction and use in Europe, roughly from the fall of the Western Roman Empire to the Renaissance. During this millennium, fortifications changed warfare, and in turn were modified to ...
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# Medieval fortification ## Fortification types {#fortification_types} ### City walls {#city_walls} An exact nature of the walls of a medieval town or city would depend on the resources available for building them, the nature of the terrain, and the perceived threat. In northern Europe, early in the period, walls wer...
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# Medieval fortification ## Construction Construction could sometimes take decades. The string of Welsh castles Edward I of England had built were an exception in that he focused much of the resources of his kingdom on their speedy construction. In addition to paid workers, forced levies of labourers put thousands of...
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# Medieval fortification ## Construction ### Doors A typical exterior wooden door might be made out of two or more layers of oak planks. The grain of the wood would run vertically on the front layer and horizontally on the back, like a simple form of plywood. The two layers would be held together by iron studs, and t...
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# Medieval fortification ## Transition to modern fortification {#transition_to_modern_fortification} From the mid-15th century onwards, the power of cannons grew and medieval walls became obsolete as they were too thin to offer any realistic protection against prolonged bombardment. As a consequence of this, medieval...
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# Montauban **Montauban** (`{{IPAc-en|US|ˌ|m|ɒ|n|t|oʊ|ˈ|b|ɒ|n|,_|ˌ|m|oʊ|n|t|oʊ|ˈ|b|ɒ̃}}`{=mediawiki}, `{{IPA|fr|mɔ̃tobɑ̃|lang|fr-Montauban.oga}}`{=mediawiki}; *Montalban* `{{IPA|oc|muntalˈβa|}}`{=mediawiki}) is a commune in the southern French department of Tarn-et-Garonne. It is the capital of the department and lies...
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# Montauban ## Sights Its fortifications have been replaced by boulevards beyond which extend numerous suburbs, while on the left bank of the Tarn is the suburb of Villebourbon, which is connected to the town by a remarkable bridge of the early 14th century. This bridge is known as *Pont Vieux* (i.e. \"Old Bridge\")....
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# Montauban ## Economy The commercial importance of Montauban is due rather to its trade in agricultural produce, horses, game and poultry, than to its industries, which include nursery-gardening, cloth-weaving, cloth-dressing, flour-milling, wood-sawing, and the manufacture of furniture, silk-gauze and straw hats. ...
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# Montauban ## Personalities Montauban was the birthplace of: - Jean-Baptiste Massip (1676--1751), 18th-century French playwright, poet, librettist - Marquis Jean-Jacques Lefranc of Pompignan (1709--1784), poet - Jacques Antoine Hippolyte, Comte de Guibert (1743--1790), general and military writer - Olympe d...
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# Montevideo Convention The **Montevideo Convention on the Rights and Duties of States** is a treaty signed at Montevideo, Uruguay, on December 26, 1933, during the Seventh International Conference of American States. At the conference, United States President Franklin D. Roosevelt and Secretary of State Cordell Hull ...
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# Meta element **Meta elements** are tags used in HTML and XHTML documents to provide structured metadata about a Web page. They are part of a web page\'s `head` section. Multiple Meta elements with different attributes can be used on the same page. Meta elements can be used to specify page description, keywords and a...
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# Meta element ## Meta element used in search engine optimization {#meta_element_used_in_search_engine_optimization} Meta elements provide information about the web page, which can be used by search engines to help categorize the page correctly. They have been the focus of a field of marketing research known as sear...
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# Meta element ## Meta element used in search engine optimization {#meta_element_used_in_search_engine_optimization} ### The `language` attribute {#the_language_attribute} The `language` attribute tells search engines what natural language the website is written in (e.g. English, Spanish or French), as opposed to the...
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# Meta element ## Meta element used in search engine optimization {#meta_element_used_in_search_engine_optimization} ### Effect on searching {#effect_on_searching} Google does not use HTML keyword or meta tag elements for indexing. The Director of Research at Google, Monika Henzinger, was quoted (in 2002) as saying, ...
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# Meta element ## HTTP message headers {#http_message_headers} Meta elements of the form `<meta http-equiv="foo" content="bar">` can be used as alternatives to HTTP headers. For example, `<meta http-equiv="expires" content="Wed, 21 June 2006 14:25:27 GMT">` would tell the browser that the page \"expires\" on June 21,...
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# Malpractice In the law of torts, **malpractice**, also known as professional negligence, is an \"instance of negligence or incompetence on the part of a professional\". Professionals who may become the subject of malpractice actions include: - **medical professionals**: a medical malpractice claim may be brought...
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# Misdemeanor A **misdemeanor** (American English, spelled **misdemeanour** elsewhere) is any \"lesser\" criminal act in some common law legal systems. Misdemeanors are generally punished less severely than more serious felonies, but theoretically more so than administrative infractions (also known as minor, petty, or...
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# Misdemeanor ## Penalties Misdemeanors usually do not result in the restriction of civil rights, but may result in loss of privileges, such as professional licenses, public offices, or public employment. Such effects are known as the collateral consequences of criminal charges. This is more common when the misdemean...
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# March 27
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# Lesser Poland Voivodeship **Lesser Poland Voivodeship** (*województwo małopolskie* `{{IPA|pl|vɔjɛˈvut͡stfɔ mawɔˈpɔlskʲɛ||LL-Q809 (pol)-KaMan-województwo małopolskie.wav}}`{=mediawiki}) is a voivodeship in southern Poland. It has an area of 15108 km2, and a population of 3,404,863 (2019). Its capital and largest city...
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# Lesser Poland Voivodeship ## History In the Early Middle Ages, the territory was inhabited by the Vistulans, an old Polish tribe. It formed part of Poland since its establishment in the 10th century, with the regional capital Kraków becoming the seat of one of Poland\'s oldest dioceses, est. in 1000, contributing t...
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# Lesser Poland Voivodeship ## Climate Located in Southern Poland, Lesser Poland is the warmest place in Poland with average summer temperatures between 23 C and 30 C during the day, often reaching 32 C to 38 C in July and August, the two warmest months of the year. The city of Tarnów, which is located in Lesser Pola...
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# Lesser Poland Voivodeship ## Administrative division {#administrative_division} Lesser Poland Voivodeship is divided into 22 counties (powiats): 3 city counties and 19 land counties. These are further divided into 182 gminas. The counties are listed in the following table (ordering within categories is by decreasi...
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# Lesser Poland Voivodeship ## Symbols Lesser Poland Voivodeship\'s symbols can be blazoned as follows: Coat of arms: *A traditional Iberian shield gules, an eagle argent displayed armed, legged, beaked, langued and crowned Or.* Flag: *Per fess argent and gules, a narrow fess Or.* ## Cuisine thumb\|upright=0.85\|...
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# Man'yōshū The `{{nihongo3|{{IPA|ja|maɰ̃joꜜːɕɯː|pron}}; literally "Collection of Ten Thousand Leaves"|万葉集|'''Man'yōshū'''}}`{=mediawiki} is the oldest extant collection of Japanese `{{transliteration|ja|[[waka (poetry)|waka]]}}`{=mediawiki} (poetry in Classical Japanese), compiled sometime after AD 759 during the Nar...
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# Man'yōshū ## Name Further information: Interpretation of the title of the Man\'yōshū The literal translation of the kanji that make up the title `{{Transliteration|ja|Man'yōshū}}`{=mediawiki} (*万 --- 葉 --- 集*) is \"ten thousand --- leaves --- collection\". The principal interpretations of this name, according to t...
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# Man'yōshū ## Poets The vast majority of the poems of the `{{Transliteration|ja|Man'yōshū}}`{=mediawiki} were composed over a period of roughly a century, with scholars assigning the major poets of the collection to one or another of the four \"periods\" discussed above. Princess Nukata\'s poetry is included in that...
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# Man'yōshū ## Plant species cited {#plant_species_cited} More than 150 species of grasses and trees are mentioned in approximately 1,500 entries of the `{{Transliteration|ja|Man'yōshū}}`{=mediawiki}. A `{{nihongo||[[:ja:万葉植物園|万葉植物園]]|Man'yō shokubutsu-en}}`{=mediawiki} is a botanical garden that attempts to contain ...
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# Maggieknockater **Maggieknockater** (*Magh an Fhùcadair*, meaning \"field of the fuller\" or \"plain of the hilly ridge\") is a hamlet on the A95 road between Craigellachie and Mulben in Scotland in the Moray council area, in the county of Banffshire. Until the early 1970s there was large apiary which was well know...
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# Millbridge, Plymouth **Millbridge** is a small neighbourhood of Plymouth, on the boundary of what used to be the towns of Plymouth and Devonport, in the English county of Devon. ## History What was originally a self-standing village (which has now been subsumed within the city) lies to the north of the toll bridge...
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# ML (programming language) ML}} `{{More citations needed|date=May 2015}}`{=mediawiki} `{{Infobox programming language | name = ML | logo = | paradigm = [[Multi-paradigm programming language|Multi-paradigm]]: [[Functional programming|functional]], [[Generic programming|generic]], [[Imperative programming|imperative]] ...
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# ML (programming language) ## Examples The following examples use the syntax of Standard ML. Other ML dialects such as OCaml and F# differ in small ways. ### Factorial The factorial function expressed as pure ML: ``` sml fun fac (0 : int) : int = 1 | fac (n : int) : int = n * fac (n - 1) ``` This describes the...
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# Mambo (music) **Mambo** is a genre of Cuban dance music pioneered by the charanga Arcaño y sus Maravillas in the late 1930s and later popularized in the big band style by Pérez Prado. It originated as a syncopated form of the danzón, known as danzón-mambo, with a final, improvised section, which incorporated the *gu...
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# Mambo (music) ## History ### 1940-1952: \"Brass\" Mambo in Mexico City {#brass_mambo_in_mexico_city} Dámaso Pérez Prado, a pianist and arranger from Matanzas, Cuba, established his residence in Havana at the beginning of the 1940s and began to work at night clubs and orchestras, such as Paulina Alvarez\'s and Casin...
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# Message transfer agent Within the Internet email system, a **message transfer agent** (**MTA**), **mail transfer agent**, or **mail relay** is software that transfers electronic mail messages from one computer to another using the Simple Mail Transfer Protocol. In some contexts, the alternative names **mail server**...
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# The Medallions **The Medallions** were an American doo-wop vocal group led by Vernon Green (1937--2000). ## History The group formed in Los Angeles, California, United States, in 1954, after Vernon Green was heard singing on the street by Walter \"Dootsie\" Williams, the owner of Dootone Records. Green -- who walk...
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# Melting **Melting**, or fusion, is a physical process that results in the phase transition of a substance from a solid to a liquid. This occurs when the internal energy of the solid increases, typically by the application of heat or pressure, which increases the substance\'s temperature to the melting point. At the ...
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# Melting ## Related concept {#related_concept} In ultrashort pulse physics, a so-called nonthermal melting may take place. It occurs not because of the increase of the atomic kinetic energy, but because of changes of the interatomic potential due to excitation of electrons. Since electrons are acting like a glue sti...
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# Martin Waldseemüller **Martin Waldseemüller** (c. 1470 -- 16 March 1520) was a German cartographer and humanist scholar. Sometimes known by the Hellenized form of his name, **Hylacomylus**, his work was influential among contemporary cartographers. His collaborator Matthias Ringmann and he are credited with the firs...
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# Martin Waldseemüller ## Life and works {#life_and_works} ### 1507 world map {#world_map} In 1506, the *Gymnasium* obtained a French translation of the Soderini Letter, a booklet attributed to Amerigo Vespucci that provided a sensational account of four alleged Vespucci voyages to explore the coast of lands recently...
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# Martin Waldseemüller ## Honours - Waldseemüller Rock in Antarctica is named after Martin Waldseemüller
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# Matthew the Apostle Matthew}} `{{Redirect|Saint Matthew||Saint Matthew (disambiguation)}}`{=mediawiki} **Matthew the Apostle** was one of the twelve apostles of Jesus. According to Christian traditions, he was also one of the four Evangelists as author of the Gospel of Matthew, and thus is also known as **Matthew t...
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# Matthew the Apostle ## Veneration Matthew is recognized as a saint in the Roman Catholic, Eastern Orthodox, Lutheran and Anglican churches (see St. Matthew\'s Church). His tomb is located in the crypt of Salerno Cathedral in southern Italy. ### Roman Catholicism {#roman_catholicism} The Roman Catholic Church cele...
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# Matthew the Apostle ## Gallery <File:Saint> Matthew2.jpg\|Saint Matthew in the Ebbo Gospels <File:MattewIslam.JPG>\|*Saint Matthew writing the Gospel with an angel holding the volume*, an Islamic miniature `{{c.|1530}}`{=mediawiki} by Kesu Das for the Mughal king <File:Caravaggio> --- The Calling of Saint Matthew.j...
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# TiVo Corporation \| net_income_year = December 31, 2017 \| assets = `{{decrease}}`{=mediawiki} US\$3,163,678,000 \| assets_year = December 31, 2017 \| num_employees = 1,700+ \| num_employees_year = 2017 \| website = `{{URL|tivo.com}}`{=mediawiki} }} **TiVo Corporation**, formerly known as the **Rovi Corporation** a...
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# TiVo Corporation ## Products ### Guides Rovi provides guides for service providers and CE manufacturers. - TotalGuide xD, a white-label media guide for mobile devices for finding, managing, and watching TV shows and movies. This also controlled the set top boxes. - TotalGuide CE, a media guide for CE manufact...
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# TiVo Corporation ## Legacy products {#legacy_products} The company historically developed technologies and products that helped protect content from being pirated. Its two core legacy products were called RipGuard and the Analog Protection System (APS). ### RipGuard Macrovision introduced its RipGuard technology ...
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# Class (set theory) In set theory and its applications throughout mathematics, a **class** is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. Classes act as a way to have set-like collections while differing from sets so as to ...
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# Class (set theory) ## Classes in formal set theories {#classes_in_formal_set_theories} ZF set theory does not formalize the notion of classes, so each formula with classes must be reduced syntactically to a formula without classes. For example, one can reduce the formula $A = \{x\mid x=x \}$ to $\forall x(x\in A\le...
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# Mathilde Roth Schechter **Mathilde Roth Schechter** (also **Matilda**; December 16, 1859 -- August 27, 1924) was the American founder of the U.S. National Women\'s League of Conservative Judaism in 1918. ## Biography Schechter was born in Breslau, Prussia (now Wrocław, Poland). She was married to Dr. Solomon Schec...
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# Mellitus **Mellitus** (`{{IPAc-en|m|ə|ˈ|l|aɪ|t|ə|s}}`{=mediawiki}; died 24 April 624) was the first bishop of London in the Saxon period, the third archbishop of Canterbury, and a member of the Gregorian mission sent to England to convert the Anglo-Saxons from their native paganism to Christianity. He arrived in 601...
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# Mellitus ## Journey to England {#journey_to_england} Pope Gregory I sent Mellitus to England in June 601, in response to an appeal from Augustine, the first Archbishop of Canterbury. Augustine needed more clergy to join the Gregorian mission that was converting the kingdom of Kent, then ruled by Æthelberht, from pa...
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# Mellitus ## Bishop of London {#bishop_of_london} Exactly when Mellitus and his party arrived in England is unknown, but he was certainly in the country by 604, when Augustine consecrated him as bishop in the province of the East Saxons, making Mellitus the first Bishop of London after the Roman departure (London wa...
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# Mellitus ## Archbishop and death {#archbishop_and_death} Mellitus succeeded Laurence as the third Archbishop of Canterbury after the latter\'s death in 619. During his tenure as archbishop, Mellitus supposedly performed a miracle in 623 by diverting a fire that had started in Canterbury and threatened the church. H...
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# Mineraloid A **mineraloid** is a naturally occurring substance that resembles a mineral, but does not demonstrate the crystallinity of a mineral. Mineraloid substances possess chemical compositions that vary beyond the generally accepted ranges for specific minerals, for example, obsidian is an amorphous glass and n...
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# Mathematical formulation of quantum mechanics The **mathematical formulations of quantum mechanics** are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear ...
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# Mathematical formulation of quantum mechanics ## History of the formalism {#history_of_the_formalism} ### The \"old quantum theory\" and the need for new mathematics {#the_old_quantum_theory_and_the_need_for_new_mathematics} In the 1890s, Planck was able to derive the blackbody spectrum, which was later used to av...
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# Mathematical formulation of quantum mechanics ## History of the formalism {#history_of_the_formalism} ### The \"new quantum theory\" {#the_new_quantum_theory} Werner Heisenberg\'s matrix mechanics was the first successful attempt at replicating the observed quantization of atomic spectra. Later in the same year, Sc...
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# Mathematical formulation of quantum mechanics ## Postulates of quantum mechanics {#postulates_of_quantum_mechanics} A physical system is generally described by three basic ingredients: states; observables; and dynamics (or law of time evolution) or, more generally, a group of physical symmetries. A classical descri...
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# Mathematical formulation of quantum mechanics ## Postulates of quantum mechanics {#postulates_of_quantum_mechanics} ### Measurement on a system {#measurement_on_a_system} #### Description of physical quantities {#description_of_physical_quantities} Physical observables are represented by Hermitian matrices on `{{...
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# Mathematical formulation of quantum mechanics ## Postulates of quantum mechanics {#postulates_of_quantum_mechanics} ### Symmetrization postulate {#symmetrization_postulate} In quantum mechanics, two particles can be distinguished from one another using two methods. By performing a measurement of intrinsic propertie...
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# Mathematical formulation of quantum mechanics ## Mathematical structure of quantum mechanics {#mathematical_structure_of_quantum_mechanics} ### Pictures of dynamics {#pictures_of_dynamics} is Dyson\'s time-ordering symbol. (This symbol permutes a product of noncommuting operators of the form $B_1(t_1)\cdot B_2(t...
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# Mathematical formulation of quantum mechanics ## Problem of measurement {#problem_of_measurement} The picture given in the preceding paragraphs is sufficient for description of a completely isolated system. However, it fails to account for one of the main differences between quantum mechanics and classical mechanic...
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# Mathematical formulation of quantum mechanics ## List of mathematical tools {#list_of_mathematical_tools} Part of the folklore of the subject concerns the mathematical physics textbook Methods of Mathematical Physics put together by Richard Courant from David Hilbert\'s Göttingen University courses. The story is to...
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# Microlith A **microlith** is a small stone tool usually made of flint or chert and typically a centimetre or so in length and half a centimetre wide. They were made by humans from around 60,000 years ago, across Europe, Africa, Asia and Australia. The microliths were used in spear points and arrowheads. Microliths ...
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# Microlith ## Types ### Laminar and non-geometric microliths {#laminar_and_non_geometric_microliths} Laminar microliths date from at least the Gravettian culture or possibly the start of the Upper Paleolithic era, and they are found all through the Mesolithic and Neolithic eras. \"Noailles\" burins and micro-gravet...
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# Microlith ## Types ### Geometric microliths {#geometric_microliths} Geometric microliths are a clearly defined type of stone tool, at least in their basic forms. They can be divided into trapezoid, triangular and lunate (half-moon) forms, although there are many subdivisions of each of these types. A microburin is ...
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