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In mathematics, a bijection, bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with one element of the other set, each element of the other set is paired with one element of the first set. There are no unpaired elements. In mathematical terms, a bijective function f: X → Y is a one-to-one and onto mapping of a set X to a set Y; the term one-to-one correspondence must not be confused with one-to-one function. A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets the existence of a bijection means they have the same number of elements. For infinite sets, the picture is more complicated, leading to the concept of cardinal number—a way to distinguish the various sizes of infinite sets. A bijective function from a set to itself is called a permutation, the set of all permutations of a set forms a symmetry group. Bijective functions are essential to many areas of mathematics including the definitions of isomorphism, diffeomorphism, permutation group, projective map.

For a pairing between X and Y to be a bijection, four properties must hold: each element of X must be paired with at least one element of Y, no element of X may be paired with more than one element of Y, each element of Y must be paired with at least one element of X, no element of Y may be paired with more than one element of X. Satisfying properties and means that a pairing is a function with domain X, it is more common to see properties and written as a single statement: Every element of X is paired with one element of Y. Functions which satisfy property are said to be "onto Y " and are called surjections. Functions which satisfy property are called injections. With this terminology, a bijection is a function, both a surjection and an injection, or using other words, a bijection is a function, both "one-to-one" and "onto". Bijections are sometimes denoted by a two-headed rightwards arrow with tail, as in f: X ⤖ Y; this symbol is a combination of the two-headed rightwards arrow, sometimes used to denote surjections, the rightwards arrow with a barbed tail, sometimes used to denote injections.

Consider the batting line-up of a baseball or cricket team. The set X will be the players on the team and the set Y will be the positions in the batting order The "pairing" is given by which player is in what position in this order. Property is satisfied. Property is satisfied since no player bats in two positions in the order. Property says that for each position in the order, there is some player batting in that position and property states that two or more players are never batting in the same position in the list. In a classroom there are a certain number of seats. A bunch of students enter the instructor asks them to be seated. After a quick look around the room, the instructor declares that there is a bijection between the set of students and the set of seats, where each student is paired with the seat they are sitting in. What the instructor observed in order to reach this conclusion was that: Every student was in a seat, No student was in more than one seat, Every seat had someone sitting there, No seat had more than one student in it.

The instructor was able to conclude that there were just as many seats as there were students, without having to count either set. For any set X, the identity function 1X: X → X, 1X = x is bijective; the function f: R → R, f = 2x + 1 is bijective, since for each y there is a unique x = /2 such that f = y. More any linear function over the reals, f: R → R, f = ax + b is a bijection; each real number y is obtained from the real number x = /a. The function f: R →, given by f = arctan is bijective, since each real number x is paired with one angle y in the interval so that tan = x. If the codomain was made larger to include an integer multiple of π/2 this function would no longer be onto, since there is no real number which could be paired with the multiple of π/2 by this arctan function; the exponential function, g: R → R, g = ex, is not bijective: for instance, there is no x in R such that g = −1, showing that g is not onto. However, if the codomain is restricted to the positive real numbers R + ≡ g would be bijective.

The function h: R → R+, h = x2 is not bijective: for instance, h = h = 1, showing that h is not one-to-one. However, if the domain is restricted to R 0 + ≡ [ 0, + ∞ ) h would be bi

Tad DeLorm

Tad DeLorm is a retired German-born American football goalkeeper who played three seasons in the North American Soccer League and three in the American Soccer League. He now works at Classical Magnet School in Connecticut, he is a baseball coach. DeLorm attended Keene State College where he was a 1977 NAIA first team All American; that year, Keene went to the NAIA national men's soccer championship where they lost to Quincy University. In December 1996, Keene State inducted DeLorm into the school's Athletic Hall of Fame. In 1978, DeLorm turned professional with the Colorado Caribous in the North American Soccer League, he played two games, both as a substitute. The Caribous moved to Atlanta. In 1980, DeLorm moved to the Minnesota Kicks. In 1981, he signed with the Detroit Express of the American Soccer League, he played for them through at least 1983. In 1982, he was the ASL's top goalkeeper. ASL Leading Goalkeeper: 1982 NASL stats Chiefs indoor Kicks indoor

Broad Brook House

The Guilford Country Store is located at 475 Coolidge Highway in Guilford, Vermont, in the 1817 Broad Brook House, one of the oldest surviving tavern houses in the state, in continuous use as a general store since 1936. The building was listed on the National Register of Historic Places in 2011; the Guilford Country Store is set on the east side of the junction of Coolidge Highway and Guilford Center Road, in the center of Guilford's main village. It is a 2-1/2 story wood frame structure, with a side gable roof, clapboard siding, a foundation, stone, it is set close to the road, with its main facade facing west toward the road. The front is a symmetrical five bays wide, the former main entrance has simple Federal period styling, with sidelight windows and a simple cornice. A gable-roofed ell extends to the rear, a shed-roof ell extends across the northern facade, with a gable above the current main entrance, its upstairs ballroom has been converted into residential space. Broad Brook House was built in 1817 by Solomon Pratt, one of East Guilford's earliest landowners and businessmen.

He built the tavern at this point on what was the major north-south route through the area. Since the building has served a variety of important roles in the community, including as a meeting space, Masonic lodge, post office and barber shop. In 1936 George Fisher purchased the building, moved the Morse general store located across the street, into it. National Register of Historic Places listings in Windham County, Vermont Media related to Broad Brook House at Wikimedia Commons

Myken Lighthouse

Myken Lighthouse is a coastal lighthouse in Rødøy Municipality in Nordland county, Norway. It is located on the small island of Jutøya in the Myken island group, about 100 kilometres southwest of the town of Bodø, it was established in 1918 and was automated in 1975. The 30,200-candela light sits on top of a 12.5-metre tall white tower. The occulting light is white, red, or green light depending on direction, occulting once every six seconds; the light can be seen for up to 13.8 nautical miles. The light sits at an elevation of 40.3 metres above sea level. The light burns continuously from 1 August until 5 May each year; the light is not on during May through July due to the midnight sun. Lighthouses in Norway List of lighthouses in Norway Norsk Fyrhistorisk Forening

Simona Poustilnik

Simona Poustilnik is a Russian biologist, historian of science, is a science journalist. She has a PhD in the history of Russian science from the Institute for the History of Science and Technology, Russian Academy of Science, her major research is in the area of the history of Russian science of system theory, Bogdanov's tectology, Russian cosmism. She works in London, she is a member of the British Society for the History of Science and the Authors and Publicists International Association. Her main research interests are on the history of 20th-century Russian philosophy, her special interest is Bogdanov's Tektology, Russian Darwinism and development of proletarian science during the first postrevolutionary decades. Now she is working on an international project, exploring interactions among science, filmmaking in Bolshevik Russia, focusing on the relationships between system thinking in Russia and Soviet Constructivism. In her research she is connecting the understanding of the Russian Darwinists of “natural podbor” as ‘fine-tuning’ by nature and Bogdanov’s concept of tektological ‘podbor’ as the universal mechanism of the construction of any organization.

As Simona Poustlinik commented at a recent conference on Bogdanov: It is remarkable the extent to which Bogdanov anticipated the ideas which were to be developed in systems thinking in the twentieth century. He anticipated not only a general theory of systems and cybernetics, but ideas which entered into systems science in the late decades and which are associated with the names of Prigogine and Maturana. Sixty papers and monographs have been published, The following represent a selection of papers published in English and Russian: Poustilnik, Simona. 2016. “Bogdanov’s Tektology: A Science of Construction”. In Early Soviet Thought: Bogdanov and the Proletkult. Spherical Book I. Tangential Points Publication Series. Editor-in-Chief: Pia Tikka. Helsinki, Espoo: Aalto University. Poustilnik, S. Tectology in the Context of Intellectual Thought in Russia. Poustilnik, S. Alexander Bogdanov and the Genesis of the Systems Theory. Poustilnik, S.. The vegetable of Proletarian Revolution. In Nesavisimaja gaseta, 2004, N 10.

Poustilnik, S.. The role of gender in evolution of the man.. In Nesavisimaja gaseta, 2004, N 09. Poustilnik, S.. Hamlet from Red Star / In Nesavisimaja gaseta, 2002. N 12 Poustilnik, S. Biological Ideas in Tektology and Discussion Papers. In Alexander Bogdanov and the Origins of Systems Thinking in Russia. 1998. Pp. 63–73, 112-116, 127-128, 216-217, 313, 314. 1998, Ashgate, UK. Poustilnik, S. Modern Systems Science: Variations on a Theme? Center for Systems Studies, Research Memorandum, 1996, No 11, 20 p. Hull, UK Poustilnik, S. Reading the Tektology: Provisional Findings and Research Directions, Center for Systems Studies, Research Memorandum, 1995, N 7, 20 p. Hull, UK Poustilnik,S. Bogdanov's Tektology: Between Science and Philosophy. In Filosofskie issledovanija, Moscow, 1995, N 3, pp. 226–241 Poustilnik, S. Principle of Assemblage as Base of A. Bogdanov's Concept) In Voprosy filosofii, Moscow, 1995, N 8, pp. 24–30 Poustilnik, S. The Ideas of Evolution in A. Bogdanov's Tektology. In The Concept of Self-Organization in a Historical Perspective, 1994, Nauka, pp. 189–198 Poustilnik, S. Ivan Pavlov.

//Science in the USSR, 1987. N 3, pp. 100–107. Poustilnik, S. Returned life. In Science in the USSR, 1988. N 5, pp. 40–43. Poustilnik, S. Evolution of Immunity. In Science in the USSR, 1989. N 2, pp. 127–128. Simona Poustilnik. ALEKSANDR BOGDANOV'S TEKTOLOGY: A SCIENCE OF CONSTRUCTION Some rare Bogdanov photos courtesy of Simona Poustilnik Red Hamlet The Science for the better world Sex in Human Evolution Vavilov and Food of the future West Indian Matriarhat Avoska from Prince Charles Pure English doctrine Heretic of Medicine Why Alice asks too clever questions Origin of Gender Ethology Persons Organizational Dynamics Tectology Alexander Bogdanov and the Origins of Systems Thinking in Russia Centre for Systems Studies of University of Hull Когда человечество, кончив блуждания… Наука для лучшего мира Человечества сны золотые Какие яблони будут цвести на Марсе Умолчание об авариях часто оправдывали секретностью

NausicaƤ (character)

Nausicaä is a fictional character from Hayao Miyazaki's science fiction manga series Nausicaä of the Valley of the Wind and his anime film of the same name. Her story is set in the future on a post-apocalyptic Earth, where Nausicaä is the princess of the Valley of the Wind, a minor kingdom, she assumes the responsibilities of her ill father and succeeds him to the throne over the course of the story. Fueled by her love for others and for life itself, Nausicaä studies the ecology of her world to understand the Sea of Corruption, a system of flora and fauna which came into being after the Seven Days of Fire. Nausicaä's abilities include commitment, her magnetic personality attracts adoration from nearly all those who meet her. Her empathy allows her to communicate with many animals. Nausicaä joins a war between adjacent territories of the remaining inhabitable land. Assuming command of the Valley's small force sets her off on a journey that will alter the course of human existence. Many experts and manga enthusiasts have interpreted the character.

Nausicaä won the seventh Animage Grand Prix, the June 1987 Grand Prix, coming second in May 1991, again coming first in December 1992. In 2014, IGN ranked her as the ninth greatest anime character of all time, saying that "She is a genuine, charismatic character, loved and respected by her people, but she's a capable, though reluctant, warrior." Although a skillful fighter, Miyazaki's Nausicaä is peace-loving. She has an unusual gift for communicating with the giant insects and is noted for her empathy toward animals, humans, as well as other beings; as an intelligent girl, Nausicaä explores the toxic wasteland, which surrounds the realms and conducts scientific experiments in an attempt to define the true nature and origins of the toxic world in which she lives. Her explorations are facilitated by her skill at "windriding": flying with an advanced glider-like craft called Mehve, equipped with a jet-assist. Nausicaä has her origins in Miyazaki's aborted anime adaption of Richard Corben's Rowlf, a comic book about princess Maryara of the Land of Canis and her dog Rowlf.

Miyazaki found similarities with the Beast. The similarities inspired in him the desire to create a character to highlight the theme of "devotion, self-giving". Finding Corben's princess "bland", Miyazaki imagined "a young girl with character, brimming with sensitivity, to contrast her with an incapable father". Named "Yara" by Miyazaki, short for Corben's Maryara, this character was a young princess left "bearing the crushing weight of her destiny" when her sick father abdicated, bestowing the burden of the kingdom on her and forcing her to bridle her personal aspirations. Miyazaki's Yara is portrayed with a dog "which always accompanied her from a young age and cared for his mistress"; this pet dog is omitted when the story develops. Canis valley becomes Valley of the Wind and the pet dog is replaced with a fictional fox squirrel. Miyazaki intended Yara to wear short pants and moccasins, exposing her bare legs "to show vigorous movements and a dynamic character", but he had to abandon that idea as it did not make sense to expose her legs in the harsh environment that began to evolve as he developed the setting for the story.

The transition from Yara to Nausicaä came when Miyazaki began to develop his own character, after the project to adapt Corben's comic fell through. The character went through a few intermediate phases. Miyazaki had taken a liking to the name "Nausicaä" and he used it to rename his main character; the name comes from the Phaeacian princess Nausicaa of the Odyssey. The Nausicaa of the Odyssey was "renowned for her love of nature and music, her fervid imagination and disregard for material possessions", traits which Dani Cavallaro sees in Miyazaki's Nausicaä. Miyazaki has written that he identified with Bernard Evslin's description of the character in Gods and Demons, translated into Japanese by Minoru Kobayashi. Miyazaki expressed disappointment, about not finding the same splendor in the character he had found in Evlin's book, when he read Homer's original poem. Another inspiration is the main character from The Princess Who Loved Insects, a Japanese tale from the Heian period, one of the short stories collected in the Tsutsumi Chūnagon Monogatari.

It tells the story of a young princess, considered to be rather eccentric by her peers because, although of marriageable age, she prefers to spend her time outdoors studying insects, rather than grooming herself in accordance with the rules and expectations of the society of her era. The princess questions why other people see only the beauty of the butterfly and do not recognise the beauty and usefulness of the caterpillar from which it must grow. Miyazaki notes that the lady would not be perceived the same way in our own time as in the Heian period, he wonders about her ultimate fate, which isn't explained in the surviving fragments of the incomplete texts. Miyazaki has said that Evslin's Nausicaa reminds him of this princess, stating that the two characters "became fused into one and created the story". Miyazaki said that Nausicaä is "governed by a kind of animism". Miyazaki felt that it was important to make Nausicaä a female because he felt that this allowed him to create more complex villains, saying, "If we try to make an adventure story with a male lead, we have no choice but to do Indiana Jones, with a Nazi or someone else, a villain in everyone's eyes."

Miyazaki said of Nausicaä that " is not a protagonist who defeats an opponent, but a protagonist who understands, or accepts. She is someone who l