the-french-artist/wikipedia_20220301.simple_sentence_embeddings huggingface dataset:
Surjective function 
 For every element b in the codomain B, there is at least one element a in the domain A such that f(a)=b.
Surjective function 
 This means that no element in the codomain is unmapped, and that the range and codomain of f are the same set.
Surjective function 
 The term surjection and the related terms injection and bijection were introduced by the group of mathematicians that called itself Nicholas Bourbaki.
Surjective function 
 In the 1930s, this group of mathematicians published a series of books on modern advanced mathematics.
Surjective function 
 The French prefix sur means above or onto and was chosen since a surjective function maps its domain on to its codomain.
Surjective function 
 where the element  is called the image of the element , and the element  a pre-image of the element .
Surjective function 
 Let f(x):ℝ→ℝ be a real-valued function y=f(x) of a real-valued argument x. (This means both the input and output are numbers.)
Surjective function 
 Graphic meaning: The function f is a surjection if every horizontal line intersects the graph of f in at least one point.
Surjective function 
 Analytic meaning: The function f is a surjection if for every real number yo we can find at least one real number xo such that yo=f(xo).
Surjective function 
 In mathematics, we can find exact (analytic) roots only of polynomials of first, second (and third) degree.
Surjective function 
 Since the domain of the polynomial is ℝ, the means that ther is at least one pre-image xo in the domain.
Surjective function 
 Note: One can make a non-surjective function into a surjection by restricting its codomain to elements of its range.
Surjective function 
 Example: The logarithmic function base 10  f(x):(0,+∞)→ℝ defined by f(x)=log(x) or y=log10(x) is a surjection (and an injection). (
Organic reaction 
 The basic organic chemistry reaction types are addition reactions, elimination reactions, substitution reactions, pericyclic reactions, rearrangement reactions, photochemical reactions and redox reactions.
Organic reaction 
 Organic reactions produce many man-made chemicals such as drugs, plastics, food additives, and fabrics.
Shikasta (novel) 
 British Nobel Prize in Literature-winner Doris Lessing wrote it as the first book in her five-book Canopus in Argos series.
Shikasta (novel) 
 The book has a subtitle, "Personal, psychological, historical documents relating to visit by Johor (George Sherban) Emissary (Grade 9) 87th of the Period of the Last Days". '
Shikasta (novel) 
 The novel is the history of the planet Shikasta under the influence of three galactic empires: Canopus, Sirius, and their shared enemy, Puttiora.
Shikasta (novel) 
 The novel shows the Earth's prehistory, how things became worse, the "Century of Destruction" (the 20th-century), and the Apocalypse (World War III).
Shikasta (novel) 
 Shikasta uses stories and images from the Old Testament and is influenced by spiritual and mystical themes in Sufism.
Shikasta (novel) 
 The story of Shikasta is retold in the third book of the Canopus series, The Sirian Experiments (1980).
Shikasta (novel) 
 Shikasta appears again in the fourth book in the series, The Making of the Representative for Planet 8 (1982).
Shikasta (novel) 
 The Zones that are briefly mentioned in Shikasta are the subject of the second book in the series, The Marriages Between Zones Three, Four and Five (1980).
HOMO/LUMO 
 For example, if a molecule has enough electrons to fill 15 MOs, the 15 MOs with the lowest energy levels will be occupied.
HOMO/LUMO 
 The 15th MO on the list would be called the "highest occupied molecular orbital" (HOMO) and the 16th MO on the list would be the "lowest unoccupied molecular orbital" (LUMO).
HOMO/LUMO 
 The band gap can sometimes serve as a measure of the excitability of the molecule: the smaller the energy, the more easily a molecule's electrons will be excited.
Roald Hoffmann 
 Roald Hoffmann (born July 18, 1937) is a Polish-born American theoretical chemist of Jewish descent.
Substituent 
 In organic chemistry and biochemistry, substituent is the name for a single atom or for a group of atoms that take the position of another atom in a molecule.
Substituent 
 The terms substituent, side chain, group, branch, or pendant group are used in the same way to describe branches from a parent structure.
Substituent 
 In polymers, side chains extend from a backbone structure, while they are attached to the alpha carbon atoms of the amino acid backbone in proteins.
Substituent 
 The substituent group is listed first with a suffix to describe how it is attached to the main carbon chain.
Substituent 
 The suffix -yl is used when naming organic compounds that contain a single bond replacing one hydrogen.
Substituent 
 The phrases most-substituted and least-substituted are often used to describe molecules and predict their products.
Substituent 
 Markovnikov's rule predicts that the hydrogen adds to the carbon of the alkene functional group that has the greater number of hydrogen substituents.
Substituent 
 Zaitsev's rule predicts that the major reaction product is the alkene with the more highly substituted (more stable) double bond.
Greater rhea 
 The species, first described by Carl Linnaeus in 1758, is found in Argentina, Bolivia, Brazil, Paraguay, and Uruguay.
Greater rhea 
 The greater rhea takes its scientific name from the Greek goddess Rhea and the Latin word for "America".
Petr Kalandra 
 Petr Kalandra (March 10, 1950 – September 7, 1995) was a Czech musician, guitarist, harmonica player, vocalist and songwriter.
Till Eulenspiegel's Merry Pranks 
 Till Eulenspiegel's Merry Pranks (German: Till Eulenspiegels lustige Streiche) is a very well-known piece of music for orchestra by Richard Strauss.
Till Eulenspiegel's Merry Pranks 
 In this work, Richard Strauss describes the adventures of Till Eulenspiegel who was the character in a series of stories written in Germany many years ago.
Till Eulenspiegel's Merry Pranks 
 There is a small clarinet (normally an E flat clarinet, although in Strauss's day he used a D clarinet) that describes the character of Till.
Till Eulenspiegel's Merry Pranks 
 He rides his horse through the market and knocks lots of things off the stalls, then flirts with the girls (the first violin plays a theme which suggests love).
Till Eulenspiegel's Merry Pranks 
 Till pleads to be let free and tries to joke his way out of his troubles, but the executioner takes no notice.
Till Eulenspiegel's Merry Pranks 
 There is a short silence, then the music returns to the opening 'Once upon a Time' theme, but the music finishes with a little joke, as if saying that someone like Till can never be destroyed.
Beatová síň slávy 
 Beatová síň slávy (Beat Hall of Fame or shortly BSS) is something like the Rock and Roll Hall of Fame.
Thomson's gazelle 
 They can be found on ranches and farmland throughout East Africa, and survive long after other species have been killed off or migrated away.
Thomson's gazelle 
 Tommies stand at about half a meter (22-26 inches) tall and weigh in between 15 and 25 kilograms (35-55 pounds).
Thomson's gazelle 
 The tommy has adapted to drier life on the open grass plains of East Africa, mainly southern Kenya and northern Tanzania.
Thomson's gazelle 
 Although tommies have many predators, including cheetahs, lions, leopards, crocodiles and hyenas, they are frequently the last animals left on an abandoned ranch or farmland.
Thomson's gazelle 
 Their major predators are cheetahs, which can run faster, but gazelles can outlast them in long chases and are able to make turns more speedily.
Thomson's gazelle 
 This small antelope-gazelle can run extremely fast, from , to 96 km/h (60 mph) and zigzag, a peculiarity which often saves it from predators.
Thomson's gazelle 
 Sometimes they are also chased by leopards, lions and hyenas, but the gazelles are faster and more agile; these predators attack especially the young or infirm individuals.
Thomson's gazelle 
 They can also be devoured by crocodiles and pythons, and their fawns are sometimes the prey of eagles, jackals, and baboons.
Thomson's gazelle 
 A noticeable behaviour of Thomson's gazelles is their bounding leap, known as stotting or pronking, used to startle predators and display strength.
Diene 
 In organic chemistry, a diene ( ) or diolefin ( ) is a hydrocarbon that contains two carbon pi bonds.
Diene 
 Cumulated dienes have the double bonds sharing a common atom as in a group of compounds called allenes.
Diene 
 Many specialized dienes have been developed to exploit this reactivity for the synthesis of natural products, e.g. Danishefsky’s diene.
Conjugated system 
 In chemistry, a conjugated system is a system of continuous and parallel p-orbitals with delocalized electrons.
Conjugated system 
 In general, conjugated systems may lower the overall energy of the molecule and increase how steady it is.
Conjugated system 
 In most cases, the atoms in a molecule are held together by single bonds (where orbitals from adjacent atoms overlap).
Conjugated system 
 Molecules which have a conjugated system have unique properties different from normal compounds created by the sharing of the delocalized electrons among many atoms.
Conjugated system 
 Conjugation is the overlap of one p-orbital with another across a sigma bond (or single bond) that is in between. (
Conjugated system 
 A conjugated system has a region of overlapping p-orbitals, bridging the single bonds that are between.
Conjugated system 
 The largest conjugated systems (with the greatest number of shared electrons) are in graphite, conductive polymers, and carbon nanotubes.
Conjugated system 
 For example, furan (see picture) is a five-membered ring with two alternating double bonds and an oxygen in position 1.
Conjugated system 
 Also, pi orbitals needed for conjugation can come from substituent groups α to the ring like: a carbonyl group (C=O), an imine group (C=N), a vinyl group (C=C), or an anion.
Conjugated system 
 Chromophores are light-absorbing parts of a molecule that can cause a compound to have a visible color.
Conjugated system 
 Chromophores are often present in various organic compounds and sometimes present in polymers that are colored or glow in the dark.
Conjugated system 
 Chromophores often consist of a series of conjugated bonds and/or ring systems, which can include C-C, C=C, C=O, or N=N bonds.
Prince Fielder 
 Prince Semien Fielder (born May 9, 1984 in Ontario, California) is an American Major League Baseball player.
Prince Fielder 
 He debuted in the MLB for the Milwaukee Brewers on June 13, 2005 when he was called up from the minor league Nashville Sounds.
Prince Fielder 
 He was sent back down but was called up again on August 17, 2005 where he finished the season with the Brewers and was used as a pinch-hitter.
Kurt Alder 
 Alder was born in the industrial area of Königshütte, Silesia (modern day Chorzów, Upper Silesia, Poland).
Kurt Alder 
 He studied chemistry at the University of Berlin from 1922, and later at the University of Kiel where his earned a PhD in 1926 for work supervised by Diels.
Kurt Alder 
 In 1936 he left Kiel to join I G Farben Industrie at Leverkusen, where he worked on synthetic rubber.
Kurt Alder 
 In 1940, he was appointed Professor of Experimental Chemistry and Chemical Technology at the  University of Cologne and Director of the Institute of Chemistry there.
Kurt Alder 
 Throughout this time and despite the many obstacles to original research in Europe at the time, he continued a systematic program of investigations of his particular interests in the synthesis of organic compounds.
Kurt Alder 
 Alder received several honorary degrees and other awards, most famously the 1950 Nobel Prize in Chemistry which he shared with his teacher Diels for their work on what is now known as the Diels–Alder reaction.
Kenichi Fukui 
 "It is only after the remarkable appearance of the brilliant work by Woodward and Hoffmann that I have become fully aware that not only the density distribution but also the nodal property of the particular orbitals have significance in such a wide variety of chemical reactions."
Woodward's rules 
 They give information about the wavelength of the absorption maximum (symbol λmax ) in an ultraviolet-visible (UV) spectrum of a compound.
Woodward's rules 
 The rules build the prediction on the type of chromophores present, the substituents on the chromophores, and changes due to the solvent.
Woodward's rules 
 A diene is either homoannular with both double bonds contained in one ring or heteroannular with two double bonds distributed between two rings.
Woodward's rules 
 This diene group has 4 alkyl substituents (labeled 1,2,3,4) and the double bond in one ring is exocyclic to the other (adding 5 nm for an exocyclic double bond).
Lemon shark 
 The first dorsal fin is low and positioned at the back of the pectoral fins, and the second dorsal is of similar shape and size and positioned at the front of the anal fin.
Lemon shark 
 The pelvic fin weakly concave (curving inwards) rear margins, and the pectoral fin's outer margin is slightly convex (curving outwards), and both fins are weakly falcate.
Lemon shark 
 The middle ridge is high, sharp and separated by deep furrows, and the back margins are opposite the primary ridges.
Lemon shark 
 Lemon sharks usually range between the lengths of , and have a growth rate of 0.21 inches per year (0.54 cm per year).
Lemon shark 
 After a gestation period of 10 to 12 months, pregnant females enter shallow nursery areas in spring and summer to give birth to litters of 4 to 17 pups.
Lemon shark 
 The pups have a very slow growth rate and remain within nursery grounds for quite a long time, where they are in less danger from predators.
Lemon shark 
 The mangroves that the young mainly inhabit are highly productive waters, creating an excellent area for feeding, but also an area of very low oxygen content.
Lemon shark 
 However, the Lemon shark has many adaptations that increase oxygen uptake, such as blood with an unusually high affinity for oxygen.
Lemon shark 
 Maturity is reached at about 6 and a half years of age, and it is believed that the Lemon shark lives for up to 27 years.
Lemon shark 
 Since Lemon sharks can blend into their surroundings so well, it is easy for someone to accidentally disrupt the shark.
Lemon shark 
 Still, many experts worry that they won’t copy all they do in the wild in captivity so they don’t usually rely on such details and observations as facts if they can’t also be confirmed in the wild.
Lemon shark 
 The Lemon Shark is gentle in nature and doesn’t seem to be aggressive towards people, including divers.
Lemon shark 
 Catfish, mullet, jacks, croakers, porcupine fish, cowfish, guitarfish, stingrays, eagle rays, crabs and crayfish make up most of the Lemon shark's diet.
Lemon shark 
 Lemon sharks will eat until full with the rate of digestion dependent on the amount of food consumed at a single time.
Lemon shark 
 The Lemon shark lives in the tropical and subtropical waters of the coastal areas of the Atlantic and Pacific Oceans.
Lemon shark 
 They are often found in shallow waters near coasts and islands, by coral reefs, mangroves, bays, and sometimes even river mouths.
Lemon shark 
 According to the International Shark Attack File, there have been only 10 unprovoked attacks by Lemon sharks, all occurring in Florida and the Caribbean.
Lemon shark 
 The Lemon shark is targeted by commercial and recreational fishermen along the U.S, Atlantic Ocean, Caribbean, and in the eastern Pacific Ocean.
Lemon shark 
 The US bottom longline fishery commonly targets this species and it is also caught as by-catch in both pelagic and gillnet fisheries.
Lemon shark 
 There is some concern that populations in the western north Atlantic and eastern Pacific Ocean are in danger due to over-fishing.
Spined pygmy shark 
 These sharks live very deep in the water (down to 6,500 feet) but they migrate up to about 650 feet at night, to hunt.
Nurse shark 
 The nurse shark (Ginglymostoma cirratum) is a bottom-dwelling shark, and is the only known species in the genus Ginglymostoma.
Nurse shark 
 The Nurse shark is common in the coastal tropical and subtropical waters of the eastern Pacific and the Atlantic Ocean.
Nurse shark 
 Nurse sharks have two spineless, rounded dorsal fins, with the first dorsal fin being much larger than the second, and they have one anal fin.
Nurse shark 
 The sub-terminal mouth is placed well in front of the eyes, the spiracles are small, and there are long barbels on the mouth.
Nurse shark 
 The young that are up to 60 cm (24 inches) long have small black spots, with an area of lightness surrounding each spot, covering the entire body.
Nurse shark 
 Studies show that Nurse sharks kept out of sunlight become slightly lighter in colour, as compared to Nurse sharks which are exposed to sunlight.
Nurse shark 
 Nurse sharks with unusally colours (such as brilliant yellow or milky white) have been reported several times.
Nurse shark 
 This means that there is no overlapping between the teeth, and that forward movements of teeth leading to shedding does not depend on other teeth.
Nurse shark 
 With sharks that have many overlapping teeth, the replacement of teeth cannot take place until the outer blocking teeth are lost.
Nurse shark 
 Averaging 2.2-2.7 metres (7.2-9 feet) in total length, and weighing 75-105 kg (165-232 pounds), adult females reach a larger size than adult males which are around 2.1-2.6 metres (7-8.5 feet) long, and weigh around 90-120 kg (198-265 pounds).
Nurse shark 
 Females reach maturity at about 2.3 metres (7.6 feet), and males reach maturity at about 2.1 metres (7 feet).
Nurse shark 
 New-born Nurse sharks range in length from 28 to 30 cm (11 to 12 inches), with growth rates of 13 cm (5 inches) and 2.3 kg (5 pounds) per year.
Nurse shark 
 In the Atlantic, it ranges from Senegal to Gabon, Rhode Island to southern Brazil, and Mexico to Peru.
Nurse shark 
 This species is common in shallow waters throughout the West Indies, south Florida and the Florida Keys.
Nurse shark 
 The Nurse shark is a nocturnal animal that rests on sandy bottoms or in caves or crevices in shallow waters during the day.
Nurse shark 
 They are usually found in groups of up to 40, as they lie very close together, sometimes even piling on one another.
Nurse shark 
 In addition to swimming near the bottom, the Nurse shark can move around on the sea floor, using its flexible, muscular pectoral fins as limbs.
Nurse shark 
 Large juveniles and adults are usually found around deep coral reefs, and rocky areas at depths of up to 3-75 metres (10-246 feet) during the daytime, and then they migrate into shallower waters of less than 20 metres (66 feet) deep after darkness.
Nurse shark 
 Young Nurse sharks up to 1.7 metres (6 feet) are usually found around shallow coral reefs, grass flats or mangrove islands in waters which are 1-4 metres (3-13 feet) deep.
Nurse shark 
 Nurse sharks have been known to repeatedly return to the same caves and crevices in which they have rested before.
Nurse shark 
 Nurse sharks are sluggish, and are not aggressive towards humans and will not attack unless they are provoked.
Nurse shark 
 They feed on fish (such as catfish, mullets, and pufferfish)  stingrays, mollusks (such as octopuses, squids, and clams),  sea snakes, and tunicates.
Nurse shark 
 They also consume algae, coral,  crustaceans (such as lobsters, shrimps, and crabs), sea urchins, snails and bivalves.
Nurse shark 
 The Nurse shark is one of the few species of sharks that can remain motionless in the water when it wants to.
Nurse shark 
 This not only helps it to conserve energy, it gives the Nurse shark an advantage when it comes to hunting.
Nurse shark 
 As it stays motionless, it's prey usually donesn't notice it, giving the Nurse shark a chance to ambush it's prey.
Nurse shark 
 Although the Nurse shark has no real predator, remains of Nurse sharks have been found in the stomachs of Tiger sharks, and Lemon sharks.
Spiny dogfish 
 It is a small species of shark, with an average length of 28-39 inches (70–100 cm), and reaching a maximum weight of 9.8 kg.
Spiny dogfish 
 The dogfish is found in the Atlantic and Pacific Ocean, and can be found from the surface to depths as deep as 1,460 metres.
Spiny dogfish 
 The spiny dogfish feeds mainly on pelagic fish such as herring, menhaden, capelin, sand lance, and mackerel.
Spiny dogfish 
 The second dorsal fin is about two-thirds the size of the first one and is located behind the pelvic fins.
Spiny dogfish 
 On the front of each dorsal fin there is a sharp spine attached to them, giving the spiny dogfish its name.
Spiny dogfish 
 The pectoral fins form nearly perfect equilateral triangles, with rounded rear tips, and slightly concave rear margins.
Spiny dogfish 
 There are rows of white spots along each side, from above the pectoral fins to above the pelvic fins.
Spiny dogfish 
 The edges of the dorsal fins and the caudal fin have a dusky-colour at birth, but this colour quickly fades.
Spiny dogfish 
 The average length of the spiny dogfish is 28-39 inches (70–100 cm), with adult males ranging from 24-35 inches (60–90 cm), and adult females ranging from 30-42 inches (76–107 cm).
Spiny dogfish 
 Mature females can weigh as much as 3.2-4.5 kg (7-10 pounds), with a maximum recorded weight of 9.8 kg (22 pounds).
Spiny dogfish 
 The all-tackle game fish record is 7.14 kg (16 pounds), and was caught off the coast of Ireland in 1989.
Spiny dogfish 
 In the western Atlantic, the spiny dogfish ranges from Greenland to Argentina, and in the eastern Atlantic it is found from Iceland and the Murmanski Coast (Russia) to South Africa, including the Mediterranean Sea and the Black Sea.
Spiny dogfish 
 In the western Pacific, the dogfish occurs from the Bering Sea to New Zealand, while in the eastern Pacific, this species is found from the Bering Sea to Chile.
Spiny dogfish 
 Spiny dogfish can be found in brackish water, but prefer seawater, and are commonly found in waters with the temperature of 7-15 °C.
Spiny dogfish 
 Spiny dogfish are found inshore and offshore, over continental and insular (island) shelve, and upper slopes.
Spiny dogfish 
 Spiny dogfish have been found in the stomachs of cod, red hake, and goosefish, as well as other dogfish.
Spiny dogfish 
 To defend itself, the dogfish curls into a ball, and strikes at predators with its spines on the dorsal fins.
Spiny dogfish 
 They feed mainly on pelagic fish such as herring, menhaden, capelin, sand lance, and mackerel, often consuming large numbers of them.
Spiny dogfish 
 They have been known to bite through fishing nets to be able to feed on the caught fish, usually releasing most of the fish.
Spiny dogfish 
 Other food items of this species includes molluscs (such as squid and octopus), crustacea (such as shrimp and crab), jellyfish, sea cucumber, algae, smaller sharks, and shark egg cases.
Spiny dogfish 
 Spiny dogfish are ovoviviparous, meaning that the embryos develop inside eggs inside the female, and are nourished by yolk-filled sacs.
Spiny dogfish 
 The dogfish poses little threat to humans, but if it is not handled properly, the spines on its dorsal fins can give a harmful wound.
Spiny dogfish 
 Also, the spiny dogfish has earned itself a bad reputation among fishermen due to its habit of biting through fishing nets to get at any fish which is caught in the nets.
Spiny dogfish 
 The spiny dogfish is the most common living shark, yet two populations in the northwest and northeast Atlantic are at great risk due to overfishing.
Spiny dogfish 
 This shark is caught for food, liver oil, and is used to make sand paper, vitamins, leather, fertiliser, and pet food.
Spiny dogfish 
 Between 1900 and 1910, when the dogfish was at its peak abundance, it was estimated that up to 27 million spiny dogfish were caught off the Massachusetts coast every year.
Spiny dogfish 
 Due to their long gestation period and the low number of pups they give birth to at a time, the spiny dogfish must be managed carefully.
Spiny dogfish 
 The fishing of spiny dogfish increased dramatically in the U.S.A during the 1990s, resulting in the population of mature females to decrease by 75%, leading to low number of pups.