text stringlengths 0 73.6k | source stringclasses 4
values |
|---|---|
Fish protein powder-Categories-The two basic categories used to classify fish protein powders are dependent on the levels of protein, fat, mineral and carbohydrate contained in the powder. The minerals are mostly naturally occurring, organic complexes of magnesium, calcium and phosphorus. The spray drying process may u... | milkshake721/2.1M-wiki-STEM |
Fish protein powder-Categories-Fish protein concentrate (FPC) - is a powder concentrate with medium level of protein (50-70%) and will contain some level of fat/oil (1-20%) in the powder form as well.
Fish protein isolate (FPi) - where the product contains less than 1% fat/oil and more than 90% protein.
New manufacturi... | milkshake721/2.1M-wiki-STEM |
Fish protein powder-Peptides vs proteins and amino acids in the digestive tract-Any animal that consumes a whole protein must break down and digest the protein order to absorb the nutrients. For humans this begins with chewing and the addition of saliva enzymes, followed by acid and protease enzyme digestion in the sto... | milkshake721/2.1M-wiki-STEM |
Fish protein powder-Nutritional aspects-Significant elements of the nutritional science of fish protein powders centers around the bioactive and antioxidant properties of the peptide fractions produced during hydrolysis and their ability to have a positive impact on many conditions including gastrointestinal issues ass... | milkshake721/2.1M-wiki-STEM |
Caffeine-Free Pepsi-Caffeine-Free Pepsi-Caffeine-Free Pepsi is a version of the cola Pepsi that omits the caffeine that is customarily part of a cola. It was introduced under the brand name "Pepsi Free" in 1982 by PepsiCo. It was 99.7 percent caffeine free. A sugar-free variant was also introduced and known as "Diet Pe... | milkshake721/2.1M-wiki-STEM |
Caffeine-Free Pepsi-Background-When it was first introduced, Caffeine-Free Pepsi's label background was red, but to avoid any confusion with Coca-Cola, the background color was changed to gold in 1987. As part of Pepsi's changing their background to blue in 1998, Pepsi Caffeine Free's background changed to blue with th... | milkshake721/2.1M-wiki-STEM |
Caffeine-Free Pepsi-Background-When introduced, Pepsi Free was available in cans, 2-liter bottles, and 20-ounce glass bottles. Caffeine-Free Pepsi is currently available in cans, 16 oz. plastic bottles and 2 liters, though availability varies from store to store (for instance, 16 oz. bottles are typically only availabl... | milkshake721/2.1M-wiki-STEM |
Caffeine-Free Pepsi-In popular culture-Two cans of Pepsi Free are seen, at separate times, in the 1983 film Mr. Mom.
Two-liter bottles and six-packs of cans of Pepsi Free appear in a refrigerator case behind Sylvester Stallone's character in the grocery store scene in the 1986 film Cobra. | milkshake721/2.1M-wiki-STEM |
Caffeine-Free Pepsi-In popular culture-Pepsi Free was the subject of a scene in the 1985 film Back to the Future. Upon entering a café in 1955, Marty McFly (Michael J. Fox) asks for a Tab (Coca-Cola's first version of a sugar-free soft drink, which was not available until 1963) and is told that he cannot have a "tab," ... | milkshake721/2.1M-wiki-STEM |
Caffeine-Free Pepsi-In popular culture-A can of Diet Pepsi Free can be seen beside Marty's alarm clock towards the beginning of the movie when Doc (Christopher Lloyd) calls him to remind him to meet him at the mall. The can is also seen toward the end of the movie when Marty wakes up in the morning at his house in 1985... | milkshake721/2.1M-wiki-STEM |
Pronunciation of GIF-Pronunciation of GIF-The pronunciation of GIF, an acronym for the Graphics Interchange Format, has been disputed since the 1990s. Popularly rendered in English as a one-syllable word, the acronym is most commonly pronounced (listen) (with a hard g as in gift) or (listen) (with a soft g as in gem), ... | milkshake721/2.1M-wiki-STEM |
Pronunciation of GIF-Pronunciation of GIF-The controversy stems partly from the fact that there is no general rule for how the letter sequence gi is to be pronounced; the hard g prevails in words such as gift, while the soft g is used in others such as ginger. In addition, some speakers enunciate each letter in the acr... | milkshake721/2.1M-wiki-STEM |
Pronunciation of GIF-Background-The Graphics Interchange Format (GIF) is an image file format developed in 1987 by Steve Wilhite at the American online service provider CompuServe. GIFs are popularly used to display short, looped animations. The acronym GIF, commonly pronounced as a monosyllable, has a disputed pronunc... | milkshake721/2.1M-wiki-STEM |
Pronunciation of GIF-Background-Other languages In French, the acronym tends to be pronounced [ʒif] (listen), with the voiced postalveolar fricative, [ʒ], as in the j in the French joie or the s in the English measure or vision, even though [dʒ], which does not occur in native vocabulary, tends to be retained in Englis... | milkshake721/2.1M-wiki-STEM |
Pronunciation of GIF-Analysis of the dispute-Cause In English, the linguistic controversy stems partly from the fact that there is no general rule for how the letter sequence gi is to be pronounced; the hard g prevails in words such as gift, while the soft g is used in others, such as ginger. In Old English, g would ma... | milkshake721/2.1M-wiki-STEM |
Pronunciation of GIF-Analysis of the dispute-In her coverage of Dow's piece, Canadian linguist Gretchen McCulloch theorizes that since the hard and soft g in this context are used with near-equal frequency, when a person first encounters the word GIF, they make a guess akin to flipping a coin by comparing it to other w... | milkshake721/2.1M-wiki-STEM |
Pronunciation of GIF-Analysis of the dispute-Arguments A 2019 analysis by linguist Marten van der Meulen found that the most common arguments employed online over the pronunciation of GIF are "system" arguments, which support one side of the debate by contending that the pronunciation should flow from a consistent rule... | milkshake721/2.1M-wiki-STEM |
Pronunciation of GIF-Analysis of the dispute-Polling A 2014 Mashable poll of more than 30,000 people worldwide found that seven in ten used the hard g. Van der Meulen's analysis found that 57.2 percent of users who offered an opinion supported the hard g, while 31.8 percent favored the soft g. The analysis also found t... | milkshake721/2.1M-wiki-STEM |
Pronunciation of GIF-Analysis of the dispute-Dictionaries Dictionary.com lists both the hard and soft g pronunciations for GIF, indicating the latter as the primary pronunciation, while the Cambridge Dictionary of American English and the Cambridge Advanced Learner's Dictionary offer only the hard g pronunciation. The ... | milkshake721/2.1M-wiki-STEM |
Pronunciation of GIF-Incidents-In May 2013, Wilhite was presented with a lifetime achievement award at the annual Webby Awards honoring excellence on the Internet. Upon accepting the award at the ceremony, Wilhite displayed a five-word slide that simply read, in all caps: "It's pronounced 'jif' not 'gif'". Here, jif re... | milkshake721/2.1M-wiki-STEM |
Mazovia encoding-Mazovia encoding-Mazovia encoding is a character set used under DOS to represent Polish text. The character set derives from code page 437, with specific positions modified to accommodate Polish letters. Notably, the Mazovia encoding maintains the block graphic characters from code page 437, distinguis... | milkshake721/2.1M-wiki-STEM |
Mazovia encoding-Mazovia encoding-The Mazovia encoding was designed in 1984 by Jan Klimowicz of IMM. It was designed as part of a project to develop and produce a Polish IBM PC clone codenamed "Mazovia 1016". The code page was specifically optimized for the peripheral devices commonly used with the Mazovia 1016 compute... | milkshake721/2.1M-wiki-STEM |
Mazovia encoding-Mazovia encoding-Some ambiguity exists in the official code page assignment for the Mazovia encoding: PTS-DOS and S/DOS support this encoding under code page 667 (CP667). The same encoding was also called code page 991 (CP991) in some Polish software, however, the FreeDOS implementation of code page 99... | milkshake721/2.1M-wiki-STEM |
Mazovia encoding-Mazovia encoding-The DOS code page switching file NECPINW.CPI for NEC Pinwriters supports the Mazovia encoding under both code pages 667 and 991. FreeDOS has meanwhile introduced support for the original Mazovia encoding under code page 790 (CP790) as well. The Fujitsu DL6400 (Pro) / DL6600 (Pro) print... | milkshake721/2.1M-wiki-STEM |
Mazovia encoding-Character set-Each character is shown with its equivalent Unicode code point. Only the second half of the table (128–255) is shown, all of the first half (0–127) being the same as ASCII and code page 437. | milkshake721/2.1M-wiki-STEM |
Mazovia encoding-Character set-Several variants of this encoding exists: Mazovia 157 (ś is at 9D instead of 9E) Fido Mazovia (ć is at 0x87 instead of 8D and Ć is at 0x80 instead of 0x95) FreeDOS Mazovia (złoty sign at 9B). FreeDOS supports this variant under code page 991, although the original definition of code page ... | milkshake721/2.1M-wiki-STEM |
Radical 89-Radical 89-Radical 89 or radical double x (爻部) meaning "trigrams" is one of the 34 Kangxi radicals (214 radicals in total) composed of 4 strokes.
In the Kangxi Dictionary, there are 16 characters (out of 49,030) to be found under this radical.
This radical does not exist in the Table of Indexing Chinese Char... | milkshake721/2.1M-wiki-STEM |
Radical 89-Literature-Fazzioli, Edoardo (1987). Chinese calligraphy : from pictograph to ideogram : the history of 214 essential Chinese/Japanese characters. calligraphy by Rebecca Hon Ko. New York: Abbeville Press. ISBN 0-89659-774-1.
Lunde, Ken (Jan 5, 2009). "Appendix J: Japanese Character Sets" (PDF). CJKV Informat... | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-Allotropes of iron-At atmospheric pressure, three allotropic forms of iron exist, depending on temperature: alpha iron (α-Fe, ferrite), gamma iron (γ-Fe, austenite), and delta iron (δ-Fe). At very high pressure, a fourth form exists, epsilon iron (ε-Fe, hexaferrum). Some controversial experimental ev... | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-Standard pressure allotropes-Alpha iron (α-Fe) Below 912 °C (1,674 °F), iron has a body-centered cubic (bcc) crystal structure and is known as α-iron or ferrite. It is thermodynamically stable and a fairly soft metal. α-Fe can be subjected to pressures up to ca. 15 GPa before transforming into a high... | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-Standard pressure allotropes-Magnetically, α-iron is paramagnetic at high temperatures. However, below its Curie temperature (TC or A2) of 771 °C (1044K or 1420 °F), it becomes ferromagnetic. In the past, the paramagnetic form of α-iron was known as beta iron (β-Fe). Even though the slight tetragonal... | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-Standard pressure allotropes-Similarly, the A2 boundary is of only minor importance compared to the A1 (eutectoid), A3 and Acm critical temperatures. The Acm, where austenite is in equilibrium with cementite + γ-Fe, is beyond the right edge in Fig. 1. The α + γ phase field is, technically, the β + γ ... | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-Standard pressure allotropes-The primary phase of low-carbon or mild steel and most cast irons at room temperature is ferromagnetic α-Fe. It has a hardness of approximately 80 Brinell. The maximum solubility of carbon is about 0.02 wt% at 727 °C (1,341 °F) and 0.001% at 0 °C (32 °F). When it dissolve... | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-Standard pressure allotropes-Mild steel (carbon steel with up to about 0.2 wt% C) consists mostly of α-Fe and increasing amounts of cementite (Fe3C, an iron carbide). The mixture adopts a lamellar structure called pearlite. Since bainite and pearlite each contain α-Fe as a component, any iron-carbon ... | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-Standard pressure allotropes-A2 critical temperature and induction heating β-Fe and the A2 critical temperature are important in induction heating of steel, such as for surface-hardening heat treatments. Steel is typically austenitized at 900–1000 °C before it is quenched and tempered. The high-frequ... | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-Standard pressure allotropes-Gamma iron (γ-Fe) When heating iron above 912 °C (1,674 °F), its crystal structure changes to a face-centered cubic (fcc) crystalline structure. In this form it is called gamma iron (γ-Fe) or austenite. γ-iron can dissolve considerably more carbon (as much as 2.04% by mas... | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-Standard pressure allotropes-Delta iron (δ-Fe) Peculiarly, above 1,394 °C (2,541 °F) iron changes back into the bcc structure, known as δ-Fe. δ-iron can dissolve as much as 0.08% of carbon by mass at 1,475 °C. It is stable up to its melting point of 1,538 °C (2,800 °F). δ-Fe cannot exist above 5.2 GP... | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-High pressure allotropes-Epsilon iron / Hexaferrum (ε-Fe) At pressures above approximately 10-13 GPa and temperatures up to around 700 K, α-iron changes into a hexagonal close-packed (hcp) structure, which is also known as ε-iron or hexaferrum; the higher-temperature γ-phase also changes into ε-iron,... | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-High pressure allotropes-Experimental high temperature and pressure An alternate stable form, if it exists, may appear at pressures of at least 50 GPa and temperatures of at least 1,500 K; it has been thought to have an orthorhombic or a double hcp structure. As of December 2011, recent and ongoing e... | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-Phase transitions-Melting and boiling points The melting point of iron is experimentally well defined for pressures less than 50 GPa. | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-Phase transitions-For greater pressures, published data (as of 2007) put the γ-ε-liquid triple point at pressures that differ by tens of gigapascals and 1000 K in the melting point. Generally speaking, molecular dynamics computer simulations of iron melting and shock wave experiments suggest higher m... | milkshake721/2.1M-wiki-STEM |
Allotropes of iron-Phase transitions-Structural phase transitions The exact temperatures at which iron will transition from one crystal structure to another depends on how much and what type of other elements are dissolved in the iron. The phase boundary between the different solid phases is drawn on a binary phase dia... | milkshake721/2.1M-wiki-STEM |
Charlotte (cake)-Charlotte (cake)-A charlotte is a type of bread pudding that can be served hot or cold. It is also referred to as an "icebox cake". Bread, sponge cake, crumbs or biscuits/cookies are used to line a mold, which is then filled with a fruit puree or custard. The baked pudding could then be sprinkled with ... | milkshake721/2.1M-wiki-STEM |
Charlotte (cake)-Charlotte (cake)-The variant charlotte russe also called charlotte parisienne, created by the French chef Antonin Carême, uses a mold lined with ladyfingers and filled with Bavarian cream.
Classically, stale bread dipped in butter was used as the lining, but sponge cake or ladyfingers may be used today... | milkshake721/2.1M-wiki-STEM |
Charlotte (cake)-History-The charlotte is known to have existed by the late-18th century. In 1796, The New-York Magazine published a poem by Joel Barlow called The Hasty-Pudding which included the following lines: Some have claimed that it was a tribute to Britain's Queen Charlotte.In 1815, Marie-Antoine Carême claims ... | milkshake721/2.1M-wiki-STEM |
Charlotte (cake)-History-In Carême's 1815 Le Pâtissier royal parisien, he mentions many varieties of charlotte: à la parisienne, à la française, à l'italienne, aux macarons d'avelines, aux gaufres aux pistaches, de pommes, de pomme d'api, d'abricots, de pêches, de pommes glacée aux abricots, de pommes au beurre, parisi... | milkshake721/2.1M-wiki-STEM |
Charlotte (cake)-Types-There are many variants. Most charlottes are served cool, so they are more common in warmer seasons. Fruit charlottes usually combine a fruit purée or preserve, like raspberry or pear, with a custard filling or whipped cream. Charlottes are not always made with fruit; some, notably charlotte russ... | milkshake721/2.1M-wiki-STEM |
Charlotte (cake)-Types-Charlotte russe Charlotte russe or charlotte à la russe is a cold dessert of Bavarian cream set in a mold lined with ladyfingers.A simplified version of charlotte russe was a popular dessert or on-the-go treat sold in candy stores and luncheonettes in New York City, during the 1930s, 1940s, and 1... | milkshake721/2.1M-wiki-STEM |
Charlotte (cake)-Etymology-The earliest attestation of "charlotte" is in a New York magazine in 1796. Its origins are unclear. It may come from the woman's name. One etymology suggests it is a corruption of the Old English word charlyt, a kind of custard, or charlets, a meat dish.It is often claimed that Carême named i... | milkshake721/2.1M-wiki-STEM |
Charlotte (cake)-Etymology-Carême's preferred name for charlotte à la russe was charlotte à la parisienne, and he says (in 1815) that "others" prefer to call it russe,: 446 so it is unlikely that he named it russe for Czar Alexander I as has been proposed. | milkshake721/2.1M-wiki-STEM |
Nailset-Nailset-A nailset or nail punch is a hand tool used for driving the exposed head of a nail or pin below the surface of a piece of wood, such as when installing decorative moulding or face-fastening wood flooring. | milkshake721/2.1M-wiki-STEM |
Nailset-Nailset-Though they vary in design, nailsets are typically made from a hard round or square steel rod which tapers at one end to a flat or slightly hollowed tip. The tip is placed against the head of the nail, while the other end of the nailset is struck with a hammer. Nailsets come with different sized tips su... | milkshake721/2.1M-wiki-STEM |
't-'t-In the Dutch language, the word 't (Dutch pronunciation: [ət]) is a contraction of the article "het", meaning "the". 't can be found as a tussenvoegsel, a word that is positioned between a person's first and last name. Careful writers should use an apostrophe (U+2019 ’ ) in front of the t – and not confuse it wit... | milkshake721/2.1M-wiki-STEM |
't-Examples-Dirk van 't Klooster Evert-Jan 't Hoen Gerard 't Hooft Haas Visser 't Hooft in 't Veld (surname) Bart Spring in 't Veld Sophie in 't Veld Jacobus Henricus van 't Hoff John van 't Schip Maarten 't Hart Tom van 't Hek Van 't Hof (surname) Van 't Wout (surname) Willem Visser 't Hooft Youp van 't Hek | milkshake721/2.1M-wiki-STEM |
Kirsanov reaction-Kirsanov reaction-The Kirsanov reaction is a method for the synthesis of certain organophosphorus compounds. In this reaction a tertiary phosphine is combined with a halogen and then an amine to give the iminophosphines, which are useful ligands and useful reagents. | milkshake721/2.1M-wiki-STEM |
Kirsanov reaction-Kirsanov reaction-A typical reaction involves triphenylphosphine with bromine to give bromotriphenylphosphonium bromide: Ph3P + Br2 → Ph3PBr+Br−This salt is treated in situ with alkylamines to give the iminophosphorane: Ph3PBr+Br− + 3 RNH2 → Ph3PNR + 2 RNH3+Br−The method is used when the conventional ... | milkshake721/2.1M-wiki-STEM |
Pasta allo scarpariello-Pasta allo scarpariello-Pasta allo scarpariello is a traditional Italian pasta dish from Naples.It is typically made with spaghetti, tomatoes, Pecorino Romano cheese, Parmigiano Reggiano cheese, basil, chili pepper, extra virgin olive oil, garlic and salt.Its name literally means "shoemaker's pa... | milkshake721/2.1M-wiki-STEM |
Epigram-Epigram-An epigram is a brief, interesting, memorable, and sometimes surprising or satirical statement. The word is derived from the Greek ἐπίγραμμα epígramma "inscription" from ἐπιγράφειν epigráphein "to write on, to inscribe", and the literary device has been employed for over two millennia.
The presence of w... | milkshake721/2.1M-wiki-STEM |
Epigram-Ancient Greek-The Greek tradition of epigrams began as poems inscribed on votive offerings at sanctuaries – including statues of athletes – and on funerary monuments, for example "Go tell it to the Spartans, passersby...". These original epigrams did the same job as a short prose text might have done, but in ve... | milkshake721/2.1M-wiki-STEM |
Epigram-Ancient Greek-Though modern epigrams are usually thought of as very short, Greek literary epigram was not always as short as later examples, and the divide between "epigram" and "elegy" is sometimes indistinct (they share a characteristic metre, elegiac couplets). In the classical period, the clear distinction ... | milkshake721/2.1M-wiki-STEM |
Epigram-Ancient Greek-Hellenistic epigrams are also thought of as having a "point" – that is, the poem ends in a punchline or satirical twist. By no means do all Greek epigrams behave this way; many are simply descriptive, but Meleager of Gadara and Philippus of Thessalonica, the first comprehensive anthologists, prefe... | milkshake721/2.1M-wiki-STEM |
Epigram-Ancient Greek-A major source for Greek literary epigram is the Greek Anthology, a compilation from the 10th century AD based on older collections, including those of Meleager and Philippus. It contains epigrams ranging from the Hellenistic period through the Imperial period and Late Antiquity into the compiler'... | milkshake721/2.1M-wiki-STEM |
Epigram-Ancient Roman-Roman epigrams owe much to their Greek predecessors and contemporaries. Roman epigrams, however, were often more satirical than Greek ones, and at times used obscene language for effect. Latin epigrams could be composed as inscriptions or graffiti, such as this one from Pompeii, which exists in se... | milkshake721/2.1M-wiki-STEM |
Epigram-Ancient Roman-Odi et amo. Quare id faciam fortasse requiris. | milkshake721/2.1M-wiki-STEM |
Epigram-Ancient Roman-Nescio, sed fieri sentio, et excrucior.I hate and I love. Maybe you'd like to know why I do? I don't know, but I feel it happening, and I am tormented.Martial, however, is considered to be the master of the Latin epigram. His technique relies heavily on the satirical poem with a joke in the last l... | milkshake721/2.1M-wiki-STEM |
Epigram-Ancient Roman-Non sunt longa quibus nihil est quod demere possis, sed tu, Cosconi, disticha longa facis.Learn what you don't know: one work of (Domitius) Marsus or learned Pedo often stretches out over a doublesided page.
A work isn't long if you can't take anything out of it, but you, Cosconius, write even a c... | milkshake721/2.1M-wiki-STEM |
Epigram-English-In early English literature the short couplet poem was dominated by the poetic epigram and proverb, especially in the translations of the Bible and the Greek and Roman poets. | milkshake721/2.1M-wiki-STEM |
Epigram-English-Two successive lines of verse that rhyme with each other are known as a couplet. Since 1600, the couplet has been featured as a part of the longer sonnet form, most notably in William Shakespeare's sonnets. Sonnet 76 is an example. The two-line poetic form as a closed couplet was also used by William Bl... | milkshake721/2.1M-wiki-STEM |
Epigram-English-The first work of English literature penned in North America was Robert Hayman's Quodlibets, Lately Come Over from New Britaniola, Old Newfoundland, which is a collection of over 300 epigrams, many of which do not conform to the two-line rule or trend. While the collection was written between 1618 and 1... | milkshake721/2.1M-wiki-STEM |
Epigram-English-During the early 20th century, the rhymed epigram couplet form developed into a fixed verse image form, with an integral title as the third line. Adelaide Crapsey codified the couplet form into a two-line rhymed verse of ten syllables per line with her image couplet poem On Seeing Weather-Beaten Trees, ... | milkshake721/2.1M-wiki-STEM |
Epigram-Poetic epigrams-What is an Epigram? a dwarfish whole, Its body brevity, and wit its soul.
— Samuel Taylor Coleridge ("Epigram", 1809)Some can gaze and not be sick But I could never learn the trick.
There's this to say for blood and breath; They give a man a taste for death.
— A. E. HousmanLittle strokes Fell gr... | milkshake721/2.1M-wiki-STEM |
Epigram-In art-"When Guns Speak, Death Settles Disputes" is Charles Marion Russell's epigrammatic title for a clash by gunfighters of the Old West in America. | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-Goldbach's conjecture-Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers.
The conjecture has been shown to hold for all integers less than 4×101... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-History-On 7 June 1742, the German mathematician Christian Goldbach wrote a letter to Leonhard Euler (letter XLIII), in which he proposed the following conjecture: Goldbach was following the now-abandoned convention of considering 1 to be a prime number, so that a sum of units would indeed be a su... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-History-A modern version of the first conjecture is: A modern version of the marginal conjecture is: And a modern version of Goldbach's older conjecture of which Euler reminded him is: These modern versions might not be entirely equivalent to the corresponding original statements. For example, if ... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-History-The third modern statement (equivalent to the second) is the form in which the conjecture is usually expressed today. It is also known as the "strong", "even", or "binary" Goldbach conjecture. A weaker form of the second modern statement, known as "Goldbach's weak conjecture", the "odd Gol... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-Verified results-For small values of n, the strong Goldbach conjecture (and hence the weak Goldbach conjecture) can be verified directly. For instance, in 1938, Nils Pipping laboriously verified the conjecture up to n = 100000. With the advent of computers, many more values of n have been checked;... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-Heuristic justification-Statistical considerations that focus on the probabilistic distribution of prime numbers present informal evidence in favour of the conjecture (in both the weak and strong forms) for sufficiently large integers: the greater the integer, the more ways there are available for... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-Heuristic justification-A very crude version of the heuristic probabilistic argument (for the strong form of the Goldbach conjecture) is as follows. The prime number theorem asserts that an integer m selected at random has roughly a 1/ln m chance of being prime. Thus if n is a large even integer a... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-Heuristic justification-Since ln n ≪ √n, this quantity goes to infinity as n increases, and one would expect that every large even integer has not just one representation as the sum of two primes, but in fact very many such representations. | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-Heuristic justification-This heuristic argument is actually somewhat inaccurate, because it assumes that the events of m and n − m being prime are statistically independent of each other. For instance, if m is odd, then n − m is also odd, and if m is even, then n − m is even, a non-trivial relatio... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-Heuristic justification-The Goldbach partition function is the function that associates to each even integer the number of ways it can be decomposed into a sum of two primes. Its graph looks as a comet, and is therefore called Goldbach's comet.Goldbach's comet suggests tight upper and lower bounds... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-Rigorous results-The strong Goldbach conjecture is much more difficult than the weak Goldbach conjecture. Using Vinogradov's method, Nikolai Chudakov, Johannes van der Corput, and Theodor Estermann showed that almost all even numbers can be written as the sum of two primes (in the sense that the f... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-Rigorous results-In 1975, Hugh Montgomery and Robert Charles Vaughan showed that "most" even numbers are expressible as the sum of two primes. More precisely, they showed that there exist positive constants c and C such that for all sufficiently large numbers N, every even number less than N is th... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-Rigorous results-In 1951, Yuri Linnik proved the existence of a constant K such that every sufficiently large even number is the sum of two primes and at most K powers of 2. János Pintz and Imre Ruzsa found in 2020 that K = 8 works. Assuming the generalized Riemann hypothesis, K = 7 also works, as... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-Related problems-Although Goldbach's conjecture implies that every positive integer greater than one can be written as a sum of at most three primes, it is not always possible to find such a sum using a greedy algorithm that uses the largest possible prime at each step. The Pillai sequence tracks ... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-Related problems-Hardy and Littlewood listed as their Conjecture I: "Every large odd number (n > 5) is the sum of a prime and the double of a prime". This conjecture is known as Lemoine's conjecture and is also called Levy's conjecture.
The Goldbach conjecture for practical numbers, a prime-like s... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-Related problems-A strengthening of the Goldbach conjecture proposed by Harvey Dubner states that every even integer greater than 4208 is the sum of two twin primes. Only 34 even integers less than 4208 are not the sum of two twin primes. Dubner has verified computationally that this list is compl... | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-In popular culture-Goldbach's Conjecture (Chinese: 哥德巴赫猜想) is the title of the biography of Chinese mathematician and number theorist Chen Jingrun, written by Xu Chi. | milkshake721/2.1M-wiki-STEM |
Goldbach's conjecture-In popular culture-The conjecture is a central point in the plot of the 1992 novel Uncle Petros and Goldbach's Conjecture by Greek author Apostolos Doxiadis, in the short story "Sixty Million Trillion Combinations" by Isaac Asimov and also in the 2008 mystery novel No One You Know by Michelle Rich... | milkshake721/2.1M-wiki-STEM |
Voluntary Control Council for Interference by Information Technology Equipment-Voluntary Control Council for Interference by Information Technology Equipment-The Voluntary Control Council for Interference by Information Technology Equipment or VCCI is the Japanese body governing RF emissions (i.e. electromagnetic inter... | milkshake721/2.1M-wiki-STEM |
Ski cross-Ski cross-Ski cross is a skiing competition which incorporates terrain features traditionally found in freestyle skiing with courses which include big-air jumps and high-banked turns. In spite of the fact that it is a timed racing event, it is often considered a type of freestyle skiing. What sets ski cross a... | milkshake721/2.1M-wiki-STEM |
Ski cross-Ski cross-Ski cross is a part of the FIS Freestyle World Ski Championships, the world championship organized by the FIS for freestyle skiing. First organized in 1986, the world championship is now held every odd year. In 2010 the sport debuted as a part of the Winter Olympic Games and has been contested ever ... | milkshake721/2.1M-wiki-STEM |
Ski cross-Overview-In a time trial or qualification round, every competitor skis down the course, which is built to encompass both naturally occurring terrain and artificial features like jumps, rollers or banks. After the time trial, the fastest 32 skiers (fastest 16 if not 32 competitors) compete in a knockout series... | milkshake721/2.1M-wiki-STEM |
Ski cross-History-The idea for a multi-racer single run with obstacles seems to have been borne at Alyeska Ski Resort in Alaska (USA) during the late 1970s. A group of racers, led by Scott Hunter an employee at Alyeska wanted to take advantage of the mountain's natural bobsled-like gullies and rollers in a race that wa... | milkshake721/2.1M-wiki-STEM |
Ski cross-History-A similar idea originated with Jim "Too Tall" Essick, one of the founders of Recreational Sports Marketing (RSM), in the late 1980s. Essick wanted to bring the excitement of motocross to skiing, in order to make ski races more exciting for spectators. The idea was pitched to several corporations, but ... | milkshake721/2.1M-wiki-STEM |
Ski cross-FIS Freestyle World Ski Championships-In addition to moguls and aerials, ski cross competitions were added to the International Ski Federation (FIS)'s FIS Freestyle Skiing World Cup calendar in 2004. | milkshake721/2.1M-wiki-STEM |
Ski cross-Winter Olympic Games-Ski cross debuted in the Olympics at the 2010 Winter Olympics where Michael Schmid won the men's event, and Ashleigh McIvor of Canada won the women's event.
In the 2014 Winter Olympics France's Men swept the podium while in the women's event, Canadians Marielle Thompson and Kelsey Serwa f... | milkshake721/2.1M-wiki-STEM |
Ski cross-Winter Olympic Games-In the 2018 Winter Olympics in Korea, Canada continued its domination of the sport. Kelsey Serwa won her second Olympic medal, this time a gold. Canadian teammate Brittany Phelan took home the silver. Swiss skier Fanny Smith won bronze. On the men's side, Brady Leman got redemption after ... | milkshake721/2.1M-wiki-STEM |
Ski cross-Winter X Games-Ski cross was in the first fifteen Winter X Games, an event which features extreme sports, and was in all Winter X Games until the 2012 Winter X Games. Ski cross, boardercross, and mono ski cross were cut from the 2013 Winter X Games due to the cost of building the cross course. | milkshake721/2.1M-wiki-STEM |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.