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118-444: Methane ( US : / ˈ m ɛ θ eɪ n / METH -ayn , UK : / ˈ m iː θ eɪ n / MEE -thayn ) is a chemical compound with the chemical formula CH 4 (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride , the simplest alkane , and the main constituent of natural gas . The abundance of methane on Earth makes it an economically attractive fuel , although capturing and storing it

236-408: A {\displaystyle a} , b {\displaystyle b} , or c {\displaystyle c} , depending on which axis the glide is along. There is also the n {\displaystyle n} glide, which is a glide along the half of a diagonal of a face, and the d {\displaystyle d} glide, which is a fourth of the way along either

354-698: A cot–caught merger , which is rapidly spreading throughout the whole country. However, the South, Inland North, and a Northeastern coastal corridor passing through Rhode Island, New York City, Philadelphia, and Baltimore typically preserve an older cot–caught distinction. For that Northeastern corridor, the realization of the THOUGHT vowel is particularly marked , as depicted in humorous spellings, like in tawk and cawfee ( talk and coffee ), which intend to represent it being tense and diphthongal : [oə] . A split of TRAP into two separate phonemes , using different

472-570: A coal deposit, while enhanced coal bed methane recovery is a method of recovering methane from non-mineable coal seams). It is associated with other hydrocarbon fuels, and sometimes accompanied by helium and nitrogen . Methane is produced at shallow levels (low pressure) by anaerobic decay of organic matter and reworked methane from deep under the Earth's surface. In general, the sediments that generate natural gas are buried deeper and at higher temperatures than those that contain oil . Methane

590-457: A hydrogen halide molecule and a methyl radical ( •CH 3 ). The methyl radical then reacts with a molecule of the halogen to form a molecule of the halomethane, with a new halogen atom as byproduct. Similar reactions can occur on the halogenated product, leading to replacement of additional hydrogen atoms by halogen atoms with dihalomethane , trihalomethane , and ultimately, tetrahalomethane structures, depending upon reaction conditions and

708-520: A pronunciations for example in gap [æ] versus gas [eə] , further defines New York City as well as Philadelphia–Baltimore accents. Most Americans preserve all historical /r/ sounds, using what is known as a rhotic accent . The only traditional r -dropping (or non-rhoticity) in regional U.S. accents variably appears today in eastern New England , New York City , and some of the former plantation South primarily among older speakers (and, relatedly, some African-American Vernacular English across

826-616: A complex phenomenon of "both convergence and divergence": some accents are homogenizing and leveling , while others are diversifying and deviating further away from one another. Having been settled longer than the American West Coast, the East Coast has had more time to develop unique accents, and it currently comprises three or four linguistically significant regions, each of which possesses English varieties both different from each other as well as quite internally diverse: New England ,

944-447: A consonant, such as in pearl , car and fort . Non-rhotic American accents, those that do not pronounce ⟨r⟩ except before a vowel, such as some accents of Eastern New England , New York City , and African-Americans , and a specific few (often older ones) spoken by Southerners , are often quickly noticed by General American listeners and perceived as sounding especially ethnic, regional, or antiquated. Rhoticity

1062-423: A face or space diagonal of the unit cell. The latter is called the diamond glide plane as it features in the diamond structure. In 17 space groups, due to the centering of the cell, the glides occur in two perpendicular directions simultaneously, i.e. the same glide plane can be called b or c , a or b , a or c . For example, group Abm2 could be also called Acm2, group Ccca could be called Cccb. In 1992, it

1180-586: A merger with the THOUGHT ( caught ) set. Having taken place prior to the unrounding of the cot vowel, it results in lengthening and perhaps raising, merging the more recently separated vowel into the THOUGHT vowel in the following environments: before many instances of /f/ , /θ/ , and particularly /s/ (as in Austria, cloth, cost, loss, off, often, etc.), a few instances before /ŋ/ (as in strong, long, wrong ), and variably by region or speaker in gone , on , and certain other words. Unlike American accents,

1298-636: A nice day , for sure); many are now distinctly old-fashioned (swell, groovy). Some English words now in general use, such as hijacking, disc jockey , boost, bulldoze and jazz , originated as American slang. American English has always shown a marked tendency to use words in different parts of speech and nouns are often used as verbs . Examples of nouns that are now also verbs are interview, advocate, vacuum, lobby, pressure, rear-end, transition, feature, profile, hashtag, head, divorce, loan, estimate, X-ray, spearhead, skyrocket, showcase, bad-mouth, vacation , major, and many others. Compounds coined in

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1416-454: A normal abelian subgroup of rank 3, called the Bravais lattice (so named after French physicist Auguste Bravais ). There are 14 possible types of Bravais lattice. The quotient of the space group by the Bravais lattice is a finite group which is one of the 32 possible point groups . A glide plane is a reflection in a plane, followed by a translation parallel with that plane. This is noted by

1534-485: A pressure of one atmosphere . As a gas, it is flammable over a range of concentrations (5.4%–17%) in air at standard pressure . Solid methane exists in several modifications . Presently nine are known. Cooling methane at normal pressure results in the formation of methane I. This substance crystallizes in the cubic system ( space group Fm 3 m). The positions of the hydrogen atoms are not fixed in methane I, i.e. methane molecules may rotate freely. Therefore, it

1652-475: A process of extensive dialect mixture and leveling in which English varieties across the colonies became more homogeneous compared with the varieties in Britain. English thus predominated in the colonies even by the end of the 17th century's first immigration of non-English speakers from Western Europe and Africa. Additionally, firsthand descriptions of a fairly uniform American English (particularly in contrast to

1770-400: A requirement for pure methane can easily be fulfilled by steel gas bottle from standard gas suppliers. Methane is the major component of natural gas, about 87% by volume. The major source of methane is extraction from geological deposits known as natural gas fields , with coal seam gas extraction becoming a major source (see coal bed methane extraction , a method for extracting methane from

1888-399: A resource that is otherwise difficult to transport for its weight, ash content, low calorific value and propensity to spontaneous combustion during storage and transport. A number of similar plants exist around the world, although mostly these plants are targeted towards the production of long chain alkanes for use as gasoline , diesel , or feedstock to other processes. Power to methane

2006-657: A series of other vowel shifts in the same region, known by linguists as the " Inland North ". The Inland North shares with the Eastern New England dialect (including Boston accents ) a backer tongue positioning of the GOOSE /u/ vowel (to [u] ) and the MOUTH /aʊ/ vowel (to [ɑʊ~äʊ] ) in comparison to the rest of the country. Ranging from northern New England across the Great Lakes to Minnesota, another Northern regional marker

2124-488: A subgroup Z . This table gives the number of space group types in small dimensions, including the numbers of various classes of space group. The numbers of enantiomorphic pairs are given in parentheses. In addition to crystallographic space groups there are also magnetic space groups (also called two-color (black and white) crystallographic groups or Shubnikov groups). These symmetries contain an element known as time reversal. They treat time as an additional dimension, and

2242-514: A survey, completed in 2003, polling English speakers across the United States about their specific everyday word choices, hoping to identify regionalisms. The study found that most Americans prefer the term sub for a long sandwich, soda (but pop in the Great Lakes region and generic coke in the South) for a sweet and bubbly soft drink , you or you guys for the plural of you (but y'all in

2360-640: A translation). For example, the diamond cubic structure does not have any point where the cubic point group applies. The lattice dimension can be less than the overall dimension, resulting in a "subperiodic" space group. For (overall dimension, lattice dimension): The 65 "Sohncke" space groups, not containing any mirrors, inversion points, improper rotations or glide planes, yield chiral crystals, not identical to their mirror image; whereas space groups that do include at least one of those give achiral crystals. Achiral molecules sometimes form chiral crystals, but chiral molecules always form chiral crystals, in one of

2478-482: A translation. A space group is thus some combination of the translational symmetry of a unit cell (including lattice centering ), the point group symmetry operations of reflection , rotation and improper rotation (also called rotoinversion), and the screw axis and glide plane symmetry operations. The combination of all these symmetry operations results in a total of 230 different space groups describing all possible crystal symmetries. The number of replicates of

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2596-453: A variation of American English in these islands. In 2021, about 245 million Americans, aged 5 or above, spoke English at home: a majority of the United States total population of roughly 330 million people. The United States has never had an official language at the federal level, but English is commonly used at the federal level and in states without an official language. 32 of the 50 states, in some cases as part of what has been called

2714-406: Is a halogen : fluorine (F), chlorine (Cl), bromine (Br), or iodine (I). This mechanism for this process is called free radical halogenation . It is initiated when UV light or some other radical initiator (like peroxides ) produces a halogen atom . A two-step chain reaction ensues in which the halogen atom abstracts a hydrogen atom from a methane molecule, resulting in the formation of

2832-794: Is a plastic crystal . The primary chemical reactions of methane are combustion , steam reforming to syngas , and halogenation . In general, methane reactions are difficult to control. Partial oxidation of methane to methanol ( C H 3 O H ), a more convenient, liquid fuel, is challenging because the reaction typically progresses all the way to carbon dioxide and water even with an insufficient supply of oxygen . The enzyme methane monooxygenase produces methanol from methane, but cannot be used for industrial-scale reactions. Some homogeneously catalyzed systems and heterogeneous systems have been developed, but all have significant drawbacks. These generally operate by generating protected products which are shielded from overoxidation. Examples include

2950-448: Is a tetrahedral molecule with four equivalent C–H bonds . Its electronic structure is described by four bonding molecular orbitals (MOs) resulting from the overlap of the valence orbitals on C and H . The lowest-energy MO is the result of the overlap of the 2s orbital on carbon with the in-phase combination of the 1s orbitals on the four hydrogen atoms. Above this energy level is a triply degenerate set of MOs that involve overlap of

3068-480: Is a free abelian subgroup of finite index, and is also the unique maximal normal abelian subgroup. He also showed that in any dimension n there are only a finite number of possibilities for the isomorphism class of the underlying group of a space group, and moreover the action of the group on Euclidean space is unique up to conjugation by affine transformations. This answers part of Hilbert's eighteenth problem . Zassenhaus (1948) showed that conversely any group that

3186-536: Is a technology that uses electrical power to produce hydrogen from water by electrolysis and uses the Sabatier reaction to combine hydrogen with carbon dioxide to produce methane. Methane can be produced by protonation of methyl lithium or a methyl Grignard reagent such as methylmagnesium chloride . It can also be made from anhydrous sodium acetate and dry sodium hydroxide , mixed and heated above 300 °C (with sodium carbonate as byproduct). In practice,

3304-546: Is abiotic. Abiotic means that methane is created from inorganic compounds, without biological activity, either through magmatic processes or via water-rock reactions that occur at low temperatures and pressures, like serpentinization . Most of Earth's methane is biogenic and is produced by methanogenesis , a form of anaerobic respiration only known to be conducted by some members of the domain Archaea . Methanogens occur in landfills and soils , ruminants (for example, cattle ),

3422-642: Is also associated with the United States, perhaps mostly in the Midwest and the South. American accents that have not undergone the cot–caught merger (the lexical sets LOT and THOUGHT ) have instead retained a LOT – CLOTH split : a 17th-century distinction in which certain words (labeled as the CLOTH lexical set ) separated away from the LOT set. The split, which has now reversed in most British English, simultaneously shifts this relatively recent CLOTH set into

3540-637: Is also home to a creole language known commonly as Hawaiian Pidgin , and some Hawaii residents speak English with a Pidgin-influenced accent. American English also gave rise to some dialects outside the country, for example, Philippine English , beginning during the American occupation of the Philippines and subsequently the Insular Government of the Philippine Islands ; Thomasites first established

3658-439: Is also sometimes used as an alternative name for the whole trigonal system.) The hexagonal lattice system is larger than the hexagonal crystal system, and consists of the hexagonal crystal system together with the 18 groups of the trigonal crystal system other than the seven whose names begin with R. The Bravais lattice of the space group is determined by the lattice system together with the initial letter of its name, which for

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3776-526: Is common in most American accents despite being now rare in England because, during the 17th-century British colonization, nearly all dialects of English were rhotic, and most North American English simply remained that way. The preservation of rhoticity in North America was also supported by continuing waves of rhotic-accented Scotch-Irish immigrants, most intensely during the 18th century (and moderately during

3894-404: Is difficult because it is a gas at standard temperature and pressure . In the Earth's atmosphere methane is transparent to visible light but absorbs infrared radiation, acting as a greenhouse gas . Methane is an organic compound , and among the simplest of organic compounds. Methane is also a hydrocarbon . Naturally occurring methane is found both below ground and under the seafloor and

4012-426: Is easier to store than hydrogen due to its higher boiling point and density, as well as its lack of hydrogen embrittlement . The lower molecular weight of the exhaust also increases the fraction of the heat energy which is in the form of kinetic energy available for propulsion, increasing the specific impulse of the rocket. Compared to liquid hydrogen , the specific energy of methane is lower but this disadvantage

4130-414: Is formed by both geological and biological processes. The largest reservoir of methane is under the seafloor in the form of methane clathrates . When methane reaches the surface and the atmosphere , it is known as atmospheric methane . The Earth's atmospheric methane concentration has increased by about 160% since 1750, with the overwhelming percentage caused by human activity. It accounted for 20% of

4248-488: Is generally transported in bulk by pipeline in its natural gas form, or by LNG carriers in its liquefied form; few countries transport it by truck. American English American English , sometimes called United States English or U.S. English , is the set of varieties of the English language native to the United States. English is the most widely spoken language in the United States ; an official language in 32 of

4366-408: Is increasing the amount of methane released from wetlands due to increased temperatures and altered rainfall patterns. This phenomenon is called wetland methane feedback . Rice cultivation generates as much as 12% of total global methane emissions due to the long-term flooding of rice fields. Ruminants, such as cattle, belch methane, accounting for about 22% of the U.S. annual methane emissions to

4484-446: Is lower than that of any other hydrocarbon, but the ratio of the heat of combustion (891 kJ/mol) to the molecular mass (16.0 g/mol, of which 12.0 g/mol is carbon) shows that methane, being the simplest hydrocarbon, produces more heat per mass unit (55.7 kJ/g) than other complex hydrocarbons. In many areas with a dense enough population, methane is piped into homes and businesses for heating , cooking, and industrial uses. In this context it

4602-459: Is mostly composed of methane, is used to produce hydrogen gas on an industrial scale. Steam methane reforming (SMR), or simply known as steam reforming, is the standard industrial method of producing commercial bulk hydrogen gas. More than 50 million metric tons are produced annually worldwide (2013), principally from the SMR of natural gas. Much of this hydrogen is used in petroleum refineries , in

4720-511: Is obtained by the reaction of CO with water via the water-gas shift reaction : This reaction is mildly exothermic (produces heat, Δ H r = −41 kJ/mol). Methane is also subjected to free-radical chlorination in the production of chloromethanes, although methanol is a more typical precursor. Hydrogen can also be produced via the direct decomposition of methane, also known as methane pyrolysis , which, unlike steam reforming, produces no greenhouse gases (GHG). The heat needed for

4838-432: Is offset by methane's greater density and temperature range, allowing for smaller and lighter tankage for a given fuel mass. Liquid methane has a temperature range (91–112 K) nearly compatible with liquid oxygen (54–90 K). The fuel currently sees use in operational launch vehicles such as Zhuque-2 and Vulcan as well as in-development launchers such as Starship , Neutron , and Terran R . Natural gas , which

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4956-420: Is often identified by Americans as a "country" accent, and is defined by the /aɪ/ vowel losing its gliding quality : [aː] , the initiation event for a complicated Southern vowel shift, including a " Southern drawl " that makes short front vowels into distinct-sounding gliding vowels . The fronting of the vowels of GOOSE , GOAT , MOUTH , and STRUT tends to also define Southern accents as well as

5074-467: Is rather easy to picture in the two-dimensional, wallpaper group case. Some of the point groups have reflections, and the reflection lines can be along the lattice directions, halfway in between them, or both. These correspond to conjugacy classes of lattice point groups in GL n ( Z ), where the lattice point group is the group of symmetries of the underlying lattice that fix a point of the lattice, and contains

5192-462: Is the common language at home, in public, and in government. Space group In crystallography , space groups are also called the crystallographic or Fedorov groups , and represent a description of the symmetry of the crystal. A definitive source regarding 3-dimensional space groups is the International Tables for Crystallography Hahn (2002) . Space groups in 2 dimensions are

5310-459: Is the extension of Z by a finite group acting faithfully is an affine space group. Combining these results shows that classifying space groups in n dimensions up to conjugation by affine transformations is essentially the same as classifying isomorphism classes for groups that are extensions of Z by a finite group acting faithfully. It is essential in Bieberbach's theorems to assume that

5428-463: Is the variable fronting of /ɑ/ before /r/ , for example, appearing four times in the stereotypical Boston shibboleth Park the car in Harvard Yard . Several other phenomena serve to distinguish regional U.S. accents. Boston , Pittsburgh , Upper Midwestern , and Western U.S. accents have fully completed a merger of the LOT vowel with the THOUGHT vowel ( /ɑ/ and /ɔ/ , respectively):

5546-402: Is usually known as natural gas , which is considered to have an energy content of 39 megajoules per cubic meter, or 1,000 BTU per standard cubic foot . Liquefied natural gas (LNG) is predominantly methane ( CH 4 ) converted into liquid form for ease of storage or transport. Refined liquid methane as well as LNG is used as a rocket fuel , when combined with liquid oxygen , as in

5664-400: Is very long. This is what gives Uranus and Neptune their blue or bluish-green colors, as light passes through their atmospheres containing methane and is then scattered back out. The familiar smell of natural gas as used in homes is achieved by the addition of an odorant , usually blends containing tert -butylthiol , as a safety measure. Methane has a boiling point of −161.5  °C at

5782-539: The Catalytica system , copper zeolites , and iron zeolites stabilizing the alpha-oxygen active site. One group of bacteria catalyze methane oxidation with nitrite as the oxidant in the absence of oxygen , giving rise to the so-called anaerobic oxidation of methane . Like other hydrocarbons , methane is an extremely weak acid . Its p K a in DMSO is estimated to be 56. It cannot be deprotonated in solution, but

5900-476: The English-only movement , have adopted legislation granting official or co-official status to English. Typically only "English" is specified, not a particular variety like American English. (From 1923 to 1969, the state of Illinois recognized its official language as "American", meaning American English.) Puerto Rico is the largest example of a United States territory in which another language – Spanish –

6018-608: The Mid-Atlantic states (including a New York accent as well as a unique Philadelphia–Baltimore accent ), and the South . As of the 20th century, the middle and eastern Great Lakes area , Chicago being the largest city with these speakers, also ushered in certain unique features, including the fronting of the LOT /ɑ/ vowel in the mouth toward [a] and tensing of the TRAP /æ/ vowel wholesale to [eə] . These sound changes have triggered

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6136-544: The Native American languages . Examples of such names are opossum , raccoon , squash , moose (from Algonquian ), wigwam , and moccasin . American English speakers have integrated traditionally non-English terms and expressions into the mainstream cultural lexicon; for instance, en masse , from French ; cookie , from Dutch ; kindergarten from German , and rodeo from Spanish . Landscape features are often loanwords from French or Spanish, and

6254-586: The Sabatier process . Methane is also a side product of the hydrogenation of carbon monoxide in the Fischer–Tropsch process , which is practiced on a large scale to produce longer-chain molecules than methane. An example of large-scale coal-to-methane gasification is the Great Plains Synfuels plant, started in 1984 in Beulah, North Dakota as a way to develop abundant local resources of low-grade lignite ,

6372-476: The TQ-12 , BE-4 , Raptor , and YF-215 engines. Due to the similarities between methane and LNG such engines are commonly grouped together under the term methalox . As a liquid rocket propellant, a methane/ liquid oxygen combination offers the advantage over kerosene / liquid oxygen combination, or kerolox, of producing small exhaust molecules, reducing coking or deposition of soot on engine components. Methane

6490-463: The asymmetric unit in a unit cell is thus the number of lattice points in the cell times the order of the point group. This ranges from 1 in the case of space group P1 to 192 for a space group like Fm 3 m, the NaCl structure . The elements of the space group fixing a point of space are the identity element, reflections, rotations and improper rotations , including inversion points . The translations form

6608-633: The conjugate base is known in forms such as methyllithium . A variety of positive ions derived from methane have been observed, mostly as unstable species in low-pressure gas mixtures. These include methenium or methyl cation CH + 3 , methane cation CH + 4 , and methanium or protonated methane CH + 5 . Some of these have been detected in outer space . Methanium can also be produced as diluted solutions from methane with superacids . Cations with higher charge, such as CH 2+ 6 and CH 3+ 7 , have been studied theoretically and conjectured to be stable. Despite

6726-714: The francophile tastes of the 19th century Victorian era Britain (for example they preferred programme for program , manoeuvre for maneuver , cheque for check , etc.). AmE almost always uses -ize in words like realize . BrE prefers -ise , but also uses -ize on occasion (see: Oxford spelling ). There are a few differences in punctuation rules. British English is more tolerant of run-on sentences , called " comma splices " in American English, and American English prefers that periods and commas be placed inside closing quotation marks even in cases in which British rules would place them outside. American English also favors

6844-495: The strength of its C–H bonds, there is intense interest in catalysts that facilitate C–H bond activation in methane (and other lower numbered alkanes ). Methane's heat of combustion is 55.5 MJ/kg. Combustion of methane is a multiple step reaction summarized as follows: Peters four-step chemistry is a systematically reduced four-step chemistry that explains the burning of methane. Given appropriate conditions, methane reacts with halogen radicals as follows: where X

6962-471: The 17 wallpaper groups which have been known for several centuries, though the proof that the list was complete was only given in 1891, after the much more difficult classification of space groups had largely been completed. In 1879 the German mathematician Leonhard Sohncke listed the 65 space groups (called Sohncke groups) whose elements preserve the chirality . More accurately, he listed 66 groups, but both

7080-759: The 18th century; apartment , shanty in the 19th century; project, condominium , townhouse , mobile home in the 20th century; and parts thereof ( driveway , breezeway, backyard ) . Industry and material innovations from the 19th century onwards provide distinctive new words, phrases, and idioms through railroading (see further at rail terminology ) and transportation terminology, ranging from types of roads ( dirt roads , freeways ) to infrastructure ( parking lot , overpass , rest area ), to automotive terminology often now standard in English internationally. Already existing English words—such as store , shop , lumber —underwent shifts in meaning; others remained in

7198-534: The 20th century. The use of English in the United States is a result of British colonization of the Americas . The first wave of English-speaking settlers arrived in North America during the early 17th century, followed by further migrations in the 18th and 19th centuries. During the 17th and 18th centuries, dialects from many different regions of England and the British Isles existed in every American colony, allowing

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7316-405: The 2p orbitals on carbon with various linear combinations of the 1s orbitals on hydrogen. The resulting "three-over-one" bonding scheme is consistent with photoelectron spectroscopic measurements. Methane is an odorless, colourless and transparent gas. It does absorb visible light, especially at the red end of the spectrum, due to overtone bands , but the effect is only noticeable if the light path

7434-429: The 50 U.S. states ; and the de facto common language used in government, education, and commerce throughout the nation. Since the late 20th century, American English has become the most influential form of English worldwide. Varieties of American English include many patterns of pronunciation, vocabulary, grammar and particularly spelling that are unified nationwide but distinct from other English dialects around

7552-622: The British form is a back-formation , such as AmE burglarize and BrE burgle (from burglar ). However, while individuals usually use one or the other, both forms will be widely understood and mostly used alongside each other within the two systems. While written American English is largely standardized across the country and spoken American English dialects are highly mutually intelligible, there are still several recognizable regional and ethnic accents and lexical distinctions. The regional sounds of present-day American English are reportedly engaged in

7670-413: The East Coast (perhaps in imitation of 19th-century London speech), even the East Coast has gradually begun to restore rhoticity, due to it becoming nationally prestigious in the 20th century. The pronunciation of ⟨r⟩ is a postalveolar approximant [ ɹ̠ ] or retroflex approximant [ ɻ ] , but a unique "bunched tongue" variant of the approximant r sound

7788-565: The Inland North. Rather than one particular accent, General American is best defined as an umbrella covering an American accent that does not incorporate features associated with some particular region, ethnicity, or socioeconomic group. Typical General American features include rhoticity , the father–bother merger , Mary–marry–merry merger , pre-nasal "short a " tensing , and other particular vowel sounds . General American features are embraced most by Americans who are highly educated or in

7906-578: The Russian mathematician and crystallographer Evgraf Fedorov and the German mathematician Arthur Moritz Schoenflies noticed that two of them were really the same. The space groups in three dimensions were first enumerated in 1891 by Fedorov (whose list had two omissions (I 4 3d and Fdd2) and one duplication (Fmm2)), and shortly afterwards in 1891 were independently enumerated by Schönflies (whose list had four omissions (I 4 3d, Pc, Cc, ?) and one duplication (P 4 2 1 m)). The correct list of 230 space groups

8024-560: The South), sneakers for athletic shoes (but often tennis shoes outside the Northeast), and shopping cart for a cart used for carrying supermarket goods. American English and British English (BrE) often differ at the levels of phonology, phonetics, vocabulary, and, to a much lesser extent, grammar and orthography. The first large American dictionary, An American Dictionary of the English Language , known as Webster's Dictionary ,

8142-528: The U.S. Several verbs ending in -ize are of U.S. origin; for example, fetishize, prioritize, burglarize, accessorize, weatherize , etc.; and so are some back-formations (locate, fine-tune, curate, donate, emote, upholster and enthuse). Among syntactic constructions that arose are outside of, headed for, meet up with, back of, etc. Americanisms formed by alteration of some existing words include notably pesky, phony, rambunctious, buddy, sundae , skeeter, sashay and kitty-corner. Adjectives that arose in

8260-563: The U.S. are for instance foothill , landslide (in all senses), backdrop , teenager , brainstorm , bandwagon , hitchhike , smalltime, and a huge number of others. Other compound words have been founded based on industrialization and the wave of the automobile: five-passenger car, four-door sedan, two-door sedan, and station-wagon (called an estate car in British English). Some are euphemistic ( human resources , affirmative action , correctional facility ). Many compound nouns have

8378-662: The U.S. are, for example, lengthy, bossy, cute and cutesy, punk (in all senses), sticky (of the weather), through (as in "finished"), and many colloquial forms such as peppy or wacky . A number of words and meanings that originated in Middle English or Early Modern English and that have been in everyday use in the United States have since disappeared in most varieties of British English; some of these have cognates in Lowland Scots . Terms such as fall ("autumn"), faucet ("tap"), diaper ("nappy"; itself unused in

8496-530: The U.S. while changing in Britain. Science, urbanization, and democracy have been important factors in bringing about changes in the written and spoken language of the United States. From the world of business and finance came new terms ( merger , downsize , bottom line ), from sports and gambling terminology came, specific jargon aside, common everyday American idioms, including many idioms related to baseball . The names of some American inventions remained largely confined to North America ( elevator [except in

8614-427: The U.S.), candy ("sweets"), skillet , eyeglasses , and obligate are often regarded as Americanisms. Fall for example came to denote the season in 16th century England, a contraction of Middle English expressions like "fall of the leaf" and "fall of the year." Gotten ( past participle of get ) is often considered to be largely an Americanism. Other words and meanings were brought back to Britain from

8732-592: The U.S., especially in the second half of the 20th century; these include hire ("to employ"), I guess (famously criticized by H. W. Fowler ), baggage , hit (a place), and the adverbs overly and presently ("currently"). Some of these, for example, monkey wrench and wastebasket , originated in 19th century Britain. The adjectives mad meaning "angry", smart meaning "intelligent", and sick meaning "ill" are also more frequent in American (and Irish) English than British English. Linguist Bert Vaux created

8850-531: The United States and the United Kingdom suggest that, while spoken American English deviated away from period British English in many ways, it is conservative in a few other ways, preserving certain features 21st-century British English has since lost. Full rhoticity (or "R-fulness") is typical of American accents, pronouncing the phoneme /r/ (corresponding to the letter ⟨r⟩ ) in all environments, including in syllable-final position or before

8968-596: The West and Midwest, and New York Latino English , spoken in the New York metropolitan area . Additionally, ethnic varieties such as Yeshiva English and " Yinglish " are spoken by some American Orthodox Jews , Cajun Vernacular English by some Cajuns in southern Louisiana , and Pennsylvania Dutch English by some Pennsylvania Dutch people. American Indian Englishes have been documented among diverse Indian tribes. The island state of Hawaii , though primarily English-speaking,

9086-547: The accents spoken in the " Midland ": a vast band of the country that constitutes an intermediate dialect region between the traditional North and South. Western U.S. accents mostly fall under the General American spectrum. Below, ten major American English accents are defined by their particular combinations of certain vowel sounds: In 2010, William Labov noted that Great Lakes, Philadelphia, Pittsburgh, and West Coast accents have undergone "vigorous new sound changes" since

9204-505: The aeronautical sense ], gasoline ) as did certain automotive terms ( truck , trunk ). New foreign loanwords came with 19th and early 20th century European immigration to the U.S.; notably, from Yiddish ( chutzpah , schmooze, bupkis, glitch ) and German ( hamburger , wiener ). A large number of English colloquialisms from various periods are American in origin; some have lost their American flavor (from OK and cool to nerd and 24/7 ), while others have not ( have

9322-421: The atmosphere. One study reported that the livestock sector in general (primarily cattle, chickens, and pigs) produces 37% of all human-induced methane. A 2013 study estimated that livestock accounted for 44% of human-induced methane and about 15% of human-induced greenhouse gas emissions. Many efforts are underway to reduce livestock methane production, such as medical treatments and dietary adjustments, and to trap

9440-537: The axial 3D point groups are magnetic 2D point groups. Number of original and magnetic groups by (overall, lattice) dimension:( Palistrant 2012 )( Souvignier 2006 ) Table of the wallpaper groups using the classification of the 2-dimensional space groups: For each geometric class, the possible arithmetic classes are Note: An e plane is a double glide plane, one having glides in two different directions. They are found in seven orthorhombic, five tetragonal and five cubic space groups, all with centered lattice. The use of

9558-679: The breakup of organic matter at elevated temperatures and pressures in deep sedimentary strata . Most methane in sedimentary basins is thermogenic; therefore, thermogenic methane is the most important source of natural gas. Thermogenic methane components are typically considered to be relic (from an earlier time). Generally, formation of thermogenic methane (at depth) can occur through organic matter breakup, or organic synthesis. Both ways can involve microorganisms ( methanogenesis ), but may also occur inorganically. The processes involved can also consume methane, with and without microorganisms. The more important source of methane at depth (crystalline bedrock)

9676-605: The chosen catalyst. Dozens of catalysts have been tested, including unsupported and supported metal catalysts, carbonaceous and metal-carbon catalysts. The reaction is moderately endothermic as shown in the reaction equation below. As a refrigerant , methane has the ASHRAE designation R-50 . Methane can be generated through geological, biological or industrial routes. The two main routes for geological methane generation are (i) organic (thermally generated, or thermogenic) and (ii) inorganic ( abiotic ). Thermogenic methane occurs due to

9794-586: The cold gas, the gas at ambient temperature is lighter than air. Gas pipelines distribute large amounts of natural gas, of which methane is the principal component. Methane is used as a fuel for ovens, homes, water heaters, kilns, automobiles, turbines, etc. As the major constituent of natural gas , methane is important for electricity generation by burning it as a fuel in a gas turbine or steam generator . Compared to other hydrocarbon fuels , methane produces less carbon dioxide for each unit of heat released. At about 891 kJ/mol, methane's heat of combustion

9912-497: The converses are not true. An inversion and a mirror implies two-fold screw axes, and so on. There are at least ten methods of naming space groups. Some of these methods can assign several different names to the same space group, so altogether there are many thousands of different names. The viewing directions of the 7 crystal systems are shown as follows. There are (at least) 10 different ways to classify space groups into classes. The relations between some of these are described in

10030-406: The country), though the vowel-consonant cluster found in "bird", "work", "hurt", "learn", etc. usually retains its r pronunciation, even in these non-rhotic American accents. Non-rhoticity among such speakers is presumed to have arisen from their upper classes' close historical contact with England, imitating London's r -dropping, a feature that has continued to gain prestige throughout England from

10148-614: The diverse regional dialects of British English) became common after the mid-18th century, while at the same time speakers' identification with this new variety increased. Since the 18th century, American English has developed into some new varieties, including regional dialects that retain minor influences from waves of immigrant speakers of diverse languages, primarily European languages. Some racial and regional variation in American English reflects these groups' geographic settlement, their de jure or de facto segregation, and patterns in their resettlement. This can be seen, for example, in

10266-742: The double quotation mark ("like this") over the single ('as here'). Vocabulary differences vary by region. For example, autumn is used more commonly in the United Kingdom, whereas fall is more common in American English. Some other differences include: aerial (United Kingdom) vs. antenna, biscuit (United Kingdom) vs. cookie/cracker, car park (United Kingdom) vs. parking lot, caravan (United Kingdom) vs. trailer, city centre (United Kingdom) vs. downtown, flat (United Kingdom) vs. apartment, fringe (United Kingdom) vs. bangs, and holiday (United Kingdom) vs. vacation. AmE sometimes favors words that are morphologically more complex, whereas BrE uses clipped forms, such as AmE transportation and BrE transport or where

10384-436: The element transforms point x into point y . In general, D = D ( lattice ) + D ( M ), where D ( M ) is a unique function of M that is zero for M being the identity. The matrices M form a point group that is a basis of the space group; the lattice must be symmetric under that point group, but the crystal structure itself may not be symmetric under that point group as applied to any particular point (that is, without

10502-401: The following table. Each classification system is a refinement of the ones below it. To understand an explanation given here it may be necessary to understand the next one down. Arithmetic crystal classes may be interpreted as different orientations of the point groups in the lattice, with the group elements' matrix components being constrained to have integer coefficients in lattice space. This

10620-510: The following two centuries) when this ethnic group eventually made up one-seventh of the colonial population. Scotch-Irish settlers spread from Delaware and Pennsylvania throughout the larger Mid-Atlantic region, the inland regions of both the South and North, and throughout the West: American dialect areas that were all uninfluenced by upper-class non-rhoticity and that consequently have remained consistently rhotic. While non-rhoticity spread on

10738-432: The gas to use its combustion energy. Most of the subseafloor is anoxic because oxygen is removed by aerobic microorganisms within the first few centimeters of the sediment . Below the oxygen-replete seafloor, methanogens produce methane that is either used by other organisms or becomes trapped in gas hydrates . These other organisms that utilize methane for energy are known as methanotrophs ('methane-eating'), and are

10856-469: The group acts as isometries; the theorems do not generalize to discrete cocompact groups of affine transformations of Euclidean space. A counter-example is given by the 3-dimensional Heisenberg group of the integers acting by translations on the Heisenberg group of the reals, identified with 3-dimensional Euclidean space. This is a discrete cocompact group of affine transformations of space, but does not contain

10974-743: The group elements can include time reversal as reflection in it. They are of importance in magnetic structures that contain ordered unpaired spins, i.e. ferro- , ferri- or antiferromagnetic structures as studied by neutron diffraction . The time reversal element flips a magnetic spin while leaving all other structure the same and it can be combined with a number of other symmetry elements. Including time reversal there are 1651 magnetic space groups in 3D ( Kim 1999 , p.428). It has also been possible to construct magnetic versions for other overall and lattice dimensions ( Daniel Litvin's papers , ( Litvin 2008 ), ( Litvin 2005 )). Frieze groups are magnetic 1D line groups and layer groups are magnetic wallpaper groups, and

11092-446: The guts of termites, and the anoxic sediments below the seafloor and the bottom of lakes. This multistep process is used by these microorganisms for energy. The net reaction of methanogenesis is: The final step in the process is catalyzed by the enzyme methyl coenzyme M reductase (MCR). Wetlands are the largest natural sources of methane to the atmosphere, accounting for approximately 20 - 30% of atmospheric methane. Climate change

11210-401: The halogen-to-methane ratio. This reaction is commonly used with chlorine to produce dichloromethane and chloroform via chloromethane . Carbon tetrachloride can be made with excess chlorine. Methane may be transported as a refrigerated liquid (liquefied natural gas, or LNG ). While leaks from a refrigerated liquid container are initially heavier than air due to the increased density of

11328-431: The history of the discovery of the space groups in detail. The space groups in three dimensions are made from combinations of the 32 crystallographic point groups with the 14 Bravais lattices , each of the latter belonging to one of 7 lattice systems . What this means is that the action of any element of a given space group can be expressed as the action of an element of the appropriate point group followed optionally by

11446-939: The hospital , BrE to hospital ; contrast, however, AmE actress Elizabeth Taylor , BrE the actress Elizabeth Taylor ). Often, these differences are a matter of relative preferences rather than absolute rules; and most are not stable since the two varieties are constantly influencing each other, and American English is not a standardized set of dialects. Differences in orthography are also minor. The main differences are that American English usually uses spellings such as flavor for British flavour , fiber for fibre , defense for defence , analyze for analyse , license for licence , catalog for catalogue and traveling for travelling . Noah Webster popularized such spellings in America, but he did not invent most of them. Rather, "he chose already existing options on such grounds as simplicity, analogy or etymology." Other differences are due to

11564-656: The influence of 18th-century Protestant Ulster Scots immigrants (known in the U.S. as the Scotch-Irish ) in Appalachia developing Appalachian English and the 20th-century Great Migration bringing African-American Vernacular English to the Great Lakes urban centers. Any phonologically unmarked North American accent falls under an umbrella known as General American. This section mostly refers to such General American features. Studies on historical usage of English in both

11682-438: The late 18th century onwards, but which has conversely lost prestige in the U.S. since at least the early 20th century. Non-rhoticity makes a word like car sound like cah or source like sauce . New York City and Southern accents are the most prominent regional accents of the country, as well as the most stigmatized and socially disfavored. Southern speech, strongest in southern Appalachia and certain areas of Texas,

11800-480: The main reason why little methane generated at depth reaches the sea surface. Consortia of Archaea and Bacteria have been found to oxidize methane via anaerobic oxidation of methane (AOM); the organisms responsible for this are anaerobic methanotrophic Archaea (ANME) and sulfate-reducing bacteria (SRB). Given its cheap abundance in natural gas, there is little incentive to produce methane industrially. Methane can be produced by hydrogenating carbon dioxide through

11918-427: The mid-nineteenth century onwards, so they "are now more different from each other than they were 50 or 100 years ago", while other accents, like of New York City and Boston, have remained stable in that same time-frame. However, a General American sound system also has some debated degree of influence nationwide, for example, gradually beginning to oust the regional accent in urban areas of the South and at least some in

12036-617: The most formal contexts, and regional accents with the most General American native features include North Midland, Western New England, and Western accents. Although no longer region-specific, African-American Vernacular English , which remains the native variety of most working- and middle-class African Americans , has a close relationship to Southern dialects and has greatly influenced everyday speech of many Americans, including hip hop culture . Hispanic and Latino Americans have also developed native-speaker varieties of English. The best-studied Latino Englishes are Chicano English , spoken in

12154-402: The past forms of a few verbs (for example, AmE/BrE: learned / learnt , burned / burnt , snuck/sneaked , dove/dived ) although the purportedly "British" forms can occasionally be seen in American English writing as well; different prepositions and adverbs in certain contexts (for example, AmE in school, BrE at school ); and whether or not a definite article is used, in very few cases (AmE to

12272-418: The point group. Conway , Delgado Friedrichs, and Huson et al. ( 2001 ) gave another classification of the space groups, called a fibrifold notation , according to the fibrifold structures on the corresponding orbifold . They divided the 219 affine space groups into reducible and irreducible groups. The reducible groups fall into 17 classes corresponding to the 17 wallpaper groups , and

12390-457: The production of chemicals and in food processing. Very large quantities of hydrogen are used in the industrial synthesis of ammonia . At high temperatures (700–1100 °C) and in the presence of a metal -based catalyst ( nickel ), steam reacts with methane to yield a mixture of CO and H 2 , known as "water gas" or " syngas ": This reaction is strongly endothermic (consumes heat, Δ H r = 206 kJ/mol). Additional hydrogen

12508-468: The reaction can also be GHG emission free, e.g. from concentrated sunlight, renewable electricity, or burning some of the produced hydrogen. If the methane is from biogas then the process can be a carbon sink . Temperatures in excess of 1200 °C are required to break the bonds of methane to produce hydrogen gas and solid carbon. However, through the use of a suitable catalyst the reaction temperature can be reduced to between 550-900 °C depending on

12626-419: The remaining 35 irreducible groups are the same as the cubic groups and are classified separately. In n dimensions, an affine space group, or Bieberbach group, is a discrete subgroup of isometries of n -dimensional Euclidean space with a compact fundamental domain. Bieberbach ( 1911 , 1912 ) proved that the subgroup of translations of any such group contains n linearly independent translations, and

12744-415: The space groups that permit this. Among the 65 Sohncke groups are 22 that come in 11 enantiomorphic pairs. Only certain combinations of symmetry elements are possible in a space group. Translations are always present, and the space group P1 has only translations and the identity element. The presence of mirrors implies glide planes as well, and the presence of rotation axes implies screw axes as well, but

12862-448: The symbol e became official with Hahn (2002) . The lattice system can be found as follows. If the crystal system is not trigonal then the lattice system is of the same type. If the crystal system is trigonal, then the lattice system is hexagonal unless the space group is one of the seven in the rhombohedral lattice system consisting of the 7 trigonal space groups in the table above whose name begins with R. (The term rhombohedral system

12980-448: The total radiative forcing from all of the long-lived and globally mixed greenhouse gases , according to the 2021 Intergovernmental Panel on Climate Change report. Strong, rapid and sustained reductions in methane emissions could limit near-term warming and improve air quality by reducing global surface ozone. Methane has also been detected on other planets, including Mars , which has implications for astrobiology research. Methane

13098-570: The traditional standard accent of (southern) England, Received Pronunciation (RP), has evolved a trap–bath split . Moreover, American accents preserve /h/ at the start of syllables, while perhaps a majority of the regional dialects of England participate in /h/ dropping , particularly in informal contexts. However, General American is also innovative in a number of its own ways: The process of coining new lexical items started as soon as English-speaking British-American colonists began borrowing names for unfamiliar flora, fauna, and topography from

13216-417: The verb-and-preposition combination: stopover, lineup, tryout, spin-off, shootout , holdup, hideout, comeback, makeover , and many more. Some prepositional and phrasal verbs are in fact of American origin ( win out, hold up, back up/off/down/out, face up to and many others). Noun endings such as -ee (retiree), -ery (bakery), -ster (gangster) and -cian (beautician) are also particularly productive in

13334-403: The way around the axis each time). The degree of translation is then added as a subscript showing how far along the axis the translation is, as a portion of the parallel lattice vector. So, 2 1 is a twofold rotation followed by a translation of 1/2 of the lattice vector. The general formula for the action of an element of a space group is where M is its matrix, D is its vector, and where

13452-772: The word corn , used in England to refer to wheat (or any cereal), came to denote the maize plant, the most important crop in the U.S. Most Mexican Spanish contributions came after the War of 1812 , with the opening of the West, like ranch (now a common house style ). Due to Mexican culinary influence, many Spanish words are incorporated in general use when talking about certain popular dishes: cilantro (instead of coriander), queso, tacos, quesadillas, enchiladas, tostadas, fajitas, burritos, and guacamole. These words usually lack an English equivalent and are found in popular restaurants. New forms of dwelling created new terms ( lot , waterfront) and types of homes like log cabin , adobe in

13570-609: The world. Any American or Canadian accent perceived as lacking noticeably local, ethnic, or cultural markers is known in linguistics as General American ; it covers a fairly uniform accent continuum native to certain regions of the U.S. but especially associated with broadcast mass media and highly educated speech. However, historical and present linguistic evidence does not support the notion of there being one single mainstream American accent . The sound of American English continues to evolve, with some local accents disappearing, but several larger regional accents having emerged in

13688-416: Was found by 1892 during correspondence between Fedorov and Schönflies. William Barlow  ( 1894 ) later enumerated the groups with a different method, but omitted four groups (Fdd2, I 4 2d, P 4 2 1 d, and P 4 2 1 c) even though he already had the correct list of 230 groups from Fedorov and Schönflies; the common claim that Barlow was unaware of their work is incorrect. Burckhardt (1967) describes

13806-406: Was suggested to use symbol e for such planes. The symbols for five space groups have been modified: A screw axis is a rotation about an axis, followed by a translation along the direction of the axis. These are noted by a number, n , to describe the degree of rotation, where the number is how many operations must be applied to complete a full rotation (e.g., 3 would mean a rotation one third of

13924-469: Was written by Noah Webster in 1828, codifying several of these spellings. Differences in grammar are relatively minor, and do not normally affect mutual intelligibility; these include: typically a lack of differentiation between adjectives and adverbs, employing the equivalent adjectives as adverbs he ran quick / he ran quickly ; different use of some auxiliary verbs ; formal (rather than notional) agreement with collective nouns ; different preferences for

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