FIM-92刺针便携式防空导弹

Description.

Light to carry and easy to operate, the FIM-92 Stinger is a passive surface-to-air missile that can be shoulder-fired by a single operator (although standard military procedure calls for two operators, team chief and gunner). The FIM-92B missile can also be fired from the M-1097 Avenger and the M6 Linebacker. The missile is also capable of being deployed from a Humvee Stinger rack, and can be used by airborne troops. A helicopter launched version exists called Air-to-Air Stinger (ATAS).  The missile is long and in diameter with fins. The missile itself weighs, while the missile with its launch tube and integral sight, fitted with a gripstock and IFF antenna, weighs approximately. It has an outward targeting range of up to 4,800 m and can engage low altitude enemy threats at up to 3,800 m. The Stinger is launched by a small ejection motor that pushes it a safe distance from the operator before engaging the main two-stage solid-fuel sustainer, which accelerates it to a maximum speed of Mach 2.54 (750 m/s). The warhead is a penetrating hit-to-kill annular blast fragmentation type with an impact fuze and a self-destruct timer.  To fire the missile, a BCU (Battery Coolant Unit) is inserted into the gripstock. This device consists of a supply of liquid argon which is injected into the seeker to cool it to operating temperature, and a thermal battery which provides power for target acquisition: a single BCU provides power and coolant for roughly 45 seconds, after which another must be inserted if the missile has not been fired. The BCUs are somewhat sensitive to abuse, and have a limited shelf life due to the pressurised liquid argon leaking. The IFF system receives power from a rechargeable battery which is part of the IFF interrogator box which plugs into the base of the gripstock's pistol grip. Guidance to the target is initially through proportional navigation, then switches to another mode that directs the missile towards the target airframe instead of its exhaust plume.  There are three main variants in use: the Stinger basic, STINGER-Passive Optical Seeker Technique (POST), and STINGER-Reprogrammable Microprocessor (RMP). These correspond to the FIM-92A, FIM-92B, and FIM-92C and later variants respectively.  The POST has a dual-detector seeker: IR and UV. This allows it to distinguish targets from countermeasures much better than the Redeye and FIM-92A, which have IR-only. While modern flares can have an IR signature that is closely matched to the launching aircraft's engine exhaust, there is a readily distinguishable difference in UV signature between flares and jet engines. The Stinger-RMP is so-called because of its ability to load a new set of software via ROM chip inserted in the grip at the depot. If this download to the missile fails during power-up, basic functionality runs off the on-board ROM. The four-processor RMP has 4 KB of RAM for each processor. Since the downloaded code runs from RAM, there is little space to spare, particularly for processors dedicated to seeker input processing and target analysis.

History.

The missile began as a program by General Dynamics to produce an improved variant of their 1967 FIM-43 Redeye. Production of the Redeye ran from 1969 to 1982, with a total production of around 85,000 missiles. The program was accepted for further development as Redeye II by the U.S. Army in 1971 and designated FIM-92; the "Stinger" appellation was chosen in 1972. Because of technical difficulties that dogged testing, the first shoulder launch was not until mid-1975. Production of the FIM-92A began in 1978. An improved Stinger with a new seeker, the FIM-92B, was produced from 1983 alongside the FIM-92A. Production of both the A and B types ended in 1987 with around 16,000 missiles produced.  The replacement FIM-92C began development in 1984, and production began in 1987. The first examples were delivered to front-line units in 1989. C-type missiles were fitted with a reprogrammable microprocessor, allowing for incremental firmware updates. Later missiles designated D received improvements to improve their ability to defeat countermeasures, and later upgrades to the D were designated G.  The FIM-92E or Block I was developed from 1992 and delivered from 1995 (certain sources state that the FIM-92D is also part of the Block I development). The main changes were again in the sensor and the software, improving the missile's performance against low-signature targets. A software upgrade in 2001 was designated F. Block II development began in 1996 using a new focal plane array sensor to improve the missile's effectiveness in "high clutter" environments and increase the engagement range to about 25,000 feet (7,600 m). Production was scheduled for 2004, but "Jane's" reports that this may be on hold.  Since 1984 the Stinger has been issued to many U.S. Navy warships for point defense, particularly in Middle Eastern waters, with a three-man team that can perform other duties when not conducting Stinger training or maintenance. Until it was decommissioned in September 1993, the U.S. Navy had at least one Stinger Gunnery Detachment attached to Beachmaster Unit Two in Little Creek Virginia. The sailors of this detachment would deploy to carrier battlegroups in teams of two to four sailors per ship as requested by Battle Group Commanders.

Service.

Falklands War.

The Stinger's combat debut occurred during the Falklands War fought between the United Kingdom and Argentina. At the onset of the conflict soldiers of the British Army's Special Air Service had been clandestinely equipped with six missiles, although they had received little instruction in their use. The sole SAS trooper who had received training on the system, and was due to train other troops, was killed in a helicopter crash on 19 May. Nonetheless, on 21 May 1982 an SAS soldier engaged and shot down an Argentine Pucará ground attack aircraft with a Stinger. On 30 May, at about 11.00 a.m., an Aerospatiale SA-330 Puma helicopter was brought down by another missile, also fired by the SAS, in the vicinity of Mount Kent. Six National Gendarmerie Special Forces were killed and eight more wounded. The main MANPADS used by both sides during the Falklands War was the Blowpipe missile.

Soviet War in Afghanistan.

In late 1985, several groups, such as Free the Eagle, began arguing the CIA was not doing enough to support the Mujahideen in the Soviet–Afghan War. Michael Pillsbury, Vincent Cannistraro, and others put enormous bureaucratic pressure on the CIA to provide the Stinger to the rebels. The idea was controversial because up to that point, the CIA had been operating with the pretense that the United States was not involved in the war directly, for various reasons. All weapons supplied up to that point were non-U.S. made weapons, like Type 56 rifles purchased from China, and AK-47 and AKM AK derivatives purchased from Egypt.  The final say-so came down to President General Muhammad Zia-ul-Haq of Pakistan, through whom the CIA had to pass all of its funding and weapons to the Mujahideen. President Zia constantly had to gauge how much he could "make the pot boil" in Afghanistan without provoking a Soviet invasion of his own country. According to George Crile III, U.S. Representative Charlie Wilson's relationship with Zia was instrumental in the final go-ahead for the Stinger introduction.  Wilson and his associates at first viewed the Stinger as "just adding another component to the lethal mix we were building." Their increasingly successful Afghanistan strategy, formed largely by Michael G. Vickers, was based on a broad mix of weapons, tactics, and logistics, not a'silver bullet solution' of a single weapon. Furthermore, the previous attempts to provide MANPADs to the Mujahideen, namely the SA-7 and Blowpipe, hadn't worked very well.  Engineer Ghaffar, of Gulbuddin Hekmatyar's Hezb-i-Islami, brought down the first Hind gunship with a Stinger on September 25, 1986 near Jalalabad. As part of Operation Cyclone, the CIA eventually supplied nearly 500 Stingers (some sources claim 1,500–2,000) to the Mujahideen in Afghanistan, and 250 launchers.  The impact of the Stinger on the outcome of the war is contested, particularly in the translation between the impact on the tactical battlefield to the strategic level withdrawal, and the influence the first had on the second. Dr. Robert F. Baumann (of the Staff College at Fort Leavenworth) described its impact on "Soviet tactical operations" as "unmistakable". This opinion was shared by Yossef Bodansky. Soviet, and later, Russian, accounts give little significance to the Stinger for strategically ending the war.  According to the 1993 US US Air Defense Artillery Yearbook, the Mujahideen gunners used the supplied Stingers to score approximately 269 total aircraft kills in about 340 engagements, a 79-percent kill ratio. If this report is accurate, Stingers would be responsible for over half of the 451 Soviet aircraft losses in Afghanistan. But these statistics are based on Mujahedin self-reporting, which is of unknown reliability. Selig Harrison rejects such figures, quoting a Russian general who claims the United States "greatly exaggerated" Soviet and Afghan aircraft losses during the war. According to Soviet figures, in 1987–1988, only 35 aircraft and 63 helicopters were destroyed by all causes. The Pakistan Army fired twenty-eight Stingers at enemy aircraft without a single kill.  According to Crile, who includes information from Alexander Prokhanov, the Stinger was a "turning point". Milt Bearden saw it as a "force multiplier" and morale booster. Representative Charlie Wilson, the politician behind Operation Cyclone, described the first Stinger Mi-24 shootdowns in 1986 as one of the three crucial moments of his experience in the war, saying "we never really won a set-piece battle before September 26, and then we never lost one afterwards." He was given the first spent Stinger tube as a gift and kept it on his office wall. That launch tube is now on exhibit at the US Army Air Defense Artillery Museum, Fort Sill, OK.  Many Russian military analysts tend to be dismissive of the impact to the Stinger. According to Alan J. Kuperman, the stingers did make an impact at first but within a few months flares, beacons, and exhaust baffles were installed to disorient the missiles, along with night operation and terrain-hugging tactics to prevent the rebels from getting a clear shot. By 1988, Kuperman states, the mujahideen had all but stopped firing them. Another source (Jonathan Steele) states that Stingers forced Soviet helicopters and ground attack planes to bomb from higher altitudes with less accuracy, but did not bring down many more aircraft than Chinese heavy machine guns and other less sophisticated anti-aircraft weaponry.  The last Stingers were supplied in 1988 after increasing reports of fighters selling them to Iran and thawing relations with Moscow. After the 1989 Soviet withdrawal from Afghanistan, the U.S. attempted to buy back the Stinger missiles, with a $55 million program launched in 1990 to buy back around 300 missiles (US$183,300 each). The U.S. government collected most of the Stingers it had delivered, but by 1996 around 600 were unaccounted for and some found their way into Croatia, Iran, Sri Lanka, Qatar, and North Korea. According to the CIA, already in August 1988 the U.S. had demanded from Qatar the return of Stinger missiles. Wilson later told CBS he "lived in terror" that a civilian airliner would be shot down by a Stinger, but he did not have misgivings about having provided Stingers to defeat the Soviets.  The story of the Stingers in Afghanistan was popularly told in the media by western sources primarily, notably in "" by George Crile, and "Ghost Wars" by Steve Coll.

Angolan Civil War.

The Reagan administration provided 310 Stingers to Jonas Savimbi's UNITA movement in Angola between 1986 and 1989. As in Afghanistan, efforts to recover missiles after the end of hostilities proved incomplete. The battery of a Stinger lasts for four or five years, so any battery supplied in the 1980s would now be inoperative but during the Syrian Civil War, insurgents showed how easily they switched to different batteries, including widespread car batteries, as power sources for several MANPADS models.

Libyan invasion of Chad.

The French army used 15 firing positions and 30 missiles purchased in 1983 for operations in Chad. The 35th Parachute Artillery Regiment made an unsuccessful fire during a Libyan bombardment on 10 September 1987 and shot down a Hercules transport aircraft on 7 July 1988.  The Chadian government received Stinger missiles from the United States, when Libya invaded the northern part of the African country. On 8 October 1987, a Libyan Su-22MK was shot down by a FIM-92A fired by Chadian forces. The pilot, Capt. Diya al-Din, ejected and was captured. He was later granted political asylum by the French government. During the recovery operation, a Libyan MiG-23MS was shot down by a FIM-92A.

Tajik civil war.

Tajik Islamist opposition forces operating from Afghanistan during the 1992–97 Tajik civil war encountered a heavy air campaign launched by Russia and Uzbekistan to prop up the government in Dushanbe that included border and cross-border raids. During one of these operations, a Sukhoi Su-24M was shot down on 3 May 1993 with a Stinger fired by fundamentalists. Both Russian pilots were rescued.

Chechen War.

Russian officials claimed several times that the Chechen militia and insurgents possessed US-made Stinger missiles. They attributed a few of their aerial losses to the American MANPADS. The presence of such missiles was confirmed by photo evidence even though their actual number and origin were not clear.  It is believed one Sukhoi Su-24 was shot down by a Stinger missile during the Second Chechen War.

Sri Lankan Civil War.

The Liberation Tigers of Tamil Eelam also managed to acquire one or several Stingers, possibly from former Mujahideen stocks, and used at least one to down a Sri Lanka Air Force Mi-24 on November 10, 1997.

United States.

As of 2000, the U.S. inventory contains 13,400 missiles. The total cost of the program is $7,281,000,000. It is rumored that the United States Secret Service has Stinger missiles to defend the President, a notion that has never been dispelled; however, U.S. Secret Service plans favor moving the President to a safer place in the event of an attack rather than shooting down the plane, lest the missile (or the wreckage of the target aircraft) hit innocents.  During the 1980s, the Stinger was used to support different US-aligned guerrilla forces, notably the Afghan Mujahidins, the Chad government against the Libyan invasion and the Angolan UNITA. The Nicaraguan contras were not provided with Stingers due to the lack of fixed wing aircraft of the Sandinista government, as such the previous generation FIM-43 Redeye was considered adequate.

Syrian civil war.

In the Syrian civil war, Turkey reportedly helped to transport a limited amount of FIM-92 Stingers to the Free Syrian Army.  On 27 February 2020, during the northwestern offensive launched in December 2019 by the Syrian government (backed by Russia, Iran and Hezbollah), Russian and Syrian aircraft (variously reportedly as Russian Su-34s and Syrian Su-22) attacked a Turkish military convoy near Idlib, killing 36 Turkish soldiers. That day, video footage emerged of alleged Turkish soldiers (who are backing Syrian opposition fighters) firing what apparently looks like a Roketsan-made Stinger against either Russian or Syrian aircraft (or possibly against both).

The FIM-92 Stinger is a Man-Portable Air-Defense System (MANPADS) that operates as an infrared homing surface-to-air missile (SAM). It can be adapted to fire from a wide variety of ground vehicles and helicopters (as an AAM). Developed in the United States, it entered service in 1981 and is used by the militaries of the United States and 29 other countries. It is principally manufactured by Raytheon Missile Systems and is produced under license by EADS in Germany and by Roketsan in Turkey, with 70,000 missiles produced.

FIM-92刺针便携式防空导弹(英语:FIM-92 Stinger)华语一般称为便携式防空导弹或肩射导弹,为小型人员携行式防空导弹,采用红外线导引热追踪以及紫外线物体追踪,由美国研发并使用于所有美军部队,1981年服役至今。在美国和其他29个国家中。主要由雷神导弹系统公司制造,授权德国的EADS和土耳其的生产导弹,已经生产超过70,000枚导弹。经证实有270架飞机和直升机被FIM-92刺针便携式防空导弹击落。


Definition.

An abelian group is a set, formula_1, together with an operation formula_2 that combines any two elements formula_3 and formula_4 of formula_1 to form another element of formula_6 denoted formula_7. The symbol formula_2 is a general placeholder for a concretely given operation. To qualify as an abelian group, the set and operation, formula_9, must satisfy five requirements known as the "abelian group axioms":  A group in which the group operation is not commutative is called a "non-abelian group" or "non-commutative group".

Facts.

Notation.

There are two main notational conventions for abelian groups – additive and multiplicative.  Generally, the multiplicative notation is the usual notation for groups, while the additive notation is the usual notation for modules and rings. The additive notation may also be used to emphasize that a particular group is abelian, whenever both abelian and non-abelian groups are considered, some notable exceptions being near-rings and partially ordered groups, where an operation is written additively even when non-abelian.

Multiplication table.

To verify that a finite group is abelian, a table (matrix) – known as a Cayley table – can be constructed in a similar fashion to a multiplication table. If the group is formula_35 under the the entry of this table contains the product formula_36. The group is abelian if and only if this table is symmetric about the main diagonal.  This is true since if the group is abelian, then formula_37. This implies that the formula_38 entry of the table equals the formula_39 entry, thus the table is symmetric about the main diagonal.

Examples.

In general, matrices, even invertible matrices, do not form an abelian group under multiplication because matrix multiplication is generally not commutative. However, some groups of matrices are abelian groups under matrix multiplication – one example is the group of formula_58 rotation matrices.

Historical remarks.

Camille Jordan named abelian groups after Norwegian mathematician Niels Henrik Abel, because Abel found that the commutativity of the group of a polynomial implies that the roots of the polynomial can be calculated by using radicals. See Section 6.5 of Cox (2004) for more information on the historical background.

Properties.

If formula_42 is a natural number and formula_48 is an element of an abelian group formula_47 written additively, then formula_62 can be defined as formula_63 (formula_42 summands) and formula_65. In this way, formula_47 becomes a module over the ring formula_52 of integers. In fact, the modules over formula_52 can be identified with the abelian groups.  Theorems about abelian groups (i.e. modules over the principal ideal domain formula_52) can often be generalized to theorems about modules over an arbitrary principal ideal domain. A typical example is the classification of finitely generated abelian groups which is a specialization of the structure theorem for finitely generated modules over a principal ideal domain. In the case of finitely generated abelian groups, this theorem guarantees that an abelian group splits as a direct sum of a torsion group and a free abelian group. The former may be written as a direct sum of finitely many groups of the form formula_70 for formula_71 prime, and the latter is a direct sum of finitely many copies of formula_52.  If formula_73 are two group homomorphisms between abelian groups, then their sum formula_74, defined by formula_75, is again a homomorphism. (This is not true if formula_76 is a non-abelian group.) The set formula_77 of all group homomorphisms from formula_47 to formula_76 thus turns into an abelian group in its own right.  Somewhat akin to the dimension of vector spaces, every abelian group has a "rank". It is defined as the maximal cardinality of a set of linearly independent elements of the group. The integers and the rational numbers have rank one, as well as every subgroup of the rationals.  The center formula_80 of a group formula_47 is the set of elements that commute with every element of formula_47. A group formula_47 is abelian if and only if it is equal to its center formula_80. The center of a group formula_47 is always a characteristic abelian subgroup of formula_47. If the quotient group formula_87 of a group by its center is cyclic then formula_47 is abelian.

Finite abelian groups.

Cyclic groups of integers modulo formula_42, formula_90, were among the first examples of groups. It turns out that an arbitrary finite abelian group is isomorphic to a direct sum of finite cyclic groups of prime power order, and these orders are uniquely determined, forming a complete system of invariants. The automorphism group of a finite abelian group can be described directly in terms of these invariants. The theory had been first developed in the 1879 paper of Georg Frobenius and Ludwig Stickelberger and later was both simplified and generalized to finitely generated modules over a principal ideal domain, forming an important chapter of linear algebra.  Any group of prime order is isomorphic to a cyclic group and therefore abelian. Any group whose order is a square of a prime number is also abelian. In fact, for every prime number formula_71 there are (up to isomorphism) exactly two groups of order formula_92, namely formula_93 and formula_94.

Classification.

The fundamental theorem of finite abelian groups states that every finite abelian group formula_47 can be expressed as the direct sum of cyclic subgroups of prime-power order; it is also known as the basis theorem for finite abelian groups. This is generalized by the fundamental theorem of finitely generated abelian groups, with finite groups being the special case when "G" has zero rank; this in turn admits numerous further generalizations.  The classification was proven by Leopold Kronecker in 1870, though it was not stated in modern group-theoretic terms until later, and was preceded by a similar classification of quadratic forms by Carl Friedrich Gauss in 1801; see history for details.  The cyclic group formula_96 of order formula_97 is isomorphic to the direct sum of formula_98 and formula_99 if and only if formula_45 and formula_42 are coprime. It follows that any finite abelian group formula_47 is isomorphic to a direct sum of the form  in either of the following canonical ways:  For example, formula_109 can be expressed as the direct sum of two cyclic subgroups of order 3 and 5: formula_110. The same can be said for any abelian group of order 15, leading to the remarkable conclusion that all abelian groups of order 15 are isomorphic.  For another example, every abelian group of order 8 is isomorphic to either formula_111 (the integers 0 to 7 under addition modulo 8), formula_112 (the odd integers 1 to 15 under multiplication modulo 16), or formula_113.  See also list of small groups for finite abelian groups of order 30 or less.

Automorphisms.

One can apply the fundamental theorem to count (and sometimes determine) the automorphisms of a given finite abelian group formula_47. To do this, one uses the fact that if formula_47 splits as a direct sum formula_116 of subgroups of coprime order, then formula_117.  Given this, the fundamental theorem shows that to compute the automorphism group of formula_47 it suffices to compute the automorphism groups of the Sylow formula_71-subgroups separately (that is, all direct sums of cyclic subgroups, each with order a power of formula_71). Fix a prime formula_71 and suppose the exponents formula_122 of the cyclic factors of the Sylow formula_71-subgroup are arranged in increasing order:  for some formula_125. One needs to find the automorphisms of  One special case is when formula_127, so that there is only one cyclic prime-power factor in the Sylow formula_71-subgroup formula_129. In this case the theory of automorphisms of a finite cyclic group can be used. Another special case is when formula_42 is arbitrary but formula_131 for formula_132. Here, one is considering formula_129 to be of the form  so elements of this subgroup can be viewed as comprising a vector space of dimension formula_42 over the finite field of formula_71 elements formula_137. The automorphisms of this subgroup are therefore given by the invertible linear transformations, so  where formula_139 is the appropriate general linear group. This is easily shown to have order  In the most general case, where the formula_122 and formula_42 are arbitrary, the automorphism group is more difficult to determine. It is known, however, that if one defines  and  then one has in particular formula_145, formula_146, and  One can check that this yields the orders in the previous examples as special cases (see Hillar, C., & Rhea, D.).

Finitely generated abelian groups.

An abelian group is finitely generated if it contains a finite set of elements (called "generators") formula_148 such that every element of the group is a linear combination with integer coefficients of elements of.  Let be a free abelian group with basis formula_149 There is a unique group homomorphism formula_150 such that This homomorphism is surjective, and its kernel is finitely generated (since integers form a Noetherian ring). Consider the matrix with integer entries, such that the entries of its th column are the coefficients of the th generator of the kernel. Then, the abelian group is isomorphic to the cokernel of linear map defined by. Conversely every integer matrix defines a finitely generated abelian group.  It follows that the study of finitely generated abelian groups is totally equivalent with the study of integer matrices. In particular, changing the generating set of is equivalent with multiplying on the left by a unimodular matrix (that is, an invertible integer matrix whose inverse is also an integer matrix). Changing the generating set of the kernel of is equivalent with multiplying on the right by an unimodular matrix.  The Smith normal form of is a matrix where and are unimodular, and is a matrix such that all non-diagonal entries are zero, the non-zero diagonal entries are the first ones, and is a divisor of for. The existence and the shape of the Smith normal proves that the finitely generated abelian group is the direct sum where is the number of zero rows at the bottom of (and also the rank of the group). This is the fundamental theorem of finitely generated abelian groups.  The existence of algorithms for Smith normal form shows that the fundamental theorem of finitely generated abelian groups is not only a theorem of abstract existence, but provides a way for computing expression of finitely generated abelian groups as direct sums.

Infinite abelian groups.

The simplest infinite abelian group is the infinite cyclic group formula_52. Any finitely generated abelian group formula_1 is isomorphic to the direct sum of formula_156 copies of formula_52 and a finite abelian group, which in turn is decomposable into a direct sum of finitely many cyclic groups of prime power orders. Even though the decomposition is not unique, the number formula_156, called the rank of formula_1, and the prime powers giving the orders of finite cyclic summands are uniquely determined.  By contrast, classification of general infinitely generated abelian groups is far from complete. Divisible groups, i.e. abelian groups formula_1 in which the equation formula_161 admits a solution formula_162 for any natural number formula_42 and element formula_3 of formula_1, constitute one important class of infinite abelian groups that can be completely characterized. Every divisible group is isomorphic to a direct sum, with summands isomorphic to formula_166 and Prüfer groups formula_167 for various prime numbers formula_71, and the cardinality of the set of summands of each type is uniquely determined. Moreover, if a divisible group formula_1 is a subgroup of an abelian group formula_47 then formula_1 admits a direct complement: a subgroup formula_172 of formula_47 such that formula_174. Thus divisible groups are injective modules in the category of abelian groups, and conversely, every injective abelian group is divisible (Baer's criterion). An abelian group without non-zero divisible subgroups is called reduced.  Two important special classes of infinite abelian groups with diametrically opposite properties are "torsion groups" and "torsion-free groups", exemplified by the groups formula_175 (periodic) and formula_166 (torsion-free).

Torsion groups.

An abelian group is called periodic or torsion, if every element has finite order. A direct sum of finite cyclic groups is periodic. Although the converse statement is not true in general, some special cases are known. The first and second Prüfer theorems state that if formula_1 is a periodic group, and it either has a bounded exponent, i.e., formula_178 for some natural number formula_42, or is countable and the formula_71-heights of the elements of formula_1 are finite for each formula_71, then formula_1 is isomorphic to a direct sum of finite cyclic groups. The cardinality of the set of direct summands isomorphic to formula_184 in such a decomposition is an invariant of formula_1. These theorems were later subsumed in the Kulikov criterion. In a different direction, Helmut Ulm found an extension of the second Prüfer theorem to countable abelian formula_71-groups with elements of infinite height: those groups are completely classified by means of their Ulm invariants.

Torsion-free and mixed groups.

An abelian group is called torsion-free if every non-zero element has infinite order. Several classes of torsion-free abelian groups have been studied extensively:  An abelian group that is neither periodic nor torsion-free is called mixed. If formula_1 is an abelian group and formula_190 is its torsion subgroup, then the factor group formula_191 is torsion-free. However, in general the torsion subgroup is not a direct summand of formula_1, so formula_1 is "not" isomorphic to formula_194. Thus the theory of mixed groups involves more than simply combining the results about periodic and torsion-free groups. The additive group formula_52 of integers is torsion-free formula_52-module.

Invariants and classification.

One of the most basic invariants of an infinite abelian group formula_1 is its rank: the cardinality of the maximal linearly independent subset of formula_1. Abelian groups of rank 0 are precisely the periodic groups, while torsion-free abelian groups of rank 1 are necessarily subgroups of formula_166 and can be completely described. More generally, a torsion-free abelian group of finite rank formula_156 is a subgroup of formula_201. On the other hand, the group of formula_71-adic integers formula_203 is a torsion-free abelian group of infinite formula_52-rank and the groups formula_205 with different formula_42 are non-isomorphic, so this invariant does not even fully capture properties of some familiar groups.  The classification theorems for finitely generated, divisible, countable periodic, and rank 1 torsion-free abelian groups explained above were all obtained before 1950 and form a foundation of the classification of more general infinite abelian groups. Important technical tools used in classification of infinite abelian groups are pure and basic subgroups. Introduction of various invariants of torsion-free abelian groups has been one avenue of further progress. See the books by Irving Kaplansky, László Fuchs, Phillip Griffith, and David Arnold, as well as the proceedings of the conferences on Abelian Group Theory published in "Lecture Notes in Mathematics" for more recent findings.

Additive groups of rings.

The additive group of a ring is an abelian group, but not all abelian groups are additive groups of rings (with nontrivial multiplication). Some important topics in this area of study are:

Relation to other mathematical topics.

Many large Abelian groups possess a natural topology, which turns them into topological groups.  The collection of all Abelian groups, together with the homomorphisms between them, forms the category formula_207, the prototype of an Abelian category.  There are still many areas of current research:  Moreover, Abelian groups of infinite order lead, quite surprisingly, to deep questions about the set theory commonly assumed to underlie all of mathematics. Take the Whitehead problem: are all Whitehead groups of infinite order also free Abelian groups? In the 1970s, Saharon Shelah proved that the Whitehead problem is:

A note on the typography.

Among mathematical adjectives derived from the proper name of a mathematician, the word "abelian" is rare in that it is often spelled with a lowercase a, rather than an uppercase A, indicating how ubiquitous the concept is in modern mathematics.

In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel.

阿贝尔群(Abelian group)也称为交换群(commutative group)或可交换群,它是满足其元素的运算不依赖于它们的次序(交换律公理)的群。阿贝尔群推广了整数集合的加法运算。阿贝尔群以挪威数学家尼尔斯·阿贝尔命名。


Rise to Power.

Shaybani was initially an Uzbek warrior leading a contingent of 3000 men in the army of the Timurid ruler of Samarkand, Sultan Ahmed Mirza under the Amir, Abdul Ali Tarkhan. However, when Ahmed Mirza went to war against Sultan Mahmud Khan, the Khan of Moghulistan, to reclaim Tashkent from him, Shaybani secretly met the Moghul Khan and agreed to betray and plunder Ahmed's army. This happened in the Battle of the Chirciq River in 1488 CE, resulting in a decisive victory for Moghulistan. Sultan Mahmud Khan gave Turkistan to Shaybani as a reward. Here, however, Shaybani oppressed the local Kazakhs, resulting in a war between Moghulistan and the Kazakh Khanate. Moghulistan was defeated in this war, but Shaybani gained power among the Uzbeks. He decided to conquer Samarkand and Bukhara from Ahmed Mirza. Sultan Mahmud's subordinate emirs convinced him to aid Shaybani in doing so, and together they marched on Samarkand.  Shaybani had five consorts:  He had three sons:

Foundation of Shaybanid Dynasty.

Continuing the policies of his grandfather, Abul-Khayr Khan, Shaybani ousted the Timurids from their capital Samarkand by 1500. He fought successful campaigns against the Timurid leader Babur, founder of the Mughal Empire. In 1505 he recaptured Samarkand and in 1507 also took Herat, the southern capital of the Timurids. Shaybani conquered Bukhara in 1506 and established the Shaybanid Dynasty of the Khanate of Bukhara. In 1508–09, he carried out many raids northward, pillaging the land of the Kazakh Khanate. However he suffered a major defeat from Kazakhs under Kasim Khan in 1510.

Foreign policy.

Shaybani Khan maintained ties with Ottoman Empire and China. In 1503, his ambassadors arrived at the court of the Ming Empire Emperor. In Alliance with the Ottoman Sultan Bayezid II (1481-1512), Shaybani Khan opposed the Safavid Shah Ismail I.

Death.

Shah Ismail I was alarmed by Shaybani's success and moved against the Uzbeks. In the Battle of Marv (1510), Muhammad Shaybani was defeated and killed when trying to escape. Shaybani Khan's army was surrounded by Ismail's 17,000-strong army and was defeated after fierce resistance. The remnants of the army ended up dying under enemy arrows. At the time of Shaybani's death, the Uzbeks controlled all of Transoxiana, that is, the area between the Syr Darya and Amu Darya rivers. After capturing Samarkand from Babur, Shaybani married Babur's sister, Khanzada Begum. Babur's liberty to leave Samarkand was made contingent upon his assent to this alliance. After Shaybani's death, Ismail I gave liberty to Khanzada Begum with her son and, at Babur's request, sent them to his court. For this reason Shaybani was succeeded not by a son but by an uncle, a cousin and a brother whose descendants would rule Bukhara until 1598 and Khwarizm (later named Khiva) until 1687.  From the accounts of Babur, i.e. the Baburnama, we came to know that the Shah of Persia Ismail beheaded Shaybani and had his skull turned into a bejeweled drinking goblet which was drunk from when entertaining; he later sent the cup to Babur as a goodwill gesture. The rest of Shaybani's body parts were either sent to various areas of the empire for display or put on a spike at the main gate of Samarkand.

Personality.

Shaybani Khan was very fond of history in his youth. In 1475, he was specially presented with a book about the life of Alexander the Great — Iskandarnamah, written in the distant Ottoman Empire.  Medieval author Nisari recognized Shaybani Khan as a scholar of the holy Koran.  The manuscript of his philosophical and religious work "Bahru’l-huda", written in the Central Asian Turkic literary language in 1508, is in London. Shaybani Khan used various works on theology when writing his essay. It contains his own views on religious issues. The author presents his own idea of the basics of Islam: repentance for sins, showing mercy, and others. Shaybani Khan shows excellent knowledge of Muslim rituals and daily duties of devout Muslims.

Muhammad Shaybani Khan (, also known as Abul-Fath Shaybani Khan or Shayabak Khan or Shahi Beg Khan, originally named "Shibägh", which means "wormwood" or "obsidian") (c. 1451 – 2 December 1510), was an Uzbek leader who consolidated various Uzbek tribes and laid the foundations for their ascendance in Transoxiana and the establishment of the Khanate of Bukhara. He was a Shaybanid or descendant of Shiban (or Shayban), the fifth son of Jochi, Genghis Khan's eldest son. His father was Sheikh Haidar, son of Abu'l-Khayr Khan.

穆罕默德·昔班尼(,1451年-1510年-12月2日)是河中地区布哈拉汗国的开国之君。他继续巩固各乌兹别克部族和奠定基础。


Schematic symbol.

In circuit diagrams, a voltmeter is represented by the letter "V" in a circle, with two emerging lines representing the two points of measurement.

Analog voltmeter.

A moving coil galvanometer can be used as a voltmeter by inserting a resistor in series with the instrument. The galvanometer has a coil of fine wire suspended in a strong magnetic field. When an electric current is applied, the interaction of the magnetic field of the coil and of the stationary magnet creates a torque, tending to make the coil rotate. The torque is proportional to the current through the coil. The coil rotates, compressing a spring that opposes the rotation. The deflection of the coil is thus proportional to the current, which in turn is proportional to the applied voltage, which is indicated by a pointer on a scale.  One of the design objectives of the instrument is to disturb the circuit as little as possible and so the instrument should draw a minimum of current to operate. This is achieved by using a sensitive galvanometer in series with a high resistance, and then the entire instrument is connected in parallel with the circuit examined.  The sensitivity of such a meter can be expressed as "ohms per volt", the number of ohms resistance in the meter circuit divided by the full scale measured value. For example, a meter with a sensitivity of 1000 ohms per volt would draw 1 milliampere at full scale voltage; if the full scale was 200 volts, the resistance at the instrument's terminals would be ohms and at full scale the meter would draw 1 milliampere from the circuit under test. For multi-range instruments, the input resistance varies as the instrument is switched to different ranges.  Moving-coil instruments with a permanent-magnet field respond only to direct current. Measurement of AC voltage requires a rectifier in the circuit so that the coil deflects in only one direction. Some moving-coil instruments are also made with the zero position in the middle of the scale instead of at one end; these are useful if the voltage reverses its polarity.  Voltmeters operating on the electrostatic principle use the mutual repulsion between two charged plates to deflect a pointer attached to a spring. Meters of this type draw negligible current but are sensitive to voltages over about 100 volts and work with either alternating or direct current.

Vacuum tube volt meters (VTVMs) and field-effect transistor volt meters (FET-VMs).

The sensitivity and input resistance of a voltmeter can be increased if the current required to deflect the meter pointer is supplied by an amplifier and power supply instead of by the circuit under test. The electronic amplifier between input and meter gives two benefits; a rugged moving coil instrument can be used, since its sensitivity need not be high, and the input resistance can be made high, reducing the current drawn from the circuit under test. Amplified voltmeters often have an input resistance of 1, 10, or 20 megohms which is independent of the range selected. A once-popular form of this instrument used a vacuum tube in the amplifier circuit and so was called the vacuum tube voltmeter, or VTVM. These were almost always powered by the local AC line current and so were not particularly portable. Today these circuits use a solid-state amplifier using field-effect transistors, hence FET-VM, and appear in handheld digital multimeters as well as in bench and laboratory instruments. These are now so ubiquitous that they have largely replaced non-amplified multimeters except in the least expensive price ranges.  Most VTVMs and FET-VMs handle DC voltage, AC voltage, and resistance measurements; modern FET-VMs add current measurements and often other functions as well. A specialized form of the VTVM or FET-VM is the AC voltmeter. These instruments are optimized for measuring AC voltage. They have much wider bandwidth and better sensitivity than a typical multifunction device.

Digital voltmeter.

A digital voltmeter (DVM) measures an unknown input voltage by converting the voltage to a digital value and then displays the voltage in numeric form. DVMs are usually designed around a special type of analog-to-digital converter called an integrating converter.  DVM measurement accuracy is affected by many factors, including temperature, input impedance, and DVM power supply voltage variations. Less expensive DVMs often have input resistance on the order of 10 MΩ. Precision DVMs can have input resistances of 1 GΩ or higher for the lower voltage ranges (e.g. less than 20 V). To ensure that a DVM's accuracy is within the manufacturer's specified tolerances, it must be periodically calibrated against a voltage standard such as the Weston cell.  The first digital voltmeter was invented and produced by Andrew Kay of Non-Linear Systems (and later founder of Kaypro) in 1954.

A voltmeter is an instrument used for measuring electrical potential difference between two points in an electric circuit. Analog voltmeters move a pointer across a scale in proportion to the voltage of the circuit; digital voltmeters give a numerical display of voltage by use of an analog-to-digital converter.

电压表为科学仪器,又称伏特计,常用于电磁学中。电压表是用来测量电压的大小,单位通常为伏特(V)。电压表一般以并联的方式连结至所需量度电压的电路元件之中。电压表的电阻一般很大,以避免使被量度的电压改变。


Biochemistry.

Phosphatases catalyze the hydrolysis of a phosphomonoester, removing a phosphate moiety from the substrate. Water is split in the reaction, with the -OH group attaching to the phosphate ion, and the H+ protonating the hydroxyl group of the other product. The net result of the reaction is the destruction of a phosphomonoester and the creation of both a phosphate ion and a molecule with a free hydroxyl group.  Phosphatases are able to dephosphorylate seemingly different sites on their substrates with great specificity. Identifying the "phosphatase code," that is, the mechanisms and rules that govern substrate recognition for phosphatases, is still a work in progress, but the first comparative analysis of all the protein phosphatases encoded across nine eukaryotic 'phosphatome' genomes is now available. Studies reveal that so called "docking interactions" play a significant role in substrate binding. A phosphatase recognizes and interacts with various motifs (elements of secondary structure) on its substrate; these motifs bind with low affinity to docking sites on the phosphatase, which are not contained within its active site. Although each individual docking interaction is weak, many interactions occur simultaneously, conferring a cumulative effect on binding specificity. Docking interactions can also allosterically regulate phosphatases and thus influence their catalytic activity.

Functions.

In contrast to kinases, phosphatase enzymes recognize and catalyze a wider array of substrates and reactions. For example, in humans, Ser/Thr kinases outnumber Ser/Thr phosphatases by a factor of ten. To some extent, this disparity results from incomplete knowledge of the human phosphatome, that is, the complete set of phosphatases expressed in a cell, tissue, or organism. Many phosphatases have yet to be discovered, and for numerous known phosphatases, a substrate has yet to be identified. However, among well-studied phosphatase/kinase pairs, phosphatases exhibit greater variety than their kinase counterparts in both form and function; this may result from the lesser degree of conservation among phosphatases.

Protein phosphatases.

A protein phosphatase is an enzyme that dephosphorylates an amino acid residue of its protein substrate. Whereas protein kinases act as signaling molecules by phosphorylating proteins, phosphatases remove the phosphate group, which is essential if the system of intracellular signaling is to be able to reset for future use. The tandem work of kinases and phosphatases constitute a significant element of the cell's regulatory network. Phosphorylation (and dephosphorylation) is among the most common modes of posttranslational modification in proteins, and it is estimated that, at any given time, up to 30% of all proteins are phosphorylated.  Two notable protein phosphatases are PP2A and PP2B. PP2A is involved in multiple regulatory processes, such as DNA replication, metabolism, transcription, and development. PP2B, also called calcineurin, is involved in the proliferation of T cells; because of this, it is the target of some drugs that seek to suppress the immune system.

Nucleotidases.

A nucleotidase is an enzyme that catalyzes the hydrolysis of a nucleotide, forming a nucleoside and a phosphate ion. Nucleotidases are essential for cellular homeostasis, because they are partially responsible for maintaining a balanced ratio of nucleotides to nucleosides. Some nucleotidases function outside the cell, creating nucleosides that can be transported into the cell and used to regenerate nucleotides via salvage pathways. Inside the cell, nucleotidases may help to maintain energy levels under stress conditions. A cell deprived of oxygen and nutrients may catabolize more nucleotides to boost levels of nucleoside triphosphates such as ATP, the primary energy currency of the cell.

In gluconeogenesis.

Phosphatases can also act on carbohydrates, such as intermediates in gluconeogenesis. Gluconeogenesis is a biosynthetic pathway wherein glucose is created from noncarbohydrate precursors; the pathway is essential because many tissues can only derive energy from glucose. Two phosphatases, glucose-6-phosphatase and fructose-1,6-bisphosphatase, catalyze irreversible steps in gluconeogenesis. Each cleaves a phosphate group from a six-carbon sugar phosphate intermediate.

Classification.

Within the larger class of phosphatase, the Enzyme Commission recognizes 104 distinct enzyme families. Phosphatases are classified by substrate specificity and sequence homology in catalytic domains. Despite their classification into over one hundred families, all phosphatases still catalyze the same general hydrolysis reaction.  In in-vitro experiments, phosphatase enzymes seem to recognize many different substrates, and one substrate may be recognized by many different phosphatases. However, when experiments have been carried out in-vivo, phosphatase enzymes have been shown to be incredibly specific. In some cases, a protein phosphatase (i.e. one defined by its recognition of protein substrates) can catalyze the dephosphorylation of nonprotein substrates. Similarly, dual-specificity tyrosine phosphatases can dephosphorylate not only tyrosine residues, but also serine residues. Thus, one phosphatase can exhibit the qualities of multiple phosphatase families.

A phosphatase is an enzyme that uses water to cleave a phosphoric acid monoester into a phosphate ion and an alcohol. Because a phosphatase enzyme catalyzes the hydrolysis of its substrate, it is a subcategory of hydrolases. Phosphatase enzymes are essential to many biological functions, because phosphorylation (e.g. by protein kinases) and dephosphorylation (by phosphatases) serve diverse roles in cellular regulation and signaling. Whereas phosphatases remove phosphate groups from molecules, kinases catalyze the transfer of phosphate groups to molecules from ATP. Together, kinases and phosphatases direct a form of post-translational modification that is essential to the cell's regulatory network. Phosphatase enzymes are not to be confused with phosphorylase enzymes, which catalyze the transfer of a phosphate group from hydrogen phosphate to an acceptor. Due to their prevalence in cellular regulation, phosphatases are an area of interest for pharmaceutical research.

磷酸酶是一种能够将对应底物去磷酸化的酶,即通过水解磷酸单酯将底物分子上的磷酸基团除去,并生成磷酸根离子和自由的羟基。磷酸酶的作用与激酶的作用正相反,激酶是磷酸化酶,可以利用能量分子,如ATP,将磷酸基团加到对应底物分子上。在许多生物体中都普遍存在的一种磷酸酶是碱性磷酸酶。


History and description.

The 8088 was designed at Intel's laboratory in Haifa, Israel, as were a large number of Intel's processors. The 8088 was targeted at economical systems by allowing the use of an eight-bit data path and eight-bit support and peripheral chips; complex circuit boards were still fairly cumbersome and expensive when it was released. The prefetch queue of the 8088 was shortened to four bytes, from the 8086's six bytes, and the prefetch algorithm was slightly modified to adapt to the narrower bus. These modifications of the basic 8086 design were one of the first jobs assigned to Intel's then-new design office and laboratory in Haifa.  Variants of the 8088 with more than 5 MHz maximal clock frequency include the 8088-2, which was fabricated using Intel's new enhanced nMOS process called HMOS and specified for a maximal frequency of 8 MHz. Later followed the 80C88, a fully static CHMOS design, which could operate with clock speeds from 0 to 8 MHz. There were also several other, more or less similar, variants from other manufacturers. For instance, the NEC V20 was a pin-compatible and slightly faster (at the same clock frequency) variant of the 8088, designed and manufactured by NEC. Successive NEC 8088 compatible processors would run at up to 16 MHz. In 1984, Commodore International signed a deal to manufacture the 8088 for use in a licensed Dynalogic Hyperion clone, in a move that was regarded as signaling a major new direction for the company.  When announced, the list price of the 8088 was US$124.80.

Differences from the 8086.

The 8088 is architecturally very similar to the 8086. The main difference is that there are only eight data lines instead of the 8086's 16 lines. All of the other pins of the device perform the same function as they do with the 8086 with two exceptions. First, pin 34 is no longer (this is the high-order byte select on the 8086—the 8088 does not have a high-order byte on its eight-bit data bus). Instead it outputs a maximum mode status,. Combined with the IO/ and DT/ signals, the bus cycles can be decoded (it generally indicates when a write operation or an interrupt is in progress). The second change is the pin that signals whether a memory access or input/output access is being made has had it sense reversed. The pin on the 8088 is IO/. On the 8086 part it is /M. The reason for the reversal is that it makes the 8088 compatible with the 8085.

Performance.

Depending on the clock frequency, the number of memory wait states, as well as on the characteristics of the particular application program, the "average" performance for the Intel 8088 ranged approximately from 0.33 to 1 million instructions per second. Meanwhile, the codice_1 and codice_2 instructions, taking two and three cycles respectively, yielded an "absolute peak" performance of between and MIPS per MHz, that is, somewhere in the range 3–5 MIPS at 10 MHz.  The speed of the execution unit (EU) and the bus of the 8086 CPU was well balanced; with a typical instruction mix, an 8086 could execute instructions out of the prefetch queue a good bit of the time. Cutting down the bus to eight bits made it a serious bottleneck in the 8088. With the speed of instruction fetch reduced by 50% in the 8088 as compared to the 8086, a sequence of fast instructions can quickly drain the four-byte prefetch queue. When the queue is empty, instructions take as long to complete as they take to fetch. Both the 8086 and 8088 take four clock cycles to complete a bus cycle; whereas for the 8086 this means four clocks to transfer two bytes, on the 8088 it is four clocks per byte. Therefore, for example, a two-byte shift or rotate instruction, which takes the EU only two clock cycles to execute, actually takes eight clock cycles to complete if it is not in the prefetch queue. A sequence of such fast instructions prevents the queue from being filled as fast as it is drained, and in general, because so many basic instructions execute in fewer than four clocks per instruction byte—including almost all the ALU and data-movement instructions on register operands and some of these on memory operands—it is practically impossible to avoid idling the EU in the 8088 at least 1⁄4 of the time while executing useful real-world programs, and it is not hard to idle it half the time. In short, an 8088 typically runs about half as fast as 8086 clocked at the same rate, because of the bus bottleneck (the only major difference).  A side effect of the 8088 design, with the slow bus and the small prefetch queue, is that the speed of code execution can be very dependent on instruction order. When programming the 8088, for CPU efficiency, it is vital to interleave long-running instructions with short ones whenever possible. For example, a repeated string operation or a shift by three or more will take long enough to allow time for the 4-byte prefetch queue to completely fill. If short instructions (i.e. ones totaling few bytes) are placed between slower instructions like these, the short ones can execute at full speed out of the queue. If, on the other hand, the slow instructions are executed sequentially, back to back, then after the first of them the bus unit will be forced to idle because the queue will already be full, with the consequence that later more of the faster instructions will suffer fetch delays that might have been avoidable. As some instructions, such as single-bit-position shifts and rotates, take literally 4 times as long to fetch as to execute, the overall effect can be a slowdown by a factor of two or more. If those code segments are the bodies of loops, the difference in execution time may be very noticeable on the human timescale.  The 8088 is also (like the 8086) slow at accessing memory. The same ALU that is used to execute arithmetic and logic instructions is also used to calculate effective addresses. There is a separate adder for adding a shifted segment register to the offset address, but the offset EA itself is always calculated entirely in the main ALU. Furthermore, the loose coupling of the EU and BIU (bus unit) inserts communication overhead between the units, and the four-clock period bus transfer cycle is not particularly streamlined. Contrast this with the two-clock period bus cycle of the 6502 CPU and the 80286's three-clock period bus cycle with pipelining down to two cycles for most transfers. Most 8088 instructions that can operate on either registers or memory, including common ALU and data-movement operations, are at least four times slower for memory operands than for only register operands. Therefore, efficient 8088 (and 8086) programs avoid repeated access of memory operands when possible, loading operands from memory into registers to work with them there and storing back only the finished results. The relatively large general register set of the 8088 compared to its contemporaries assists this strategy. When there are not enough registers for all variables that are needed at once, saving registers by pushing them onto the stack and popping them back to restore them is the fastest way to use memory to augment the registers, as the stack PUSH and POP instructions are the fastest memory operations. The same is probably not true on the 80286 and later; they have dedicated address ALUs and perform memory accesses much faster than the 8088 and 8086.  Finally, because calls, jumps, and interrupts reset the prefetch queue, and because loading the IP register requires communication between the EU and the BIU (since the IP register is in the BIU, not in the EU, where the general registers are), these operations are costly. All jumps and calls take at least 15 clock cycles. Any conditional jump requires four clock cycles if not taken, but if taken, it requires 16 cycles in addition to resetting the prefetch queue; therefore, conditional jumps should be arranged to be not taken most of the time, especially inside loops. In some cases, a sequence of logic and movement operations is faster than a conditional jump that skips over one or two instructions to achieve the same result.  Intel datasheets for the 8086 and 8088 advertised the dedicated multiply and divide instructions (MUL, IMUL, DIV, and IDIV), but they are very slow, on the order of 100–200 clock cycles each. Many simple multiplications by small constants (besides powers of 2, for which shifts can be used) can be done much faster using dedicated short subroutines. The 80286 and 80386 each greatly increased the execution speed of these multiply and divide instructions.

Selection for use in the IBM PC.

The original IBM PC was the most influential microcomputer to use the 8088. It used a clock frequency of 4.77 MHz (4/3 the NTSC colorburst frequency). Some of IBM's engineers and other employees wanted to use the IBM 801 processor, some would have preferred the new Motorola 68000, while others argued for a small and simple microprocessor, such as the MOS Technology 6502 or Zilog Z80, which had been used in earlier personal computers. However, IBM already had a history of using Intel chips in its products and had also acquired the rights to manufacture the 8086 family.  IBM chose the 8088 over the 8086 because Intel offered a better price for the former and could supply more units. Another factor was that the 8088 allowed the computer to be based on a modified 8085 design, as it could easily interface with most nMOS chips with 8-bit databuses, i.e. existing and mature, and therefore economical, components. This included ICs originally intended for support and peripheral functions around the 8085 and similar processors (not exclusively Intel's), which were already well known by many engineers, further reducing cost.  The descendants of the 8088 include the 80188, 80186, 80286, 80386, 80486, and later software-compatible processors, which are in use today.

The Intel 8088 (""eighty-eighty-eight"", also called iAPX 88) microprocessor is a variant of the Intel 8086. Introduced on June 1, 1979, the 8088 had an eight-bit external data bus instead of the 16-bit bus of the 8086. The 16-bit registers and the one megabyte address range were unchanged, however. In fact, according to the Intel documentation, the 8086 and 8088 have the same execution unit (EU)—only the bus interface unit (BIU) is different. The original IBM PC was based on the 8088, as were its clones.

Intel 8088 是一个 Intel 以 8086 为基础的 微处理器,拥有 16 位元 暂存器 和 8 位元外部 资料总线。这是原本 IBM PC 上所使用的处理器。 8088 使用 8 位元的设计,所针对的是较为经济之系统。在它推出时候,大的资料总线宽度电路板还是相当地昂贵。8088 的预取(prefetch) 贮列(queue) 是 4 字节,相对于 8086 的是 6 字节。8088 的后代包括到现在还在使用的intel 80188、80288(不再制造或使用)、和 80388 微控制器(microcontroller)。 到目前为止使用 8088 之最重要的微电脑是 IBM PC。原本的 PC 处理器是以 4.77 MHz 的时脉频率执行。 显然地 IBM 自家工程师想要使用 Motorola 68000,并且它后来被用在已经遗忘的 IBM 仪器 9000 实验室电脑中,但是 IBM 已经拥有制造 8086 家族的授权,以作为给 Intel 气泡式内存 设计的授权之交换。使用 8 位元 8088 版本的一个因素是,它可以使用现有 Intel 8085 形态的元件,允许以修改 8085 设计的方式为基础制造电脑。68000 的元件在当时并非广泛可以得到,虽然可以使用 Motorola 6800 元件来达成一种程度。Intel 的泡沫式内存在当时市场上推出有一段时间,但是由于从日本公司来的低廉价格所产生的激烈竞争,Intel 离开了内存市场并且专注在处理器上。 相容可以取代的芯片 NEC V20 是由 NEC 所制造,改进了约 20 % 的功率改善。


Structure.

The sternum is a long, flat bone, forming the middle portion of the front of the chest. The top of the sternum supports the clavicles (collarbones) and its edges join with the costal cartilages of the first two pairs of ribs. The inner surface of the sternum is also the attachment of the sternopericardial ligaments. Its top is also connected to the sternocleidomastoid muscle. The sternum consists of three main parts, listed from the top:  In its natural position, the sternum is angled obliquely, downward and forward. It is slightly convex in front and concave behind; broad above, shaped like a "T", becoming narrowed at the point where the manubrium joins the body, after which it again widens a little to below the middle of the body, and then narrows to its lower extremity. In adults the sternum is on average about 17 cm, longer in the male than in the female.

Manubrium.

The manubrium () is the broad upper part of the sternum. It has a quadrangular shape, narrowing from the top, which gives it four borders. The suprasternal notch (jugular notch) is located in the middle at the upper broadest part of the manubrium. This notch can be felt between the two clavicles. On either side of this notch are the right and left clavicular notches.  The manubrium joins with the body of the sternum, the clavicles and the cartilages of the first pair of ribs. The inferior border, oval and rough, is covered with a thin layer of cartilage for articulation with the body. The lateral borders are each marked above by a depression for the first costal cartilage, and below by a small facet, which, with a similar facet on the upper angle of the body, forms a notch for the reception of the costal cartilage of the second rib. Between the depression for the first costal cartilage and the demi-facet for the second is a narrow, curved edge, which slopes from above downward towards the middle. Also, the superior sternopericardial ligament attaches the pericardium to the posterior side of the manubrium.

Body.

The body, or gladiolus, is the longest part. It is flat and considered to have only a front and back surface. It is flat on the front, directed upward and forward, and marked by three transverse ridges which cross the bone opposite the third, fourth, and fifth articular depressions. The pectoralis major attaches to it on either side. At the junction of the third and fourth parts of the body is occasionally seen an orifice, the sternal foramen, of varying size and form. The posterior surface, slightly concave, is also marked by three transverse lines, less distinct, however, than those in front; from its lower part, on either side, the transversus thoracis takes origin.  The sternal angle is located at the point where the body joins the manubrium. The sternal angle can be felt at the point where the sternum projects farthest forward. However, in some people the sternal angle is concave or rounded. During physical examinations, the sternal angle is a useful landmark because the second rib attaches here.  Each outer border, at its superior angle, has a small facet, which with a similar facet on the manubrium, forms a cavity for the cartilage of the second rib; below this are four angular depressions which receive the cartilages of the third, fourth, fifth, and sixth ribs. The inferior angle has a small facet, which, with a corresponding one on the xiphoid process, forms a notch for the cartilage of the seventh rib. These articular depressions are separated by a series of curved interarticular intervals, which diminish in length from above downward, and correspond to the intercostal spaces. Most of the cartilages belonging to the true ribs, articulate with the sternum at the lines of junction of its primitive component segments. This is well seen in some other vertebrates, where the parts of the bone remain separated for longer.  The upper border is oval and articulates with the manubrium, at the sternal angle. The lower border is narrow, and articulates with the xiphoid process.

Xiphoid process.

Located at the inferior end of the sternum is the pointed xiphoid process. Improperly performed chest compressions during cardiopulmonary resuscitation can cause the xiphoid process to snap off, driving it into the liver which can cause a fatal hemorrhage.  The sternum is composed of highly vascular tissue, covered by a thin layer of compact bone which is thickest in the manubrium between the articular facets for the clavicles. The inferior sternopericardial ligament attaches the pericardium to the posterior xiphoid process.

Joints.

The cartilages of the top five ribs join with the sternum at the sternocostal joints. The right and left clavicular notches articulate with the right and left clavicles, respectively. The costal cartilage of the second rib articulates with the sternum at the sternal angle making it easy to locate.  The transversus thoracis muscle is innervated by one of the intercostal nerves and superiorly attaches at the posterior surface of the lower sternum. Its inferior attachment is the internal surface of costal cartilages two through six and works to depress the ribs.

Development.

The sternum develops from two cartilaginous bars one on the left and one on the right, connected with the cartilages of the ribs on each side. These two bars fuse together along the middle to form the cartilaginous sternum which is ossified from six centers: one for the manubrium, four for the body, and one for the xiphoid process.  The ossification centers appear in the intervals between the articular depressions for the costal cartilages, in the following order: in the manubrium and first piece of the body, during the sixth month of fetal life; in the second and third pieces of the body, during the seventh month of fetal life; in its fourth piece, during the first year after birth; and in the xiphoid process, between the fifth and eighteenth years.  The centers make their appearance at the upper parts of the segments, and proceed gradually downward. To these may be added the occasional existence of two small "episternal" centers, which make their appearance one on either side of the jugular notch; they are probably vestiges of the episternal bone of the monotremata and lizards.  Occasionally some of the segments are formed from more than one center, the number and position of which vary [Fig. 6]. Thus, the first piece may have two, three, or even six centers.  When two are present, they are generally situated one above the other, the upper being the larger; the second piece has seldom more than one; the third, fourth, and fifth pieces are often formed from two centers placed laterally, the irregular union of which explains the rare occurrence of the sternal foramen [Fig. 7], or of the vertical fissure which occasionally intersects this part of the bone constituting the malformation known as "fissura sterni;" these conditions are further explained by the manner in which the cartilaginous sternum is formed.  More rarely still the upper end of the sternum may be divided by a fissure. Union of the various centers of the body begins about puberty, and proceeds from below upward [Fig. 5]; by the age of twenty-five they are all united.  The xiphoid process may become joined to the body before the age of thirty, but this occurs more frequently after forty; on the other hand, it sometimes remains ununited in old age. In advanced life the manubrium is occasionally joined to the body by bone. When this takes place, however, the bony tissue is generally only superficial, the central portion of the intervening cartilage remaining unossified.  In early life, the sternum's body is divided into four segments, not three, called "sternebrae" (singular: "sternebra").

Clinical significance.

Bone marrow biopsy.

Because the sternum contains bone marrow, it is sometimes used as a site for bone marrow biopsy. In particular, patients with a high BMI (obese or grossly overweight) may present with excess tissue that makes access to traditional marrow biopsy sites such as the pelvis difficult.

Sternal opening.

A somewhat rare congenital disorder of the sternum sometimes referred to as an anatomical variation is a sternal foramen, a single round hole in the sternum that is present from birth and usually is off-centered to the right or left, commonly forming in the 2nd, 3rd, and 4th segments of the breastbone body. Congenital sternal foramina can often be mistaken for bullet holes. They are usually without symptoms but can be problematic if acupuncture in the area is intended.

Fractures.

Fractures of the sternum are rather uncommon. They may result from trauma, such as when a driver's chest is forced into the steering column of a car in a car accident. A fracture of the sternum is usually a comminuted fracture. The most common site of sternal fractures is at the sternal angle. Some studies reveal that repeated punches or continual beatings, sometimes called "breastbone punches", to the sternum area have also caused fractured sternums. Those are known to have occurred in contact sports such as hockey and football. Sternal fractures are frequently associated with underlying injuries such as pulmonary contusions, or bruised lung tissue.

Dislocation.

A manubriosternal dislocation is rare and usually caused by severe trauma. It may also result from minor trauma where there is a precondition of arthritis.

Sternotomy.

The breastbone is sometimes cut open (a median sternotomy) to gain access to the thoracic contents when performing cardiothoracic surgery.

Resection.

The sternum can be totally removed (resected) as part of a radical surgery, usually to surgically treat a malignancy, either with or without a mediastinal lymphadenectomy (Current Procedural Terminology codes # 21632 and # 21630, respectively).

Bifid sternum or sternal cleft.

A bifid sternum is an extremely rare congenital abnormality caused by the fusion failure of the sternum. This condition results in sternal cleft which can be observed at birth without any symptom.

Other animals.

The sternum, in vertebrate anatomy, is a flat bone that lies in the middle front part of the rib cage. It is endochondral in origin. It probably first evolved in early tetrapods as an extension of the pectoral girdle; it is not found in fish. In amphibians and reptiles it is typically a shield-shaped structure, often composed entirely of cartilage. It is absent in both turtles and snakes. In birds it is a relatively large bone and typically bears an enormous projecting keel to which the flight muscles are attached. Only in mammals does the sternum take on the elongated, segmented form seen in humans.

Arthropods.

In arachnids, the sternum is the ventral (lower) portion of the cephalothorax. It consists of a single sclerite situated between the coxa, opposite the carapace.

Etymology.

English "sternum" is a translation of Ancient Greek, '. The Greek writer Homer used the term to refer to the "male chest", and the term,'to refer to the "chest of both sexes". The Greek physician Hippocrates used στέρνον to refer to the "chest", and στῆθος to the "breastbone". The Greek physician Galen was the first to use in the present meaning of "breastbone". The sternum as the solid bony part of the chest can be related to Ancient Greek, "()", meaning "firm" or "solid". The English term breastbone is actually more like the Latin "os pectoris", derived from classical Latin "os", bone and "pectus", chest or breast. Confusingly, "pectus" is also used in classical Latin as "breastbone".

The sternum or breastbone is a long flat bone located in the central part of the chest. It connects to the ribs via cartilage and forms the front of the rib cage, thus helping to protect the heart, lungs, and major blood vessels from injury. Shaped roughly like a necktie, it is one of the largest and longest flat bones of the body. Its three regions are the manubrium, the body, and the xiphoid process. The word "sternum" originates from the Ancient Greek στέρνον, meaning "chest".

胸骨("Sternum")是胸腔中前方一块扁平,剑状的骨,接有肋 。


Names.

Different disciplines generally call this diacritic by different names. Typography tends to use the term "caron". Linguistics more often uses "haček" (with no long mark), largely due to the influence of the Prague School (particularly on Structuralist linguists who subsequently developed alphabets for previously unwritten languages of the Americas). Pullum's and Ladusaw's "Phonetic Symbol Guide" (Chicago, 1996) uses the term "wedge".  The term "caron" is used in the official names of Unicode characters (e.g., "Latin capital letter Z with caron"). Its earliest known use was in the United States Government Printing Office Style Manual of 1967, and it was later used in character sets such as DIN 31624 (1979), ISO 5426 (1980), ISO/IEC 6937 (1983) and ISO/IEC 8859-2 (1985). Its actual origin remains obscure, but some have suggested that it may derive from a fusion of caret and macron. Though this may be folk etymology, it is plausible, particularly in the absence of other suggestions.  The "Oxford English Dictionary" gives 1953 as the earliest citation for "háček". In Czech, "háček" () means "small hook", the diminutive form of "hák" (), "hook". The name appears in most English dictionaries, but they treat the long mark (acute accent) differently. British dictionaries, such as the "OED", "ODE", "CED", write "háček" (with the mark) in the headwords, while American ones, such as the "Merriam-Webster", "NOAD", "AHD", omit the acute and write "haček", however, the "NOAD" gives "háček" as an alternative spelling.  In Slovak it is called "mäkčeň" (, i.e., "softener" or "palatalization mark"), in Serbo-Croatian "kvaka" or "kvačica" ("angled hook" or "small angled hook"), in Slovenian "strešica" ("little roof") or "kljukica" ("little hook"), in Lithuanian "paukščiukas" ("little bird") or "varnelė" ("little jackdaw"), in Estonian "katus" ("roof"), in Finnish "hattu" ("hat"), and in Lakota "ičášleče" ("wedge").

Origin.

The caron evolved from the dot above diacritic, which Jan Hus introduced into Czech orthography (along with the acute accent) in his "De Orthographia Bohemica" (1412). The original form still exists in Polish "ż". However, Hus's work was hardly known at that time, and "háček" became widespread only in the 16th century with the introduction of printing.

Usage.

For the fricatives "š", "ž", and the affricate "č" only, the caron is used in most northwestern Uralic languages that use the Latin alphabet, such as Karelian, Veps, Northern Sami and Inari Sami (though not in Southern Sami). Estonian and Finnish use "š" and "ž" (but not "č"), but only for transcribing foreign names and loanwords (albeit common loanwords such as "šekki" or "tšekk" 'check'); the sounds (and letters) are native and common in Karelian, Veps and Sami.  In Italian, "š", "ž", and "č" are routinely used as in Slovenian to transcribe Slavic names in the Cyrillic script since in native Italian words, the sounds represented by these letters must be followed by a vowel, and Italian uses "ch" for, not. Other Romance languages, by contrast, tend to use their own orthographies, or in a few cases such as Spanish, borrow English "sh" or "zh".  The caron is also used in the Romany alphabet. The Faggin-Nazzi writing system for the Friulian language makes use of the caron over the letters "c", "g", and "s".  The caron is also often used as a diacritical mark on consonants for romanization of text from non-Latin writing systems, particularly in the scientific transliteration of Slavic languages. Philologists and the standard Finnish orthography often prefer using it to express sounds for which English require a digraph ("sh, ch", and "zh") because most Slavic languages use only one character to spell the sounds (the key exceptions are Polish "sz" and "cz"). Its use for that purpose can even be found in the United States because certain atlases use it in romanization of foreign place names. On the typographical side, Š/š and Ž/ž are likely the easiest among non-Western European diacritic characters to adopt for Westerners because the two are part of the Windows-1252 character encoding.  It is also used as an accent mark on vowels to indicate the tone of a syllable. The main example is in Pinyin for Chinese in which it represents a falling-rising tone. It is used in transliterations of Thai to indicate a rising tone.

Phonetics.

The caron represents a rising tone in the International Phonetic Alphabet. It is used in the Uralic Phonetic Alphabet for indicating postalveolar consonants and in Americanist phonetic notation to indicate various types of pronunciation.  The caron below represents voicing.

Writing and printing carons.

In printed Czech and Slovak text, the caron combined with certain letters (lower-case ť, ď, ľ, and upper-case Ľ) is reduced to a small stroke. That is optional in handwritten text.  In Lazuri orthography, the lower-case "k" with caron sometimes has its caron reduced to a stroke while the lower-case "t" with caron preserves its caron shape.  Although the stroke looks similar to an apostrophe, there is a significant difference in kerning. Using an apostrophe in place of a caron looks very unprofessional, but it can be found on goods produced in foreign countries and imported to Slovakia or the Czech Republic (compare t’ to ť, L’ahko to Ľahko). (Apostrophes appearing as palatalization marks in some Finnic languages, such as Võro and Karelian, are not forms of caron either.) Foreigners also sometimes mistake the caron for the acute accent (compare Ĺ to Ľ, ĺ to ľ).

List of letters.

Balto-Slavic.

The following are the Czech and Slovak letters and digraphs with the caron (Czech: "háček", Slovak: "mäkčeň"):  In the Lower Sorbian and Upper Sorbian languages, the following letters and digraphs have the caron:  Balto-Slavic Serbo-Croatian, Slovenian, Latvian and Lithuanian use č, š and ž. The digraph dž is also used in these languages but is considered a separate letter only in Serbo-Croatian. The Belarusian Lacinka alphabets also contain the digraph (as a separate letter), and Latin transcriptions of Bulgarian and Macedonian may use them at times, for transcription of the letter-combination ДЖ (Bulgarian) and the letter Џ (Macedonian).

Uralic.

Of Uralic languages, Estonian (and transcriptions to Finnish) use Š/š and Ž/ž, and Karelian and some Sami languages use Č/č, Š/š and Ž/ž. Dž is not a separate letter. (Skolt Sami has more: see below.) Č is present because it may be phonemically geminate: in Karelian, the phoneme 'čč' is found, and is distinct from 'č', which is not the case in Finnish or Estonian, for which only one length is recognized for 'tš'. (Incidentally, in transcriptions, Finnish orthography has to employ complicated notations like "mettšä" or even the "mettshä" to express Karelian "meččä".) On some Finnish keyboards, it is possible to write those letters by typing "s" or "z" while holding right Alt key or AltGr key.  Notice that they are "not" palatalized but postalveolar consonants. For example, Estonian "Nissi" (palatalized) is distinct from "nišši" (postalveolar). Palatalization is typically ignored in spelling, but some Karelian and Võro orthographies use an apostrophe (') or an acute accent ( ́). In Finnish and Estonian, "š" and "ž" (and in Estonian, very rarely "č") appear in loanwords and foreign proper names only and when not available, they can be substituted with 'h':'sh' for 'š', in print.  Skolt Sami uses Ʒ/ʒ (ezh) to mark the alveolar affricate, thus Ǯ/ǯ (ezh-caron or edzh (edge)) marks the postalveolar affricate. In addition to Č, Š, Ž and Ǯ, Skolt Sami also uses the caron to mark palatal stops Ǧ and Ǩ. More often than not, they are geminated: "vuäǯǯad" "to get".

Others.

Finnish Romani uses Ȟ/ȟ.  Lakota uses Č/č, Š/š, Ž/ž, Ǧ/ǧ (voiced post-velar fricative) and Ȟ/ȟ (plain post-velar fricative).  The DIN 31635 standard for transliteration of Arabic uses Ǧ/ǧ to represent the letter. "", on account of the inconsistent pronunciation of J in European languages, the variable pronunciation of the letter in educated Arabic, and the desire of the DIN committee to have a one-to-one correspondence of Arabic to Latin letters in its system.  Romanization of Pashto uses Č/č, Š/š, Ž/ž, X̌/x̌, to represent the letters چ, ش, ژ, ښ, respectively. Additionally, Ṣ̌/ṣ̌ and Ẓ̌/ẓ̌ are used by the southern Pashto dialect only (replaced by X̌/x̌ and Ǵ/ǵ in the north).  The latter Š/š is also used to transcribe the phoneme in Sumerian and Akkadian cuneiform, and the phoneme in Semitic languages represented by the letter shin (Phoenician and its descendants).

Other uses.

The caron is also used in Mandarin Chinese pinyin romanization and orthographies of several other tonal languages to indicate the "falling-rising" tone (similar to the pitch made when asking "Huh?"). The caron can be placed over the vowels: ǎ, ě, ǐ, ǒ, ǔ, ǚ. The alternative to a caron is a number 3 after the syllable: hǎo = hao3, as the "falling-rising" tone is the third tone in Mandarin.  The caron is used in the New Transliteration System of D'ni in the symbol š to represent the sound (English "sh").  Many alphabets of African languages use the caron to mark the rising tone, as in the African reference alphabet.  The caron is also used for Cypriot Greek letters that have a different sound from Standard Modern Greek: σ̌ κ̌ π̌ τ̌ ζ̌ in words like τζ̌αι ("and"), κάτ̌τ̌ος ("cat").  A-caron (ǎ) is also used to transliterate the Cyrillic letter Ъ (er golyam) in Bulgarian-it represents the mid back unrounded vowel.

Software.

Unicode.

For legacy reasons, most letters that carry carons are precomposed characters in Unicode, but a caron can also be added to any letter by using the combining character, for example: b̌ q̌ J̌.  The characters Č, č, Ě, ě, Š, š, Ž, ž are a part of the Unicode Latin Extended-A set because they occur in Czech and other official languages in Europe, while the rest are in Latin Extended-B, which often causes an inconsistent appearance.  Unicode also encodes, for example: p̬.

A caron (), háček or haček ( or ; plural "háčeks" or "háčky") also known as a hachek, wedge, check, kvačica, mäkčeň, inverted circumflex, inverted hat, flying bird, is a diacritic (ˇ) commonly placed over certain letters in the orthography of some Baltic, Slavic, Finnic, Samic, Berber, and other languages to indicate a change in the related letter's pronunciation (c > č; > ).

抑扬符(ˇ)(英语:caron 或 英语:háček,来自捷克文 :;"háček"的意思是"钩子";hachek、check),又名楔子(wedge)、反向扬抑符(inverted circumflex)、反向帽(inverted hat)等,是个置于字母上的附加符号,有用于波罗的语族、斯拉夫语族、芬兰语支、萨米语、柏柏尔语族等等的语言在音变上的使用。该符号也在汉语拼音代表第三声。


Uses.

Syllable weight.

In Greco-Roman metrics and in the description of the metrics of other literatures, the macron was introduced and is still widely used to mark a long (heavy) syllable. Even relatively recent classical Greek and Latin dictionaries are still concerned with indicating only the length (weight) of syllables; that is why most still do not indicate the length of vowels in syllables that are otherwise metrically determined. Many textbooks about Ancient Rome and Greece use the macron even if it was not actually used at that time.

Vowel length.

The following languages or transliteration systems use the macron to mark long vowels:

Tone.

The following languages or alphabets use the macron to mark tones:

Omission.

Sometimes the macron marks an omitted "n" or "m", like the tilde:

Letter extension.

The macron is used in the orthography of a number of vernacular languages of the Solomon Islands and Vanuatu, particularly those first transcribed by Anglican missionaries. The macron has no unique value, and is simply used to distinguish between two different phonemes.  Thus, in several languages of the Banks Islands, including Mwotlap, the simple "m" stands for, but an "m" with a macron (m̄) is a rounded labial-velar nasal ; while the simple "n" stands for the common alveolar nasal, an "n" with macron (n̄) represents the velar nasal ; the vowel ē stands for a (short) higher by contrast with plain "e" ; likewise ō contrasts with plain "o".  In Hiw orthography, the consonant "r̄" stands for the prestopped velar lateral approximant. In Araki, the same symbol "r̄" encodes the alveolar trill – by contrast with "r", which encodes the alveolar flap.  In Bislama (orthography before 1995), Lamenu and Lewo, a macron is used on two letters "". "m̄" represents, and "p̄" represents. The orthography after 1995 (which has no diacritics) has these written as "mw" and "pw".  In Kokota, "ḡ" is used for the velar stop, but "g" without macron is the voiced velar fricative.  In Marshallese, a macron is used on four letters –'– whose pronunciations differ from the unmarked '. Marshallese uses a vertical vowel system with three to four vowel phonemes, but traditionally their allophones have been written out, so vowel letters with macron are used for some of these allophones. Though the standard diacritic involved is a macron, there are no other diacritics used "above" letters, so in practice other diacritics can and have been used in less polished writing or print, yielding nonstandard letters like ", depending on displayability of letters in computer fonts.

Other uses.

Also, in some instances, a diacritic will be written like a macron, although it represents another diacritic whose standard form is different:

Medicine.

In medical prescriptions and other handwritten notes, macrons mean:

Mathematics and science.

The overline is a typographical symbol similar to the macron, used in a number of ways in mathematics and science, for example to represent complex conjugation:  formula_1  It is also used in Hermann–Mauguin notation.

Music.

In music, the tenuto marking resembles the macron.  The macron is also used in German lute tablature to distinguish repeating alphabetic characters.

Technical notes.

The Unicode Standard encodes combining and precomposed macron characters:  Macron-related Unicode characters not included in the table above:  In LaTeX a macron is created with the command "\=", for example: M\=aori for Māori. In OpenOffice, if the extension Compose Special Characters is installed, a macron may be added by following the letter with a hyphen and pressing the user's predefined shortcut key for composing special characters. A macron may also be added by following the letter with the character's four-digit hex-code, and pressing the user's predefined shortcut key for adding unicode characters.

A macron () is a diacritical mark: it is a straight bar placed above a letter, usually a vowel. Its name derives from Ancient Greek ("makrón") "long", since it was originally used to mark long or heavy syllables in Greco-Roman metrics. It now more often marks a long vowel. In the International Phonetic Alphabet, the macron is used to indicate a mid-tone; the sign for a long vowel is instead a modified triangular colon.

长音符号(Macron;;长音符), 由希腊语 ("makros") 意「巨大」,形为 ̄,原意为指示响音成为长响音。相反为短音符号 ̆,用以指示短音的响音。这些是语音学上的消歧义。