title: Dialect continuum

text: The Germanic dialects spoken on the island of Great Britain comprise areal varieties of English in England and of Scots in Scotland. Those of large areas north and south of the border are often mutually intelligible. In contrast, the Orcadian dialect of Scots is very different from the dialects of English in southern England—but they are linked by a chain of intermediate varieties.


title: Dialect continuum

text: The western continuum of Romance languages comprises, from West to East: in Portugal, Portuguese; in Spain, Galician, Leonese or Asturian, Castilian or Spanish, Aragonese and Catalan or Valencian; in France, Occitan, Franco-Provençal, standard French and Corsican which is closely related to Italian; in Italy, Piedmontese, Italian, Lombard, Emilian, Romagnol, Gallo-Picene, Venetian, Friulian, Ladin; and in Switzerland, Lombard and Romansh. This continuum is sometimes presented as another example, but the major languages in the group (i.e. Portuguese, Spanish, French and Italian) have had separate standards for longer than the languages in the Continental West Germanic group, and so are not commonly classified as dialects of a common language.


title: Dialect continuum

text: Focusing instead on the local Romance lects that pre-existed the establishment of national or regional standard languages, all evidence and principles point to "Romania continua" as having been, and to varying extents in some areas still being, what Charles Hockett called an L-complex, i.e. an unbroken chain of local differentiation such that, in principle and with appropriate caveats, intelligibility (due to sharing of features) attenuates with distance. This is perhaps most evident today in Italy, where, especially in rural and small-town contexts, local Romance is still often employed at home and work, and geolinguistic distinctions are such that while native speakers from any two nearby towns can understand each other with ease, they can also spot from linguistic features that the other is from elsewhere.


title: Dialect continuum

text: In recent centuries, the intermediate dialects between the major Romance languages have been moving toward extinction, as their speakers have switched to varieties closer to the more prestigious national standards. That has been most notable in France, owing to the French government's refusal to recognise minority languages, but it has occurred to some extent in all Western Romance speaking countries. Language change has also threatened the survival of stateless languages with existing literary standards, such as Occitan.


title: Dialect continuum

text: The Romance languages of Italy are a less arguable example of a dialect continuum. For many decades since Italy's unification, the attitude of the French government towards the ethnolinguistic minorities was copied by the Italian government.


title: Dialect continuum

text: The eastern Romance continuum is dominated by Romanian. Outside Romania and Moldova, across the other south-east European countries, various Romanian language groups are to be found: pockets of various Romanian and Aromanian subgroups survive throughout Bulgaria, Serbia, North Macedonia, Greece, Albania and Croatia (in Istria).


title: Dialect continuum

text: Conventionally, on the basis of extralinguistic features (such as writing systems or the former western frontier of the Soviet Union), the North Slavic continuum is split into East and West Slavic continua. From the perspective of linguistic features alone, only two Slavic (dialect) continua can be distinguished, namely, North and South.


title: Dialect continuum

text: The North Slavic continuum covers the East Slavic and West Slavic languages. East Slavic includes Russian, Belarusian, Rusyn and Ukrainian; West Slavic languages of Czech, Polish, Slovak, Silesian, Kashubian, and Upper and Lower Sorbian.


title: Dialect continuum

text: Ukrainian dialects and to a lesser degree Belarusian have been influenced by neighbouring Polish, due to the historical ties with the Polish–Lithuanian Commonwealth.


title: Dialect continuum

text: All South Slavic languages form a dialect continuum. It comprises, from West to East, Slovenia, Croatia, Bosnia and Herzegovina, Montenegro, Serbia, North Macedonia, and Bulgaria. Standard Slovene, Macedonian, and Bulgarian are each based on a distinct dialect, but the Bosnian, Croatian, Montenegrin, and Serbian standard varieties of the pluricentric Serbo-Croatian language are all based on the same dialect, Shtokavian.


title: Dialect continuum

text: Therefore, Croats, Serbs, Bosniaks and Montenegrins communicate fluently with each other in their respective standardized varieties. In Croatia, native speakers of Shtokavian may struggle to understand distinct Kajkavian or Chakavian dialects, as might the speakers of the two with each other. Likewise in Serbia, the Torlakian dialect differs significantly from Standard Serbian. Serbian is a Western South Slavic standard, but Torlakian is largely transitional with the Eastern South Slavic languages (Bulgarian and Macedonian). Collectively, the Torlakian dialects with Macedonian and Bulgarian share many grammatical features that set them apart from all other Slavic languages, such as the complete loss of its grammatical case systems and adoption of features more commonly found among analytic languages.


title: Dialect continuum

text: The barrier between "East South Slavic" and "West South Slavic" is historical and natural, caused primarily by a one-time geographical distance between speakers. The two varieties started diverging early on (circa 11th century CE) and evolved separately ever since without major mutual influence, as evidenced by distinguishable Old Slavonic, while the western dialect of common Old Slavic was still spoken across the modern Serbo-Croatian area in the 12th and early 13th centuries. An intermediate dialect linking western and eastern variations inevitably came into existence over time – Torlakian – spoken across a wide radius on which the tripoint of Bulgaria, North Macedonia and Serbia is relatively pivotal.


title: Dialect continuum

text: The other major language family in Europe besides Indo-European are the Uralic languages. The Sami languages, sometimes mistaken for a single language, are a dialect continuum, albeit with some disconnections like between North, Skolt and Inari Sami. The Baltic-Finnic languages spoken around the Gulf of Finland form a dialect continuum. Thus, although Finnish and Estonian are separate languages, there is no definite linguistic border or isogloss that separates them. This is now more difficult to recognize because many of the intervening languages have declined or become extinct.


title: Dialect continuum

text: The Goidelic languages consist of Irish, Scottish and Manx. Prior to the 19th and 20th centuries, the continuum existed throughout Ireland, the Isle of Man and Scotland. Many intermediate dialects have become extinct or have died out leaving major gaps between languages such as in the islands of Rathlin, Arran or Kintyre and also in the Irish counties or Antrim, Londonderry and Down.


title: Dialect continuum

text: The current Goidelic speaking areas of Ireland are also separated by extinct dialects but remain mutually intelligible.


title: Dialect continuum

text: Arabic is a standard case of diglossia. The standard written language, Modern Standard Arabic, is based on the Classical Arabic of the Qur'an, while the modern vernacular dialects (or languages) branched from ancient Arabic dialects, from North Western Africa through Egypt, Sudan, and the Fertile Crescent to the Arabian Peninsula and Iraq. The dialects use different analogues from the Arabic language inventory and have been influenced by different substrate and superstrate languages. Adjacent dialects are mutually understandable to a large extent, but those from distant regions are more difficult to be understood.


title: Dialect continuum

text: The difference between the written standard and the vernaculars is apparent also in the written language, and children have to be taught Modern Standard Arabic in school to be able to read it.


title: Dialect continuum

text: All modern Aramaic languages descend from a dialect continuum that historically existed before the Islamicization of the Levant and Mesopotamia. Northeastern Neo-Aramaic, including distinct varieties spoken by both Jews and Christians, is a dialect continuum although greatly disrupted by population displacement during the twentieth century.


title: Dialect continuum

text: The Kurdish language is considered as a dialect continuum of many varieties and the three main varieties are Northern Kurdish (Kurmanji), Central Kurdish (Sorani), and Southern Kurdish (Xwarîn).


title: Dialect continuum

text: The Persian language in its various varieties (Tajiki and Dari), is representative of a dialect continuum. The divergence of Tajik was accelerated by the shift from the Perso-Arabic alphabet to a Cyrillic one under the Soviets. Western dialects of Persian show greater influence from Arabic and Oghuz Turkic languages, but Dari and Tajik tend to preserve many classical features in grammar and vocabulary. Also the Tat language, a dialect of Persian, is spoken in Azerbaijan.


title: Dialect continuum

text: Turkic languages are best described as a dialect continuum. Geographically this continuum starts at the Balkans in the west with Balkan Turkish, includes Turkish in Turkey and Azerbaijani language in Azerbaijan, extends into Iran with Azeri and Khalaj, into Iraq with Turkmen, across Central Asia to include Turkmenistan, Uzbekistan, Kazakhstan, Kyrgyzstan, to southern Regions of Tajikistan and into Afghanistan. In the south, the continuum starts in northern Afghanistan, northward to Chuvashia. In the east it extends to the Republic of Tuva, the Xinjiang autonomous region in Western China with the Uyghur language and into Mongolia with Khoton. The entire territory is inhabited by Turkic speaking peoples. There are three varieties of Turkic geographically outside the continuum: Chuvash, Yakut and Dolgan. They have been geographically separated from the other Turkic languages for an extensive period of time, and Chuvash language stands out as the most divergent from other Turkic languages.


title: Dialect continuum

text: The Turkic continuum makes internal genetic classification of the languages problematic. Chuvash, Khalaj and Yakut are generally classified as significantly distinct, but the remaining Turkic languages are quite similar, with a high degree of mutual intelligibility between not only geographically adjacent varieties but also among some varieties some distance apart. Structurally, the Turkic languages are very close to one another, and they share basic features such as SOV word order, vowel harmony and agglutination.


title: Dialect continuum

text: Many of the Indo-Aryan languages of the Indian subcontinent form a dialect continuum. What is called "Hindi" in India is frequently Standard Hindi, the Sanskritized register of the colloquial Hindustani spoken in the Delhi area, the other register being Urdu. However, the term Hindi is also used for the different dialects from Bihar to Rajasthan and, more widely, some of the Eastern and Northern dialects are sometimes grouped under Hindi. The Indo-Aryan Prakrits also gave rise to languages like Gujarati, Assamese, Maithili, Bengali, Odia, Nepali, Marathi, Konkani and Punjabi.


title: Dialect continuum

text: The differences are similar to those within the Romance languages, which are similarly descended from a language spread by imperial expansion over substrate languages 2000 years ago.


title: Dialect continuum

text: Unlike Europe, however, Chinese political unity was restored in the late 6th century and has persisted (with interludes of division) until the present day.


title: Dialect continuum

text: There are no equivalents of the local standard literary languages that developed in the numerous independent states of Europe.


title: Dialect continuum

text: Chinese dialectologists have divided the local varieties into a number of dialect groups, largely based on phonological developments in comparison with Middle Chinese.


title: Dialect continuum

text: Most of these groups are found in the rugged terrain of the southeast, reflecting the greater variation in this area, particularly in Fujian.


title: Dialect continuum

text: Moreover, in many cases the transitions between groups are smooth, as a result of centuries of interaction and multilingualism.


title: Dialect continuum

text: The boundaries between the northern Mandarin area and the central groups, Wu, Gan and Xiang, are particularly weak, due to the steady flow of northern features into these areas.


title: Dialect continuum

text: Transitional varieties between the Wu, Gan and Mandarin groups have been variously classified, with some scholars assigning them to a separate Hui group.


title: Dialect continuum

text: There are sharper boundaries resulting from more recent expansion between Hakka and Yue, and between Southwestern Mandarin and Yue, but even here there has been considerable convergence in contact areas.


title: Dialect continuum

text: Cree is a group of closely related Algonquian languages that are distributed from Alberta to Labrador in Canada. They form the Cree-Montagnais-Naskapi dialect continuum, with around 117,410 speakers. The languages can be roughly classified into nine groups, from west to east:


title: Dialect continuum

text: Various Cree languages are used as languages of instruction and taught as subjects: Plains Cree, Eastern Cree, Montagnais, etc. Mutual intelligibility between some dialects can be low. There is no accepted standard dialect.


title: Dialect continuum

text: Ojibwa (Chippewa) is a group of closely related Algonquian languages in Canada, which is distributed from British Columbia to Quebec, and the United States, distributed from Montana to Michigan, with diaspora communities in Kansas and Oklahoma. With Cree, the Ojibwe dialect continuum forms its own continuum, but the Oji-Cree language of this continuum joins the Cree–Montagnais–Naskapi dialect continuum through Swampy Cree. The Ojibwe continuum has 70,606 speakers. Roughly from northwest to southeast, it has these dialects:


title: Dialect continuum

text: Unlike the Cree–Montagnais–Naskapi dialect continuum, with distinct n/y/l/r/ð dialect characteristics and noticeable west-east k/č(ch) axis, the Ojibwe continuum is marked with vowel syncope along the west-east axis and ∅/n along the north-south axis.


title: Lignum vitae

text: Lignum vitae () is a wood, also called guayacan or guaiacum, and in parts of Europe known as Pockholz or pokhout, from trees of the genus "Guaiacum". The trees are indigenous to the Caribbean and the northern coast of South America (e.g: Colombia and Venezuela) and have been an important export crop to Europe since the beginning of the 16th century. The wood was once very important for applications requiring a material with its extraordinary combination of strength, toughness, and density. It is also the national tree of the Bahamas, and the Jamaican national flower.


title: Lignum vitae

text: The wood is obtained chiefly from "Guaiacum officinale" and "Guaiacum sanctum", both small, slow-growing trees. All species of the genus "Guaiacum" are now listed in Appendix II of CITES (the Convention on International Trade in Endangered Species of Wild Fauna and Flora) as potentially endangered species. "G. sanctum" is listed as Near Threatened by the IUCN Red List. Demand for the wood has been reduced by modern materials science, which has led to polymer, alloys and composite materials that can take lignum vitae's place.


title: Lignum vitae

text: "Lignum vitae" is Latin for "wood of life". The plant derives its name from its medicinal uses; lignum vitae resin has been used to treat a variety of medical conditions from coughs to arthritis, and chips of the wood can also be used to brew a tea.


title: Lignum vitae

text: Other names for lignum vitae include (Spanish for "holy wood"), Aura palo santo and "bastard greenheart" (not to be confused with true greenheart "Chlorocardium rodiei", a popular wood in shipbuilding, cabinetry, and woodturning but a completely different timber). Lignum vitae is also one of the numerous hard, dense woods loosely referred to as "ironwood".


title: Lignum vitae

text: Lignum vitae is hard and durable, and is also the densest wood traded (average dried density: ~79 lbs/ft or ~1,260 kg/m); it will easily sink in water. On the Janka scale of hardness, which measures hardness of woods, lignum vitae ranks highest of the trade woods, with a Janka hardness of 4,500 lbf (compared with Olneya at 3,260 lbf, African blackwood at 2,940 lbf, hickory at 1,820 lbf, red oak at 1,290 lbf, yellow pine at 690 lbf, and Balsa at 100 lbf). The densest of all woods is "Allocasuarina luehmannii". Krugiodendron typically has a higher density, among many other woods that vary by sample.


title: Lignum vitae

text: Various other hardwoods may also be called lignum vitae and should not be confused with it. The best-known come from "Bulnesia arborea" and "Bulnesia sarmientoi" (in the same subfamily as "Guaiacum") and are known as verawood or Argentine lignum vitae; they are somewhat similar in appearance and working qualities as genuine lignum vitae. Some hardwoods from Australasia (e.g., "Vitex lignum-vitae" and some species of "Acacia" and "Eucalyptus") are also referred to as lignum vitae.


title: Lignum vitae

text: The tree is slow-growing and relatively small in stature, even when mature and old. It bears small, purplish-blue flowers which result in paired orange dehiscent fruits. The bark is mottled.


title: Lignum vitae

text: Due to the density of the wood, cricket bails, in particular "heavy bails" used in windy conditions, are sometimes made of lignum vitae. It is also sometimes used to make lawn bowls, croquet mallets, and skittles balls. The wood also has seen widespread historical usage in mortars and pestles and for wood carvers' mallets.


title: Lignum vitae

text: It was the traditional wood used for the British police truncheon until recently, due to its density (and strength), combined with the relative softness of wood compared to metal, thereby tending to bruise or stun rather than simply cut the skin.


title: Lignum vitae

text: The belaying pins and deadeyes aboard USS "Constitution" and many other sailing ships were made from lignum vitae. Due to its density and natural oils, they rarely require replacement, despite the severity of typical marine weathering conditions, and also resisted jamming in their mortise holes. The sheaves of blocks on sailing vessels were made of lignum vitae until the introduction of modern synthetics.


title: Lignum vitae

text: Due to lignum vitae's toughness, it can also be used as a lap in the process of cutting gems. The wood is covered with powdered industrial diamond, attached to a spindle, and used to smooth rough surfaces of gems.


title: Lignum vitae

text: Master clockmaker John Harrison used lignum vitae in the bearings and gears of his pendulum clocks and his first three marine chronometers (all of which were large clocks rather than watches), since the wood is self-lubricating. The use of lignum vitae eliminates the need for horological lubricating oil; 18th-century horological oil would become viscous and reduce the accuracy of a timepiece under unfavourable conditions (including those that prevail at sea).


title: Lignum vitae

text: For the same reason it was widely used in water-lubricated shaft bearings for ships and hydro-electric power plants, and in the stern-tube bearings of ship propeller shafts until the 1960s saw the introduction of sealed white metal bearings. According to the San Francisco Maritime National Park Association website, the shaft bearings on the WWII submarine were made of this wood. The aft main shaft strut bearings for , the world's first nuclear-powered submarine, were composed of this wood. Also, the bearings in the original 1920s turbines of the Conowingo hydroelectric plant on the lower Susquehanna River were made from lignum vitae. The shaft bearings on the horizontal turbines at the Pointe du Bois generating station in Manitoba are made from lignum vitae. Other hydroelectric plant turbine bearings, many of them still in service, were fabricated with lignum vitae and are too numerous to list here.


title: Lignum vitae

text: The United Railroads of San Francisco (an ancestor of the San Francisco Municipal Railway) began installing insulators made of composite materials to support the heavy 600-volt DC feeder wires for their trolley system in 1904. These lines were damaged, along with most everything else, during the 1906 earthquake and the fires that followed. Rebuilding the trolley system and expanding it to replace cable car routes destroyed in the quake created a huge demand for insulators, a demand manufacturers further east were unable to meet. The properties of lignum vitae, namely its ability to withstand high stress (from heavy cables on long spans and the strain of lines rounding corners) and high temperature (due to the feeder cables becoming very hot during peak operating hours), and its ready availability from the holds of the ships in the harbor (used as dunnage and ballast) made it an ideal 'temporary' solution. Many remained into service well into the 1970s, with the last few pieces replaced in the 2000s in favor of an underground feeder system.


title: Lignum vitae

text: It was also used extensively in the manufacture of British Railways Mark 1 Rolling Stock, as a "bump stop" in the bogies (the frame that carries the wheels).


title: Lignum vitae

text: Pioneering calypsonian/vaudevillian Sam Manning recorded a song titled "Lignum Vitae" in the 1920s. His reference was doubly salacious, referring to both the bark tea's contraceptive qualities and the phallic symbolism of the hard wood.


title: Lignum vitae

text: Benvenuto Cellini recounts using lignum vitae (presumably in tea form) to cure himself of a venereal disease (the so-called "French Pox", presumably Syphilis).


title: Lignum vitae

text: According to T. H. White's version of the King Arthur story "The Once and Future King", lignum vitae, from which the wand of Merlin is made, has magical powers.


title: Lignum vitae

text: Gabriel García Márquez's novel "Love in the Time of Cholera" includes a bathtub made of this wood in one of the main characters' homes. His novel "Chronicle of a Death Foretold" also refers to the use of this wood in making a cane for the blind Poncio Vicario.


title: Lignum vitae

text: In Charles Dickens' novel "Bleak House", one of the characters, Matthew Bagnet is referred to as lignum vitae, "... in compliment to the extreme hardness and toughness of his physiognomy."


title: Lignum vitae

text: In Philip Pullman's novel, The Secret Commonwealth, the heroine Lyra Belacqua carries a truncheon made from lignum vitae as a weapon.


title: Limit inferior and limit superior

text: In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting (that is, eventual and extreme) bounds on the sequence. They can be thought of in a similar fashion for a function (see limit of a function). For a set, they are the infimum and supremum of the set's limit points, respectively. In general, when there are multiple objects around which a sequence, function, or set accumulates, the inferior and superior limits extract the smallest and largest of them; the type of object and the measure of size is context-dependent, but the notion of extreme limits is invariant.


title: Limit inferior and limit superior

text: Limit inferior is also called infimum limit, limit infimum, liminf, inferior limit, lower limit, or inner limit; limit superior is also known as supremum limit, limit supremum, limsup, superior limit, upper limit, or outer limit.


title: Limit inferior and limit superior

text: The limits superior and inferior can equivalently be defined using the concept of subsequential limits of the sequence formula_11. An element formula_12 of the extended real numbers formula_13 is a "subsequential limit" of formula_11 if there exists a strictly increasing sequence of natural numbers formula_15 such that formula_16. If formula_17 is the set of all subsequential limits of formula_11, then


title: Limit inferior and limit superior

text: If the terms in the sequence are real numbers, the limit superior and limit inferior always exist, as the real numbers together with ±∞ (i. e. the extended real number line) are complete. More generally, these definitions make sense in any partially ordered set, provided the suprema and infima exist, such as in a complete lattice.


title: Limit inferior and limit superior

text: Whenever the ordinary limit exists, the limit inferior and limit superior are both equal to it; therefore, each can be considered a generalization of the ordinary limit which is primarily interesting in cases where the limit does "not" exist. Whenever lim inf "x" and lim sup "x" both exist, we have


title: Limit inferior and limit superior

text: Limits inferior/superior are related to big-O notation in that they bound a sequence only "in the limit"; the sequence may exceed the bound. However, with big-O notation the sequence can only exceed the bound in a finite prefix of the sequence, whereas the limit superior of a sequence like e may actually be less than all elements of the sequence. The only promise made is that some tail of the sequence can be bounded above by the limit superior plus an arbitrarily small positive constant, and bounded below by the limit inferior minus an arbitrarily small positive constant.


title: Limit inferior and limit superior

text: The limit superior and limit inferior of a sequence are a special case of those of a function (see below).


title: Limit inferior and limit superior

text: In mathematical analysis, limit superior and limit inferior are important tools for studying sequences of real numbers. Since the supremum and infimum of an unbounded set of real numbers may not exist (the reals are not a complete lattice), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the complete totally ordered set [−∞,∞], which is a complete lattice.


title: Limit inferior and limit superior

text: Consider a sequence formula_11 consisting of real numbers. Assume that the limit superior and limit inferior are real numbers (so, not infinite).


title: Limit inferior and limit superior

text: As mentioned earlier, it is convenient to extend formula_37 to formula_38 Then, formula_39 in formula_40 converges if and only if


title: Limit inferior and limit superior

text: in which case formula_42 is equal to their common value. (Note that when working just in formula_43 convergence to formula_44 or formula_45 would not be considered as convergence.) Since the limit inferior is at most the limit superior, the following conditions hold formula_46


title: Limit inferior and limit superior

text: If formula_47 and formula_48, then the interval formula_49 need not contain any of the numbers formula_50 but every slight enlargement formula_51 for arbitrarily small formula_52 will contain formula_1 for all but finitely many indices formula_54 In fact, the interval formula_49 is the smallest closed interval with this property. We can formalize this property like this: there exist subsequences formula_56 and formula_57 of formula_1 (where formula_59 and formula_60 are monotonous) for which we have formula_61


title: Limit inferior and limit superior

text: In the particular case that one of the sequences actually converges, say formula_77 then the inequalities above become equalities (with formula_78 or formula_79 being replaced by formula_80).


title: Limit inferior and limit superior

text: If formula_85 exists (including the case formula_86) and formula_87 then formula_88 provided that formula_89 is not of the form formula_84


title: Limit inferior and limit superior

text: The value of this limit inferior is conjectured to be 2 – this is the twin prime conjecture – but has only been proven to be less than or equal to 246. The corresponding limit superior is formula_98, because there are arbitrary gaps between consecutive primes.


title: Limit inferior and limit superior

text: Assume that a function is defined from a subset of the real numbers to the real numbers. As in the case for sequences, the limit inferior and limit superior are always well-defined if we allow the values +∞ and -∞; in fact, if both agree then the limit exists and is equal to their common value (again possibly including the infinities). For example, given formula_99, we have formula_100 and formula_101. The difference between the two is a rough measure of how "wildly" the function oscillates, and in observation of this fact, it is called the oscillation of "f" at "0". This idea of oscillation is sufficient to, for example, characterize Riemann-integrable functions as continuous except on a set of measure zero. Note that points of nonzero oscillation (i.e., points at which "f" is "badly behaved") are discontinuities which, unless they make up a set of zero, are confined to a negligible set.


title: Limit inferior and limit superior

text: There is a notion of lim sup and lim inf for functions defined on a metric space whose relationship to limits of real-valued functions mirrors that of the relation between the lim sup, lim inf, and the limit of a real sequence. Take a metric space formula_102, a subspace formula_103 contained in formula_102, and a function formula_105. Define, for any limit point formula_80 of formula_103,


title: Limit inferior and limit superior

text: Note that as ε shrinks, the supremum of the function over the ball is monotone decreasing, so we have


title: Limit inferior and limit superior

text: This finally motivates the definitions for general topological spaces. Take "X", "E" and "a" as before, but now let "X" be a topological space. In this case, we replace metric balls with neighborhoods:


title: Limit inferior and limit superior

text: The power set ℘("X") of a set "X" is a complete lattice that is ordered by set inclusion, and so the supremum and infimum of any set of subsets (in terms of set inclusion) always exist. In particular, every subset "Y" of "X" is bounded above by "X" and below by the empty set ∅ because ∅ ⊆ "Y" ⊆ "X". Hence, it is possible (and sometimes useful) to consider superior and inferior limits of sequences in ℘("X") (i.e., sequences of subsets of "X").


title: Limit inferior and limit superior

text: The difference between the two definitions involves how the topology (i.e., how to quantify separation) is defined. In fact, the second definition is identical to the first when the discrete metric is used to induce the topology on "X".


title: Limit inferior and limit superior

text: In this case, a sequence of sets approaches a limiting set when the elements of each member of the sequence approach the elements of the limiting set. In particular, if formula_117 is a sequence of subsets of formula_118 then:


title: Limit inferior and limit superior

text: This is the definition used in measure theory and probability. Further discussion and examples from the set-theoretic point of view, as opposed to the topological point of view discussed below, are at set-theoretic limit.


title: Limit inferior and limit superior

text: By this definition, a sequence of sets approaches a limiting set when the limiting set includes elements which are in all except finitely many sets of the sequence "and" does not include elements which are in all except finitely many complements of sets of the sequence. That is, this case specializes the general definition when the topology on set "X" is induced from the discrete metric.


title: Limit inferior and limit superior

text: under which a sequence of points {"x"} converges to point "x" ∈ "X" if and only if "x" = "x" for all except finitely many "k". Therefore, "if the limit set exists" it contains the points and only the points which are in all except finitely many of the sets of the sequence. Since convergence in the discrete metric is the strictest form of convergence (i.e., requires the most), this definition of a limit set is the strictest possible.


title: Limit inferior and limit superior

text: In this sense, the sequence has a limit so long as every point in "X" either appears in all except finitely many "X" or appears in all except finitely many "X".


title: Limit inferior and limit superior

text: Using the standard parlance of set theory, set inclusion provides a partial ordering on the collection of all subsets of "X" that allows set intersection to generate a greatest lower bound and set union to generate a least upper bound. Thus, the infimum or meet of a collection of subsets is the greatest lower bound while the supremum or join is the least upper bound. In this context, the inner limit, lim inf "X", is the largest meeting of tails of the sequence, and the outer limit, lim sup "X", is the smallest joining of tails of the sequence. The following makes this precise.


title: Limit inferior and limit superior

text: The following are several set convergence examples. They have been broken into sections with respect to the metric used to induce the topology on set "X".


title: Kufa

text: Kufa ( ), also spelled Kufah, is a city in Iraq, about south of Baghdad, and northeast of Najaf. It is located on the banks of the Euphrates River. The estimated population in 2003 was 110,000. Currently, Kufa and Najaf are joined into a single urban area that is mostly commonly known to the outside world as 'Najaf'.


title: Kufa

text: Along with Samarra, Karbala, Kadhimiya and Najaf, Kufa is one of five Iraqi cities that are of great importance to Shi'ite Muslims. The city was founded in 638 CE (17 Hijrah) during the reign of the second Rashidun Caliph, Umar ibn Al-Khattab, and it was the final capital of the last Rashidun Caliph, Ali ibn Abi Talib. Kufa was also the founding capital of the Abbasid Caliphate. During the Islamic Golden Age it was home to the grammarians of Kufa. Kufic script is named for the city.


title: Kufa

text: After the Arab victory against the Byzantine Empire at Battle of Yarmouk in 636, Kufa was founded and given its name in 637–638 CE, about the same time as Basra. Kufa and Basra were the two "amsar" (garrison cities) of Iraq, serving as military bases and administrative centers. The Companion of the Prophet Saʻd ibn Abī Waqqas founded it as an encampment adjacent to the Lakhmid Arab city of Al-Hirah, and incorporated it as a city of seven divisions. Non-Arabs knew the city under alternate names: "Hīrah" and "Aqulah", before the consolidations of ʻAbdu l-Mālik in 691. Umar, who assigned the land of the Jews in Arabia to his warriors, ordered the relocation of the Jews of Khaybar to a strip of land in Kufa, in 640. In the 640s, the Kufan commons were agitated that Umar's governor was distributing the spoils of war unfairly. In 642 ʻUmar summoned Saʻd to Medina with his accusers. Despite finding Sa'd to be innocent, Umar deposed him to avert ill feelings. At first, Umar appointed Ammar ibn Yasir and secondly Basra's first Governor Abū Mūsā al-Ashʻarī; but the Kufan instigators accepted neither. ʻUmar and the Kufans finally agreed on Al-Mughīrah ibn Shuʻbah.


title: Kufa

text: It was also conquered for few years by the Thaqafids dynasty led by Mokhtar Al Thaqafi after conquering Basra and other parts of Iraq.


title: Kufa

text: Following Umar's death (644), his successor Uthman replaced Mughirah with Al-Walid ibn Uqba in 645. This happened while the Arabs were continuing their conquest of western Persia under Uthman ibn Abi al-As from Tawwaj, but late in the 640s, these forces suffered setbacks.


title: Kufa

text: Uthman in 650 reorganised the Iranian frontier; both Basra and Kufa received new governors (Sa'id ibn al-'As in Kufa's case), and the east came under Basra's command while north of that remained under Kufa's. The few but noticeable trouble makers in Kufa sought in 654 and had Sa'id deposed and instead showed satisfaction with the return of Abu Musa, which Uthman approved seeking to please all. Kufa remained a source of instigations albeit from a minority. In 656 when the Egyptian instigators, in co-operation with those in Kufa, marched onto the Caliph Uthman in Medina, Abu Musa counselled the instigators to no avail.


title: Kufa

text: Upon Uthman's assassination by rebels, governor Abu Musa attempted to restore a non-violent atmosphere in Kufa. The Muslims in Medina and elsewhere supported the right of Ali ibn Abu Talib to the caliphate. In order to manage the military frontiers more efficiently, Ali shifted the capital from Medina to Kufa.


title: Kufa

text: The people of Syria and their governor, Muawiyah, who seized the Caliphate for himself and his family by using the confusion caused by the assassination of Caliph Uthman and being disturbed by the brutal assassination of the Caliph Uthman, demanded retribution. As Muawiyah mounted his campaign to hold Ali responsible for the murder of Uthman, factions developed. In an already emotionally charged atmosphere, Muawiyah's refusal to give allegiance to Ali as the Caliph without Ali avenging Uthman first eventually, led to war.


title: Kufa

text: While praying in the Great Mosque of Kufa, Ali was attacked by the Kharijite Abd-al-Rahman ibn Muljam. He was wounded by ibn Muljam's poison-coated sword while prostrating in the Fajr prayer.


title: Kufa

text: Muawiyah I appointed Ziyad ibn Abihi Al the Governor of Kufa, after Hasan's migration to Medina, which was a peace treaty which dictated he abdicate his right to caliphate to avoid an open war among Muslims. Some of Hasan's followers, like Hujr ibn Adi, were unhappy with the peace treaty, and did not change their ways according to the edicts of the new Governor. This became increasingly noticeable, since it created a rebellion against the ruler. However, Ziyad ibn Abihi was an equally keen strategist and politician, and was able to put down all challenges posed by the rebels against his rule.


title: Kufa

text: Throughout the Umayyad era, as was the case since the inception of the city by Umar ibn Khattab, there were those among Kufa's inhabitants who were rebellious to their rulers. Yazid I was declared as the Second Umayyad Caliph which led to a rebellion among Kufans and they turned to Muhammad's grandson Husayn for help and leadership. Yazid appointed Ubayd Allah ibn Ziyad as the new Governor to put down the rebellion, and kill Husayn if he did not acknowledge his Caliphate, culminating in the Battle of Karbala. There was a period of relative calm during the short reign of Al-Mukhtar's rulership, and the Umayyad-era Governorship of Al-Hajjaj.


title: Kufa

text: In 749, the Abbasids under al-Hasan ibn Qahtaba took Kufa and made it their capital. In 762, they moved their seat to Baghdad. Under the Umayyad and early Abbasid decades, Kufa's importance gradually shifted from caliphal politics to Islamic theory and practice. The city was sacked by the Qarmatians in 905, 924, and 927, and it never fully recovered from the destruction.


title: Kufa

text: Wael Hallaq notes that by contrast with Medina and to a lesser extent Syria, in Iraq there was no unbroken Muslim or Ishmaelite population dating back to the prophet Muhammad's time. Therefore, Maliki (and Azwa'i) appeals to the practice "amal" () of the community could not apply. Instead the people of Iraq relied upon those Companions of the Muhammad who settled there, and upon such factions from the Hijaz whom they respected most. A primary founder of a Sunni school of thought, Abu Hanifa, was a Kufan who had supported the Zaydi Revolt in the 730s; and his jurisprudence was systematised and defended against non-Iraqi rivals (starting with Malikism) by other Kufans, such as al-Shaybani.


title: Kufa

text: Shirazi's "Tabaqat", which Hallaq labels "an important early biographical work dedicated to jurists", covered 84 "towering figures" of Islamic jurisprudence; to which Kufa provided 20. It was therefore a center surpassed only by Medina (22), although Basra came close (17). Kufans could claim that the more prominent of Muhammad's Companions had called that city home: not only Ibn Abu Waqqas, Abu Musa, and Ali; but also Abd Allah ibn Mas'ud, Salman the Persian, Ammar ibn Yasir, and Huzayfa ibn Yaman. Among its jurists prior to Abu Hanifa, Hallaq singles out Sa'id ibn Jubayr, Ibrahim al-Nakha‘i, and Hammad ibn Abi Sulayman; and considers Amir al-Sha‘bi a pioneer in the science of judicial precedent.


title: Kufa

text: Additionally, Imam Muhammad al-Baqir and his son Jafar al-Sadiq made decisions from Medina that contributed to the law of Kufa; and to this day Shi‘ite law follows their example. Imam Abu Hanifa too learnt from al-Baqir and especially al-Sadiq. As a result, while Hanafi school is doctrinally Sunni, in practical terms Hanafi law is closer to Imami law than either is to the other schools of jurisprudence i.e. of Malik, Shafi‘i, and Ibn Hanbal.


title: Kufa

text: Kufa was also among the first centers of Qur'anic interpretation, which Kufans credited to the exegete Mujahid (until he escaped to Mecca in 702). It further recorded general traditions as Hadith; in the 9th century, Yahya ibn ‘Abd al-Hamid al-Himmani compiled many of these into a Musnad.


title: Kufa

text: Given Kufa's opposition to Damascus, Kufan traditionists had their own take on Umayyad history. The historian Abu Mikhnaf al-Azdi (d. 774) compiled their accounts into a rival history, which became popular under Abbasid rule. This history does not survive but later historians like Tabari quoted from it extensively.


title: Kufa

text: Kufa is also where the kufic script was developed, the earliest script of the Arabic language. As the scholar al-Qalqashandi maintained, "The Arabic script ["khatt"] is the one which is now known as Kufic. From it evolved all the present hands." The angular script which later came to be known as Kufic had its origin about a century earlier than the founding of the town of Kufa, according to Moritz in the "Encyclopaedia of Islam". The kufic script was derived from one of the four pre-Islamic Arabic scripts, the one called "al-Hiri" (used in Hirah). (The other three were "al-Anbari" (from Anbar), "al-Makki" (from Mecca) and "al-Madani" (from Medina)). Ibn al-Nadim (died ca. 999) the author of the famous "Kitab al-Fihrist", an index of Arabic books, dedicates the a section of the first chapter to calligraphy. He was the first to use the word 'kufic' to characterize this script, which reached a state of decorative perfection in the 8th century, when surahs were used to decorate ceramics, for representations of nature were strictly forbidden under the Islamic regime. Al-Fihrist contains the biographies of many of the grammarian philologists from the school of Kufa and from its rival school of Basra. A third chapter treats of the grammarians from both schools.


title: Kufa

text: Kufan coins were among the numerous silver coins of various origins found in 1989 by the mouth of Dvina, right next to Arkhangelsk in the extreme north of Russia. The Kufan coins were the only non-European ones in the hoard, and testify to the very wide-ranging indirect trading links which Kufa had at one time. It is estimated the hoard was buried in the beginning of the 12th century, when Kufa was already long past the peak of its fortunes, but the coins might have arrived at the far north at a much earlier time.


title: Kufa

text: Kufa began to come under constant attack in the 11th century and eventually shrank and lost its importance. Over the last century, the population of Kufa began to grow again. It continues to be an important pilgrimage site for Shi'ite Muslims.


title: Kufa

text: The town has produced several Shi'ite Muslim scholars. It also contains buildings of importance to Shi'ites:


title: Shane Watson

text: Shane Robert Watson (born 17 June 1981) is an Australian former cricketer, and occasional captain in all formats, who has played for Australia's national cricket team. He is a right-handed batsman and a right-handed fast-medium swing bowler who played international cricket between 2002 and 2016. He was the world No. 1 T20I all-rounder for 150 weeks, including an all-time record of 120 consecutive weeks (13 Oct 2011 – 30 January 2014). He was the last player to retire from Australia's golden era of the early 2000s.


title: Shane Watson

text: Watson holds several records in T20Is, ODIs and T20s. According to "Forbes", Watson was the highest-paid non-Indian cricketer in the world for five consecutive years between 2011 and 2015.


title: Shane Watson

text: He is considered one of the most influential white ball all-rounders in this era and won the "Player of the Series" or "Most Valuable Player" award in a number of crucial tournaments, including the 2009 Champions Trophy, 2012 World T20, 2008 IPL and 2013 IPL. He is one of the two players to score a century and take a hat-trick in the Indian Premier League along with Rohit Sharma.


title: Shane Watson

text: On 2 November 2020, he announced his retirement from all forms of cricket. Ahead of IPL 2022, Watson joined Delhi Capitals as assistant coach of the franchise.


title: Shane Watson

text: Shane Watson was an AIS Australian Cricket Academy scholarship holder in 2000. He started his first-class cricketing career for Tasmania after leaving his home state of Queensland, but returned to play for his native Queensland as his international career was beginning. He also played for Hampshire in the English County Championship in 2005.


title: Shane Watson

text: Watson was selected for his first Australian team in early 2002, being selected to tour South Africa with the Test team after topping the Pura Cup wicket-taking charts for Tasmania, as well as steady middle-order batting performances. Watson did make his ODI debut on tour, replacing Steve Waugh, who was sacked after the team failed to make the ODI finals in the preceding Australian summer. Watson continued as a regular member of the ODI team until he suffered three stress fractures in his back, at the start of 2003, missing the 2003 Cricket World Cup. He was replaced by his Queensland teammate Andrew Symonds, who proceeded to establish his position as the all rounder after scoring 143* and 91* during the tournament.


title: Shane Watson

text: Watson returned to regular ODI duty in the 2004–05 season, as a bowling all rounder. He also made his test debut in the Third Test against Pakistan as the fifth bowler, to allow Australia to play two spinners and three pace bowlers on a dry Sydney Cricket Ground pitch.


title: Shane Watson

text: Australian selectors included Watson as the fifth bowler and all rounder in all Test matches following the 2005 Ashes series. Watson played against the ICC World XI in the role, but he dislocated his shoulder in just his second Test in that designated role against the West Indies, after diving to field a ball. Watson was again replaced by Symonds and was unable to represent Australia for the remainder of the summer.


title: Shane Watson

text: This changed when Watson opened the batting for Australia at the 2006 ICC Champions Trophy, alongside wicket-keeper Adam Gilchrist, instead of Simon Katich. After failing in the first two matches against the West Indies and England, Watson made a 50 in Australia's victory over India, which sealed their place in the semi-finals, he then took 2 wickets and scored 57 not out in the finals to seal the win. In the 2009 ICC Champions Trophy held in South Africa, Watson again played a prominent role, making two consecutive 100s against England and New Zealand in semi-final and final, helping Australia to defend their title.


title: Shane Watson

text: Watson was named in the squad for the 2006–07 Ashes series against England. However, he came off the ground in a one-day domestic game the week before the first Test with a suspected hamstring tear, which ruled him out for the first three Tests. Michael Clarke was called up in Watson's place, and responded with a half-century, and then a century to cement Clarke's place in the team.


title: Shane Watson

text: Watson was expected to be fit for the fourth Test on Boxing Day and the MCG in Melbourne, and because of Damien Martyn's unexpected retirement, it looked likely that Watson would be included in the side. However, another injury setback in a match for Queensland ruled Watson out for the rest of the Ashes series. Watson eventually returned in February to the ODI side, replacing Cameron White in the all rounder position, However he again broke down with injury during the 29th match of 2007 Cricket World Cup and missed two matches of the Super 8's before returning in fine style scoring an unbeaten 65 off 32 balls against New Zealand. Injury again struck Watson in the early stages of the 2007 ICC World Twenty20 as he missed most of the tournament due to hamstring strain. He was then out of action for the 2007–08 Australian season.


title: Shane Watson

text: After Symonds was omitted from the Australian team for disciplinary reasons, Watson took the all rounder's position for the tour of India in late 2008, batting at No. 6. During the Third Test in Delhi, he was involved in a series of confrontations with Indian opener Gautam Gambhir, who scored a double century and reached his century by lofting Watson over midwicket for six.


title: Shane Watson

text: After returning to Australia, Symonds was recalled to the Test team and both all rounders played in the First Test against New Zealand in Brisbane. As the pitch was a green, rain-affected moist surface expected to favour seamers, spinner Jason Krejza was dropped to accommodate two seam bowling all rounders. After the match, which Australia won, Watson was dropped as spinner Nathan Hauritz was included and Symonds retained. Symonds continued to perform poorly, and there were calls for Watson to take his place, but both men then fell injured at the end of the year, Watson with a stress fracture. Watson returned to international duty in the ODI series against Pakistan in the UAE, scoring a century.


title: Shane Watson

text: He returned to the Australian Test side for the 3rd Ashes Test match at Edgbaston on 30 July 2009 as an opener. In a rain interrupted match he made 62 and 53 batting alongside Simon Katich. He scored his second highest Test score of 96 against the West Indies in the Second Test in Adelaide in December 2009. He and Katich put on a century stand and he had reached 96 at stumps, only to inside edge his first ball of the next morning onto his stumps while attempting to hit a boundary to reach his century. In the Third Test, he made 89 in another century stand with Katich. In the second innings, he removed opposition captain Chris Gayle and then charged towards him, screaming in celebration directly in front of him. This earned him a fine from the match referee, and considerable criticism from much of the Australian public.


title: Shane Watson

text: In the First Test against Pakistan, he made 93 runs on Boxing Day and featured in his third century stand in as many matches with Katich, but was run out after a mix-up with Katich in which both players ended up running towards the same end, again falling short of his debut Test hundred. On Day four, Watson finally made his first Test hundred, which came in interesting style, by hitting the ball hard to the fielder at point who put the catch down. When Ponting declared, he remained not out on 120. Watson was awarded man of the match on 30 December for his role in Australia's Test victory.


title: Shane Watson

text: In the second innings of the Second Test at the SCG, Watson fell short of another century, dismissed for 97. During this Test, the Australian Cricket Media Association presented Watson with Australian Cricketer of the Year Award.


title: Shane Watson

text: In the first test of Australia's 2010 tour of India, Watson opened his account with his second test century – an attritional 126 runs off 338 balls on a slow, low Mohali pitch. The innings capped an excellent start to the tour, as he also scored a century in each innings of the warm-up match, albeit at a much brisker pace. He topscored again in the second innings with a run-a-ball 56, which proved vital in setting a competitive target as Australia's middle order again collapsed in spectacular fashion following his dismissal.


title: Shane Watson

text: During this period as an opener, he had the highest Australian Test batting average (50.40) for 2 calendar years (2009–2010).


title: Shane Watson

text: On 30 March 2011, Watson was named test and ODI vice-captain. On 11 April 2011 he made 185 not out off 96 balls against Bangladesh. Watson made several records in this match, which include most sixes, highest score by an Australian batsman, fastest 150, most runs from boundaries, highest individual score while chasing in an ODI and highest score in the second innings of an ODI match, dethroning MS Dhoni's 183 not out against Sri Lanka in 2005. But his record of highest individual score while chasing in an ODI was broken when Fakhar Zaman scored 193 in a losing cause on 4 April 2021 in the 2nd ODI against South Africa while chasing 342.


title: Shane Watson

text: During 2010–2013, he won a series of Australian "Player of the Year" awards, including Allan Border Medal in 2010 and 2011.


title: Shane Watson

text: Before the start of 2012 ICC World Twenty20, there were no expectations on Australia as it was ranked only 10th in the world. After two stages of the tournament, Australia were placed at sixth, moving up four places and became one of the favourites to win the tournament. This is the only time a team's place in the rankings has changed so drastically in a short time, due to four straight wins against top-ranked teams. Much of this success was due to an in-form Shane Watson.


title: Shane Watson

text: In the first match against Ireland at R.Premadasa Stadium in Colombo, Watson opened the bowling and took 3–26 (the wickets of opener-captain William Porterfield, keeper-batsman Niall O'Brien and all-rounder Kevin O'Brien); he then scored 51 from 30 balls to help his side win the match in 15.1 overs. He was subsequently named as Man of the Match. In the next match against the West Indies he again opened the bowling and batting, taking 2–29 from 4 overs (the wickets of Chris Gayle & Kieron Pollard). He then scored 41 not out from 24 balls to win the Man of the Match award as his side won by 17 runs (by the Duckworth-Lewis method). Against India, he was used as second change bowler and took 3–34. It was he who had changed the game by taking the wickets of Yuvraj Singh and opener Irfan Pathan in the 11th over. He also dismissed Suresh Raina in the last over. He followed it up with 72 from 42 balls (7 sixes and 2 fours) making a mockery of the target 141. Against South Africa he took 2–29 (the wickets of Hashim Amla and AB de Villiers), following it up with 70 from 47 balls to win his fourth consecutive Man of the Match award. At the completion of the group stages and Super Eight stages, Watson had the most runs, wickets and sixes. His dominance with both bat and ball made him the unanimous choice of the experts to be named Player of the Tournament.


title: Shane Watson

text: Before the 3rd Test against India in March 2013, the team management of Michael Clarke, who was also a selector at the time, and coach Mickey Arthur, dropped four players from the 3rd test, which included vice-captain Shane Watson, along with James Pattinson, Mitchell Johnson and Usman Khawaja for failing to make a presentation on team performance. Watson had subsequently flown back to Australia due to the birth of his first child. Michael Clarke and coach Mickey Arthur were severely criticized and ridiculed by the public, media and former players for such a silly decision. Watson returned to the team for the fourth and final test of the series, and captained the test side (due to an injury to Clarke) for the only time in his career. After the tour, Watson resigned as vice-captain, while Cricket Australia sacked Mickey Arthur as coach and stripped Michael Clarke as a selector in the following weeks.


title: Shane Watson

text: Shane Watson was named as one of the members of Australia's 15-man World Cup squad on 11 January 2015. He played in all but one of Australia's World Cup matches, as Australia went on to win the tournament.


title: Shane Watson

text: Watson had a disappointing start to his World Cup campaign, dismissed for a first ball duck in Australia's first match of the tournament against England, and dismissed for 23 against New Zealand in a losing effort. As a result of his poor form, Watson was dropped for Australia's match against Afghanistan, and was replaced by James Faulkner. However, he was reinstated for Australia's next match against Sri Lanka , scoring 67 off 41 balls, and taking 1/71 off 7 overs as Australia prevailed by 64 runs. In Australia's final group stage match, against Scotland, Watson scored 24 runs from 23 balls and took 1/18 off three overs as Australia defeated Scotland by 7 wickets and qualified for the knockout stage.


title: Shane Watson

text: In Australia's quarter final match against Pakistan, Watson was on the receiving end of a memorable fierce bowling spell from Wahab Riaz, a spell which won Riaz plaudits from numerous cricketers past and present


title: Shane Watson

text: , with Michael Clarke referring to Riaz's performance 'as good as I've faced in ODI cricket for a long time' and Kevin Pietersen describing the spell as the "Best spell of bowling by a foreigner on Aussie soil for years". After being dropped by Rahat Ali at square leg at 4 runs, Watson went on to score 64 not out from 66 balls as Australia recorded a 6 wicket victory with 97 balls to spare.


title: Shane Watson

text: Watson played in Australia's 95 run semi-final victory over India, with Watson scoring 28 runs from 30 balls. Watson played in the 2015 Cricket World Cup Final, scoring 2 not out as Australia prevailed over New Zealand by 7 wickets, winning their fifth Cricket World Cup as a result.


title: Shane Watson

text: On 31 January 2016, Watson was named T20I captain and became one of the few Australians to captain in all formats, he opened the innings after a long gap and scored 124*, which made several records, including becoming the first Australian batsman to score a century in all three formats of the game.


title: Shane Watson

text: He retired from international cricket in 2016 and became the last player to retire from Australia's golden era of the early 2000s. He was named Australia's T20 International Player of the Year on 23 January 2017.


title: Shane Watson

text: Watson played for Rajasthan Royals in seven of the first eight seasons of the Indian Premier League, signing for the side for the inaugural IPL season in 2008. He was the Player of the Tournament during the season, but missed the second season whilst on international duty. In 2013 he scored his first Twenty20 century playing against Chennai Super Kings, scoring 101 runs from 61 balls, hitting six fours and six sixes. He again won the Player of the Tournament in 2013. He captained the side in 2014 and was the highest-paid overseas player.


title: Shane Watson

text: After the suspension of Rajasthan for two season, he played for Royal Challengers Bangalore in 2016. He captained the side for some matches during the 2017 season but was signed by Chennai Super Kings for the following season. He scored his third and fourth IPL centuries during the 2018 season, and remained with the side in 2019, losing the 2019 final. He played his final IPL season in 2020 for Chennai.


title: Shane Watson

text: Watson signed with Australian Big Bash League franchise Sydney Thunder in 2015 and was a member of the team that won the BBL that season. He was the captain of the team. He played for the side until the end of the 2018/19 season.


title: Shane Watson

text: In 2016 Watson was announced as one of the icon players for the first season of the Pakistan Super League. He played for Islamabad United initially, moving to Quetta Gladiators in subsequent seasons. The same year he was a marquee player in the Caribbean Premier League, playing in the league for two seasons.


title: Shane Watson

text: Watson is married to broadcaster Lee Furlong. They have two children. In 2017, Watson launched a sports clinic, "Let’s Activate", for children. It teaches the basics of sports skills, using songs, movement, dance and sports activities. Watson has his own podcast called "Lessons Learnt with the Greats".


title: Shane Watson

text: Watson scored 14 centuries in international cricket, four in Test matches, nine in ODIs and one in a Twenty20 International.


title: Parallel ATA

text: Parallel ATA (PATA), originally , also known as IDE, is a standard interface designed for IBM PC-compatible computers. It was first developed by Western Digital and Compaq in 1986 for compatible hard drives and CD or DVD drives. The connection is used for storage devices such as hard disk drives, floppy disk drives, and optical disc drives in computers.


title: Parallel ATA

text: The standard is maintained by the X3/INCITS committee. It uses the underlying (ATA) and Packet Interface (ATAPI) standards.


title: Parallel ATA

text: The Parallel ATA standard is the result of a long history of incremental technical development, which began with the original AT Attachment interface, developed for use in early PC AT equipment. The ATA interface itself evolved in several stages from Western Digital's original Integrated Drive Electronics (IDE) interface. As a result, many near-synonyms for ATA/ATAPI and its previous incarnations are still in common informal use, in particular Extended IDE (EIDE) and Ultra ATA (UATA). After the introduction of SATA in 2003, the original ATA was renamed to Parallel ATA, or PATA for short.


title: Parallel ATA

text: Parallel ATA cables have a maximum allowable length of . Because of this limit, the technology normally appears as an internal computer storage interface. For many years, ATA provided the most common and the least expensive interface for this application. It has largely been replaced by SATA in newer systems.


title: Parallel ATA

text: The standard was originally conceived as the "AT Bus Attachment," officially called "AT Attachment" and abbreviated "ATA" because its primary feature was a direct connection to the 16-bit ISA bus introduced with the IBM PC/AT. The original ATA specifications published by the standards committees use the name "AT Attachment". The "AT" in the IBM PC/AT referred to "Advanced Technology" so ATA has also been referred to as "Advanced Technology Attachment". When a newer Serial ATA (SATA) was introduced in 2003, the original ATA was renamed to Parallel ATA, or PATA for short.


title: Parallel ATA

text: Physical ATA interfaces became a standard component in all PCs, initially on host bus adapters, sometimes on a sound card but ultimately as two physical interfaces embedded in a Southbridge chip on a motherboard. Called the "primary" and "secondary" ATA interfaces, they were assigned to base addresses 0x1F0 and 0x170 on ISA bus systems. They were replaced by SATA interfaces.


title: Parallel ATA

text: The first version of what is now called the ATA/ATAPI interface was developed by Western Digital under the name "Integrated Drive Electronics" (IDE). Together with Control Data Corporation (the hard drive manufacturer) and Compaq Computer (the initial customer), they developed the connector, the signaling protocols and so on, with the goal of remaining software compatible with the existing ST-506 hard drive interface. The first such drives appeared internally in Compaq PCs in 1986. and were first separately offered by Conner Peripherals as the CP342 in June 1987.


title: Parallel ATA

text: The term "Integrated Drive Electronics" refers to the fact that the drive controller is integrated into the drive, as opposed to a separate controller situated at the other side of the connection cable to the drive. On an IBM PC compatible, CP/M machine, or similar, this was typically a card installed on a motherboard. The interface cards used to connect a parallel ATA drive to, for example, an ISA Slot, are not drive controllers: they are merely bridges between the host bus and the ATA interface. Since the original ATA interface is essentially just a 16-bit ISA bus in disguise, the bridge was especially simple in case of an ATA connector being located on an ISA interface card. The integrated controller presented the drive to the host computer as an array of 512-byte blocks with a relatively simple command interface. This relieved the mainboard and interface cards in the host computer of the chores of stepping the disk head arm, moving the head arm in and out, and so on, as had to be done with earlier ST-506 and ESDI hard drives. All of these low-level details of the mechanical operation of the drive were now handled by the controller on the drive itself. This also eliminated the need to design a single controller that could handle many different types of drives, since the controller could be unique for the drive. The host need only to ask for a particular sector, or block, to be read or written, and either accept the data from the drive or send the data to it.


title: Parallel ATA

text: The interface used by these drives was standardized in 1994 as ANSI standard X3.221-1994, "AT Attachment Interface for Disk Drives". After later versions of the standard were developed, this became known as "ATA-1".


title: Parallel ATA

text: A short-lived, seldom-used implementation of ATA was created for the IBM XT and similar machines that used the 8-bit version of the ISA bus. It has been referred to as "XT-IDE", "XTA" or "XT Attachment".


title: Parallel ATA

text: In 1994, about the same time that the ATA-1 standard was adopted, Western Digital introduced drives under a newer name, Enhanced IDE (EIDE). These included most of the features of the forthcoming ATA-2 specification and several additional enhancements. Other manufacturers introduced their own variations of ATA-1 such as "Fast ATA" and "Fast ATA-2".


title: Parallel ATA

text: The new version of the ANSI standard, "AT Attachment Interface with Extensions ATA-2" (X3.279-1996), was approved in 1996. It included most of the features of the manufacturer-specific variants.


title: Parallel ATA

text: ATA-2 also was the first to note that devices other than hard drives could be attached to the interface:


title: Parallel ATA

text: As mentioned in the previous sections, ATA was originally designed for, and worked only with hard disk drives and devices that could emulate them. The introduction of ATAPI (ATA Packet Interface) by a group called the Small Form Factor committee (SFF) allowed ATA to be used for a variety of other devices that require functions beyond those necessary for hard disk drives. For example, any removable media device needs a "media eject" command, and a way for the host to determine whether the media is present, and these were not provided in the ATA protocol.


title: Parallel ATA

text: The Small Form Factor committee approached this problem by defining ATAPI, the "ATA Packet Interface". ATAPI is actually a protocol allowing the ATA interface to carry SCSI commands and responses; therefore, all ATAPI devices are actually "speaking SCSI" other than at the electrical interface. In fact, some early ATAPI devices were simply SCSI devices with an ATA/ATAPI to SCSI protocol converter added on. The SCSI commands and responses are embedded in "packets" (hence "ATA Packet Interface") for transmission on the ATA cable. This allows any device class for which a SCSI command set has been defined to be interfaced via ATA/ATAPI.


title: Parallel ATA

text: ATAPI devices are also "speaking ATA", as the ATA physical interface and protocol are still being used to send the packets. On the other hand, ATA hard drives and solid state drives do not use ATAPI.


title: Parallel ATA

text: ATAPI devices include CD-ROM and DVD-ROM drives, tape drives, and large-capacity floppy drives such as the Zip drive and SuperDisk drive.


title: Parallel ATA

text: The SCSI commands and responses used by each class of ATAPI device (CD-ROM, tape, etc.) are described in other documents or specifications specific to those device classes and are not within ATA/ATAPI or the T13 committee's purview. One commonly used set is defined in the MMC SCSI command set.


title: Parallel ATA

text: ATAPI was adopted as part of ATA in INCITS 317-1998, "AT Attachment with Packet Interface Extension (ATA/ATAPI-4)".


title: Parallel ATA

text: The ATA/ATAPI-4 standard also introduced several "Ultra DMA" transfer modes. These initially supported speeds from 16 MByte/s to 33 MByte/second. In later versions, faster Ultra DMA modes were added, requiring new 80-wire cables to reduce crosstalk. The latest versions of Parallel ATA support up to 133 MByte/s.


title: Parallel ATA

text: Ultra ATA, abbreviated UATA, is a designation that has been primarily used by Western Digital for different speed enhancements to the ATA/ATAPI standards. For example, in 2000 Western Digital published a document describing "Ultra ATA/100", which brought performance improvements for the then-current ATA/ATAPI-5 standard by improving maximum speed of the Parallel ATA interface from 66 to 100 MB/s. Most of Western Digital's changes, along with others, were included in the ATA/ATAPI-6 standard (2002).


title: Parallel ATA

text: The terms "integrated drive electronics" (IDE), "enhanced IDE" and "EIDE" have come to be used interchangeably with ATA (now Parallel ATA, or PATA).


title: Parallel ATA

text: In addition, there have been several generations of "EIDE" drives marketed, compliant with various versions of the ATA specification. An early "EIDE" drive might be compatible with ATA-2, while a later one with ATA-6.


title: Parallel ATA

text: Nevertheless, a request for an "IDE" or "EIDE" drive from a computer parts vendor will almost always yield a drive that will work with most Parallel ATA interfaces.


title: Parallel ATA

text: Another common usage is to refer to the specification version by the fastest mode supported. For example, ATA-4 supported Ultra DMA modes 0 through 2, the latter providing a maximum transfer rate of 33 megabytes per second. ATA-4 drives are thus sometimes called "UDMA-33" drives, and sometimes "ATA-33" drives. Similarly, ATA-6 introduced a maximum transfer speed of 100 megabytes per second, and some drives complying with this version of the standard are marketed as "PATA/100" drives.


title: Parallel ATA

text: Initially, the size of an ATA drive was stored in the system x86 BIOS using a type number (1 through 45) that predefined the C/H/S parameters and also often the landing zone, in which the drive heads are parked while not in use. Later, a "user definable" format called C/H/S or cylinders, heads, sectors was made available. These numbers were important for the earlier ST-506 interface, but were generally meaningless for ATA—the CHS parameters for later ATA large drives often specified impossibly high numbers of heads or sectors that did not actually define the internal physical layout of the drive at all. From the start, and up to ATA-2, every user had to specify explicitly how large every attached drive was. From ATA-2 on, an "identify drive" command was implemented that can be sent and which will return all drive parameters.


title: Parallel ATA

text: Owing to a lack of foresight by motherboard manufacturers, the system BIOS was often hobbled by artificial C/H/S size limitations due to the manufacturer assuming certain values would never exceed a particular numerical maximum.


title: Parallel ATA

text: The first of these BIOS limits occurred when ATA drives reached sizes in excess of 504 MiB, because some motherboard BIOSes would not allow C/H/S values above 1024 cylinders, 16 heads, and 63 sectors. Multiplied by 512 bytes per sector, this totals bytes which, divided by bytes per MiB, equals 504 MiB (528 MB).


title: Parallel ATA

text: The second of these BIOS limitations occurred at 1024 cylinders, 256 heads, and 63 sectors, and a problem in MS-DOS limited the number of heads to 255. This totals to bytes (8032.5 MiB), commonly referred to as the 8.4 gigabyte barrier. This is again a limit imposed by x86 BIOSes, and not a limit imposed by the ATA interface.


title: Parallel ATA

text: It was eventually determined that these size limitations could be overridden with a small program loaded at startup from a hard drive's boot sector. Some hard drive manufacturers, such as Western Digital, started including these override utilities with large hard drives to help overcome these problems. However, if the computer was booted in some other manner without loading the special utility, the invalid BIOS settings would be used and the drive could either be inaccessible or appear to the operating system to be damaged.


title: Parallel ATA

text: Later, an extension to the x86 BIOS disk services called the "Enhanced Disk Drive" (EDD) was made available, which makes it possible to address drives as large as 2 sectors.


title: Parallel ATA

text: The first drive interface used 22-bit addressing mode which resulted in a maximum drive capacity of two gigabytes. Later, the first formalized ATA specification used a 28-bit addressing mode through LBA28, allowing for the addressing of 2 () sectors (blocks) of 512 bytes each, resulting in a maximum capacity of 128 GiB (137 GB).


title: Parallel ATA

text: ATA-6 introduced 48-bit addressing, increasing the limit to 128 PiB (144 PB). As a consequence, any ATA drive of capacity larger than about 137 GB must be an ATA-6 or later drive. Connecting such a drive to a host with an ATA-5 or earlier interface will limit the usable capacity to the maximum of the interface.


title: Parallel ATA

text: Some operating systems, including Windows XP pre-SP1, and Windows 2000 pre-SP3, disable LBA48 by default, requiring the user to take extra steps to use the entire capacity of an ATA drive larger than about 137 gigabytes.


title: Parallel ATA

text: Older operating systems, such as Windows 98, do not support 48-bit LBA at all. However, members of the third-party group MSFN have modified the Windows 98 disk drivers to add unofficial support for 48-bit LBA to Windows 95 OSR2, Windows 98, Windows 98 SE and Windows ME.


title: Parallel ATA

text: Some 16-bit and 32-bit operating systems supporting LBA48 may still not support disks larger than 2 TiB due to using 32-bit arithmetic only; a limitation also applying to many boot sectors.


title: Parallel ATA

text: Parallel ATA (then simply called ATA or IDE) became the primary storage device interface for PCs soon after its introduction. In some systems, a third and fourth motherboard interface was provided, allowing up to eight ATA devices to be attached to the motherboard. Often, these additional connectors were implemented by inexpensive RAID controllers.


title: Parallel ATA

text: Soon after the introduction of Serial ATA (SATA) in 2003, use of Parallel ATA declined. The first motherboards with built-in SATA interfaces usually had only a single PATA connector (for up to two PATA devices), along with multiple SATA connectors. Some PCs and laptops of the era have a SATA hard disk and an optical drive connected to PATA.


title: Parallel ATA

text: As of 2007, some PC chipsets, for example the Intel ICH10, had removed support for PATA. Motherboard vendors still wishing to offer Parallel ATA with those chipsets must include an additional interface chip. In more recent computers, the Parallel ATA interface is rarely used even if present, as four or more Serial ATA connectors are usually provided on the motherboard and SATA devices of all types are common.


title: Parallel ATA

text: With Western Digital's withdrawal from the PATA market, hard disk drives with the PATA interface were no longer in production after December 2013 for other than specialty applications.


title: Parallel ATA

text: Parallel ATA cables transfer data 16 bits at a time. The traditional cable uses 40-pin female connectors attached to a 40- or 80-conductor ribbon cable. Each cable has two or three connectors, one of which plugs into a host adapter interfacing with the rest of the computer system. The remaining connector(s) plug into storage devices, most commonly hard disk drives or optical drives. Each connector has 39 physical pins arranged into two rows, with a gap or key at pin 20.


title: Parallel ATA

text: Round parallel ATA cables (as opposed to ribbon cables) were eventually made available for 'case modders' for cosmetic reasons, as well as claims of improved computer cooling and were easier to handle; however, only ribbon cables are supported by the ATA specifications.


title: Parallel ATA

text: In the ATA standard, pin 20 is defined as a mechanical key and is not used. This pin's socket on the female connector is often obstructed, requiring pin 20 to be omitted from the male cable or drive connector; it is thus impossible to plug it in the wrong way round.


title: Parallel ATA

text: However, some flash memory drives can use pin 20 as VCC_in to power the drive without requiring a special power cable; this feature can only be used if the equipment supports this use of pin 20.


title: Parallel ATA

text: Pin 28 of the gray (slave/middle) connector of an 80-conductor cable is not attached to any conductor of the cable. It is attached normally on the black (master drive end) and blue (motherboard end) connectors. This enables cable select functionality.


title: Parallel ATA

text: Pin 34 is connected to ground inside the blue connector of an 80-conductor cable but not attached to any conductor of the cable, allowing for detection of such a cable. It is attached normally on the gray and black connectors.


title: Parallel ATA

text: A 44-pin variant PATA connector is used for 2.5 inch drives inside laptops. The pins are closer together and the connector is physically smaller than the 40-pin connector. The extra pins carry power.


title: Parallel ATA

text: ATA's cables have had 40 conductors for most of its history (44 conductors for the smaller form-factor version used for 2.5" drives—the extra four for power), but an 80-conductor version appeared with the introduction of the "UDMA/66" mode. All of the additional conductors in the new cable are grounds, interleaved with the signal conductors to reduce the effects of capacitive coupling between neighboring signal conductors, reducing crosstalk. Capacitive coupling is more of a problem at higher transfer rates, and this change was necessary to enable the 66 megabytes per second (MB/s) transfer rate of "UDMA4" to work reliably. The faster "UDMA5" and "UDMA6" modes also require 80-conductor cables.


title: Parallel ATA

text: Though the number of conductors doubled, the number of connector pins and the pinout remain the same as 40-conductor cables, and the external appearance of the connectors is identical. Internally, the connectors are different; the connectors for the 80-conductor cable connect a larger number of ground conductors to the ground pins, while the connectors for the 40-conductor cable connect ground conductors to ground pins one-to-one. 80-conductor cables usually come with three differently colored connectors (blue, black, and gray for controller, master drive, and slave drive respectively) as opposed to uniformly colored 40-conductor cable's connectors (commonly all gray). The gray connector on 80-conductor cables has pin 28 CSEL not connected, making it the slave position for drives configured cable select.


title: Parallel ATA

text: The image on the right shows PATA connectors after removal of strain relief, cover, and cable. Pin one is at bottom left of the connectors, pin 2 is top left, etc., except that the lower image of the blue connector shows the view from the opposite side, and pin one is at top right.


title: Parallel ATA

text: The connector is an insulation-displacement connector: each contact comprises a pair of points which together pierce the insulation of the ribbon cable with such precision that they make a connection to the desired conductor without harming the insulation on the neighboring conductors. The center row of contacts are all connected to the common ground bus and attach to the odd numbered conductors of the cable. The top row of contacts are the even-numbered sockets of the connector (mating with the even-numbered pins of the receptacle) and attach to every other even-numbered conductor of the cable. The bottom row of contacts are the odd-numbered sockets of the connector (mating with the odd-numbered pins of the receptacle) and attach to the remaining even-numbered conductors of the cable.


title: Parallel ATA

text: Note the connections to the common ground bus from sockets 2 (top left), 19 (center bottom row), 22, 24, 26, 30, and 40 on all connectors. Also note (enlarged detail, bottom, looking from the opposite side of the connector) that socket 34 of the blue connector does not contact any conductor but unlike socket 34 of the other two connectors, it does connect to the common ground bus. On the gray connector, note that socket 28 is completely missing, so that pin 28 of the drive attached to the gray connector will be open. On the black connector, sockets 28 and 34 are completely normal, so that pins 28 and 34 of the drive attached to the black connector will be connected to the cable. Pin 28 of the black drive reaches pin 28 of the host receptacle but not pin 28 of the gray drive, while pin 34 of the black drive reaches pin 34 of the gray drive but not pin 34 of the host. Instead, pin 34 of the host is grounded.


title: Parallel ATA

text: The standard dictates color-coded connectors for easy identification by both installer and cable maker. All three connectors are different from one another. The blue (host) connector has the socket for pin 34 connected to ground inside the connector but not attached to any conductor of the cable. Since the old 40 conductor cables do not ground pin 34, the presence of a ground connection indicates that an 80 conductor cable is installed. The conductor for pin 34 is attached normally on the other types and is not grounded. Installing the cable backwards (with the black connector on the system board, the blue connector on the remote device and the gray connector on the center device) will ground pin 34 of the remote device and connect host pin 34 through to pin 34 of the center device. The gray center connector omits the connection to pin 28 but connects pin 34 normally, while the black end connector connects both pins 28 and 34 normally.


title: Parallel ATA

text: If two devices are attached to a single cable, one must be designated as "Device 0" (in the past, commonly designated "master") and the other as "Device 1" (in the past, commonly designated as "slave"). This distinction is necessary to allow both drives to share the cable without conflict. The "Device 0" drive is the drive that usually appears "first" to the computer's BIOS and/or operating system. In most personal computers the drives are often designated as "C:" for the "Device 0" and "D:" for the "Device 1" referring to one active primary partitions on each.


title: Parallel ATA

text: The terms "device" and "drive" are used interchangeably in the industry, as in "master drive" or "master device."


title: Parallel ATA

text: The mode that a device must use is often set by a jumper setting on the device itself, which must be manually set to "Device 0" ("Master") or "Device 1" ("Slave"). If there is a single device on a cable, it should be configured as "Device 0". However, some certain era drives have a special setting called "Single" for this configuration (Western Digital, in particular). Also, depending on the hardware and software available, a "Single" drive on a cable will often work reliably even though configured as the "Device 1" drive (most often seen where an optical drive is the only device on the secondary ATA interface).


title: Parallel ATA

text: The words "primary" and "secondary" typically refers to the two IDE cables, which can have two drives each (primary master, primary slave, secondary master, secondary slave).


title: Parallel ATA

text: A drive mode called "cable select" was described as optional in ATA-1 and has come into fairly widespread use with ATA-5 and later. A drive set to "cable select" automatically configures itself as "Device 0" or "Device 1", according to its position on the cable. Cable select is controlled by pin 28. The host adapter grounds this pin; if a device sees that the pin is grounded, it becomes the "Device 0" (master) device; if it sees that pin 28 is open, the device becomes the "Device 1" (slave) device.


title: Parallel ATA

text: This setting is usually chosen by a jumper setting on the drive called "cable select", usually marked "CS", which is separate from the "Device 0/1" setting.


title: Parallel ATA

text: Note that if two drives are configured as "Device 0" and "Device 1" manually, this configuration does not need to correspond to their position on the cable. Pin 28 is only used to let the drives know their position on the cable; it is not used by the host when communicating with the drives. In other words, the manual master/slave setting using jumpers on the drives takes precedence and allows them to be freely placed on either connector of the ribbon cable.


title: Parallel ATA

text: With the 40-conductor cable, it was very common to implement cable select by simply cutting the pin 28 wire between the two device connectors; putting the slave "Device 1" device at the end of the cable, and the master "Device 0" on the middle connector. This arrangement eventually was standardized in later versions. However, it had one drawback: if there is just one master device on a 2-drive cable, using the middle connector, this results in an unused stub of cable, which is undesirable for physical convenience and electrical reasons. The stub causes signal reflections, particularly at higher transfer rates.


title: Parallel ATA

text: Starting with the 80-conductor cable defined for use in ATAPI5/UDMA4, the master "Device 0" device goes at the far-from-the-host end of the cable on the black connector, the slave "Device 1" goes on the grey middle connector, and the blue connector goes to the host (e.g. motherboard IDE connector, or IDE card). So, if there is only one ("Device 0") device on a two-drive cable, using the black connector, there is no cable stub to cause reflections (the unused connector is now in the middle of the ribbon). Also, cable select is now implemented in the grey middle device connector, usually simply by omitting the pin 28 contact from the connector body.


title: Parallel ATA

text: The parallel ATA protocols up through ATA-3 require that once a command has been given on an ATA interface, it must complete before any subsequent command may be given. Operations on the devices must be serializedwith only one operation in progress at a timewith respect to the ATA host interface. A useful mental model is that the host ATA interface is busy with the first request for its entire duration, and therefore can not be told about another request until the first one is complete. The function of serializing requests to the interface is usually performed by a device driver in the host operating system.


title: Parallel ATA

text: The ATA-4 and subsequent versions of the specification have included an "overlapped feature set" and a "queued feature set" as optional features, both being given the name "Tagged Command Queuing" (TCQ), a reference to a set of features from SCSI which the ATA version attempts to emulate. However, support for these is extremely rare in actual parallel ATA products and device drivers because these feature sets were implemented in such a way as to maintain software compatibility with its heritage as originally an extension of the ISA bus. This implementation resulted in excessive CPU utilization which largely negated the advantages of command queuing. By contrast, overlapped and queued operations have been common in other storage buses; in particular, SCSI's version of tagged command queuing had no need to be compatible with APIs designed for ISA, allowing it to attain high performance with low overhead on buses which supported first party DMA like PCI. This has long been seen as a major advantage of SCSI.


title: Parallel ATA

text: The Serial ATA standard has supported native command queueing (NCQ) since its first release, but it is an optional feature for both host adapters and target devices. Many obsolete PC motherboards do not support NCQ, but modern SATA hard disk drives and SATA solid-state drives usually support NCQ, which is not the case for removable (CD/DVD) drives because the ATAPI command set used to control them prohibits queued operations.


title: Parallel ATA

text: There are many debates about how much a slow device can impact the performance of a faster device on the same cable. There is an effect, but the debate is confused by the blurring of two quite different causes, called here "Lowest speed" and "One operation at a time".


title: Parallel ATA

text: On early ATA host adapters, both devices' data transfers can be constrained to the speed of the slower device, if two devices of different speed capabilities are on the same cable.


title: Parallel ATA

text: For all modern ATA host adapters, this is not true, as modern ATA host adapters support "independent device timing". This allows each device on the cable to transfer data at its own best speed. Even with earlier adapters without independent timing, this effect applies only to the data transfer phase of a read or write operation.


title: Parallel ATA

text: This is caused by the omission of both overlapped and queued feature sets from most parallel ATA products. Only one device on a cable can perform a read or write operation at one time; therefore, a fast device on the same cable as a slow device under heavy use will find it has to wait for the slow device to complete its task first.


title: Parallel ATA

text: However, most modern devices will report write operations as complete once the data is stored in their onboard cache memory, before the data is written to the (slow) magnetic storage. This allows commands to be sent to the other device on the cable, reducing the impact of the "one operation at a time" limit.


title: Parallel ATA

text: The impact of this on a system's performance depends on the application. For example, when copying data from an optical drive to a hard drive (such as during software installation), this effect probably will not matter. Such jobs are necessarily limited by the speed of the optical drive no matter where it is. But if the hard drive in question is also expected to provide good throughput for other tasks at the same time, it probably should not be on the same cable as the optical drive.


title: Parallel ATA

text: ATA devices may support an optional security feature which is defined in an ATA specification, and thus not specific to any brand or device. The security feature can be enabled and disabled by sending special ATA commands to the drive. If a device is locked, it will refuse all access until it is unlocked.


title: Parallel ATA

text: A device can have two passwords: A User Password and a Master Password; either or both may be set. There is a Master Password identifier feature which, if supported and used, can identify the current Master Password (without disclosing it).


title: Parallel ATA

text: A device can be locked in two modes: High security mode or Maximum security mode. Bit 8 in word 128 of the IDENTIFY response shows which mode the disk is in: 0 = High, 1 = Maximum.


title: Parallel ATA

text: In High security mode, the device can be unlocked with either the User or Master password, using the "SECURITY UNLOCK DEVICE" ATA command. There is an attempt limit, normally set to 5, after which the disk must be power cycled or hard-reset before unlocking can be attempted again. Also in High security mode, the SECURITY ERASE UNIT command can be used with either the User or Master password.


title: Parallel ATA

text: In Maximum security mode, the device can be unlocked only with the User password. If the User password is not available, the only remaining way to get at least the bare hardware back to a usable state is to issue the SECURITY ERASE PREPARE command, immediately followed by SECURITY ERASE UNIT. In Maximum security mode, the SECURITY ERASE UNIT command requires the Master password and will completely erase all data on the disk. Word 89 in the IDENTIFY response indicates how long the operation will take.


title: Parallel ATA

text: While the ATA lock is intended to be impossible to defeat without a valid password, there are purported workarounds to unlock a device.


title: Parallel ATA

text: Due to a short cable length specification and shielding issues it is extremely uncommon to find external PATA devices that directly use PATA for connection to a computer. A device connected externally needs additional cable length to form a U-shaped bend so that the external device may be placed alongside, or on top of the computer case, and the standard cable length is too short to permit this. For ease of reach from motherboard to device, the connectors tend to be positioned towards the front edge of motherboards, for connection to devices protruding from the front of the computer case. This front-edge position makes extension out the back to an external device even more difficult. Ribbon cables are poorly shielded, and the standard relies upon the cabling to be installed inside a shielded computer case to meet RF emissions limits.


title: Parallel ATA

text: External hard disk drives or optical disk drives that have an internal PATA interface, use some other interface technology to bridge the distance between the external device and the computer. USB is the most common external interface, followed by Firewire. A bridge chip inside the external devices converts from the USB interface to PATA, and typically only supports a single external device without cable select or master/slave.


title: Parallel ATA

text: Compact Flash in its "IDE mode" is essentially a miniaturized ATA interface, intended for use on devices that use flash memory storage. No interfacing chips or circuitry are required, other than to directly adapt the smaller CF socket onto the larger ATA connector. (Although most CF cards only support IDE mode up to PIO4, making them much slower in IDE mode than their CF capable speed)


title: Parallel ATA

text: The ATA connector specification does not include pins for supplying power to a CF device, so power is inserted into the connector from a separate source. The exception to this is when the CF device is connected to a 44-pin ATA bus designed for 2.5-inch hard disk drives, commonly found in notebook computers, as this bus implementation must provide power to a standard hard disk drive.


title: Parallel ATA

text: CF devices can be designated as devices 0 or 1 on an ATA interface, though since most CF devices offer only a single socket, it is not necessary to offer this selection to end users. Although CF can be hot-pluggable with additional design methods, by default when wired directly to an ATA interface, it is not intended to be hot-pluggable.


title: Parallel ATA

text: The following table shows the names of the versions of the ATA standards and the transfer modes and rates supported by each. Note that the transfer rate for each mode (for example, 66.7 MB/s for UDMA4, commonly called "Ultra-DMA 66", defined by ATA-5) gives its maximum theoretical transfer rate on the cable. This is simply two bytes multiplied by the effective clock rate, and presumes that every clock cycle is used to transfer end-user data. In practice, of course, protocol overhead reduces this value.


title: Parallel ATA

text: Congestion on the host bus to which the ATA adapter is attached may also limit the maximum burst transfer rate. For example, the maximum data transfer rate for conventional PCI bus is 133 MB/s, and this is shared among all active devices on the bus.


title: Parallel ATA

text: In addition, no ATA hard drives existed in 2005 that were capable of measured sustained transfer rates of above 80 MB/s. Furthermore, sustained transfer rate tests do not give realistic throughput expectations for most workloads: They use I/O loads specifically designed to encounter almost no delays from seek time or rotational latency. Hard drive performance under most workloads is limited first and second by those two factors; the transfer rate on the bus is a distant third in importance. Therefore, transfer speed limits above 66 MB/s really affect performance only when the hard drive can satisfy all I/O requests by reading from its internal cache—a very unusual situation, especially considering that such data is usually already buffered by the operating system.


title: Parallel ATA

text: , mechanical hard disk drives can transfer data at up to 524 MB/s, which is far beyond the capabilities of the PATA/133 specification. High-performance solid state drives can transfer data at up to 7000–7500 MB/s.


title: Parallel ATA

text: Only the Ultra DMA modes use CRC to detect errors in data transfer between the controller and drive. This is a 16-bit CRC, and it is used for data blocks only. Transmission of command and status blocks do not use the fast signaling methods that would necessitate CRC. For comparison, in Serial ATA, 32-bit CRC is used for both commands and data.


title: Parallel ATA

text: ATAPI devices with removable media, other than CD and DVD drives, are classified as ARMD (ATAPI Removable Media Device) and can appear as either a super-floppy (non-partitioned media) or a hard drive (partitioned media) to the operating system. These can be supported as bootable devices by a BIOS complying with the ATAPI Removable Media Device BIOS Specification, originally developed by Compaq Computer Corporation and Phoenix Technologies. It specifies provisions in the BIOS of a personal computer to allow the computer to be bootstrapped from devices such as Zip drives, Jaz drives, SuperDisk (LS-120) drives, and similar devices.