Later research dealt also with numberings of other classes like classes of recursively enumerable sets. Goncharov discovered for example a class of recursively enumerable sets for which the numberings fall into exactly two classes with respect to recursive isomorphisms.
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In computability theory a numbering is the assignment of natural numbers to a set of objects such as functions, rational numbers, graphs, or words in some language. A numbering can be used to transfer the idea of computability and related concepts, which are originally defined on the natural numbers using computable functions, to these different types of objects. Common examples of numberings include Gödel numberings in first-order logic and admissible numberings of the set of partial computable functions.
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As of April 2013, the Korean, Japanese, Taiwanese, Southeast Asian and North American regional servers have upgraded to the new "Return to Orpesia" series. However, the Korean servers reverted to the original version numberings on January 9, 2013, reason being that the new "B" version series caused confusion. Thus, IMC decided to revert to the original numberings which is still used by its internal development team. Subsequent patches to other regional servers also followed suit.
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Using an encoding such as Gödel numberings, any string can be encoded as a natural number, via which a decision problem can be defined as a subset of the natural numbers.
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Note: Different sources give different numberings for the rounds of the competition. Some record five rounds prior to the quarter-finals; others note a qualifying round followed by four full rounds.
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Because polyhedral face numberings of this type are used as "spindown life counters" in the game Magic: The Gathering, name the canonical polyhedron realization of this dual polyhedron as "the Lich's nemesis".
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A numbering is an enumeration of functions; it has two parameters, e and x and outputs the value of the e-th function in the numbering on the input x. Numberings can be partial-recursive although some of its members are total recursive, that is, computable functions. Admissible numberings are those into which all others can be translated. A Friedberg numbering (named after its discoverer) is a one-one numbering of all partial-recursive functions; it is necessarily not an admissible numbering.
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Psalm 7 from a medieval French manuscript. Psalm 7 is the 7th psalm from the Book of Psalms. Its authorship is traditionally assigned to King David. The Greek and Masoretic numberings are the same for this psalm.
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Note: Different sources give different numberings for the rounds of the competition. Some record five rounds prior to the quarter-finals; others note a preliminary round followed by four full rounds. The first of these notations is used in this article.
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III, c.38. In the original 1922 road numberings, A491 was assigned to the Shrewsbury, Welshpool, Mallwyd and Cemmaes Road route, now part of the A458 and A470. The route between Wall Heath and Bromsgrove was assigned the A449 number.
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Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage. The former numbering scheme is used in this article.
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Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage. The former numbering scheme is used in this article.
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Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage. The former numbering scheme is used in this article.
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In September 2004, the 4th Ring Road underwent a massive sign change. Exit numberings were unified at last—bidirectionally (this was previously not the case). A new overpass in the northern stretch was put into operation in October 2004, near the Beichen area.
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Neon is a chemical element with the symbol Ne and atomic number 10. It is a noble gas.Group 18 refers to the modern numbering of the periodic table. Older numberings described the rare gases as Group 0 or Group VIIIA (sometimes shortened to 8).
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The S&DR; George England 2-4-0 were steam locomotives of 2-4-0 wheel arrangement built by George England for the Somerset and Dorset Railway (S&DR;) and its predecessor, the Somerset Central Railway (SCR). There were frequent re-numberings, which explains the presence of two number 11s.
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The numberings following no. 54 were added by several other people at a later time (19th century), in sequences that do not coincide perfectly. The collection was acquired by Henry Aldrich and donated to Christ Church, Oxford as part of his bequest to the college following his death in 1710.
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Note: Different sources give different numberings for the rounds of the competition. Some record five rounds prior to the quarter-finals; others note a preliminary round followed by four full rounds. The former system is used in this article. Tied matches were decided by golden goal extra time and penalty shoot-outs.
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The Schenker edition gives three different bar numberings for this variation, two of which imply the omission of some of the bars. Neither preface identifies the sources leading to these numberings.Heinrich Schenker (ed.) translated with new preface by Carl Schachter (1975): Ludwig van Beethoven: Complete Piano Sonatas, vol. 2, Dover Publications Inc.
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In computability theory, a Friedberg numbering is a numbering (enumeration) of the set of all uniformly recursively enumerable sets that has no repetitions: each recursively enumerable set appears exactly once in the enumeration (Vereščagin and Shen 2003:30). The existence of such numberings was established by Richard M. Friedberg in 1958 (Cutland 1980:78).
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Undefined forms appearing in works such as MMC-081 have also been interpreted as organic overgrowth or vines. Il Lee attaches no descriptive titles to his artwork. Instead, the artist uses his own system of letters and numbers to catalogue his work. Successive numberings such as SBK-089, SBK-0810, and SBK-0811 infer a sequence of related output.
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Because complex priority arguments can be technical and difficult to follow, it has traditionally been considered desirable to prove results without priority arguments, or to see if results proved with priority arguments can also be proved without them. For example, Kummer published a paper on a proof for the existence of Friedberg numberings without using the priority method.
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In the National League's inaugural season, Blockhouse Bay became the first team to win the league and cup double. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage. The former numbering scheme is used in this article.
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By using Gödel numberings, the primitive recursive functions can be extended to operate on other objects such as integers and rational numbers. If integers are encoded by Gödel numbers in a standard way, the arithmetic operations including addition, subtraction, and multiplication are all primitive recursive. Similarly, if the rationals are represented by Gödel numbers then the field operations are all primitive recursive.
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The 2006 Chatham Cup was the 79th annual nationwide knockout football competition in New Zealand. Up to the last 16 of the competition, the cup was run in three regions (northern, central, and southern), with an open draw from the quarter-finals on. In all, 137 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition.
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The 2007 Chatham Cup was the 80th annual nationwide knockout football competition in New Zealand. Up to the last 16 of the competition, the cup was run in three regions (northern, central, and southern), with an open draw from the quarter-finals on. In all, 123 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition.
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The 1999 Chatham Cup was the 72nd annual nationwide knockout football competition in New Zealand. Up to the last 16 of the competition, the cup was run in three regions (northern, central, and southern), with an open draw from the quarter-finals on. In all, 132 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition.
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Issues 9 through 12 were 128 pages, and the remaining issues were 112 pages. The issues were numbered consecutively throughout; the first eight issues were given volume numberings as well, with two volumes of four numbers each. Issues 30 through 39 of Nebula were distributed in the US; they were stamped at 35 cents and post-dated four months, thus the American copies ran from September 1958 to June 1959.
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In 1929, the Ambassador Bridge opened, offering the first direct and permanent link to Detroit. This caused a cascade of route re-numberings in the Windsor and Maidstone areas. Highway 2 was rerouted along North Talbot Road, and diverted onto the newly built Provincial Road, leading northwest to Howard Avenue. At Howard, the road turned west along Tecumseh Road to Ouellette Avenue, turning north and terminating at the ferry docks.
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The 1968 Chatham Cup was the 41st annual nationwide knockout football competition in New Zealand. Early stages of the competition were run on a regional basis. In all, 93 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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The 1969 Chatham Cup was the 42nd annual nationwide knockout football competition in New Zealand. Early stages of the competition were run on a regional basis. In all, 89 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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Note: Different sources give different numberings for the rounds of the competition. Some record six rounds prior to the quarter-finals; others note a preliminary round followed by five rounds proper. In an early round of the competition, Norwest United were thrashed 21-0 by Metro - a competition record which still stands. It was equalled in 2005, when Central United scored 21 - again against the unfortunate Norwest United.
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The rooted product is especially relevant for trees, as the rooted product of two trees is another tree. For instance, Koh et al. (1980) used rooted products to find graceful numberings for a wide family of trees. If H is a two-vertex complete graph K2, then for any graph G, the rooted product of G and H has domination number exactly half of its number of vertices.
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73 Three decades later, in 2005 and 2006, this route was successfully climbed by a group of Russian mountaineers."Following the traces of Dr. Frederick Cook", SH Paro No evidence of Cook's purported journey between the "Gateway" and the summit has been found. His claim to have reached the summit is not supported by his photos' vistas, his two sketch maps' markers, and peak-numberings for points attained.Bryce. (1997). DIO pp. 60–61.
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However, routes with similar numberings, especially short secondary routes, tend to be located within close proximity to each other. Mile markers for state routes in Tennessee are based on the mileage for each county, and not the entire route. The route's number is displayed in small text at the bottom of each mile marker. State routes that are overlaid on U.S. Routes are not signed; the route numbers are only displayed on the mile markers.
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During 2019, all of the High Capacity Class 450/5 units were formed back in to their original seating formations, with first class re-added as a result, as part of the refurbishment programme. As such, all of the units were renumbered back in to their original 450/0 numberings. The work took place at Eastleigh Works (Arlington Rail) and the last unit left Eastleigh early May, thus bringing an end to the 450/5 subclass.
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This draws on a wealth of imagery in religious writings, ultimately going back to Psalm 41/42: "As a deer pants for flowing streams, so pants my soul for you, O God..".Cohen, 142-149; Psalm 41 in the Vulgate Bible, 42 in Protestant numberings. ESV text, from biblegateway Alternatively it can be seen as an essentially decorative piling-up of different groups of subject matter with no overall complex meaning intended, but an impressive effect.
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When a molecule contains identical nuclei--which is commonly the case--there are a number of minima related by the permutations of the identical nuclei. The minima, distinguished by different numberings of identical nuclei, can be partitioned in equivalent classes. Two minima are equivalent if they can be transformed into one other by rotating the molecule, that is, without surmounting any energy barrier (bond breaking or bond twisting). The molecules with minima in different equivalent classes are called versions.
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In computability theory, the theorem, or universal Turing machine theorem, is a basic result about Gödel numberings of the set of computable functions. It affirms the existence of a computable universal function, which is capable of calculating any other computable function. The universal function is an abstract version of the universal Turing machine, thus the name of the theorem. Roger's equivalence theorem provides a characterization of the Gödel numbering of the computable functions in terms of the smn theorem and the UTM theorem.
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This chart uses standard numberings for octaves where middle C corresponds to C4. In the MIDI language middle C is referred to as MIDI note number 60. The lowest note that a pipe organ can sound (with a true pipe) is C−1 (or CCCC), which is 8 Hz, below the range of human hearing and not visible on this chart. However, if acoustic combination (a note and its fifth) counts, the lowest note is C−2 (or CCCCC), which is 4 Hz.
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The 1971 Chatham Cup was the 44th annual nationwide knockout football competition in New Zealand. Early stages of the competition were run on a regional basis, with the National League teams receiving a bye until the later stages of the competition. In all, 99 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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The 1972 Chatham Cup was the 45th annual nationwide knockout football competition in New Zealand. Early stages of the competition were run on a regional basis, with the National League teams receiving a bye until the later stages of the competition. In all, 99 teams took part in the competition. Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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Recess Monkey has created several dozen self-produced video works. In tandem with their release of 2009's Field Trip album, they released two 90 minute DVDs in the Field Trips With Recess Monkey series. Each DVD is broken into four short episodes and the volumes are known by their episode numberings, Episodes 1-4 and Episodes 5-8. The DVDs blended music videos with live performances, interviews and were hosted by the band's fictitious hand puppet band manager Mayor Monkey.
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In a show of speed, within the first 100 hours, new exit numberings were put up for almost all of the western stretch of the 4th Ring Road (despite new/old signs being alternated on a different stretch of the ring road). Reaction to the new signs are mixed. There is a definitive plus side: the exits are now matched with their equivalent exit/bridge names on the 3rd and 5th ring roads. Unfortunately, many complain of an information overkill.
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In 1985 the second generation of E-road numbering was implemented, leading to an update of the National Road network as well. With the N91 now heading south to Almere and Utrecht, the N93 was extended northwards. The section leading to the border with Belgium was abandoned and subsequently downgraded. While the N-road numbers were originally signposted everywhere, they were gradually replaced on road signs by the formerly administrative Rijksweg and provincial numberings, starting in 1976 and 1978 respectively.
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There was no standard interface for using higher-resolution SVGA graphics modes supported by later video cards. Each manufacturer developed their own methods of accessing the screen memory, including different mode numberings and different bank switching arrangements. The latter were used to address large images within a single 64kB segment of memory. Previously, the VGA standard had used planar video memory arrangements to the same effect, but this did not easily extend to the greater colour depths and higher resolutions offered by SVGA adapters.
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The 1975 Chatham Cup was the 48th annual nationwide knockout football competition in New Zealand. Early stages of the competition were run in three regions (northern, central, and southern), with the National League teams receiving a bye until the later stages of the competition. In all, 123 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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The 1977 Chatham Cup was the 50th annual nationwide knockout football competition in New Zealand. Early stages of the competition were run in three regions (northern, central, and southern), with the National League teams receiving a bye until the Fourth Round of the competition. In all, 142 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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The 1978 Chatham Cup was the 51st annual nationwide knockout football competition in New Zealand. Early stages of the competition were run in three regions (northern, central, and southern), with the National League teams receiving a bye until the Fourth Round of the competition. In all, 144 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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The 1979 Chatham Cup was the 52nd annual nationwide knockout football competition in New Zealand. Early stages of the competition were run in three regions (northern, central, and southern), with the National League teams receiving a bye until the Fourth Roundof the competition. In all, 131 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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The 1980 Chatham Cup was the 53rd annual nationwide knockout football competition in New Zealand. Early stages of the competition were run in three regions (northern, central, and southern), with the National League teams receiving a bye until the Fourth Round of the competition. In all, 93 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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The 1981 Chatham Cup was the 54th annual nationwide knockout football competition in New Zealand. Early stages of the competition were run in three regions (northern, central, and southern), with the National League teams receiving a bye until the Fourth Round of the competition. In all, 124 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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The 1983 Chatham Cup was the 56th annual nationwide knockout football competition in New Zealand. Early stages of the competition were run in three regions (northern, central, and southern), with the National League teams receiving a bye until the fourth round of the competition. In all, 139 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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The 1982 Chatham Cup was the 55th annual nationwide knockout football competition in New Zealand. Early stages of the competition were run in three regions (northern, central, and southern), with the National League teams receiving a bye until the Fourth Round of the competition. In all, 125 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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On classical computers, ear decompositions of 2-edge-connected graphs and open ear decompositions of 2-vertex-connected graphs may be found by greedy algorithms that find each ear one at a time. A simple greedy approach that computes at the same time ear decompositions, open ear decompositions, st-numberings and -orientations in linear time (if exist) is given in . The approach is based on computing a special ear decomposition named chain decomposition by one path-generating rule. shows that non-separating ear decompositions may also be constructed in linear time.
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In library science, the number of pages in a book forms part of its physical description, coded in subfield $300a in MARC 21 and in subfield $215a in UNIMARC. This description consists of the number of pages (or a list of such numberings separated by commas, if the book contains separately-numbered sections), followed by the abbreviation "p." for "page(s)". The number of pages is written in the same style (Arabic or Roman numerals, uppercase or lowercase, etc.) as the numbering in each section. Unnumbered pages are not described.
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The uniformity of their spacing makes this type of sundial easy to construct. If the dial plate material is opaque, both sides of the equatorial dial must be marked, since the shadow will be cast from below in winter and from above in summer. With translucent dial plates (e.g. glass) the hour angles need only be marked on the sun-facing side, although the hour numberings (if used) need be made on both sides of the dial, owing to the differing hour schema on the sun-facing and sun-backing sides.
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The 1974 Chatham Cup was the 47th annual nationwide knockout football competition in New Zealand. Early stages of the competition were run in three regions, with the National League teams receiving a bye until the later stages of the competition. In all, 114 teams took part in the competition, at that time a record number. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock- out stage.
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The 1984 Chatham Cup was the 57th annual nationwide knockout football competition in New Zealand. Early stages of the competition were run in three regions (northern, central, and southern), with the National League teams receiving a bye until the fourth round (last 32) of the competition. In all, 128 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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The 1985 Chatham Cup was the 58th annual nationwide knockout football competition in New Zealand. Early stages of the competition were run in three regions (northern, central, and southern), with the National League teams receiving a bye into the Fourth Round (last 32) of the competition. In all, 141 teams took part in the competition. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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The 32nd Division part in the battle of Moscow did not escape the notice of the Soviet high command and it was given the title 29th Guards Rifle Division and the 17th Rifle Regiment received the Order of the Red Banner. Its regiments were given new Guards unit numberings as the 87th, 90th, and 93rd Guards Rifle Regiments. The next appearance of the division in battle was in the Ukraine in January 1944 with the 37th Army. Later that year it was moved to the Baltic area and was the first Soviet division into Riga.
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In the 60s he developed an axiomatic complexity theory which was independent of concrete machine models. The theory is based on Gödel numberings and the Blum axioms. Even though the theory is not based on any machine model it yields concrete results like the compression theorem, the gap theorem, the honesty theorem and the Blum speedup theorem. Some of his other work includes a protocol for flipping a coin over a telephone, median of medians (a linear time selection algorithm), the Blum Blum Shub pseudorandom number generator, the Blum- Goldwasser cryptosystem, and more recently CAPTCHAs.
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The 1976 Chatham Cup was the 49th annual nationwide knockout football competition in New Zealand. Early stages of the competition were run in three regions (northern, central, and southern), with the National League teams receiving a bye until the later stages of the competition. In all, 146 teams took part in the competition - a record for the time. Note: Different sources give different numberings for the rounds of the competition: some start round one with the beginning of the regional qualifications; others start numbering from the first national knock-out stage.
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In the 1985 Plan, these were generically referred as "other roads". Many of the 1945 Plan's estradas nacionais were not included in the post-1985 highway plans, and were declassified from the National Road Network in anticipation of their transfer to municipal authorities. Although some were transferred, many municipalities did not assume responsibility for the management of these roads; a number of them continue to be administered by the national roads agency. Despite being declassified, most of the roads retained their designations, keeping their old numberings and N prefixes, including those that are administered by the municipalities.
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András Ádám conjectured that these linear maps are the only ways of renumbering a circulant graph while preserving the circulant property: that is, if and are isomorphic circulant graphs, with different numberings, then there is a linear map that transforms the numbering for into the numbering for . However, Ádám's conjecture is now known to be false. A counterexample is given by graphs and with 16 vertices each; a vertex in is connected to the six neighbors , , and modulo 16, while in the six neighbors are , , and modulo 16. These two graphs are isomorphic, but their isomorphism cannot be realized by a linear map.
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Since then, the Enchiridion has been repeatedly republished, with considerable additions by different editors. As a result, the numberings in more recent editions in no way correspond to those in the original. The numbering that scholars in recent decades (since 1963) have usually cited for the entries is that introduced in the edition prepared by Adolf Schönmetzer, S.J., which explains the abbreviation "DS" (for "Denzinger-Schönmetzer") that is used to specify this numbering, which is very different from that in earlier editions. Peter Hünermann is the most recent editor and the 43rd edition has been published in English by Ignatius Press.
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An early example of a how-to book is the 1569 book A booke of the arte and maner, how to plant and graffe all sortes of trees: With divers other new practice, by one of the Abbey of Saint Vincent in Fraunce by Leonard Mascall. A well known full-length book in the genre is How to Win Friends and Influence People, written by Dale Carnegie in 1936. A similar concept can be seen in many of the For Dummies series of tutorials and also in many other introductory surveys titled with the suffix "101" (based on academic numberings of entry-level courses).
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In computability theory the '' theorem', (also called the translation lemma, parameter theorem, and the parameterization theorem) is a basic result about programming languages (and, more generally, Gödel numberings of the computable functions) (Soare 1987, Rogers 1967). It was first proved by Stephen Cole Kleene (1943). The name ' comes from the occurrence of an S with subscript n and superscript m in the original formulation of the theorem (see below). In practical terms, the theorem says that for a given programming language and positive integers m and n, there exists a particular algorithm that accepts as input the source code of a program with m + n free variables, together with m values.
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The retrospective assignment of "No. 1" to this concerto (and the consequent redesignation of the Violin Concerto Bartók composed in 1936–39 as "No. 2") has met with some resistance, especially from Hungarian scholars and musicologists, on grounds that the composer had "annulled" this concerto, not only by excluding it from his list of mature works but also by extracting the first movement and reworking it in 1911 as the first of Two Portraits, Op. 5. The objection has also been made that, even though an early String Quartet, composed in Pozsony, and an early Sonata for Violin and Piano have been published, the traditional numberings of the String Quartets and the Violin Sonatas have not been changed .
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The latest content theme for the Korean server is "Return to Orpesia". After defeating the evil Viscount Montoro, the player gets the opportunity to return to the old continent of Orpesia, where Bristia, the defeated enemy of Vespanola, announces the opening of a sea route to the New World, linking the midway island of Viron (Byron) to the Bristian port city of Kielce. The player then gets involved in a new main quest line and aids the Bristian Liberation Army to free their homeland from Vespanolan hegemony. With the release of the "Return to Orpesia" expansion, version numberings have returned to 1.0, with an added "B", which either stands for "Bristia" or "Beginning" to symbolize a major milestone in the game's content and storyline.
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The anime adaptation of , produced by the Japanese animation studio Kyoto Animation and directed by Tatsuya Ishihara, contained 14 episodes which aired in Japan between April 2 and July 2, 2006. It was originally aired in a nonlinear order, with the prologue and first seven chapters of the first novel intermixed with chapters from some of the later novels. The "next episode" previews feature two different episode numberings: one number from Haruhi, who numbers the episodes in chronological order, and one number from Kyon, who numbered them in broadcast order. The DVD releases start with "Episode 00" and are then shown in chronological order. The anime was licensed and distributed by Bandai Entertainment over four DVDs released between May and November 2007. A complete box set was released on July 29, 2008. It was broadcast in Italy on Rai 4 between October 24, 2010 and February 6, 2011. Each of the North American releases offered a limited edition collector's set featuring the English dub DVD in chronological order, a subbed-only disc containing the episodes in broadcast order, and an official CD release of the opening, ending, and insert songs appearing in the show.
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