title: Graph coloring

text: As stated above, formula_50 A conjecture of Reed from 1998 is that the value is essentially closer to the lower bound,


title: Graph coloring

text: The chromatic number of the plane, where two points are adjacent if they have unit distance, is unknown, although it is one of 5, 6, or 7. Other open problems concerning the chromatic number of graphs include the Hadwiger conjecture stating that every graph with chromatic number "k" has a complete graph on "k" vertices as a minor, the Erdős–Faber–Lovász conjecture bounding the chromatic number of unions of complete graphs that have at most one vertex in common to each pair, and the Albertson conjecture that among "k"-chromatic graphs the complete graphs are the ones with smallest crossing number.


title: Graph coloring

text: When Birkhoff and Lewis introduced the chromatic polynomial in their attack on the four-color theorem, they conjectured that for planar graphs "G", the polynomial formula_52 has no zeros in the region formula_53. Although it is known that such a chromatic polynomial has no zeros in the region formula_54 and that formula_55, their conjecture is still unresolved. It also remains an unsolved problem to characterize graphs which have the same chromatic polynomial and to determine which polynomials are chromatic.


title: Graph coloring

text: Determining if a graph can be colored with 2 colors is equivalent to determining whether or not the graph is bipartite, and thus computable in linear time using breadth-first search or depth-first search. More generally, the chromatic number and a corresponding coloring of perfect graphs can be computed in polynomial time using semidefinite programming. Closed formulas for chromatic polynomials are known for many classes of graphs, such as forests, chordal graphs, cycles, wheels, and ladders, so these can be evaluated in polynomial time.


title: Graph coloring

text: If the graph is planar and has low branch-width (or is nonplanar but with a known branch decomposition), then it can be solved in polynomial time using dynamic programming. In general, the time required is polynomial in the graph size, but exponential in the branch-width.


title: Graph coloring

text: Brute-force search for a "k"-coloring considers each of the formula_56 assignments of "k" colors to "n" vertices and checks for each if it is legal. To compute the chromatic number and the chromatic polynomial, this procedure is used for every formula_57, impractical for all but the smallest input graphs.


title: Graph coloring

text: Using dynamic programming and a bound on the number of maximal independent sets, "k"-colorability can be decided in time and space formula_58. Using the principle of inclusion–exclusion and Yates's algorithm for the fast zeta transform, "k"-colorability can be decided in time formula_59 for any "k". Faster algorithms are known for 3- and 4-colorability, which can be decided in time formula_60 and formula_61, respectively. Exponentially faster algorithms are also known for 5- and 6-colorability, as well as for restricted families of graphs, including sparse graphs.


title: Graph coloring

text: The contraction formula_62 of a graph "G" is the graph obtained by identifying the vertices "u" and "v", and removing any edges between them. The remaining edges originally incident to "u" or "v" are now incident to their identification ("i.e.", the new fused node "uv"). This operation plays a major role in the analysis of graph coloring.


title: Graph coloring

text: due to , where "u" and "v" are non-adjacent vertices, and formula_64 is the graph with the edge added. Several algorithms are based on evaluating this recurrence and the resulting computation tree is sometimes called a Zykov tree. The running time is based on a heuristic for choosing the vertices "u" and "v".


title: Graph coloring

text: where "u" and "v" are adjacent vertices, and formula_66 is the graph with the edge removed. formula_67 represents the number of possible proper colorings of the graph, where the vertices may have the same or different colors. Then the proper colorings arise from two different graphs. To explain, if the vertices "u" and "v" have different colors, then we might as well consider a graph where "u" and "v" are adjacent. If "u" and "v" have the same colors, we might as well consider a graph where "u" and "v" are contracted. Tutte's curiosity about which other graph properties satisfied this recurrence led him to discover a bivariate generalization of the chromatic polynomial, the Tutte polynomial.


title: Graph coloring

text: These expressions give rise to a recursive procedure called the "deletion–contraction algorithm", which forms the basis of many algorithms for graph coloring. The running time satisfies the same recurrence relation as the Fibonacci numbers, so in the worst case the algorithm runs in time within a polynomial factor of formula_68 for "n" vertices and "m" edges. The analysis can be improved to within a polynomial factor of the number formula_69 of spanning trees of the input graph. In practice, branch and bound strategies and graph isomorphism rejection are employed to avoid some recursive calls. The running time depends on the heuristic used to pick the vertex pair.


title: Graph coloring

text: The greedy algorithm considers the vertices in a specific order formula_70,…,formula_71 and assigns to formula_72 the smallest available color not used by formula_72's neighbours among formula_70,…,formula_75, adding a fresh color if needed. The quality of the resulting coloring depends on the chosen ordering. There exists an ordering that leads to a greedy coloring with the optimal number of formula_76 colors. On the other hand, greedy colorings can be arbitrarily bad; for example, the crown graph on "n" vertices can be 2-colored, but has an ordering that leads to a greedy coloring with formula_77 colors.


title: Graph coloring

text: For chordal graphs, and for special cases of chordal graphs such as interval graphs and indifference graphs, the greedy coloring algorithm can be used to find optimal colorings in polynomial time, by choosing the vertex ordering to be the reverse of a perfect elimination ordering for the graph. The perfectly orderable graphs generalize this property, but it is NP-hard to find a perfect ordering of these graphs.


title: Graph coloring

text: If the vertices are ordered according to their degrees, the resulting greedy coloring uses at most formula_78 colors, at most one more than the graph's maximum degree. This heuristic is sometimes called the Welsh–Powell algorithm. Another heuristic due to Brélaz establishes the ordering dynamically while the algorithm proceeds, choosing next the vertex adjacent to the largest number of different colors. Many other graph coloring heuristics are similarly based on greedy coloring for a specific static or dynamic strategy of ordering the vertices, these algorithms are sometimes called sequential coloring algorithms.


title: Graph coloring

text: The maximum (worst) number of colors that can be obtained by the greedy algorithm, by using a vertex ordering chosen to maximize this number, is called the Grundy number of a graph.


title: Graph coloring

text: Two well-known polynomial-time heuristics for graph colouring are the DSatur and recursive largest first (RLF) algorithms.


title: Graph coloring

text: Similarly to the greedy colouring algorithm, DSatur colours the vertices of a graph one after another, expending a previously unused colour when needed. Once a new vertex has been coloured, the algorithm determines which of the remaining uncoloured vertices has the highest number of different colours in its neighbourhood and colours this vertex next. This is defined as the "degree of saturation" of a given vertex.


title: Graph coloring

text: The recursive largest first algorithm operates in a different fashion by constructing each color class one at a time. It does this by identifying a maximal independent set of vertices in the graph using specialised heuristic rules. It then assigns these vertices to the same color and removes them from the graph. These actions are repeated on the remaining subgraph until no vertices remain.


title: Graph coloring

text: The worst-case complexity of DSatur is formula_79, where formula_80 is the number of vertices in the graph. The algorithm can also be implemented using a binary heap to store saturation degrees, operating in formula_81 where formula_82 is the number of edges in the graph. This produces much faster runs with sparse graphs. The overall complexity of RLF is slightly higher than DSatur at formula_83.


title: Graph coloring

text: In the field of distributed algorithms, graph coloring is closely related to the problem of symmetry breaking. The current state-of-the-art randomized algorithms are faster for sufficiently large maximum degree Δ than deterministic algorithms. The fastest randomized algorithms employ the multi-trials technique by Schneider et al.


title: Graph coloring

text: In a symmetric graph, a deterministic distributed algorithm cannot find a proper vertex coloring. Some auxiliary information is needed in order to break symmetry. A standard assumption is that initially each node has a "unique identifier", for example, from the set {1, 2, ..., "n"}. Put otherwise, we assume that we are given an "n"-coloring. The challenge is to "reduce" the number of colors from "n" to, e.g., Δ + 1. The more colors are employed, e.g. O(Δ) instead of Δ + 1, the fewer communication rounds are required.


title: Graph coloring

text: A straightforward distributed version of the greedy algorithm for (Δ + 1)-coloring requires Θ("n") communication rounds in the worst case − information may need to be propagated from one side of the network to another side.


title: Graph coloring

text: The simplest interesting case is an "n"-cycle. Richard Cole and Uzi Vishkin show that there is a distributed algorithm that reduces the number of colors from "n" to "O"(log "n") in one synchronous communication step. By iterating the same procedure, it is possible to obtain a 3-coloring of an "n"-cycle in "O"( "n") communication steps (assuming that we have unique node identifiers).


title: Graph coloring

text: The function , iterated logarithm, is an extremely slowly growing function, "almost constant". Hence the result by Cole and Vishkin raised the question of whether there is a "constant-time" distributed algorithm for 3-coloring an "n"-cycle. showed that this is not possible: any deterministic distributed algorithm requires Ω( "n") communication steps to reduce an "n"-coloring to a 3-coloring in an "n"-cycle.


title: Graph coloring

text: The technique by Cole and Vishkin can be applied in arbitrary bounded-degree graphs as well; the running time is poly(Δ) + "O"( "n"). The technique was extended to unit disk graphs by Schneider et al. The fastest deterministic algorithms for (Δ + 1)-coloring for small Δ are due to Leonid Barenboim, Michael Elkin and Fabian Kuhn. The algorithm by Barenboim et al. runs in time "O"(Δ) + ("n")/2, which is optimal in terms of "n" since the constant factor 1/2 cannot be improved due to Linial's lower bound. use network decompositions to compute a Δ+1 coloring in time formula_84.


title: Graph coloring

text: The problem of edge coloring has also been studied in the distributed model. achieve a (2Δ − 1)-coloring in "O"(Δ +  "n") time in this model. The lower bound for distributed vertex coloring due to applies to the distributed edge coloring problem as well.


title: Graph coloring

text: Decentralized algorithms are ones where no message passing is allowed (in contrast to distributed algorithms where local message passing takes places), and efficient decentralized algorithms exist that will color a graph if a proper coloring exists. These assume that a vertex is able to sense whether any of its neighbors are using the same color as the vertex i.e., whether a local conflict exists. This is a mild assumption in many applications e.g. in wireless channel allocation it is usually reasonable to assume that a station will be able to detect whether other interfering transmitters are using the same channel (e.g. by measuring the SINR). This sensing information is sufficient to allow algorithms based on learning automata to find a proper graph coloring with probability one.


title: Graph coloring

text: Graph coloring is computationally hard. It is NP-complete to decide if a given graph admits a "k"-coloring for a given "k" except for the cases "k" ∈ {0,1,2} . In particular, it is NP-hard to compute the chromatic number. The 3-coloring problem remains NP-complete even on 4-regular planar graphs. On graphs with maximal degree 3 or less, however, Brooks' theorem implies that the 3-coloring problem can be solved in linear time. Further, for every "k" > 3, a "k"-coloring of a planar graph exists by the four color theorem, and it is possible to find such a coloring in polynomial time.


title: Graph coloring

text: The best known approximation algorithm computes a coloring of size at most within a factor O("n"(log log "n")(log n)) of the chromatic number. For all "ε" > 0, approximating the chromatic number within "n" is NP-hard.


title: Graph coloring

text: It is also NP-hard to color a 3-colorable graph with 4 colors and a "k"-colorable graph with "k" colors for sufficiently large constant "k".


title: Graph coloring

text: Computing the coefficients of the chromatic polynomial is #P-hard. In fact, even computing the value of formula_85 is #P-hard at any rational point "k" except for "k" = 1 and "k" = 2. There is no FPRAS for evaluating the chromatic polynomial at any rational point "k" ≥ 1.5 except for "k" = 2 unless NP = RP.


title: Graph coloring

text: For edge coloring, the proof of Vizing's result gives an algorithm that uses at most Δ+1 colors. However, deciding between the two candidate values for the edge chromatic number is NP-complete. In terms of approximation algorithms, Vizing's algorithm shows that the edge chromatic number can be approximated to within 4/3,


title: Graph coloring

text: and the hardness result shows that no (4/3 − "ε" )-algorithm exists for any "ε > 0" unless P = NP. These are among the oldest results in the literature of approximation algorithms, even though neither paper makes explicit use of that notion.


title: Graph coloring

text: Vertex coloring models to a number of scheduling problems. In the cleanest form, a given set of jobs need to be assigned to time slots, each job requires one such slot. Jobs can be scheduled in any order, but pairs of jobs may be in "conflict" in the sense that they may not be assigned to the same time slot, for example because they both rely on a shared resource. The corresponding graph contains a vertex for every job and an edge for every conflicting pair of jobs. The chromatic number of the graph is exactly the minimum "makespan", the optimal time to finish all jobs without conflicts.


title: Graph coloring

text: Details of the scheduling problem define the structure of the graph. For example, when assigning aircraft to flights, the resulting conflict graph is an interval graph, so the coloring problem can be solved efficiently. In bandwidth allocation to radio stations, the resulting conflict graph is a unit disk graph, so the coloring problem is 3-approximable.


title: Graph coloring

text: A compiler is a computer program that translates one computer language into another. To improve the execution time of the resulting code, one of the techniques of compiler optimization is register allocation, where the most frequently used values of the compiled program are kept in the fast processor registers. Ideally, values are assigned to registers so that they can all reside in the registers when they are used.


title: Graph coloring

text: The textbook approach to this problem is to model it as a graph coloring problem. The compiler constructs an "interference graph", where vertices are variables and an edge connects two vertices if they are needed at the same time. If the graph can be colored with "k" colors then any set of variables needed at the same time can be stored in at most "k" registers.


title: Graph coloring

text: The problem of coloring a graph arises in many practical areas such as pattern matching, sports scheduling, designing seating plans, exam timetabling, the scheduling of taxis, and solving Sudoku puzzles.


title: Graph coloring

text: An important class of "improper" coloring problems is studied in Ramsey theory, where the graph's edges are assigned to colors, and there is no restriction on the colors of incident edges. A simple example is the theorem on friends and strangers, which states that in any coloring of the edges of formula_86, the complete graph of six vertices, there will be a monochromatic triangle; often illustrated by saying that any group of six people either has three mutual strangers or three mutual acquaintances. Ramsey theory is concerned with generalisations of this idea to seek regularity amid disorder, finding general conditions for the existence of monochromatic subgraphs with given structure.


title: Tinnu Anand

text: Tinu Anand (born Virender Raj Anand, 12 October 1945) is an Indian actor, director, writer and producer in Hindi cinema and a few Telugu and Tamil films.


title: Tinnu Anand

text: He is the son of veteran writer Inder Raj Anand, brother of producer Bittu Anand and uncle of director Siddharth Anand. He did his schooling from Mayo College in India. He is Married to Shahnaz, daughter of veteran actor Agha (actor).


title: Tinnu Anand

text: His father, Inder Raj Anand, was a well-known writer in the film industry, but he did not want Tinnu, or his younger brother Bittu, to enter this industry. Inder Raj Anand would say that it was not the place for them. In the words of Tinnu Anand: "..when I told him I wanted to direct films, he was very upset. Ultimately, though, he saw that I didn't want to do anything else. So he sent me to the best school - the Satyajit Ray School. Mr. Ray and my father were friends, so my father asked him to take me under his wing."


title: Tinnu Anand

text: "In the evening, I was given the dirty job of offering Amitabh Rs.5000 for the entire film, whether it took a year or five.. Amitabh reluctantly agreed as he was desperate to act. He got the role of the poet's friend in "Saat Hindustani". When my father got the letter from Satyajit Ray saying I could work with him, I had to give up "Saat Hindustani". So I left for Calcutta and Amitabh got the role of the poet that I was supposed to play.


title: Tinnu Anand

text: (on working with actors who consistently show up quite late and put in only a few hours) "I give all the credit to Veeru (Devgan) who taught me how to unlearn what I had learnt. He told me that if you have to survive in this industry with actors like these, you should learn how to shoot a film when the actor's not there!" and: "I felt very proud when I showed Amitabh a scene between him and Amjad Khan in a dubbing studio one day. He was shocked and said 'But I never shot with Amjad'".


title: Tinnu Anand

text: Anand also worked as an assistant director to Satyajit Ray for five years, in Bengali films, "Goopy Gyne Bagha Byne" (1969), "Aranyer Din Ratri" (1970), "Pratidwandi" (1970), "Seemabaddha" (1971) to "Ashani Sanket" (1973).


title: Tinnu Anand

text: Anand portrayed an important role in "Ghajini" in 2008. In an interview, Tinu Anand spoke about his early days and also praised Amitabh Bachchan for his generosity.


title: Flag of Chile

text: The flag of Chile consists of two equal-height horizontal bands of white and red, with a blue square the same height as the white band in the canton, which bears a white five-pointed star in the center. It was adopted on 18 October 1817. The Chilean flag is also known in Spanish as "La Estrella Solitaria" ("The Lone Star").


title: Flag of Chile

text: It has a 3:2 ratio between length and width, it is divided horizontally into two bands of equal height (the lower being red). The upper area is divided once: into a square (blue), with a single centered white star; and into a rectangle (white), whose lengths are in proportion 1:2. It is in the stars and stripes flag family.


title: Flag of Chile

text: The star represents Venus significant to the country's indigenous Mapuches symbolizing a guide to progress and honor while other interpretations say it refers to an independent state; blue symbolizes the sky and the Pacific Ocean, white is for the snow-covered Andes, and red stands for the blood spilled to achieve independence.


title: Flag of Chile

text: According to the epic poem "La Araucana", the colours were derived from those from the flag flown by the Mapuche during the Arauco War. "Flag Day" is held each year on the ninth of July to commemorate the 77 soldiers who died in the 1882 Battle of La Concepción.


title: Flag of Chile

text: The first records on the possible use of flags by indigenous peoples date back to the War of Arauco, the most famous being the use described in the late 16th-century epic poem "La Araucana". In Canto XXI, Alonso de Ercilla described Talcahuano, warrior and chief of the Mapuche who work the lands near the present-day city that bears his name, bearing emblems of blue, white and red.


title: Flag of Chile

text: Two flags have been documented as used by Mapuche troops. However, these descriptions were made late in the eighteenth century without certainty about the age of them. One consisted of a five-pointed white star on a blue background similar to the canton of the current Chilean flag, while the second had a white eight-pointed star centered on a blue diamond with border zigzagged over a black background. The latter flag appears to be waved by the chief Lautaro in the best-known artistic representation of it, created by painter Pedro Subercaseaux.


title: Flag of Chile

text: The main symbol of this flag is the star of Arauco, called guñelve, representing the flower of the canelo and the bright star of Venus. In the independence of Chile, Bernardo O'Higgins said that guñelve was the direct inspiration for creating the Chilean flag with the Lone Star.


title: Flag of Chile

text: In the case of the colonizing troops, they used several Spanish flags. Each battalion had its own flag, which could incorporate different elements including the heraldic coat of arms of the King of Spain. One of the symbols most commonly used was the Cross of Burgundy, a jagged, red saltire crossed on a white cloth. The Cross of Burgundy was one of the main symbols of the Spanish Empire overseas, so it flew over the warships and was carried by the militia in the colonial territory during the Spanish colonization of the Americas.


title: Flag of Chile

text: In 1785, Carlos III established a uniform flag for all ships of the Spanish Armada, similar to the current flag of Spain. The use of this red-and-yellow flag would be extended in 1793 to "maritime towns, castles and coastal defenses." Despite the establishment of this new flag, the cross of Burgundy would still often used by colonial entities.


title: Flag of Chile

text: At the onset of the Chilean War of Independence, the First Government Junta was proclaimed on 18 September 1810, marking Chile's first step toward independence. It would be during the government of Jose Miguel Carrera in which the desire for emancipation would gain more strength. Nevertheless, the junta was established (at least nominally) as a way of controlling the government during the absence of King Fernando VII, so that the symbols of government remained Hispanic. Therefore, one of the first acts of his government would be the implementation of national symbols, such as an insignia, a coat of arms and a distinctive flag to identify the patriots. The first flag, according to tradition, would have been embroidered by the sister of the ruler, Javiera Carrera, and would be presented and raised for the first time on 4 July 1812 at a dinner with the United States consul Joel Roberts Poinsett to celebrate the anniversary of U.S. independence, an event having a great influence on the locals' struggle for independence.


title: Flag of Chile

text: Named the flag of the "Patria Vieja" ("Old Fatherland"), the flag had three horizontal stripes of blue, white and yellow. For some, the bands represent the three branches of government: majesty popular, law and force, respectively; to others, the stripes represent features of nature: the sky, the snowy Andes and fields of golden wheat, respectively. The following 30 September, during a celebration in the capital to commemorate the first government junta, the Chilean coat of arms, also called "Patria Vieja", was solemnly adopted and included in the center of the flag.


title: Flag of Chile

text: Although the blue-white-yellow flag of the "Patria Vieja" was the most recognized, other versions utilized a different arrangement of the colors, such as white-blue-yellow, for example. On other occasions, the red Cross of Santiago was included in the upper left corner together with the coat of arms in the center. The cross originates from the victory of the patriot troops in the Battle of El Roble, where within the possessions of the captured war booty was a distinctive insignia of the Order of St. James, an important symbol of Spanish pride.


title: Flag of Chile

text: In 1813 after the royalist invasion and the outbreak of the War of Independence, the Spanish symbols were abolished and the tricolor flag was formally adopted by the patriotic forces in a ceremony at the Plaza Mayor of Santiago. Months later in 1814, Carrera left political and military power, and Francisco de la Lastra was chosen as Supreme director. The war of independence began at great losses for the patriot side, and so signed the Treaty of Lircay on 3 May 1814. This agreement reaffirmed the Spanish sovereignty over the territory of Chile, among other things, and as one of its direct consequences, the Spanish flag was readopted at the expense of the tricolor.


title: Flag of Chile

text: The flag of the "Patria Vieja" would wave again after Carrera's return to power 23 July 1814 until the Battle of Rancagua (1–2 October) where the royalist victory ended the patriot government and began the "Reconquista" (or "Reconquest") from 1814 to 1817, restoring the imperial standard. The tricolor flag was last flown for the last time in the Battle of Los Papeles ("Batalla de los Papeles"), but it would appear again raised in the ships that José Miguel Carrera brought in 1817 and during his campaigns in Argentina (1820–1821). The Reconquista ended with the victory of Liberation Army of the Andes ("Ejército Liberatador de los Andes") in the Battle of Chacabuco on 12 February 1817. In this battle, the patriot troops fought with the army colonel and the flag of the Army of the Andes, inspired by the flag of Argentina, without readopting the blue-white-yellow standard.


title: Flag of Chile

text: Today, the flag of the "Patria Vieja" is used during memorial services for moose Chilean historical period, conducted by the National Institute ("Instituto Nacional General José Miguel Carrera"), which Carrera's government founded (10 August 1813). The emblem, adopted as a symbol at the beginning of carrerismo, was subsequently adopted by Chilean nationalism movement. For example, the flag with a red lightning bolt emblem superimposed was the insignia of the National Socialist Movement of Chile between 1932 and 1938.


title: Flag of Chile

text: The victory at the Battle of Chacabuco on 26 May 1817 gave way to a new period known as the "Patria Nueva" ("New Fatherland"). A new flag was adopted that day, known today as the Flag of the Transition ("Bandera de la Transición"), and it is recognized as the first national flag and the last flag used until the one used currently. It was widely publicized at the time that the design was attributed to Juan Gregorio de Las Heras. This flag had three equal stripes: blue, white, and red, which is identical to the flag of pre-communist Yugoslavia. The bottom red strip replaced the yellow from the flag of 1812. The origin of the flag's colors would be based on the description given by Alonso de Ercilla as those of the insignia of the Mapuche troops. The significances of these colors were equivalent to those of the "Patria Vieja", except that the yellow replaced the red to represent the blood that had been shed during the many conflicts.


title: Flag of Chile

text: Despite initial enthusiasm, the flag did not obtain official legalization and disappeared five months later. One reason for its suppression was that it was easily confused with both the flag of the Netherlands and the tricolor of revolutionary France, from which it was inspired.


title: Flag of Chile

text: According to the "General History of Chile" by Diego Barros Arana, the last time the Flag of the Transition was unfurled was at the ceremony to commemorate the Battle of Rancagua, two weeks before the adoption of the current national flag. However, there is information about a possible third flag between the Transitional and final, which would have exchanged the order of white and blue stripes and incorporated the five-pointed white star on the central strip, but that is no certainty, and it is not accepted by the majority of Chilean historians.


title: Flag of Chile

text: The design of the current Chilean flag is commonly attributed to Bernardo O'Higgins's Minister of War, José Ignacio Zenteno, having been designed by the Spanish soldier Antonio Arcos, although historians argue that it was Gregorio de Andía y Varela who drew it.


title: Flag of Chile

text: The flag was made official on 18 October 1817 by a decree, of which only indirect references to the absence of a copy thereof, which was officially presented during the Pledge of Independence ceremony on 12 February 1818, a ceremony in which the bearer was Tomás Guido.


title: Flag of Chile

text: The original flag was designed according to the Golden Ratio, which is reflected in the relation between the widths of the white and blue parts of the flag, as well as several elements in blue canton. The star does not appear upright in the center of the rectangular canton, instead the upper point appears slightly inclined toward the pole in such a way that the projection of its sides divide the length of the canton golden proportion. Additionally, in the center is printed the National Coat of Arms, known from the previous Flag of the Transition and adopted in 1817.


title: Flag of Chile

text: The adoption of the star configuration goes back to the star used by the Mapuches. According to O'Higgins, the star of the flag was the Star of Arauco. In Mapuche iconography, the morning star or Venus, (Mapudungun: "Wünelfe" or the Hispanicized "Guñelve") was represented through the figure of an octagram star or a foliated cross. Although, the star which was finally adopted bore a star having five points with the design of the "guñelve" remaining reflected in an asterisk inserted in the center of the star, representing the combination of European and indigenous traditions.


title: Flag of Chile

text: These designs soon fell into oblivion due to the difficulty in the flag's construction. So, the embroidered seal and the eight-pointed asterisk disappeared while the star was kept completely upright. In 1854 the proportion was determined in keeping with the colors of the flag, leaving the canton as a square and the ratio of hoist to fly set to 2:3. Finally, in 1912, the diameter of the star was established, the precedence of the colors in the presidential flag and decorative cockade was determined, setting the order as blue, white and red from top to bottom or from left to right of the viewer.


title: Flag of Chile

text: All of these arrangements would later be recast into Supreme Decree No. 1534 of 1967 from the Ministry of the Interior during the government of Eduardo Frei Montalva. In this document, the national emblems, coat of arms, the rosette or cockade, and the presidential standard were established. Meanwhile, the Political Constitution of Chile of 1980 establishes in the first clause of article 222 that all inhabitants of the republic should respect Chile and its national emblems.


title: Flag of Chile

text: Few records remain of the original design, the most valuable being that of the flag used in the Declaration of Independence, which had a width of two meters and a length just over two feet. The flag was protected by various hereditary institutions until it was stolen in 1980 by members of the Revolutionary Left Movement as a protest against the military dictatorship. This group kept the specimen and returned it in late 2003 to the National Historical Museum, where it can be found today.


title: Flag of Chile

text: There is a rather popular legend in Chile that claims this third Chilean flag won a "Most Beautiful National Flag in the World" contest. Its most common version states that this happened in 1907 in Blankenberge, Belgium, in the coast of the Baltic Sea . Other versions of this story say this happened in the 19th century, or that the Chilean flag was placed second after the French flag; there are even variations that talk about Chile's national anthem, placing it either in the first place or second, after La Marseillaise. The fact that the only documented version of this story gets basic details wrong (Belgium has a coast on the North Sea, not the Baltic Sea) doesn't reflect well on its historical accuracy.


title: Flag of Chile

text: The flag of the U.S. state of Texas is similar to the Chilean flag. The flag of Texas was designed and adopted on 25 January 1839; whereas Chile adopted a flag similar to today's Chilean flag 22 years earlier on 18 October 1817.


title: Flag of Chile

text: Like Texas, on 17 January 1840; a coalition of nobles from the Mexican states of Coahuila, Nuevo León, and Tamaulipas advocated secession from Mexico to form their own federal republic called the Republic of the Rio Grande with Laredo (today part of Texas) as the capital but unlike Texas, was never formally recognized and ended on 6 November of the same year. Its flag was similar to that of Texas' in that there were three stars with a red hoist, and black and white bars on the side instead of one star with a blue hoist and white and red bars.


title: Flag of Chile

text: In 1822 during the Peruvian War of Independence, troops from both the Liberating Expedition of Peru ("Expedición Libertadora del Perú") and the United Liberating Army of Peru ("Ejército Unido Libertador del Perú") used a standard that was identical to the modern flag of Chile, except their flag had three stars in the canton, representing the three nations united by the cause of independence: the Argentine provinces, Chile and Peru.


title: Flag of Chile

text: On the other hand, the Chilean flag would have served as inspiration for the supporters of Cuban independence at the start the Ten Years' War in the so-called War Cry of Yara (Spanish: "Grito de Yara") in 1868. The leader of this revolution, Carlos Manuel de Céspedes, would have been inspired to create the first Cuban flag named "La Demajagua" in honor of the place where the revolt began. Two main differences are that the red and blue colors are inverted and that the red canton extends to the middle of the fly instead of one-third as on the Chilean flag.


title: Flag of Chile

text: Céspedes would have been inspired by the Chilean flag as a way of honoring the efforts of Benjamín Vicuña Mackenna on behalf of Chile to achieve independence of Cuba after the Spanish defeat in the Chincha Islands War. According to Cespedes's son, his father "imagined a new flag that bore the same colors as that of the Carreras and O'Higgins and that would differentiate itself from the disposition of those colors." However, the flag would not have much success, and an earlier design would become the definitive Cuban flag.


title: Flag of Chile

text: The flag of Liberia, founded in 1847, also includes a single star on the canton, but it has multiple horizontal stripes similar to the United States Flag.


title: Flag of Chile

text: Also, the Flag of Malacca, a state in Malaysia, is similar, having the same colors (except the yellow star and moon) and a similar canton design, although the proportions and color order are different.


title: Flag of Chile

text: The state of Amazonas in Brazil also adopted a similar flag in 1982. Its flag also has an elongated blue canton with multiple stars.


title: Flag of Chile

text: The Catamarca province in Argentina adopted a flag in 2011 that has nearly the same colour design, but the blue is paler, and with a yellow border and a sun with two olive branches in the center.


title: Flag of Chile

text: The construction of the flag of Chile, at present, is officially defined in Supreme Decree No. 1,534 of the Ministry of the Interior, published in 1967, on the use of national emblems, which systematized and consolidated various laws and regulations on the subject. (Other laws include Law No. 2,597 of 11 January 1912, concerning the colors and proportions of the national flag, the presidential sash and rosette or cockade, and Supreme Decree No. 5805 of the Ministry of the Interior, published 26 August 1927, sets the size of the national flag for use in buildings and public offices.) According to the decree, the ratio between length and width of the flag is 3:2, being divided horizontally into two bands of equal size. While the lower section corresponds to the color red, the upper area is divided once in a blue square and a white rectangle whose lengths are in proportion 1:2, respectively. The star is located in the center of the blue canton and is constructed on a circle whose diameter is half the side of the canton.


title: Flag of Chile

text: The exact color shades are not defined by law, but they are listed as "turqui blue", "white" and "red". Approximations below:


title: Flag of Chile

text: According to Chilean law, public use of the flag is allowed without prior authorization. Before October 2011 its use was prohibited, without the approval of the provincial governor. (An exception was made in 2010 during the bicentennial celebrations, where display of the flag was permitted during the whole month of September.) This rule, however, was rarely enforced, as the flag was widely used on street celebrations, stadiums or rallies, without penal consequences.


title: Flag of Chile

text: Public buildings and private residences are required to display the flag on Navy Day (21 May), National Day (18 September) and Army Day (19 September). If the flag is displayed incorrectly or not displayed at all during these days, the person responsible may be fined.


title: Flag of Chile

text: According to the protocol concerned, the flag should be hoisted from the tip of a white mast, and if done in company with other flags different, they must be of equal or lesser size. The Chilean flag must be set to the left if the sum of the flags is an even number or the center if the sum is an odd number. The flag must also be the first to be lifted and lowered the last.


title: Flag of Chile

text: The Chilean flag can be displayed hanging either vertically or horizontally from a building or wall. In both cases, the blue square should be to the viewer's upper left.


title: Flag of Chile

text: Article 22 of the 1980 Constitution of Chile states that all inhabitants of the Republic owe respect to Chile and to its national emblems. The national emblems of Chile are the national flag, the coat of arms of the Republic and the national anthem. Pursuant to article 6 of the State Security Act of Chile (Decreto No. 890 de 1975), it is a felony against the public order to publicly mistreat the flag, the coat of arms, the name of the motherland or the national anthem.


title: Flag of Chile

text: Chile is administratively divided into 16 regions in which the internal government corresponds to the intendant. Some regional governments have adopted their own insignias, though most lack relevance, being principally used for public, regional organizations. The only exception is the flag of the Magallanes and Antartica Chilena Region, which has been adopted as a symbol of identity Magellan by its inhabitants.


title: Flag of Chile

text: The regional flags can be found in the Access Hall of the National Congress of Chile in the city of Valparaíso. Many communes and cities also have their own flags.


title: Flag of Chile

text: In memory of the brave heroes of the Battle of La Concepcion in 1882, on 9 July each year, the very day the final Chilean soldiers in La Concepcion died in defense of the Chilean nation, this "Pledge to the Flag" ("Juramento de la Bandera") is recited at all installations and military bases of the Chilean Army and on graduation parades of the Chilean Navy and Chilean Air Force across the nation in remembrance of this moment in Chilean history. If done for the Carabineros de Chile, it is on the service anniversary (27 April) and passing out parades of enlisted personnel.


title: Aleksandar Kolarov

text: Aleksandar Kolarov (; born 10 November 1985) is a Serbian former professional footballer. Although primarily a left-back, Kolarov could also operate as a centre-back and anywhere along the left flank and was known for his overlapping attacking runs on the wing, his powerful ball-striking ability with his left foot, and his accuracy from free kicks. He was named Serbian Player of the Year in 2011.


title: Aleksandar Kolarov

text: Kolarov began his career at Red Star Belgrade, but he did not break through and moved onto Čukarički in 2004. Two years later, he joined OFK Beograd before moving abroad for the first time by signing for Lazio in Serie A, where he won the Coppa Italia and Supercoppa Italiana in 2009. In 2010, he joined Manchester City, with which he won two Premier League titles, the FA Cup and the League Cup.


title: Aleksandar Kolarov

text: Kolarov made his senior international debut for Serbia in 2008 and earned 94 caps. Kolarov was a member of Serbia's squads for the 2008 Olympics, 2010 FIFA World Cup and the 2018 FIFA World Cup.


title: Aleksandar Kolarov

text: Kolarov's football career started in the Red Star Belgrade youth system. He later joined the youth system of Obilić.


title: Aleksandar Kolarov

text: In 2004, 18-year-old Kolarov moved across Belgrade to Čukarički, which played in the top-tier Serbia-Montenegro League. Signing a three-year contract, he finished the 2003–04 season in the club's youth setup and during the summer of 2004 was introduced to the first-team squad. Making 27 league appearances in his debut season, the youngster left a good impression but could not help the beleaguered team avoid relegation.


title: Aleksandar Kolarov

text: Kolarov started the 2005–06 campaign for Čukarički in the second-tier league competition, but during the winter break controversially transferred to top-tier league club OFK Beograd.


title: Aleksandar Kolarov

text: Kolarov joined OFK Beograd in February 2006 and finished out the season with them, scoring his first league goal.


title: Aleksandar Kolarov

text: In the summer of 2007, OFK Beograd sold Kolarov to Italian side Lazio (the third placed team in previous season's Serie A standings) for a €925,000 transfer fee.


title: Aleksandar Kolarov

text: Kolarov's first goal for Lazio came at the Stadio Oreste Granillo in Reggio Calabria on 30 September 2007, as he hit a rocket from 38 metres to secure a draw against lowly Reggina. During his first season in Rome, the 21-year-old Serb also participated in the UEFA Champions League for the first time, making his debut on 24 October 2007 away at Werder Bremen in a 2–1 victory.


title: Aleksandar Kolarov

text: In his second season in Italy, Kolarov established himself as Lazio's first choice at left back, scoring a spectacular goal against Lecce at the Stadio Via del Mare. It got even better for the Serbian in the second "Derby della Capitale" of the season, against city rivals Roma. With Lazio 3–2 up, Kolarov received the ball in defence from goalkeeper Fernando Muslera and proceeded to run the length of the pitch virtually unopposed. Having run 85 metres, Kolarov then slotted the ball past a helpless Doni in the Roma goal. On 13 May 2009, Kolarov played in the 2009 Coppa Italia Final against Sampdoria. The match finished 1–1 after extra time, and Kolarov scored one of Lazio's penalties in the resultant penalty shoot-out, helping Lazio win the trophy and capping a great season for the Serbian.


title: Aleksandar Kolarov

text: Lazio and 2008–09 Serie A champions Inter Milan travelled to Beijing in August 2009 to play the 2009 Supercoppa Italiana. Kolarov picked up his second winner's medal, with Lazio defeating Inter 2–1. As the 2009–10 season drew to an end, Kolarov was instantly linked with a move away from Lazio, with Manchester City and Real Madrid supposedly interested.


title: Aleksandar Kolarov

text: On 24 July 2010, it was announced that Kolarov had signed for Manchester City for a reported £16 million transfer fee. On 14 August, Kolarov made his Premier League debut in the 0–0 draw against Tottenham Hotspur at White Hart Lane. On 18 January 2011, Kolarov scored his first goal for the club in a 4–2 victory over Leicester City in the FA Cup, while on 2 February 2011, Kolarov recorded his first Premier League goal from a free kick in a 2–2 draw against Birmingham City. He played the full 90 minutes as City won the 2011 FA Cup Final.


title: Aleksandar Kolarov

text: The summer 2011 arrival of Gaël Clichy to the club marginalized Kolarov's role in the squad and he saw his first team opportunities greatly reduced. On 14 September 2011, he scored an equaliser for City in the 1–1 draw against Napoli in their first 2011–12 Champions League group stage match. On 1 October 2011, he started and played the full 90 minutes in the left-back slot against Blackburn Rovers at Ewood Park in a 0–4 away victory in the Premier League. On 31 March 2012, he added another with a long-range swing which earned City a point against Sunderland at home, after coming back from 3–1 down. He ended that season with 12 league appearances, enough for a medal, as Manchester City won the 2011–12 Premier League title in dramatic circumstances on the last day of the season. On 18 September 2012, he scored a free kick in a 3–2 Champions League defeat at Real Madrid. He went on to score in the League Cup loss to Aston Villa, while in their match against Sunderland, he scored another free-kick just five minutes into the match.


title: Aleksandar Kolarov

text: Kolarov scored from the penalty spot in City's 3–2 comeback victory over Bayern Munich in the final match of their Champions League group stage on 10 December 2013, securing his side a spot in the knockout stages of the Champions League for the first time in club history. He scored his only league goal of the 2013–14 season on 1 January 2014, netting past goalkeeper Gerhard Tremmel as City defeated Swansea City by a score of 3–2. On 11 May, he won his second Premier League trophy with Manchester City after making 30 appearances in the league, and 44 in all competitions. In June 2014, Kolarov signed a new three-year deal with City, keeping him at the club until 2017.


title: Aleksandar Kolarov

text: On 22 July 2017, Roma confirmed they had signed Kolarov on a three-year deal for a fee of €5 million.


title: Aleksandar Kolarov

text: Kolarov scored on his debut for the club on 20 August, scoring the winning goal in a 1–0 win over Atalanta. On 18 October, in the UEFA Champions League, he scored in a 3–3 draw with Chelsea. Four days later, he scored the winning goal in a 1–0 win over Torino.


title: Aleksandar Kolarov

text: On 26 September, Kolarov scored his first goal of the 2018–19 season in a 4–0 win over Frosinone. On 29 September, he scored against his former club and city rivals Lazio in a 3–1 win, becoming just the second player in history to have scored for both clubs in a Rome derby.


title: Aleksandar Kolarov

text: On 8 September 2020, Kolarov joined Inter Milan on a reported one-year deal, with an option to extend for a further year, for a fee of €1.5 million.


title: Aleksandar Kolarov

text: Kolarov was a part of the successful Serbia under-21 side which reached the final of the 2007 U-21 Championships held in the Netherlands. As a key member of that side, Kolarov was named in the UEFA Team of the tournament. In the semi-final clash with Belgium, he scored a free-kick from long range.


title: Aleksandar Kolarov

text: In June 2010, he was selected in Serbia's squad for the 2010 FIFA World Cup, where he appeared in group stage matches against Ghana and Germany.


title: Aleksandar Kolarov

text: Kolarov played a major roles in UEFA Euro 2012 qualifiers and friendlies. Kolarov was eventually rewarded for an impressive 2011 with the Serbian Footballer of the Year award.


title: Aleksandar Kolarov

text: On 11 September 2012, Kolarov scored his first goal for Serbia during a 6–1 win against Wales in a 2014 World Cup qualifier. On 7 June 2013, he scored from a free kick against Belgium in a 2014 World Cup qualifier. On 7 September 2014, he scored the equalizer in a 1–1 draw with France.


title: Aleksandar Kolarov

text: Having helped Serbia qualify for the 2018 FIFA World Cup, their first international tournament for eight years, he was also included in the final 23-man squad for that competition. Kolarov scored the only goal of their opening match against Costa Rica from a free kick. He captained Serbia in all three group stage matches.


title: Aleksandar Kolarov

text: Kolarov's switch from Čukarički to OFK Beograd in February 2006, during the 2005–06 season winter break, was highly controversial. Under contract with Čukarički at the time, Kolarov filed a request to be released dated 31 January 2006 on the grounds of "contract expiry" despite the contract being valid until January 2007. Soon after handing in his request, Kolarov publicly stated his desire to join OFK. Seeing that they had a disgruntled player on their hands, Čukarički set a €300,000 transfer fee for Kolarov due to the fact he still had one more year left on his contract with the club. OFK, for their part, simply ignored this fact and simply signed Kolarov without paying a fee. Over the coming years, Čukarički took the case in front of Football Association of Serbia (FSS), where all of their official complaints were rejected.


title: Aleksandar Kolarov

text: A year-and-a-half later, during the summer of 2007, when Kolarov was sold by OFK to Lazio for €800,000, Čukarički club president Aleksandar Mihajlović went public with an accusation that Kolarov "was stolen from Čukarički by OFK Beograd". For that, he was punished by the FSS on the verbal offence grounds and given a year-long ban on performing any functions in Serbian football.


title: Aleksandar Kolarov

text: The entire Kolarov case was featured in early 2008 on B92 television's investigative journalism programme "Insajder" which focused on criminal activities in Serbian football. The programme claims that Kolarov's case was part of a wide initiative by FSS president Zvezdan Terzić (formerly the president of OFK) who made sure young promising players signed for OFK and then raise their transfer price by making sure they get playing time in the under-21 national team.


title: Aleksandar Kolarov

text: In December 2012, Kolarov appeared in a Christmas video uploaded to Manchester City's website, reciting the carol "Jingle Bells" in a deadpan style that went viral on the internet. In December 2013, following the popularity of the previous year's video, Kolarov delivered his rendition of "Santa Claus Is Coming to Town" which also went viral following much anticipation.


title: Chicken or the egg

text: The chicken or the egg causality dilemma is commonly stated as the question, "which came first: the chicken or the egg?" The dilemma stems from the observation that all chickens hatch from eggs and all chicken eggs are laid by chickens. "Chicken-and-egg" is a metaphoric adjective describing situations where it is not clear which of two events should be considered the "cause" and which should be considered the "effect", to express a scenario of infinite regress, or to express the difficulty of sequencing actions where each seems to depend on others being done first. Plutarch posed the question as a philosophical matter in his essay "The Symposiacs", written in the 1st century CE.


title: Chicken or the egg

text: The question represents an ancient folk paradox addressing the problem of origins and first cause. Aristotle, writing in the fourth century BCE, concluded that this was an infinite sequence, with no true origin. Plutarch, writing four centuries later, specifically highlighted this question as bearing on a "great and weighty problem (whether the world had a beginning)". In the fifth century CE, Macrobius wrote that while the question seemed trivial, it "should be regarded as one of importance".


title: Chicken or the egg

text: By the end of the 16th century, the well-known question seemed to have been regarded as settled in the Christian world, based on the origin story of the Bible. In describing the creation of animals, it allows for a first chicken that did not come from an egg. However, later enlightenment philosophers began to question this solution. Carlo Dati in the mid 17th-century published an erudite satire on the subject.


title: Chicken or the egg

text: Although the question is typically used metaphorically, evolutionary biology provides literal answers, made possible by the Darwinian principle that species evolve over time, and thus that chickens had ancestors that were not chickens, similar to a view expressed by the Greek philosopher Anaximander when addressing the paradox.


title: Chicken or the egg

text: If the question refers to eggs in general, the egg came first. The first amniote egg—that is, a hard-shelled egg that could be laid on land, rather than remaining in water like the eggs of fish or amphibians—appeared around 312 million years ago. In contrast, chickens are domesticated descendants of red junglefowl and probably arose little more than eight thousand years ago, at most.


title: Chicken or the egg

text: If the question refers to "chicken" eggs specifically, the answer is complicated. The process by which the chicken arose through the interbreeding and domestication of multiple species of wild jungle fowl is poorly understood, and the point at which this evolving organism became a chicken is a somewhat arbitrary distinction. Whatever criteria one chooses, an animal nearly identical to the modern chicken (i.e., a proto-chicken) laid a fertilized egg that had DNA making it a modern chicken due to mutations in the mother's ovum, the father's sperm, or the fertilised zygote.


title: Chicken or the egg

text: It has been suggested that the actions of a protein found in modern chicken eggs may make the answer different. In the uterus, chickens produce ovocleidin-17 (OC-17), which causes the formation of the thickened calcium carbonate shell around their eggs. Because OC-17 is expressed by the hen and not the egg, the bird in which the protein first arose, though having hatched from a non-reinforced egg, would then have laid the first egg having such a reinforced shell: the chicken would have preceded this first 'modern' chicken egg. However, the presence of OC-17 or a homolog in other species, such as turkeys and finches suggests that such eggshell-reinforcing proteins are common to all birds, and thus long predate the first chickens.


title: ISO metric screw thread

text: The ISO metric screw thread is the most commonly used type of general-purpose screw thread worldwide. They were one of the first international standards agreed when the International Organization for Standardization (ISO) was set up in 1947.


title: ISO metric screw thread

text: The "M" designation for metric screws indicates the nominal outer diameter of the screw thread, in millimetres. This is also referred to as the "major" diameter in the information below. It indicates the diameter of smooth-walled hole that a male thread (e.g. on a bolt) will pass through easily to create a well-located connection to an internally threaded component (e.g. a nut) on the other side. That is, an M6 screw has a nominal outer diameter of 6 millimetres and will therefore be a well-located, co-axial fit in a hole drilled to 6 mm diameter.


title: ISO metric screw thread

text: The design principles of ISO general-purpose metric screw threads ("M" series threads) are defined in international standard ISO 68-1. Each thread is characterized by its major diameter, "D" ("D" in the diagram), and its pitch, "P". ISO metric threads consist of a symmetric V-shaped thread. In the plane of the thread axis, the flanks of the V have an angle of 60° to each other. The thread depth is 0.54125 × pitch. The outermost and the innermost of the height "H" of the V-shape are cut off from the profile.


title: ISO metric screw thread

text: The relationship between the height "H" and the pitch "P" is found using the following equation where "θ" is half the included angle of the thread, in this case 30°:


title: ISO metric screw thread

text: In an external (male) thread (e.g. on a bolt), the major diameter "D" and the minor diameter "D" define "maximum" dimensions of the thread. This means that the external thread must end flat at "D", but can be rounded out below the minor diameter "D". Conversely, in an internal (female) thread (e.g. in a nut), the major and minor diameters are "minimum" dimensions; therefore the thread profile must end flat at "D" but may be rounded out beyond "D". In practice this means that one can measure the diameter over the threads of a bolt to find the nominal diameter "D", and the inner diameter of a nut is "D".


title: ISO metric screw thread

text: The minor diameter "D" and effective pitch diameter "D" are derived from the major diameter and pitch as


title: ISO metric screw thread

text: A metric ISO screw thread is designated by the letter M followed by the value of the nominal diameter "D" (the maximum thread diameter) and the pitch "P", both expressed in millimetres and separated by the multiplication sign, "×" (e.g. M8×1.25). If the pitch is the normally used "coarse" pitch listed in ISO 261 or ISO 262, it can be omitted (e.g. M8).


title: ISO metric screw thread

text: The length of a machine screw or bolt is indicated by a following "×" and the length expressed in millimetres (e.g. M8×1.25×30 or M8×30).


title: ISO metric screw thread

text: Tolerance classes defined in ISO 965-1 can be appended to these designations, if required (e.g. M500– 6g in external threads). External threads are designated by lowercase letter, g or h. Internal threads are designated by upper case letters, G or H.


title: ISO metric screw thread

text: ISO 261 specifies a detailed list of preferred combinations of outer diameter "D" and pitch "P" for ISO metric screw threads. ISO 262 specifies a shorter list of thread dimensions – a subset of ISO 261.


title: ISO metric screw thread

text: The "coarse" pitch is the commonly used default pitch for a given diameter. In addition, one or two smaller "fine" pitches are defined, for use in applications where the height of the normal "coarse" pitch would be unsuitable (e.g. threads in thin-walled pipes). The terms "coarse" and "fine" have (in this context) no relation to the manufacturing quality of the thread.


title: ISO metric screw thread

text: In addition to coarse and fine threads, there is another division of extra fine, or "superfine" threads, with a very fine pitch thread. Superfine pitch metric threads are occasionally used in automotive components, such as suspension struts, and are commonly used in the aviation manufacturing industry. This is because extra fine threads are more resistant to coming loose from vibrations. Fine and superfine threads also have a greater minor diameter than coarse threads, which means the bolt or stud has a greater cross-sectional area (and therefore greater load-carrying capability) for the same nominal diameter.


title: ISO metric screw thread

text: Below are some common spanner (wrench) sizes for metric screw threads. Hexagonal (generally abbreviated to "hex") head widths (width across flats, spanner size) are for DIN 934 hex nuts and hex head bolts. Other (usually smaller) sizes may occur to reduce weight or cost.


title: ISO metric screw thread

text: Japan has a JIS metric screw thread standard that largely follows the ISO, but with some differences in pitch and head sizes.


title: Ahmed Raza Khan Barelvi

text: Ahmed Raza Khan, commonly known as Aala Hazrat, Ahmed Raza Khan Barelvi, or Ahmed Rida Khan in Arabic, (14 June 1856 CE or 10 Shawwal 1272 AH – 28 October 1921 CE or 25 Safar 1340 AH), was an Islamic scholar, jurist, mufti, philosopher, theologian, ascetic, Sufi, poet, and mujaddid in British India.


title: Ahmed Raza Khan Barelvi

text: He wrote on law, religion, philosophy and the sciences, and because he mastered many subjects in both rational and religious sciences, Francis Robinson, one of the leading Western scholars of South Asian Islam, considers him to be a polymath.


title: Ahmed Raza Khan Barelvi

text: He was reformer in north India who wrote extensively in defense of Muhammad and popular Sufi practices and became the leader of a movement called "Ahl-i Sunnat wa Jamàat". He influenced millions of people, today the movement has around 200 million in the region.


title: Ahmed Raza Khan Barelvi

text: Ahmed Raza Khan Barelvi's father, Naqi Ali Khan, was the son of Raza Ali Khan. Ahmed Raza Khan Barelvi belonged to the Barech tribe of Pushtuns. The Barech formed a tribal grouping among the Rohilla Pushtuns of North India who founded the state of Rohilkhand. Khan's ancestors migrated from Qandahar during the Mughal rule and settled in Lahore.


title: Ahmed Raza Khan Barelvi

text: Khan was born on 14 June 1856 in Mohallah Jasoli, Bareilly, the North-Western Provinces. The name corresponding to the year of his birth was "Al Mukhtaar". His birth name was Muhammad. Khan used the appellation "Abdul Mustafa" ("servant of the chosen one") prior to signing his name in correspondence.


title: Ahmed Raza Khan Barelvi

text: According to official Biography written by Molana Zafar Uddin Bihari , some of his famous teachers included:


title: Ahmed Raza Khan Barelvi

text: In the year 1294 A.H. (1877), at the age of 22 years, Ahmed Raza became the Mureed (disciple) of Shah Aale Rasool Marehrawi. His Murshid bestowed him with Khilafat in the several Sufi Silsilas. Some Islamic scholars received permission from him to work under his guidance.


title: Ahmed Raza Khan Barelvi

text: Imam Ahmed Raza wrote extensively in defense of his views, countered the Wahabism and Deobandi movements, and, by his writing and activity, became the leader of Ahle Sunnat movement. The movement is spread across the globe with followers in Pakistan, India, South Africa and Bangladesh. The movement now has over 200 million followers globally. The movement was largely a rural phenomenon when begun but is currently popular among urban, educated Pakistanis and Indians as well as South Asian diaspora throughout the world.


title: Ahmed Raza Khan Barelvi

text: The efforts of Khan and his associate scholars to establish a movement to counter the Deobandi and Ahl-i Hadith movements resulted to in the institutionalization of diverse Sufi movements and their allies in various parts of the world.


title: Ahmed Raza Khan Barelvi

text: Ahmed Raza Khan died on 28 October 1921 (25 Safar 1340 AH) at the age of 65, in his home at Bareilly due to complications related to his diabetes. He is buried in his hometown of Bareilly.


title: Ahmed Raza Khan Barelvi

text: Imam Ahmed Raza Khan wrote several hundred books in Arabic, Persian and Urdu, including the thirty-volume fatwa compilation "Fatawa Razaviyya", and "Kanzul Iman" (Translation & Explanation of the Qur'an). Several of his books have been translated into European and South Asian languages.


title: Ahmed Raza Khan Barelvi

text: "Kanzul Iman" (Urdu and Arabic: کنزالایمان) is a 1910 Urdu paraphrase translation of the Qur'an by Khan. It is associated with the Hanafi jurisprudence within Sunni Islam, and is a widely read version of translation in the Indian Subcontinent.


title: Ahmed Raza Khan Barelvi

text: It has been translated into English, Hindi, Bengali, Dutch, Turkish, Sindhi, Gujarati, Pashto and also recently translated in Gojri language by Mufti Nazir Ahmed Qadri.


title: Ahmed Raza Khan Barelvi

text: "Husamul Haramain" or Husam al Harmain Ala Munhir kufr wal mayn (The Sword of the Haramayn at the throat of unbelief and falsehood) 1906, is a treatise which declared infidels the founders of the Deobandi, Ahl-i Hadith and Ahmadiyya movements on the basis that they did not have the proper veneration of Muhammad and finality of prophethood in their writings. In defense of his verdict he obtained confirmatory signatures from 268 scholars in South Asia, and some from scholars in Mecca and Medina. The treatise is published in Arabic, Urdu, English, Turkish and Hindi.


title: Ahmed Raza Khan Barelvi

text: "Fatawa-e-Razvia" or the full name Al Ataya fi-Nabaviah Fatwa Razaviah (translates to Verdicts of Imam Ahmed Raza by the blessings of the Prophet) is the main fatwa (Islamic verdicts on various issues) book of his movement. It has been published in 30 volumes and in approx. 22,000 pages. It contains solution to daily problems from religion to business and from war to marriage.


title: Ahmed Raza Khan Barelvi

text: He wrote "na'at" (devotional poetry in praise of Muhammad) and always discussed him in the present tense. His main book of poetry is "Hadaiq-e-Bakhshish".


title: Ahmed Raza Khan Barelvi

text: His poems, which deal for the most part with the qualities of Muhammad, often have a simplicity and directness.


title: Ahmed Raza Khan Barelvi

text: His Urdu couplets, entitled "Mustafa jaane rahmat pe lakhon salaam" (Millions of salutations on Mustafa, the Paragon of mercy), are recited in the mosques globally. They contain praise of Muhammad, his physical appearance (verses 33 to 80), his life and times, praise of his family and companions, praise of the awliya and saleheen (the saints and the pious).


title: Ahmed Raza Khan Barelvi

text: In 1323 Hijri (1905), Ahmad Raza went for his second Haj. Allamah Shaikh Saleh Kamal a Alim of Makkatul Mukarrama, he presented five questions to Ahmad Raza on behalf of the Ulema of Makkatul Mukarrama, this question was asked by Makkatul Mukarrama Wahabi Ulema regarding Knowledge of the Unseen (Ilm-e-Ghaib) Prophet of Islam. At that time Ahmed Raza was suffering from high fever, despite the illness he tried to answer all the questions, he answered in such detail that the answer took the form of a book, and this book was named Al Daulatul Makkiya Bil Madatul Ghaibiya.


title: Ahmed Raza Khan Barelvi

text: Khan saw an intellectual and moral decline of Muslims in British India. His movement was a mass movement, defending popular Sufism, which grew in response to the influence of the Deobandi movement in South Asia and the Wahhabi movement elsewhere.


title: Ahmed Raza Khan Barelvi

text: Imam Ahmed Raza Khan supported Tawassul, Mawlid, Muhammad's awareness of complete knowledge of the unseen, and other practices which were opposed by Salafis and Deobandis.


title: Ahmed Raza Khan Barelvi

text: This concept was interpreted by Shah Abdul Aziz in Tafsir Azizi in these words: The prophet is observing everybody, knows their good and bad deeds, and knows the strength of faith (Imaan) of every individual Muslim and what has hindered his spiritual progress.


title: Ahmed Raza Khan Barelvi

text: He reached judgments with regard to certain practices and faith in his book Fatawa-e-Razvia, including:


title: Ahmed Raza Khan Barelvi

text: Mirza Ghulam Ahmad of Qadian claimed to be the Messiah, Prophet and Mahdi awaited by some Muslims as well as a Ummati Nabi, a subordinate prophet to Muhammad who came to restore Islam to the pristine form as practiced by Muhammad and early Sahaba. Khan declared Mirza Ghulam Ahmad a heretic and apostate and called him and his followers disbelievers ("kuffar").


title: Ahmed Raza Khan Barelvi

text: The theological difference with Deobandi school begun when Maulana Ahmed Raza Khan Qadri objected in writing to some of the following beliefs of Deobandi scholars.


title: Ahmed Raza Khan Barelvi

text: When Ahmed Raza Khan visited Mecca and Medina for pilgrimage in 1905, he prepared a draft document entitled "Al Motamad Al Mustanad" ("The Reliable Proofs"). In this work, Ahmad Raza branded Deobandi leaders such as Ashraf Ali Thanwi, Rashid Ahmad Gangohi, and Muhammad Qasim Nanotwi and those who followed them as "kuffar". Khan collected scholarly opinions in the Hejaz and compiled them in an Arabic language compendium with the title, "Hussam al Harmain" ("The Sword of Two Sanctuaries"), a work containing 34 verdicts from 33 ulama (20 Meccan and 13 Medinese).


title: Ahmed Raza Khan Barelvi

text: Ahmed Raza Khan wrote various books against beliefs and faith of Shia Muslims and declared various practices of Shia as kufr. He considered most Shiites of his day apostates because, he believed, they repudiated necessities of religion.


title: Ahmed Raza Khan Barelvi

text: Ahmed Raza Khan declared Wahabis as disbelievers ("kuffar") and collected many fatwas of various scholars against the Wahhabi movement founded by Muhammad ibn Abd al-Wahhab, who was predominant in the Arabian peninsula, just as he had done with the Ahmadis and Deobandis. Until this day, Khan's followers remain opposed to the Wahhabi and their beliefs.


title: Ahmed Raza Khan Barelvi

text: In 1905, Khan, on the request of contemporaries from Hijaz, wrote a verdict on the permissibility of using paper as a form of currency, entitled "Kifl-ul-Faqeehil fehim Fe Ahkam-e-Kirtas Drahim".


title: Ahmed Raza Khan Barelvi

text: Unlike other Muslim leaders in the region at the time, Khan and his movement opposed the Indian independence movement due to its leadership under Mahatma Gandhi, who was not a Muslim.


title: Ahmed Raza Khan Barelvi

text: Imam Ahmed Raza Khan declared that India was Dar al-Islam and that Muslims enjoyed religious freedom there. According to him, those arguing the contrary merely wanted to take advantage of the provisions allowing Muslims living under non-Muslim rule to collect interest from commercial transactions and had no desire to fight Jihad or perform Hijra. Therefore, he opposed labelling British India to be Dar al-Harb ("abode of war"), which meant that waging holy war against and migrating from India were inadmissible as they would cause disaster to the community. This view of Khan's was similar to other reformers Syed Ahmed Khan and Ubaidullah Al Ubaidi Suhrawardy.


title: Ahmed Raza Khan Barelvi

text: The Muslim League mobilized the Muslim masses to campaign for Pakistan, and many of Khan's followers played a significant and active role in the Pakistan Movement at educational and political fronts.


title: Ahmed Raza Khan Barelvi

text: Many religious schools, organizations, and research institutions teach Khan's ideas, which emphasize the primacy of Islamic law along with the adherence to Sufi practices and personal devotion to Muhammad.


title: Ahmed Raza Khan Barelvi

text: Imam Ahmed Raza Khan had two sons and five daughters. His sons Hamid Raza Khan and Mustafa Raza Khan Qadri are celebrated scholars of Islam. Hamid Raza Khan was his appointed successor. After him Mustafa Raza Khan succeeded his father, who then appointed Akhtar Raza Khan as his successor. His son, Mufti Asjad Raza Khan now succeeds him as the spiritual leader.


title: Ally Financial

text: Ally Financial is a bank holding company organized in Delaware and headquartered in Detroit, Michigan. The company provides financial services including car finance, online banking via a direct bank, corporate lending, vehicle insurance, mortgage loans, and an electronic trading platform to trade financial assets.


title: Ally Financial

text: Ally is one of the largest car finance companies in the U.S., providing car financing and leasing for 4.5 million customers and originating 1.4 million car loans annually. It is on the list of largest banks in the United States by assets and has 2.0 million depositors. Its electronic trading platform has approximately 350,000 funded accounts. The company has sold more than 5 million vehicles, including 270,000 vehicles sold in 2019 via its SmartAuction online marketplace for auto auctions, launched in 2000.


title: Ally Financial

text: The company was founded in 1919 by General Motors (GM) as the General Motors Acceptance Corporation (GMAC) to provide financing to automotive customers. In 1939, the company founded Motors Insurance Corporation and entered the vehicle insurance market.


title: Ally Financial

text: In 1985, while GM was under the leadership of Roger Smith, who sought to diversify the company, GMAC formed GMAC Mortgage and acquired Colonial Mortgage as well as the servicing arm of Norwest Mortgage, which included an $11 billion mortgage portfolio.


title: Ally Financial

text: In 1991, the company was forced to write-off $275 million in bad debt as part of a $436 million loss suffered from fraud committed by John McNamara, who ran a Ponzi scheme.


title: Ally Financial

text: In 1998, the company formed GMAC Real Estate. In 1999, GMAC Mortgage acquired Ditech. In 2000, the company formed GMAC Bank, a direct bank. In 2005, the company formed GMAC ResCap as a holding company for its mortgage operations.


title: Ally Financial

text: In 2006, General Motors sold a 51% interest in GMAC to Cerberus Capital Management, a private equity firm. Also that year, GMAC sold a controlling interest of GMAC Commercial Holdings (its real estate division renamed Capmark) to Goldman Sachs, Kohlberg Kravis Roberts, and Five Mile Capital Partners. GMAC Real Estate was sold to Brookfield Asset Management. In 2009, Capmark filed for bankruptcy and its North American loan origination and servicing business was acquired by Berkadia, a joint venture of Leucadia National and Berkshire Hathaway.


title: Ally Financial

text: On December 24, 2008, the Federal Reserve accepted the company's application to become a bank holding company. In January 2009, the company closed Nuvell Financial Services, its subprime lending division.


title: Ally Financial

text: As a result of losses in GMAC ResCap, the United States Department of the Treasury invested $17.2 billion in the company in 2008–2009. The Treasury sold its last stake in the company in 2014, recovering $19.6 billion from its $17.2 billion investment.


title: Ally Financial

text: In April 2009 the bank announced plans to move its Charlotte office from Ballantyne to on four floors of 440 South Church, with possible expansion later. At the time, the bank had 265 Charlotte employees in three business units.


title: Ally Financial

text: In May 2009, GMAC Bank was rebranded as Ally Bank. In May 2010, GMAC re-branded itself as Ally Financial. In September 2010, the company sold its resort finance business to Centerbridge Partners. In 2012, the company sold its Canadian banking operations to Royal Bank of Canada for $3.8 billion. In April 2014, it became a public company via an initial public offering. In 2015, it moved its headquarters to One Detroit Center, which was subsequently renamed Ally Detroit Center. In June 2016, the company acquired TradeKing, a stockbrokerage, for $275 million, which was re-branded as Ally Invest.


title: Ally Financial

text: In May 2016, Ally Bank re-entered the mortgage business with the launch of its direct-to-consumer offering called Ally Home. In April 2019, Ally Home partnered with Better.com to launch a digital mortgage platform.


title: Ally Financial

text: In October 2019 Ally announced completion of its acquisition of Health Credit Services (HCS). HCS is a technology-focused patient financing company that is based in Charlotte, North Carolina.


title: Ally Financial

text: On May 3, 2021 Ally Charlotte Center officially the bank occupies 725,000 square of the building and is the only office tenant of the building. All 2,100 Charlotte-based employees and contractors will relocate to the new building from other Charlotte offices, which includes 440 South Church, 11605 N. Community House Road, WeWork space at 128 S. Tryon St, 1401 W. Morehead St, and 2101 Rexford Road. Ally will move into the building in phases as determined by teams.


title: Ally Financial

text: In December of 2021, Ally acquired Fair Square Financial, a credit card company, for $750 million and subsequently rebranded the subsidiary and product as Ally Credit Card.


title: Ally Financial

text: The company sponsors the Miami International Auto Show, the "Time" Dealer of the Year award, and The Ally Challenge.


title: Ally Financial

text: In 2019, Ally became the primary sponsor for seven-time NASCAR Cup Series champion Jimmie Johnson at Hendrick Motorsports, a sponsorship that runs through 2023. As GMAC, the company previously had primary sponsorships with Hendrick Motorsports from 1998 through 2007 with drivers Jack Sprague, Ricky Hendrick, Brian Vickers and Casey Mears, including Vickers' 2003 NASCAR Busch Series championship victory. Alex Bowman took over the No. 48 Ally Chevrolet in 2021 after Johnson transitioned from NASCAR to the IndyCar Series; before the season began, Ally also acquired the naming rights to the Cup Series' race at Nashville Superspeedway to name it the Ally 400.


title: Ally Financial

text: Ally is also a sponsor of the National Women's Soccer League and of a team in Major League Soccer, Charlotte FC.


title: Ally Financial

text: In 2021, Ally continued to sponsor Jimmie Johnson in IMSA WeatherTech SportsCar Championship with his No.48 Cadillac DPi-V.R entry in IMSA Michelin Endurance Cup rounds alongside Kamui Kobayashi and Simon Pagenaud. Also, Mike Rockenfeller joined the team for Rolex 24 at Daytona.


title: Ally Financial

text: In December 2013, the Consumer Financial Protection Bureau (CFPB) and United States Department of Justice ordered the company to pay $80 million in consumer monetary damages and $18 million in civil penalties after determining that 235,000 minority borrowers paid higher interest rates for auto loans originated between April 2011 and December 2013 because of the company's discriminatory pricing system. The higher rates resulted from the company's specific policy of allowing dealers to charge, at their discretion, a "dealer markup" above Ally's established "buy rate" and then compensating dealers based on the markup. Ally provided an incentive for dealers to charge higher rates, in violation of the Equal Credit Opportunity Act.


title: Ammonia solution

text: Ammonia solution, also known as ammonia water, ammonium hydroxide, ammoniacal liquor, ammonia liquor, aqua ammonia, aqueous ammonia, or (inaccurately) ammonia, is a solution of ammonia in water. It can be denoted by the symbols NH(aq). Although the name ammonium hydroxide suggests an alkali with composition , it is actually impossible to isolate samples of NHOH. The ions and OH do not account for a significant fraction of the total amount of ammonia except in extremely dilute solutions.


title: Ammonia solution

text: In aqueous solution, ammonia deprotonates a small fraction of the water to give ammonium and hydroxide according to the following equilibrium:


title: Ammonia solution

text: In a 1 M ammonia solution, about 0.42% of the ammonia is converted to ammonium, equivalent to pH = 11.63


title: Ammonia solution

text: because [NH] = 0.0042 M, [OH] = 0.0042 M, [NH] = 0.9958 M, and pH = 14 + log[OH] = 11.62. The base ionization constant is


title: Ammonia solution

text: Like other gases, ammonia exhibits decreasing solubility in solvent liquids as the temperature of the solvent increases. Ammonia solutions decrease in density as the concentration of dissolved ammonia increases. At , the density of a saturated solution is 0.88 g/ml and contains 35.6% ammonia by mass, 308 grams of ammonia per litre of solution, and has a molarity of approximately 18 mol/L. At higher temperatures, the molarity of the saturated solution decreases and the density increases. Upon warming saturated solutions, ammonia gas is released.


title: Ammonia solution

text: In contrast to anhydrous ammonia, aqueous ammonia finds few non-niche uses outside of cleaning agents.


title: Ammonia solution

text: Diluted (1–3%) ammonia is also an ingredient of numerous cleaning agents, including many window cleaning formulas. Because aqueous ammonia is a gas dissolved in water, as the water evaporates from a window, the gas evaporates also, leaving the window streak-free.


title: Ammonia solution

text: In addition to use as an ingredient in cleansers with other cleansing ingredients, ammonia in water is also sold as a cleaning agent by itself, usually labeled as simply "ammonia". It may be sold plain, lemon-scented (and typically colored yellow), or pine-scented (green). Commonly available ammonia with soap added is known as "cloudy ammonia".


title: Ammonia solution

text: In industry, aqueous ammonia can be used as a precursor to some alkyl amines, although anhydrous ammonia is usually preferred. Hexamethylenetetramine forms readily from aqueous ammonia and formaldehyde. Ethylenediamine forms from 1,2-dichloroethane and aqueous ammonia.


title: Ammonia solution

text: In the early years of the twentieth century, the vapor absorption cycle using water-ammonia systems was popular and widely used, but after the development of the vapor compression cycle it lost much of its importance because of its low coefficient of performance (about one fifth of that of the vapor compression cycle). Both the Electrolux refrigerator and the Einstein refrigerator are well known examples of this application of the ammonia solution.


title: Ammonia solution

text: Ammonia is used to produce monochloramine, which is used as a disinfectant. Chloramine is preferred over chlorination for its ability to remain active in stagnant water pipes longer, reducing the risk of waterborne infections.


title: Ammonia solution

text: Ammonia is used by aquarists for the purposes of setting up a new fish tank using an ammonia process called fishless cycling. This application requires that the ammonia contain no additives.


title: Ammonia solution

text: Baking ammonia (ammonium bicarbonate) was one of the original chemical leavening agents. It was obtained from deer antlers. It is useful as a leavening agent, because ammonium carbonate is heat activated. This characteristic allows bakers to avoid both yeast's long proofing time and the quick CO dissipation of baking soda in making breads and cookies rise. It is still used to make ammonia cookies and other crisp baked goods, but its popularity has waned because of ammonia's off-putting smell and concerns over its use as a food ingredient compared to modern-day baking powder formulations. It has been assigned E number E527 for use as a food additive in the European Union.


title: Ammonia solution

text: Aqueous ammonia is used as an acidity regulator to bring down the acid levels in food. It is classified in the United States by the Food and Drug Administration as generally recognized as safe (GRAS) when using the food grade version. Its pH control abilities make it an effective antimicrobial agent.


title: Ammonia solution

text: In furniture-making, Ammonia fuming was traditionally used to darken or stain wood containing tannic acid. After being sealed inside a container with the wood, fumes from the ammonia solution react with the tannic acid and iron salts naturally found in wood, creating a rich, dark stained look to the wood. This technique was commonly used during the arts and crafts movement in furniture – a furniture style which was primarily constructed of oak and stained using these methods.


title: Ammonia solution

text: Ammonia solution is used to treat straw, producing "ammoniated straw" making it more edible for cattle.


title: Ammonia solution

text: Aqueous ammonia is used in traditional qualitative inorganic analysis as a complexant and base. Like many amines, it gives a deep blue coloration with copper(II) solutions. Ammonia solution can dissolve silver oxide residues, such as that formed from Tollens' reagent. It is often found in solutions used to clean gold, silver, and platinum jewelry, but may have adverse effects on porous gem stones like opals and pearls.


title: Oldsmobile V8 engine

text: The Oldsmobile V8, also referred to as the Rocket, is series of engines that was produced by Oldsmobile from 1949 until 1990. The Rocket, along with the 1949 Cadillac V8, were the first post-war OHV crossflow cylinder head V8 engines produced by General Motors. Like all other GM divisions, Olds continued building its own V8 engine family for decades, adopting the corporate Chevrolet 350 small-block and Cadillac Northstar engine only in the 1990s. All Oldsmobile V8s were manufactured at plants in Lansing, Michigan while the engine block and cylinder heads were cast at Saginaw Metal Casting Operations.


title: Oldsmobile V8 engine

text: All Oldsmobile V8s use a 90° bank angle, and most share a common stroke dimension: for early Rockets, for later Generation 1 engines, and for Generation 2 starting in 1964. The , , , and engines are commonly called small-blocks.<ref name="Hot Rod, 3/86, p.54">"Hot Rod", 3/86, p.54.</ref> , , and V8s have a higher deck height ( "versus" ) to accommodate a stroke crank to increase displacement. These taller-deck models are commonly called "big-blocks", and are taller and wider than their "small-block" counterparts.


title: Oldsmobile V8 engine

text: The Rocket V8 was the subject of many first and lasts in the automotive industry. It was the first mass-produced OHV V8, in 1949.


title: Oldsmobile V8 engine

text: The factory painted "small-blocks" gold or blue (flat black on the late model ), while "big-blocks" could be red, green, blue, or bronze.


title: Oldsmobile V8 engine

text: As is the case with all pre-1972 American passenger car engines, published horsepower and torque figures for those years were SAE "Gross," as opposed to 1972 and later SAE Net ratings (which are indicative of what actual production engines produce in their "as installed" state - with all engine accessories, full air cleaner assembly, and complete production exhaust system in place).


title: Oldsmobile V8 engine

text: The first Oldsmobile V8 was of a flathead design that was developed by Northway Engine Works before GM assumed operations. It was installed in the Oldsmobile Light Eight and was related to the Cadillac flathead V8 engine.


title: Oldsmobile V8 engine

text: The first generation of Oldsmobile V8s ranged from 1949-1964. Each engine in this generation is quite similar with the same size block and heads.


title: Oldsmobile V8 engine

text: The engine had hydraulic lifters, an oversquare bore:stroke ratio, a counterweighted forged crankshaft, aluminum pistons, floating wristpins, and a dual-plane intake manifold. The 303 was produced from 1949-1953. Bore was and stroke was . Cadillac used a distantly related engine which appeared in three different sizes through to the 1962 model year; though the Oldsmobile and Cadillac motors were not physically related, many lessons learned by one division were incorporated into the other's design, and the result were two engines known for their excellent power-to-weight ratio, fuel economy, and smooth, strong, reliable running.


title: Oldsmobile V8 engine

text: The original Oldsmobile V8 was to have been marketed as "Kettering Power" after chief engineer Charles Kettering, but company policy prohibited the use of his name. Instead, influenced by the Space Race between the United States and the USSR, the legendary Rocket was born, available in Oldsmobile's 88, Super 88, and 98 models. The engine proved so popular, the division's 88 models were popularly called Rocket 88s.


title: Oldsmobile V8 engine

text: The 303 was available from 1949 until 1953. From 1949 until 1951, the 2-barrel carburetor 303 produced and . Its output of 0.45 hp per cubic inch was 7% better than the 0.42 hp per cubic inch of the popular and widely produced 1949 Ford Flathead V8. 1952 88 and Super 88 V8s used a 4-barrel carburetor for and , while 4-barrel 1953 versions raised compression from 7.5:1 to 8.0:1 for and .


title: Oldsmobile V8 engine

text: The version was produced from 1954 until 1956. Bore was increased to (same as the later 283 Chevy) and stroke remained the same at . Two-barrel carburetion was standard; all high performance 324s came with four-barrel carburetors. The 324 was shared with GMC trucks.


title: Oldsmobile V8 engine

text: The 1955 model upped the compression to 8.5:1 for and in the 88 and and in the Super 88 and 98. For engines built during the first part of 1955, the 324 skirted pistons had a reputation for failing due to the cast aluminum skirt separating from its steel interior brace. This problem did not appear until the engine had over on it. By late 1956, many Olds dealers learned about the problem. Compression was up again in 1956 for and in the 88 and and in the Super 88 and 98.


title: Oldsmobile V8 engine

text: Making its debut in 1957 as standard equipment on all Olds models, the 371 was produced through 1960. Bore was up to and stroke was increased to for . 1959 and 1960 371s used green painted valve covers. 4-barrel models used 9.25:1 compression in 1957 and 10:1 in 1958 for and and and respectively. A 1958 2-barrel version produced and , but had problems with early camshaft failures due to the high preload valve spring forces. Following the Automobile Manufacturer Association ban on factory supported racing, power ratings went down for the 1959 and 1960 88 models: and for 1959 and and for 1960. It was no longer available in cars in 1961.


title: Oldsmobile V8 engine

text: This engine was used in GMC heavy trucks as the "370" of 232 gross HP at 4200 RPM and torque 355 gross lbs-ft at 2600 RPM from 1957 to 1959.It had hardened valve seats and other features for heavy duty usage.


title: Oldsmobile V8 engine

text: Introduced in the middle of the 1957 model year, the 1957 and 1958 J-2 Golden Rocket had three two-barrel (twin choke) carburetors with a vacuum-operated linkage. Only the center carburetor was mechanically connected to the throttle pedal, and it was the only one equipped with a choke. When the center carburetor was opened to 60° or more engine vacuum drawn from the windshield wiper pump would simultaneously open the front and rear carburetors. These carburetors did not open progressively; they were either open or closed. The J-2 engine also had a slightly thinner head gasket, raising compression to 10.0:1. It was advertised with gross power and torque ratings of at 4600 rpm and at 2800 rpm. Oldsmobile charged $83 for the J-2 option with the three-speed manual (or in the 98), $314 dollars with the automatic.


title: Oldsmobile V8 engine

text: In practice, owners who did not regularly drive hard enough to engage the front and rear carburetors experienced problems with the linkage and carburetor throats becoming clogged, and some J-2-equipped cars had the front and rear carburetors removed and blocked off. Moreover, correct tuning was a continual headache. The package was expensive to produce, and Oldsmobile discontinued it after 1958.


title: Oldsmobile V8 engine

text: Bore was up to for the largest first-generation Rocket, the . 394s were produced from 1959–1964 and were available on many Olds models. Most 394s used 2-barrel carburetors, but special high-compression 4-barrel versions were available starting in 1961.


title: Oldsmobile V8 engine

text: Power for the base engine was up to 315 hp (235 kW), even though compression was down a quarter point, to 9.75:1.


title: Oldsmobile V8 engine

text: The 394 replaced the 371 in Super 88 and 98 cars for 1959 and 1960 and a detuned version was used in the 88 for 1961 and the Dynamic 88 for 1962-1964.


title: Oldsmobile V8 engine

text: The 1961 through 1963 Sky Rocket (and 1964 Rocket) was a high-compression, four-barrel engine. The 10:1 compression 1961 model produced and , while the 10.25:1 1962-1964 version upped power to and . A special 1963 10.5:1 version was also produced with .


title: Oldsmobile V8 engine

text: The high-compression four-barrel 394 cu. in. 1964 Starfire produced and for the 1963-4 Starfire and 98 Custom-Sports Coupe. It was optional on 1964 98s and Super 88s.


title: Oldsmobile V8 engine

text: From 1961-1963, Oldsmobile manufactured its own version of the Buick-designed, all-aluminum 215 cubic inch V8 engine for the F-85 compact. Known variously as the Rockette, Cutlass, and Turbo-Rocket by Oldsmobile (and as Fireball and Skylark by Buick), it was a compact, lightweight engine measuring long, wide, and high (same as the small-block Chevy), with a dry weight of only . The Oldsmobile engine was very similar to the Buick engine, but not identical: it had larger wedge combustion chambers with flat-topped (rather than domed) pistons, six bolts rather than five per cylinder, and slightly larger intake valves; the valves were actuated by shaft-mounted rocker arms like the Buick and Pontiac versions, but the shafts and rockers were unique to Oldsmobile. With an 8.75:1 compression ratio and a 2-barrel carburetor, the Olds 215 had the same rated hp, at 4800 rpm, as the Buick 215, with of torque at 2400 rpm. With a 4-barrel carburetor and 10.25:1 compression, the Olds 215 made at 4800 rpm and at 3200 rpm with a manual transmission. With a 4-barrel carburetor and 10.75:1 compression, the Olds 215 made at 4800 rpm and at 3200 rpm with an automatic. The Buick version was rated at 200 hp with an 11:1 compression ratio.


title: Oldsmobile V8 engine

text: The Buick version of the 215 V8 went on to become the well known Rover V8, which still remains in limited production, utilizing the Buick-style pistons, heads, and valve train gear.


title: Oldsmobile V8 engine

text: The Oldsmobile engine block formed the basis of the Repco 3-liter engine used by Brabham to win the 1966 and 1967 Formula One world championships. The early Repco engines produced up to , and featured new SOHC cylinder heads and iron cylinder liners. The 1967 and later versions of the Repco engine had proprietary engine blocks.


title: Oldsmobile V8 engine

text: In the mid-1980s, hot rodders discovered the 215 could be stretched to as much as , using the Buick 300 crankshaft, new cylinder sleeves, and an assortment of non-GM parts. It could also be fitted with high-compression cylinder heads from the Morgan +8. Using the 5 liter Rover block and crankshaft, a maximum displacement of is theoretically possible.


title: Oldsmobile V8 engine

text: In 1962 and 1963 Oldsmobile built a turbocharged version of the 215, designated "Turbo-Rocket". The turbocharger fitted to the V8 engine was a small-diameter Garrett T5 model with integral wastegate, manufactured by Garrett AiResearch, and produced a maximum of 5 psi (34 kPa) boost at 2200 rpm. The engine had 10.25:1 compression and a single-barrel carburetor. It was rated at at 4600 rpm and at 3200 rpm. In development, the high compression ratio combined with the charged load created problems with spark knock on hard throttle applications, which led Olds to develop and utilize a novel water-injection system that sprayed metered amounts of distilled water and methyl alcohol (dubbed "Turbo-Rocket Fluid") into the intake manifold air-stream to cool the intake charge. If the fluid reservoir was empty, a complex double-float and valve assembly in the Turbo-Rocket Fluid path would set a second butterfly (positioned between the throttle butterfly and the turbocharger) into the closed position, limiting the amount of boost pressure. Many customers did not keep the reservoir filled, or had mechanical problems with the turbocharger system which resulted in many of the turbo-charger installations being removed and a conventional 4 barrel carburetor and manifold installed in its place.


title: Oldsmobile V8 engine

text: The "Turbo-Rocket" V8 was offered exclusively on the Oldsmobile Jetfire, a special version of the Cutlass compact hardtop coupe, which is noteworthy as it is one of the world's first (in fact the second) turbocharged passenger car ever offered for public sale. The Chevrolet Corvair Spyder Turbo, likewise a forced induction i.e turbo-powered car, predated the Oldsmobile Jetfire Turbo, however by only a few weeks, thus being the world's very first turbocharged commercially sold vehicle.


title: Oldsmobile V8 engine

text: The second generation of Oldsmobile V8s was produced from 1964-1990. Most of these engines were very similar, using the same bore centers and a deck height, raised on "big-block" versions to . Big-block and Diesel versions also increased the main bearing journal to for increased strength. All generation-2 small-block Olds V8s used a stroke of . The big-block engines initially used a forged crankshaft with a stroke of 3.975" for the 1965-1967 425 and 400 CID versions; starting in 1968, both the and the big blocks used a stroke of , with crankshaft material changed to cast iron except in a few rare cases.


title: Oldsmobile V8 engine

text: These were wedge-head engines with a unique combustion chamber that resulted from a valve angle of only 6°. This was much flatter than the 23° of the small-block Chevrolet and 20° of the Ford small-block wedge heads. This very open and flat chamber was fuel efficient and had lower than average emissions output. It was the only GM engine to meet US emission standards using a carburetor all the way up to 1990.


title: Oldsmobile V8 engine

text: The first second-generation Oldmobile V8 "Jetfire Rocket" introduced in 1964 and produced through 1967. It was released one year earlier than the tall deck 425, and debuted the standard stroke; bore was . 330s were painted gold and had forged steel crankshafts. The 4 barrel versions had a larger diameter harmonic damper, the 2 barrel only a balancer hub without the rubberized outer ring.


title: Oldsmobile V8 engine

text: The version was the second tall-deck "big-block" Olds. Two distinct versions of the 400 CID engine were made:


title: Oldsmobile V8 engine

text: The 1966-1967 4-4-2 V8 was a short stroke engine which featured B and C cast large-valve cylinder heads and hydraulic lifters of larger diameter, as well as push-rods of different length and diameter than the standard Olds Rocket V8. It was rated at and of torque with a Rochester 4-barrel, and with the L69 tri 2-barrel option in 1966. A nominal 360 hp was claimed in 1967 when equipped with a W30 camshaft, 4-barrel, and outside air induction, 502 of which were factory produced. They were all painted Bronze and had V and G stamped on the cylinder heads.