In general, the maximum independent set problem cannot be approximated to a constant factor in polynomial time (unless P = NP). In fact, Max Independent Set in general is Poly-APX-complete, meaning it is as hard as any problem that can be approximated to a polynomial factor. However, there are efficient approximation algorithms for restricted classes of graphs. In planar graphs, the maximum independent set may be approximated to within any approximation ratio c < 1 in polynomial time; similar polynomial-time approximation schemes exist in any family of graphs closed under taking minors.
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In the Byzantine period, the book-hand, which in earlier times had more than once approximated to the contemporary cursive, diverged widely from it.
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In that example the grain is approximated to , though the grain can also be approximated to , depending on the medication and manufacturer. The apothecaries' system has its own system of notation, in which the unit's symbol or abbreviation is followed by the quantity in lower case Roman numerals. For amounts less than one, the quantity is written as a fraction, or for one half, ss (or variations such as ss., ṡṡ, or s̅s̅).
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The gaster shows a distinct constriction on the upper surface between the first and second segments, which is narrow but very deep. The total body length is approximated to be .
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With an air dielectric cable, which is approximated to with low-loss cable, the velocity of propagation is very close to c, the speed of light in vacuo.Connor, pp. 10, 19-20.
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A ringed kingfisher's clutch size is approximated to be 3-6 eggs, which are incubated for about 22 days.Skutch, A.F. (1972). "Studies of tropical American birds". Publ. Nuttall Ornithol. Club. no. 10.
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There are more than seven types of biwa, characterised by number of strings, sounds it could produce, type of plectrum, and their use. As the biwa does not play in tempered tuning, pitches are approximated to the nearest note.
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A couple of songs and dramatic sequences were filmed in Bangkok and Pattaya. This is the second Assamese film, after Ahir Bhairav, for which shooting took place outside of India. The budget of the film was approximated to be .
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The question of Yuri's birthday remains open, though taking into account all the above mentioned information Yuri's birth date can be approximated to the end of 1080s - first half of 1090s. But then it means that Gytha was indeed his mother.
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The party represented many of the German nationalist positions, which approximated to those of Nazi Germany. Historians differ as to whether the SdP was from its beginning a Nazi front organization, or evolved into one.Eleanor L. Turk. The History of Germany.
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On the abyssal circulation of the world ocean. – I. Stationary planetary flow patterns on a sphere. Deep Sea Research (1953), 6, 140-154. This slow upward movement is approximated to be about 1 centimeter (0.5 inch) per day over most of the ocean.
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A common goal in Bayesian experimental design is to maximise the expected Kullback–Leibler divergence between the prior and the posterior. When posteriors are approximated to be Gaussian distributions, a design maximising the expected Kullback–Leibler divergence is called Bayes d-optimal.
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David Gauntlett, Media Gender and Identity, Routledge, 2002. . About Giddens' work on modernity and self- identity. Google Print. A democracy of the emotions—the democratising of everyday life—is an ideal, more or less approximated to in the diverse contexts of everyday life.
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PTAS (polynomial time approximation scheme) consists of problems that can be approximated to within any constant factor besides 1 in time that is polynomial to the input size, but the polynomial depends on such factor. This class is a subset of APX.
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It is NP-hard to compute the thickness of a given graph, and NP-complete to test whether the thickness is at most two.. However, the connection to arboricity allows the thickness to be approximated to within an approximation ratio of 3 in polynomial time.
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Vein 10 free, whereas vein 11 curved and approximated to vein 12. Hindwings with vein 3 from near angle of cell. Veins 4 and 5 from angle and approximated for a short distance. Vein 6 absent and vein 7 anastomosing (fused) with vein 8.
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The cargo moves towards the cooler electrode (Figure 2.2) due to the thermal gradient in the longer nanotube induced by the high current that is passed through it. The maximum velocity was approximated to 1 µm/s which is comparable to the speeds attained by kinesin biomotors.
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Vein 7 straight and well separated from veins 8 and 9. Vein 10 free, whereas vein 11 curved and approximated to vein 12. Hindwings with vein 3 from near angle of cell. Veins 4 and 5 from angle and veins 6 and 7 from upper angle.
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SCRAMSPACE was designed and built at Brisbane, Australia. It took 3 years to build and was estimated to cost around $14 million. It was approximated to fly at around Mach 8. It was the first and the largest research project funded by the Australian Space Research Program.
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The river Munneru flows on the western side of the city. census of India, Khammam urban agglomeration has a population of 3,13,504. However, on 19 October 2012, the civic body of Khammam was upgraded to Municipal corporation Post upgradation to corporation Khammam population is approximated to be 3,07,000.
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Chorioamnionitis is approximated to occur in about 4% of births in the United States. However, many other factors can increase the risk of chorioamnionitis. For example, in births with premature rupture of membranes (PROM), between 40 and 70% involve chorioamnionitis. Furthermore, clinical chorioamnionitis is implicated in 12% of all cesarean deliveries.
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Bennard B Perlman: Robert Henri: His Life and Art, page 17. Courier Dover Publications, 1991. While at the Pont-Aven artist's colony he painted a picture that became known as The Talisman, under the close supervision of Gauguin. The picture was an extreme exercise in Cloisonnism that approximated to pure abstraction.
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On the other hand, he approximated to Otto III, Holy Roman Emperor and eventually named him literally with the title of compadre, which meant "the co-father of the Venetian Doge's children". Otto specially liked this, and became the children's godfather.Katus László: Németország történeti gyökerei. In: Rubicon, 1999 1-2, pp.
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Almost all countries from the former Soviet Union lack freedom of panorama. Exceptions are three countries whose copyright laws were amended recently. The first was Moldova in July 2010, when the law in question was approximated to EU standards. Armenia followed in April 2013 with an updated Armenian law on copyright.
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The ECF grades approximately 200,000 games a year. The grading season runs from 1 June to 31 May. An ECF grade can be approximated to an Elo rating by multiplying by 7.5 and adding 700. An ECF grade of 100 is approximately 1450 Elo, while 200 ECF equals 2200 Elo.
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Cav1.3 channels are regulated by negative feedback to achieve Ca2+ homeostasis. Calcium ions are a critical second messenger, intrinsic to intracellular signal transduction. Extracellular calcium levels are approximated to be 12000-fold greater than intracellular levels. During calcium-dependent processes, the intracellular level of calcium rises by up to 100-fold.
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Its duration is approximated to be from the end of the 2nd century till the middle of the 9th century. In this cemetery 134 tombs were discovered with 118 being cremated and 16 simple burials. There were 500 pots discovered which were used either as burials or as cremators for the dead.
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7-limit 8:7 septimal whole tone . In music, a secor is the interval of 116.7 cents () named after George Secor. Secor devised it to allow a close approximation, generated from a single interval, to Harry Partch's 43 tone just intonation scale. All 11-limit consonances are approximated to within 3.32 cents.
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The Birmingham Larger Urban Zone, a Eurostat measure of the functional city-region approximated to local government districts, has a population of 2,357,100 in 2004. In addition to Birmingham itself, the LUZ includes the Metropolitan Boroughs of Dudley, Sandwell, Solihull and Walsall, along with the districts of Lichfield, Tamworth, North Warwickshire and Bromsgrove.
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The generation length of the species is approximated to be six years. They maintain small groups, typically foraging in tropical woodland vegetation and often observed hunting over open running water. Collectors of the museum specimens noted that the species was more difficult to shoot, flying closer to the cliffs than V. caurinus.
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Planck's Law. The Sun is approximately 6000K in surface temperature and the emission peaks at visible light. The Earth, approximated to 300K also emit non-visible radiation. In remote sensing, the electromagnetic radiation acts as the information carrier, with a distance of tens to thousands of kilometers distance between the sensor and the target.
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H. Esmaeilzadeh, et al. "Neural acceleration for general-purpose approximate programs", MICRO, 2012 ; Approximate system : In an approximate system, different subsystems of the system such as the processor, memory, sensor, and communication modules are synergistically approximated to obtain a much better system-level Q-E trade- off curve compared to individual approximations to each of the subsystems.
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8 thousand men under leadership of professor Władysław Raczkowski sang the hymn Gaude Mater Polonia. The performance of Ojczyzna by Feliks Nowowiejski with his companionship of ten brass bands have caused the peculiar appealing of the audience. The number of people singing at once at the day of the opening is approximated to 12 000 or 13 000.
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The area covered by this enumeration district approximated to that of the former Wolverton Urban District and included Stony Stratford CP, Wolverton and Greenleys CP, New Bradwell CP, Stantonbury CP and part of Great Linford CP.Map of Wolverton/Stony Stratford Urban Sub-area As of March 2020, the 2001 boundaries are no longer shown, invalidating this citation.
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However, Guangdong Province, Hainan Province, and Guangxi were the Chinese regions most extensively impacted. The typhoon brought record wind gusts into Guangxi. In those three regions combined, 13,000 homes were estimated to have collapsed and a large swath of farmland was damaged. Two people were killed in China and economic losses approximated to ¥2.1 billion (US$253 million).
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Theologians of the early Christian period differed in the usage of this term. In Antiochene circles, it connoted the humanity or divinity of Christ conceived as a concrete set of characteristics or attributes. In Alexandrine thinking, it meant a concrete individual or independent existent and approximated to hypostasis without being a synonym.Kelly, J.N.D. Early Christian Doctrines A&C; Black(1965) p.
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This computer-based generation of fractal objects is an endless process. In theory, images can be calculated infinitely but in practice are approximated to a certain level of detail. Mandelbrot used quadratic formulas described by the French mathematician Gaston Julia. The maximum fractal dimension that can be produced varies according to type and is sometimes limited according to the method implemented.
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The holotype specimen of Thanatotheristes degrootorum (TMP 2010.5.7) is based on a right maxilla, right jugal, right postorbital, right surangular, right quadrate, right laterosphenoid, left frontal, and both dentaries. The length of the skull has been approximated to be . It was smaller than the closely related Daspletosaurus, but the holotype individual was not osteologically mature at the time of death.
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Because the ESR decreases with increasing frequencies. the ripple current data sheet value, specified at 100/120 Hz, can be higher at higher frequencies. In cases like this manufacturers specify correction factors for ripple current values at higher frequencies. For example, the ripple current at 10 kHz can usually be approximated to be 30 to 40% higher than the 100/120 value.
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Post-infectious origins have been approximated to make up anywhere between 30–80% of NDPH patients in different studies. Viruses that have been implicated include Epstein-Barr virus, herpes simplex virus and cytomegalovirus. Non-specific upper respiratory infections including rhinitis and pharyngitis are most often cited by patients. In one study, 46.5% patients recalled a specific trigger with a respiratory tract illness being the most common.
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Within these regions, the screened potential experienced by an electron is approximated to be spherically symmetric about the given nucleus. In the remaining interstitial region, the potential is approximated as a constant. Continuity of the potential between the atom- centered spheres and interstitial region is enforced. In the interstitial region of constant potential, the single electron wave functions can be expanded in terms of plane waves.
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Both brianite and panethite were clear and transparent with no crystal faces; and neither present any discernible cleavage. Panethite is a biaxial negative, pale amber in its color and the estimated 2V was approximated to be 51˚. The refractive indices are α=1.567, β=1.576, γ = 1.579 all ±0.001 (Fuchs, 1967). Even though panethite lacks the lamellar structure that brianite shows, panethite shows simple twinning.
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The simplest form of this approximation centers non-overlapping spheres (referred to as muffin tins) on the atomic positions. Within these regions, the potential experienced by an electron is approximated to be spherically symmetric about the given nucleus. In the remaining interstitial region, the screened potential is approximated as a constant. Continuity of the potential between the atom-centered spheres and interstitial region is enforced.
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They reasoned that the equilibrium value of commodities approximated to prices charged by the producer when those commodities were in elastic supply and that these producer prices corresponded to the embodied labor, i.e. the cost of the labor (essentially the wages paid) that was required to produce the commodities. The Ricardian socialists viewed profit, interest and rent as deductions from this exchange-value. These ideas embodied early conceptions of market socialism.
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The forewings are white irregularly irrorated (sprinkled) with light greyish ochreous and with a black dot towards the costa near the base. The stigmata are rather large and black, the plical very obliquely beyond the first discal, the second discal approximated to the tornus. There is a marginal series of black dots around the posterior part of the costa and termen. The hindwings are very pale yellowish grey.
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The Lokstene Shrine of Dievturi was inaugurated on 6 May 2017 and is operated by the LDS. It was financed by the entrepreneur Dagnis Čākurs and is located on a small island in the Daugava river, close to the town Pļaviņas. As of 2018, the LDS consisted of a board and eight local groups. The total number of organized Dievturi was approximated to between 600 and 800 people.
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In a multilevel cache hierarchy, the miss pattern of the higher level cache becomes the re-reference pattern of the immediate lower level cache. Hartstein et al. found that whereas the cache misses for lower levels do not follow a strict power law, as long as the lower level cache is considerably larger than the higher level cache, the miss rate function can be approximated to the power law.
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Early in 1945, a Blohm & Voss (B&V;) aircraft designer called Thieme began work on Drawing Number Ae 607, within the standard drawing numbering system at B&V.; His design for a jet fighter was radically different from anything that B&V; had done before. A flying wing, it approximated to a 45° delta planform. Reports of its existence were not confirmed until 2017, when the drawing was published.
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Palpi upturned, the 2nd joint broadly scaled in front, the 3rd porrect (extending forward) and lying on the hair of 2nd joint; maxillary palpi filiform and as long as the labial; frons rounded; antennae of male minutely ciliated; patagia extending beyond the metathorax; tibiae with the outer spurs half the length of the inner; abdomen long, male with the anal tuft large. Forewing with the costa arched towards apex; the outer margin oblique; the inner margin lobed before middle and somewhat excised towards outer angle; vein 3 from angle of cell; 4, 5 approximated for about one-third length; 7 curved and approximated to 8 and 9; 10 closely approximated to 8 and 9. Hindwing with the costa arched at middle; vein 2 from near angle of cell; 3 from the angle; 4 and 5 not approximated towards origin; 6 and 7 shortly stalked and curved, 7 anastomosing (fusing) slightly with 8. The wingspan is about 40 mm.
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In classical mechanics, anharmonicity is the deviation of a system from being a harmonic oscillator. An oscillator that is not oscillating in harmonic motion is known as an anharmonic oscillator where the system can be approximated to a harmonic oscillator and the anharmonicity can be calculated using perturbation theory. If the anharmonicity is large, then other numerical techniques have to be used. As a result, oscillations with frequencies 2\omega and 3\omega etc.
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In India, the major maternal lineages are various M subclades, followed by R and U sublineages. These mitochondrial haplogroups' coalescence times have been approximated to date to 50,000 BP. The major paternal lineages represented by Y chromosomes are haplogroups R1a1, R2, H, L and Haplogroup J2. Some researchers have argued that Y-DNA Haplogroup R1a1 (M17) is of autochthonous South Asian origin. However, proposals for a Central Asian origin for R1a1 are also quite common.
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The shotgun approach is approximated to be 94% accurate, while the rest of the chromosome is about 53% accurate using the second approach. This data from the second approach, released in collaboration with the IWGSC, will be used along with the physical-map based approach to individual chromosomes, including Feuillet’s sequencing of 3B, to produce the full genome by 2017. Sequencing the wheat genome completely is important for producers all over the world.
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He was able to see the spiritual condition of people. In a state of mind which must have approximated to that of William Blake, he tells us that he saw upon one occasion the soul of a tree. He could also, he asseverated, recall the memory of some of his past lives. He was told through a sensitive that these had been many, that he had lived in trees and animals, and that he had been a prince.
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Stenoma redintegrata is a moth of the family Depressariidae. It is found in Bolivia."Stenoma Zeller, 1839" at Markku Savela's Lepidoptera and Some Other Life Forms The wingspan is about 17 mm. The forewings are pale fuscous, the veins marked with fine rather dark fuscous lines and with slender whitish interneural streaks edged below with fine rather dark fuscous lines closely approximated to the veins beneath them (so that there are pairs of closely adjacent dark lines).
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Graffiti on the Wychbury Obelisk Who put Bella in the Wych Elm? is graffiti which that appeared in 1944 following the 1943 discovery by four children of the skeletonised remains of a woman inside a wych elm in Hagley Wood, Hagley (located in the estate of Hagley Hall), in Worcestershire, England. The victim—whose murder is approximated to have occurred in 1941—remains unidentified, and the current location of her skeleton and autopsy report is unknown.
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959–960Colin Humphreys, The Mystery of the Last Supper Cambridge University Press 2011 , pp. 188–190 Several scholars have argued that the modern precision of marking the time of day should not be read back into the gospel accounts, written at a time when no standardization of timepieces, or exact recording of hours and minutes was available, and time was often approximated to the closest three-hour period.Steven L. Cox, Kendell H Easley, 2007 Harmony of the Gospels pp.
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The Burgher population worldwide is approximated to be around 100,000, concentrated mostly in the United Kingdom, Canada, Australia and New Zealand. A large community of Sri Lankans exists in Australia today, of which many are descendants of the migration over the last 50 years. Evident in the many Sri Lanka-Australia Associations, old boys’ and old girls’ school associations are maintained as a reaffirmation of their identity and wish to continue ties with their motherland, Sri Lanka.
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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, 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.
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At the 1981 Census, the Burghers (Dutch and Portuguese) were almost 40,000 (0.3% of the population of Sri Lanka). Many Burghers emigrated to other countries. There are still 100 families in Batticaloa and Trincomalee and 80 Kaffir families in Puttalam that still speak the Portuguese Creole; they have been out of contact with Portugal since 1656. The Burgher population worldwide is approximated to be around 100,000, concentrated mostly in the United Kingdom, Canada, Australia and New Zealand.
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The dark blue was popular amongst ITV contractors because it closely approximated to black on a black and white television set. The version of the logo included the word 'COLOUR', boasting the new technology. In 1979, the ident was modified once more to remove the word colour and to give it a more dynamic form up. The result was the yellow logo flying down onto a black background before the outline extended out towards the screen, set to a synthesised tune.
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The Mid-Atlantic Ridge spreading center pulls the lithosphere apart, creating normal faults which expose sub-surface rocks to seawater. Olivine, the mineral responsible for Lost City's serpentinization. The Atlantis Massif is described as an ultramafic oceanic core complex of the Mid- Atlantic Ridge, with upper mantle rock being exposed to seawater through faulting from tectonic extension associated with oceanic spreading centers. The spreading half-rate is approximated to about 12 mm/yr, classifying it as a slow-spreading ridge.
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Chau had traveled to meet supporters in the Mekong Delta region, where he was introduced to Hien. Hien and his wealthy landowners group agreed to become the dominant financiers of the Đông Du (Eastern Study) movement, which funded young nationalists in traveling to Japan, where they would study and participate in activism for Vietnam's independence from abroad.Marr, p. 105. In 1907, he donated a substantial amount of his financial resources to the support of the overseas students, approximated to be around 20,000 piastres.
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Cambridge University Press, . This defense wall constructed in a unique position to block the southern exit of the Daryal Pass before it widens into the plain of modern Tbilisi was presumably a preventive measure against the Alans who frequently raided the Roman frontiers from across the Caucasus. Armazi stele of Serapit. During this period, Armazi was governed by a hereditary pitiakhsh, whose rank approximated to that of viceroy or satrap, and was second in the official Iberian hierarchy after the king.
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Encouraged by Eusebius of Nicomedia, the Melitians went into schism and elected a rival patriarch named Theonas with the support of the Arians. A certain Pistos, a friend of Arius, was even ordained a bishop in the Melitian church. It is unclear if or to what extent the Melitians' Christology had been influenced by or approximated to Arianism in this period. In several letters, the Melitians accused Athanasius of beating their bishops, even of murdering one, and of desecrating Melitian liturgical vessels.
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Modern large wind turbines are typically actively controlled to face the wind direction measured by a wind vane situated on the back of the nacelle. By minimizing the yaw angle (the misalignment between wind and turbine pointing direction), the power output is maximized and non- symmetrical loads minimized. However, since the wind direction varies quickly the turbine will not strictly follow the direction and will have a small yaw angle on average. The power output losses can simply be approximated to fall with (cos(yaw angle))3.
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The date of its construction is approximated to 360 BC, and it was located at the west of the terrace supporting the entire complex of the "Marmaria". Although only the foundations are extant, its plan has been fully restored: It was based on a crepidoma consisting of three levels and had a prostyle in antis consisting of six columns on the façade. It also had a cella and a vestibule. The cella was separated from the pronaos by a gate in the Ionian order.
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In computational physics, N-body simulations (also called N-particle simulations) are simulations of dynamical systems of particles under the influence of certain conditions, such as being subject to gravity. These simulations are very common in cosmology and computational fluid dynamics. N refers to the number of particles considered. As simulations with higher N are more computationally intensive, systems with large numbers of actual particles will often be approximated to a smaller number of particles, and simulation algorithms need to be optimized through various methods.
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Around 250 BC, the Greek mathematician Archimedes created an algorithm to approximate with arbitrary accuracy. In the 5th century AD, Chinese mathematics approximated to seven digits, while Indian mathematics made a five-digit approximation, both using geometrical techniques. The first exact formula for , based on infinite series, was discovered a millennium later, when in the 14th century the Madhava–Leibniz series was discovered in Indian mathematics. The invention of calculus soon led to the calculation of hundreds of digits of , enough for all practical scientific computations.
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There are many descendants of Ethiopian Beta Israel, whose ancestors converted to Christianity and who are now returning to the Mosaic Israelite faith. This group of people is known as the Falash Mura. They are admitted entrance to Israel, although not as Israelites, thus enabling the Israeli government to set quotas to their immigration and make citizenship dependent on Orthodox conversion to modern Judaism. Although nobody knows for certain the exact population of the Falash Mura in Ethiopia, it is approximated to be 20,000-26,000.
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For the 2001 Census, the Office for National Statistics designated urban sub-areas called Walnut Tree and Browns Wood that are far bigger than the districts of that name.KS01 Usual resident population: Census 2001, Key Statistics for urban areas (lines 1808 to 1815). The Walnut Tree and Browns Wood urban sub-areas together approximated to that part of the former Newport Pagnell Rural District that is west of the River Ouzel and east of the M1. The ONS discontinued this usage in the 2011 Census.
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That is, an input polygon or the convex hull of an input point set must be subdivided into triangles that meet edge-to-edge and vertex-to-vertex, in such a way as to minimize the sum of the perimeters of the triangles. The problem is NP-hard for point set inputs, but may be approximated to any desired degree of accuracy. For polygon inputs, it may be solved exactly in polynomial time. The minimum weight triangulation has also sometimes been called the optimal triangulation.
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The number of inches in that measurement is approximated to be the number of degrees of curvature. Due to the limitation of how specific train equipment can make a turn at maximum speeds, there is a limitation of minimum curve radius to control the sharpness of all curves along a given route. Although most countries use radius for measurement of curvature, the term maximum degree of curvature is still used outside of the United States such as in India, but with the radius as the unit.
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Hele-Shaw flow is defined as Stokes flow between two parallel flat plates separated by an infinitesimally small gap, named after Henry Selby Hele-Shaw, who studied the problem in 1898. Various problems in fluid mechanics can be approximated to Hele-Shaw flows and thus the research of these flows is of importance. Approximation to Hele-Shaw flow is specifically important to micro-flows. This is due to manufacturing techniques, which creates shallow planar configurations, and the typically low Reynolds numbers of micro-flows.
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He was a contemprary of Raphael, with whom he studied in the school of Pietro Perugino. The two artists were close friends, and the influence of Raphael is so evident in the works of Alfano that they have frequently been attributed to the more famous artist. Towards the close of his life Alfani gradually changed his style and approximated to that of the later Florentine school. The date of his death, according to some, was 1540, while others say he was alive in 1553.
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Arno Penzias and Robert Wilson announce the discovery of a weak radio signal coming from all parts of the sky. Scientists figure out that this must be emitted by an object at a temperature of -270 °C. Soon it is recognized as the remnant of the very hot radiation from the Big Bang that created the universe 13 billion years ago, see Cosmic microwave background. This radio signal is emitted by the electron in hydrogen flipping from pointing up or down and is approximated to happen once in a million years for every particle.
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In 1998, Mikkel Thorup claimed that map graphs can be recognized in polynomial time.. However, the high exponent of the algorithm that he sketched makes it impractical, and Thorup has not published the details of his method and its proof. The maximum independent set problem has a polynomial- time approximation scheme for map graphs, and the chromatic number can be approximated to within a factor of two in polynomial time.. The theory of bidimensionality leads to many other approximation algorithms and fixed- parameter tractable algorithms for optimization problems on map graphs....
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In the 1850s Anlaby Common was enclosed land in open countryside to the east of the village of Anlaby. The area included a number of farms, and two large houses, Spring Villa (built 1840), and East Ella (built 1842). The Hull and Kirk Ella Trust road (later Anlaby Road) ran east west through the area; a northern border approximated to Derringham Dike/Spring Bank waterway and road, whilst to the south was Hessle common across fields.Ordnance Survey Sheet 240 1853 By the 1890s the Hull, Barnsley and West Riding Junction Railway (HB&WRJnc.Rlwy.
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The population was approximated to be around twenty-two, excluding slaves, in 1790, and dropped to less than ten by the early 19th century. The colony continued to survive until it was destroyed in 1832 by a slave revolt and the resulting fire. Historian Natalie Zemon Davis is working on a history of 18th century Jodensavanne, focusing on David Isaac Cohen Nassy (born 1747) and relations between blacks and whites in the Jewish community. An article titled 'Regaining Jerusalem' was published in 2016 by Davis, detailing a celebration of Passover within Jodensavanne.
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Leichter, Howard M.: A Comparative Approach to Policy Analysis: Health Care Policy in Four Nations, p. 226 By the 1960s, life and health expectancies in the Soviet Union approximated to those in the US and in non-Soviet Europe. The effectiveness of the model declined with underinvestment, with the quality of care beginning to decline by the early 1980s, though in 1985 the Soviet Union had four times the number of doctors and hospital beds per head compared with the USA. The quality of Soviet medical care became low by developed-world standards.
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The planet mass for which migration can be approximated to Type I depends on the local gas pressure scale height and, to a lesser extent, the kinematic viscosity of the gas. In warm and viscous disks, Type I migration may apply to larger mass planets. In locally isothermal disks and far from steep density and temperature gradients, co-rotation torques are generally overpowered by the Lindblad torques. Regions of outward migration may exist for some planetary mass ranges and disk conditions in both local isothermal and non-isothermal disks.
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The border between the North Korean and South Korean EEZs in the Yellow Sea cannot be determined because of potential overlap and disputes over certain islands. In the Sea of Japan, the North Korean EEZ can be approximated to be trapezoidal-shaped. The border between North Korea and Russia's respective EEZs is the only such border that has been determined in Northeast Asia. Here, the EEZ does not cause many problems, even with regards to South Korea, because the sea is not thought to be rich in resources.
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With the introduction of rifling and elongated shells replacing the old roundshot, guns could fire projectiles of nearly twice the previous weight possible for a given bore (calibre). The rifling gave a far greater range for a given propellant charge, hence a minimal increase in gunpowder was needed for the heavier shells. While the La Hitte guns retained the traditional 4 designation, the number now approximated to kg rather than the livre (French pound) as previously. Hence the Canon de campagne de 4 La Hitte fired a shell weighing nearly 4 kg.
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The Villa Magna Condominium Complex was an urban development that was planned to rise on a plot in Brickell, downtown Miami, Florida. It was approved in 2006 by the city council and the Federal Aviation Administration and construction was slated to begin in April 2007. The ending date was approximated to be late 2008 or early 2009; however, the housing crisis of the late 2000s halted the project. The project was revived as The Towers by Foster + Partners in 2016, after FAA approval of supertall heights (>1,000 ft).
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Henrichemont, formerly known as Boisbelle, is a commune in the Cher department in the Centre-Val de Loire region of France. The village was created and named in honour of Henri IV in 1609 by Maximilien de Béthune, Duke of Sully to be the capital of the principality of Boisbelle and possibly a refuge for the protestants of the region. The principality approximated to the territories of the former canton of Henrichemont. The hamlet of La Borne is home to a restored tradition of stoneware pottery, attracting world-renowned artists and writers to stay there.
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Kim was born on Jeju Island. Adopted by the head of a gisaeng house at the age of 12, she became a government gisaeng ― a type of Korean traditional entertainer who is designated and reserved specifically for government officials. After discovering a talent in business and commerce, she later became one of the most successful female merchants on the island. When Jeju was struck by a deadly famine in 1795 (the 19th year of King Jeongjo, Kim sold all her assets and donated approximately 90% of her money (approximated to be in today's currency) to save millions of lives.
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Since the principles governing the workings of the oculometer rely on a relatively simple concept (electro-optical sensing of the eye), it ensures that the oculometer will be functional whenever the user is seeing. Additionally, the position of the reflection of the collimated beam from the cornea can be approximated to be on the plane of the pupil. This implies minimal parallax error between the corneal reflection and the center of the pupil, thus making the oculometer insensitive to changes in the head position during measurements. These properties of the oculometer ensures minimal interference with the routine activities of the user during measurements.
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Such problems cannot be approximated to any multiplicative factor by a bounded-error probabilistic algorithm unless NP = RP, because any multiplicative approximation would distinguish the values 0 and 1, effectively solving the decision version in bounded-error probabilistic polynomial time. In particular, under the same assumption, this rules out the possibility of a fully polynomial time randomised approximation scheme (FPRAS). For other points, more complicated arguments are needed, and the question is the focus of active research. , it is known that there is no FPRAS for computing P(G, x) for any x > 2, unless NP = RP holds.
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However, under a scanning electron microscope, the conductive polymer is irregular due to agglomerations of the polymeric binder. Up to date, there is not a comprehensive model capable of predicting all the non-linearities observed in force-sensing resistors. The multiple phenomena occurring in the conductive polymer turn out to be too complex such to embrace them all simultaneously; this condition is typical of systems encompassed within condensed matter physics. However, in most cases, the experimental behavior of force-sensing resistors can be grossly approximated to either the percolation theory or to the equations governing quantum tunneling through a rectangular potential barrier.
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A sparsest cut of a graph G=(V,E) is a partition for which the ratio of the number of edges connecting the two partitioned components over the product of the numbers of nodes of both components is minimized. This is a NP-hard problem, and it can be approximated to within O(\log n) factor using Theorem 2. Also, a sparsest cut problem with weighted edges, weighted nodes or directed edges can be approximated within an O(\log p) factor where is the number of nodes with nonzero weight according to Theorem 3, 4 and 5.
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Baran is a village situated on the edge of Baran Nai, a hill torrent that ranges from the Sindh to Balochistan provinces of Pakistan, at the foot of the Kirthar Mountains range. The population is approximated to be less than ten thousand with the 95% population being the Gabol Baloch tribe with Sardar Nabil Ahmed Khan Gabol as the tribal head. Baran receives most of its precipitation from monsoon rains, and gives a very green looks as the rain water helps grow savannah. The region is rich in wildlife including the Sindh Ibex, deer, partridge, fox, hare and many species of small birds.Sindhwildlife.com.
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The barbat (also called “barbiton”) is unlike the instrument depicted on Greek vase paintings. The Greek barbiton, however, although it underwent many changes, retained until the end the characteristics of the instruments of the Greek kithara whose strings were strummed and plucked, whereas the rebab was sounded by means of the bow at the time of its introduction into Europe. At some period not yet determined, which we can but conjecture, the barbat approximated to the form of the large lute. An instrument called barbiton was known in the early part of the 16th century and during the 17th century.
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Babylonian mathematics usually approximated to 3, sufficient for the architectural projects of the time (notably also reflected in the description of Solomon's Temple in the Hebrew Bible).See #Imputed biblical value. "There has been concern over the apparent biblical statement of ≈ 3 from the early times of rabbinical Judaism, addressed by Rabbi Nehemiah in the 2nd century." The Babylonians were aware that this was an approximation, and one Old Babylonian mathematical tablet excavated near Susa in 1936 (dated to between the 19th and 17th centuries BCE) gives a better approximation of as = 3.125, about 0.528 percent below the exact value.
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The forewings are dark fuscous with the basal two-fifths darker with a strong purple gloss, limited by a cloudy irregularly waved pale greyish-ochreous transverse line, sometimes little marked. There is a large rounded purple-blackish apical blotch, limited by a similar less marked line from three-fifths of the costa to the dorsum before the tornus, approximated to the first above the middle but nearly obsolete there, the space between these two lines somewhat irrorated (sprinkled) with pale greyish ochreous. The hindwings are fuscous, lighter towards the apex, the basal half suffused with blackish fuscous.Transactions of the Entomological Society of London.
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Recent work suggests that the area outside the South Ireland End Moraine was inundated by Irish Ice during and after the LGM. At the same time parts of the area outside the South Wales End Moraine must also have been inundated by ice. Another puzzle is the extent to which the long profile of the Irish Sea Glacier, at the time of its maximum extent, approximated to the classic equilibrium profile. Work in analogous situations in Marie Byrd Land, Antarctica, suggests that the ice surface altitude over the mountains might have been around 800m lower than predicted.
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77 These rites took place on 24 March, called the day of blood (dies sanguinis), after the ceremony. In consequence of this practice, which approximated to the rites dedicated to Cybele in Asia Minor, both Enyo and Bellona became identified with her Cappadocian aspect, Ma."Cults of Enyo and Ma" at Theoi The Roman Campus Martius area, in which Bellona’s temple was situated, had extraterritorial status. Ambassadors from foreign states, who were not allowed to enter the city proper, stayed in this complex. Since the area of the temple was outside the pomerium, the Senate met there with ambassadors and received victorious generals prior to their triumphs.
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In 1867, mill property on streams that connected with Lake Michigan on the western side of the state had a total value of approximately two million dollars; property on the eastern side was valued over five million dollars. The total number of saw mills in Michigan was approximated to be 665. The logging industry led to the development of many towns including Grayling, Manistee, Muskegon and Alpena. With the decline of the lumbering business in the mid to late 1900s, it also led to many forgotten ghost towns such as Alcona and Killmaster—now Gustin Township, Michigan, and the 25 ghost towns in Benzie County.
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Reviewers also praised the game enabling the promotion of physical exercise. Terri Schwartz (IGN) said it was "secretly the best exercise app out there" and that it changed her daily walking routine. Patrick Allen (Lifehacker) wrote an article with tips about how to work out using Pokémon Go. Julia Belluz (Vox) said it could be the "greatest unintentional health fad ever" and wrote that one of the results of the game that the developers may not have realized was that "it seems to be getting people moving". Users took an extra 194 steps per day once they started using the app, which approximated to 26% more than usual.
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The coincidence of the Carrington super flare and the super geomagnetic event of 1859 was evidence that plasma was ejected from the Sun during a flare event. Chapman and Ferraro proposed that a plasma was emitted by the Sun in a burst as part of a flare event which disturbed the planet's magnetic field in a manner known as a geomagnetic storm. The collision frequency of particles in the plasma in the interplanetary medium is very low and the electrical conductivity is so high that it could be approximated to an infinite conductor. A magnetic field in a vacuum cannot penetrate a volume with infinite conductivity.
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Iron smelting occurred in the Ife region. The yield and efficiency were quite high as the iron smelting process yielded ore grade near 80 percent iron oxide, lean slag possessed less than 60 percent iron oxide, and no greater than the required amount of iron oxide in the slag was left for slag formation. While more excavation is needed to produce a more accurate estimate for the age of the smelting site, it can be approximated to likely being precolonial, during the Late Iron Age. Igbo Olokun, also known as Olokun Grove, may be one of the earliest workshops for producing glass in West Africa.
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Owing to these early developments, the typical example of entropy change ΔS is that associated with phase change. In solids, for example, which are typically ordered on the molecular scale, usually have smaller entropy than liquids, and liquids have smaller entropy than gases and colder gases have smaller entropy than hotter gases. Moreover, according to the third law of thermodynamics, at absolute zero temperature, crystalline structures are approximated to have perfect "order" and zero entropy. This correlation occurs because the numbers of different microscopic quantum energy states available to an ordered system are usually much smaller than the number of states available to a system that appears to be disordered.
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It is conceivable that the five superstring theories are approximated to a theory in higher dimensions possibly involving membranes. Because the action for this involves quartic terms and higher so is not Gaussian, the functional integrals are very difficult to solve and so this has confounded the top theoretical physicists. Edward Witten has popularised the concept of a theory in 11 dimensions, called M-theory, involving membranes interpolating from the known symmetries of superstring theory. It may turn out that there exist membrane models or other non-membrane models in higher dimensions—which may become acceptable when we find new unknown symmetries of nature, such as noncommutative geometry.
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However, since the Sun's gravitational field is much stronger than Earth's, the two-body solution is insufficient. The characteristic energy with respect to Sun was negative, and MAVEN – instead of heading to infinity – entered an elliptical orbit around the Sun. But the maximal velocity on the new orbit could be approximated to 33.5 km/s by assuming that it reached practical "infinity" at 3.5 km/s and that such Earth-bound "infinity" also moves with Earth's orbital velocity of about 30 km/s. The InSight mission to Mars launched with a C3 of 8.19 km2/s2. The Parker Solar Probe (via Venus) plans a maximum C3 of 154 km2/s2.
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When a force is applied, these materials elastically store and release energy, which does not result in energy loss in the form of heat. Yet, MRE and other elastography imaging techniques typically utilize a mechanical parameter estimation that assumes biological tissues to be linearly elastic and isotropic for simplicity purposes. The effective shear modulus \mu can be expressed with the following equation: \mu=E/[2(1+ u)] where E is the elastic modulus of the material and u is the Poisson’s ratio. The Poisson’s ratio for soft tissues is approximated to equal 0.5, resulting in the ratio between the elastic modulus and shear modulus to equal 3.
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Palmetto Bend Dam was begun in 1968 and completed in 1980 by the United States Bureau of Reclamation at a cost of approximately $92 million. The resulting reservoir covered the ghost town of Texana, which had been founded in 1832 near the junction of the Navidad and Lavaca rivers. A bill to convey to Texas ownership of the dam and reservoir project was introduced by Congressman Ron Paul on August 2, 1999. After paying the "adjusted net present value of current repayment obligations" (an amount approximated to be $45 million in September 2000), Texas assumed responsibility for all aspects of operation, maintenance, and replacement of the dam and reservoir, a responsibility transferred to the Lavaca-Navidad River Authority.
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On this basis England had 56 Primary Urban Areas in 2007. As Primary Urban Areas were created to allow statistical comparisons, and the majority of statistics are produced based on administrative or electoral geographies, Primary Urban Areas are approximated to local authority and ward level, or to an additional measure called a tract - similar in size to a ward but designed to be subject to fewer revisions over time. It is for these approximate areas that statistics are available. Wards and tracts, being smaller, allow a greater degree of precision in comparing PUAs, but using local authority-based definitions allow PUA comparisons to be made using the wider range of statistics available at this level.
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In computational complexity theory, a gap reduction is a reduction to a particular type of decision problem, known as a c-gap problem. Such reductions provide information about the hardness of approximating solutions to optimization problems. In short, a gap problem refers to one wherein the objective is to distinguish between cases where the best solution is above one threshold from cases where the best solution is below another threshold, such that the two thresholds have a gap in between. Gap reductions can be used to demonstrate inapproximability results, as if a problem may be approximated to a better factor than the size of gap, then the approximation algorithm can be used to solve the corresponding gap problem.
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Restoration Based only on the size of the skull, the full body size of Loxomma is approximated to be 14 feet long, although it is hard to tell definitively without the presence of any post-cranial bones. They lived between the water and the land feeding on live fish as is evident in the shape of their jaw hinge and their two-edged teeth. Because the nasal bones are paired and the nasal apertures are both anterior and pharyngeal, it is indicated that they did breathe air. The location of the orbits on the skull are raised up higher than the snout allowing for the animal to stick out its eyes while the rest of the body is underwater.
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Solar mass ( = ) is also often used in astronomy when talking about masses of stars or galaxies; for example, Alpha Centauri A has the mass of 1.1 suns, and the Milky Way has a mass of approximately . Solar mass also has a special use when estimating orbital periods and distances of 2 bodies using Kepler's laws: a3 = MtotalT2, where a is length of semi-major axis in AU, T is orbital period in years and Mtotal is the combined mass of objects in . In case of planet orbiting a star, Mtotal can be approximated to mean the mass of the central object. More specifically in the case of Sun and Earth the numbers reduce to Mtotal ~ 1, a ~ 1 and T ~ 1.
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With current extinction rates approximated to be 100 to 1,000 times the background extinction rate, it is feared that a de-extinction program might lessen public concerns over the current mass extinction crisis, if it is believed that these species can simply be brought back to life. As the editors of a Scientific American article on de-extinction pose: Should we bring back the woolly mammoth only to let elephants become extinct in the meantime? The main driving factor for the extinction of most species in this era (post 10,000 BC) is the loss of habitat, and temporarily bringing back an extinct species will not recreate the environment they once inhabited. Proponents of de-extinction, such as George Church, speak of many potential benefits.
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While everyday wind waves have a wavelength (from crest to crest) of about and a height of roughly , a tsunami in the deep ocean has a much larger wavelength of up to . Such a wave travels at well over , but owing to the enormous wavelength the wave oscillation at any given point takes 20 or 30 minutes to complete a cycle and has an amplitude of only about .Earthsci.org, Tsunamis This makes tsunamis difficult to detect over deep water, where ships are unable to feel their passage. The velocity of a tsunami can be calculated by obtaining the square root of the depth of the water in metres multiplied by the acceleration due to gravity (approximated to 10 m/s2).
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In the latest official census of 2000, Dandong's total resident population (which includes the districts of Zhenxing, Yuanbao and Zhen'an) was 780,414 people, while Dandong proper had a total population of 2.4 million. In 2005, the resident population was approximated to be 751,914 with a floating population of 176,926, for a total of 928,840. However, the non-agricultural (urban) population is said to consist of only 79.52% of the resident population (597,930). It is unclear what the floating population consists of or where they live, but it is suspected that most of the migrant population is people from the countryside looking for work, local and foreign businessmen, and students. In 2000, there were 244,430 family households (with a pop. of 741,882) and 4,955 collective households (with a pop.
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The vertex cover problem involves finding a set of vertices that touches every edge of the graph. It is NP-hard but can be approximated to within an approximation ratio of two, for instance by taking the endpoints of the matched edges in any maximal matching. Evidence that this is the best possible approximation ratio of a polynomial- time approximation algorithm is provided by the fact that, when represented as a semidefinite program, the problem has an integrality gap of two; this gap is the ratio between the solution value of the integer solution (a valid vertex cover) and of its semidefinite relaxation. According to the unique games conjecture, for many problems such as this the optimal approximation ratio is provided by the integrality gap of their semidefinite relaxation.
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Strict reduction is the simplest type of approximation-preserving reduction. In a strict reduction, the approximation ratio of a solution y' to an instance x' of a problem B must be at most as good as the approximation ratio of the corresponding solution y to instance x of problem A. In other words: : R_A(x, y) \le R_B(x', y') for x' = f(x), y = g(y'). Strict reduction is the most straightforward: if a strict reduction from problem A to problem B exists, then problem A can always be approximated to at least as good a ratio as problem B. Strict reduction preserves membership in both PTAS and APX. There exists a similar concept of an S-reduction, for which c_A(x, y) = c_B(x', y'), and the optima of the two corresponding instances must have the same cost as well.
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As showed, this characterization allows the optimal resilience to be computed in polynomial time by transforming the problem into an instance of the maximum flow problem. For unit disks with bounded ply (the maximum number of disks that have a common intersection) there exists a polynomial-time approximation scheme for the resilience, that can be generalized to barrier shapes of the same size as each other with bounded aspect ratios. For unit disks without assuming bounded ply, the problem of computing the resilience may be approximated to within a constant factor, using the fact that for this shape of barrier the optimal path can only cross each barrier a constant number of times, so the barrier thickness and barrier resilience are within a constant factor of each other. Similar methods can be generalized to non-uniform sensors of approximately equal size.
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Inspired by the circular restricted three-body problem, the four-body problem can be greatly simplified by considering a smaller body to have a small mass compared to the other three massive bodies, which in turn are approximated to describe circular orbits. This is known as the bicircular restricted four-body problem (also known as bicircular model) and it can be traced back to 1960 in a NASA report written by Su-Shu Huang. This formulation has been highly relevant in the astrodynamics, mainly to model spacecraft trajectories in the Earth-Moon system with the addition of the gravitational attraction of the Sun. The former formulation of the bicircular restricted four-body problem can be problematic when modelling other systems that not the Earth-Moon-Sun, so the formulation was generalized by Negri and Prado to expand the application range and improve the accuracy without loss of simplicity.
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The platinum record for Michael Jackson's Thriller, approximated to have sold 66 million copies worldwide, as the world's best-selling album Most albums are studio albums — that is, they are recorded in a recording studio with equipment meant to give those overseeing the recording as much control as possible over the sound of the album. They minimize external noises and reverberations and have highly sensitive microphones and sound mixing equipment. In some studios, each member of a band records their part in separate rooms (or even at separate times, while listening to the other parts of the track with headphones to keep the timing right). In recent years, with the advent of email, it has become possible for musicians to record their part of a song in another studio in another part of the world, and send their contribution over email to be included in the final product.
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The wingspan is 23–30 mm. Forewing violet grey, with a partial rosy-brown flush; the costa, cell, and median area dark fuscous, the costa often remaining pale; inner and outer lines dark, conversely edged with pale, the inner strongly outcurved below middle, closely approximated to the erect lower half of outer line; a black bar from line to line along submedian fold; claviform stigma obsolete, or minute; orbicular grey, with edge only black margined, the margin straight and forming nearly a straight line with the lower half of outer line; submarginal line pale grey, the shade before it red brown, the terminal area dark grey; hindwing greyish fuscous; in the ab. constricta ab. nov. [Warren] principally confined to the males, the median area between the two lines is narrowed and much darker, especially in the two folds, and the red flush is less developed; — the form subarcta Stgr.
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The cost of the great ocean liner approximated to £350,000, and she has a register of 12,077 tons, with a capacity for carrying many hundreds of passengers in the three classes. The chief dining saloon is superb, and so are the smoking, reading, and drawing rooms set apart for first-class travellers. Even the apartments reserved for second class passengers are fitted in a much more, costly fashion than are the best hotels in this city, while the third- class dining saloon is a spacious chamber the full width of the ship, and well lighted from both sides. The acme of comfort has been reached in the staterooms, which are as large and as airy as many bedrooms ashore, while the suites consisting of staterooms, bathroom, sitting-room, and maids' room were so attractive that they instilled a desire for ocean travel into many hearts.
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The Cayley Formation's age was approximated to be about the same as Mare Imbrium based on the local frequency of impact craters. The considerable distance between the Descartes site and previous Apollo landing sites would be beneficial for the network of geophysical instruments,Brzostowski and Brzostowski, pp 414-416 portions of which were deployed on each Apollo expedition beginning with Apollo 12. At the Alphonsus, three scientific objectives were determined to be of primary interest and paramount importance: the possibility of old, pre-Imbrium impact material from within the crater's wall, the composition of the crater's interior and the possibility of past volcanic activity on the floor of the crater at several smaller "dark halo" craters. Geologists feared, however, that samples obtained from the crater might have been contaminated by the Imbrium impact, thus preventing Apollo 16 from obtaining samples of pre-Imbrium material.
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After Wehrmacht raids, hundreds of Antwerp Jews were taken in furniture vans from their homes to Mechelen transit camp. Soon afterwards, Reeder ordered their release at the direct request of Queen Elisabeth of Bavaria and Cardinal Jozef-Ernest van Roey, and the attempt was not repeated. It was hence reported as "impossible" by local SS units charged with meeting Final Solution targets to find enough stateless and foreign Jews to fill another Auschwitz transport after 20 September 1943, though 1,800 Jews of various privileged categories were taken in 1944 to camps including Theresienstadt and Bergen-Belsen. This meant that although 43,000 Jews left Belgium under the Final Solution up until the end of occupation in 1945, many of these in the early months of occupation, this approximated to the number of non-Belgian Jews who had been resident in Belgium before the war, according to lists compiled by de Foy.
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Simon used the analogy of a pair of scissors, where one blade represents "cognitive limitations" of actual humans and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment. Many economics models assume that people are on average rational, and can in large enough quantities be approximated to act according to their preferences. With bounded rationality, Simon's goal was "to replace the global rationality of economic man with a kind of rational behavior that is compatible with the access to information and the computational capacities that are actually possessed by organisms, including man, in the kinds of environments in which such organisms exist." In short, the concept of bounded rationality revises notions of "perfect" rationality to account for the fact that perfectly rational decisions are often not feasible in practice because of the intractability of natural decision problems and the finite computational resources available for making them.
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The hardness proof of the exact boson sampling problem can be achieved following two distinct paths. Specifically, the first one uses the tools of the computational complexity theory and combines the following two facts: # Approximating the probability p(t_1, t_2, ..., t_N) of a specific measurement outcome at the output of a linear interferometer to within a multiplicative constant is a #P-hard problem (due to the complexity of the permanent) # If a polynomial-time classical algorithm for exact boson sampling existed, then the above probability p(t_1, t_2, ..., t_N) could have been approximated to within a multiplicative constant in the BPPNPcomplexity class, i.e. within the third level of the polynomial hierarchy When combined together these two facts along with the Toda's theorem result in the collapse of the polynomial hierarchy, which as mentioned above is highly unlikely to occur. This leads to the conclusion that there is no classical polynomial-time algorithm for the exact boson sampling problem.
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Since the early 1970s it was known that many optimization problems could not be solved in polynomial time unless P = NP, but in many of these problems the optimal solution could be efficiently approximated to a certain degree. In the 1970s, Teofilo F. Gonzalez and Sartaj Sahni began the study of hardness of approximation, by showing that certain optimization problems were NP-hard even to approximate to within a given approximation ratio. That is, for these problems, there is a threshold such that any polynomial-time approximation with approximation ratio beyond this threshold could be used to solve NP-complete problems in polynomial time.. In the early 1990s, with the development of PCP theory, it became clear that many more approximation problems were hard to approximate, and that (unless P = NP) many known approximation algorithms achieved the best possible approximation ratio. Hardness of approximation theory deals with studying the approximation threshold of such problems.
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Travel to Work Areas were selected to approximate city regions as one of the main units of comparison used by the State of the English Cities report and database, commissioned and maintained by the Communities and Local Government department of the UK Government.Robinson, Phillipa "And city regions......", State of the Cities Database, Presentation to North East Regional Information Partnership This has greatly increased the amount of information available about Travel to Work Areas, although the State of the Cities only publishes data for the 56 Travel to Work Areas-based around Primary Urban Areas in England. Travel to Work Areas in Scotland and Wales and those covering only rural areas are not included.\- State of the Cities - Making sense of cities - Travel to work areas (TTWAs) Department for Communities and Local Government To increase the range of statistics available the State of the Cities also publishes data for Travel to Work Areas approximated to local authority boundaries.
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It was first proposed by Apollonius of Perga at the end of the 3rd century BC. It was developed by Apollonius of Perga and Hipparchus of Rhodes, who used it extensively, during the 2nd century BC, then formalized and extensively used by Ptolemy of Thebaid in his 2nd century AD astronomical treatise the Almagest. Epicyclical motion is used in the Antikythera mechanism, an ancient Greek astronomical device for compensating for the elliptical orbit of the Moon, moving faster at perigee and slower at apogee than circular orbits would, using four gears, two of them engaged in an eccentric way that quite closely approximates Kepler's second law. Epicycles worked very well and were highly accurate, because, as Fourier analysis later showed, any smooth curve can be approximated to arbitrary accuracy with a sufficient number of epicycles. However, they fell out of favour with the discovery that planetary motions were largely elliptical from a heliocentric frame of reference, which led to the discovery that gravity obeying a simple inverse square law could better explain all planetary motions.
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At some point he also entered holy orders. In 1580 Kett resigned his fellowship and studied medicine, graduating MD in 1581, and in 1585 "Francis Kett, doctor of phisick" published 'The Glorious and Beautiful Garland of Man's Glorification, containing the godly misterie of heavenly Jerusalem', a book dedicated to Queen Elizabeth: and also in 1585 But in 1588 Edmund Scambler, the Bishop of Norwich, brought charges of heresy against him. Kett's views, if the charges against him were accurate, seem to have approximated to Arianism: he believed Jesus was not God but a good man who had suffered "only as Jesus already, and shall suffer hereafter as Christ" (that is, that having returned to earth Jesus would "suffer againe for the sinnes of the world" and eventually become divine). Kett also had millenarian beliefs, claiming that "Christ is now in his human nature gathering a church in Erthe in Judea"; and that "this year of our Lord 1588 divers Jews shall be sent to divers countries to publish the new covenant".
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2.1028 recognized amongst contemporary Platonists three principal views concerning the ideal numbers, and their relation to the ideas and to mathematical numbers: #those who, like Plato, distinguished ideal and mathematical numbers; #those who, like Xenocrates, identified ideal numbers with mathematical numbers #those who, like Speusippus, postulated mathematical numbers only Aristotle has much to say against the Xenocratean interpretation of the theory, and in particular points out that, if the ideal numbers are made up of arithmetical units, they not only cease to be principles, but also become subject to arithmetical operations. In the derivation of things according to the series of the numbers he seems to have gone further than any of his predecessors.Theophrastus, Met. c. 3 He approximated to the Pythagoreans in this, that (as is clear from his explanation of the soul) he regarded number as the conditioning principle of consciousness, and consequently of knowledge also; he thought it necessary, however, to supply what was wanting in the Pythagorean assumption by the more accurate definition, borrowed from Plato, that it is only insofar as number reconciles the opposition between the same and the different, and has raised itself to self-motion, that it is soul.
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It is NP-complete to test whether there exists a connected dominating set with size less than a given threshold, or equivalently to test whether there exists a spanning tree with at least a given number of leaves. Therefore, it is believed that the minimum connected dominating set problem and the maximum leaf spanning tree problem cannot be solved in polynomial time. When viewed in terms of approximation algorithms, connected domination and maximum leaf spanning trees are not the same: approximating one to within a given approximation ratio is not the same as approximating the other to the same ratio. There exists an approximation for the minimum connected dominating set that achieves a factor of , where Δ is the maximum degree of a vertex in G.. The maximum leaf spanning tree problem is MAX-SNP hard, implying that no polynomial time approximation scheme is likely.. However, it can be approximated to within a factor of 2 in polynomial time.. Both problems may be solved, on -vertex graphs, in time .. The maximum leaf problem is fixed-parameter tractable, meaning that it can be solved in time exponential in the number of leaves but only polynomial in the input graph size.
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