But otherwise, they should be allowed to have a lower set-aside.
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You do this until your weight comes down to a new, lower set point.
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Mr. Kreidler of Washington approved two sets of rates but is only allowing insurers to charge the lower set.
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FCC Chairman Tom Wheeler has argued that injecting competition into the market would lower set-top box prices and spur innovation.
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At about 0620 GMT, MSCI's broadest index of Asia-Pacific shares outside Japan was 23.83% lower, set for its weakest performance since Dec. 4.
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While a pared-down approach means a lower set of costs (half the price of traditional geothermal systems) and quicker installation, that doesn't mean that upfront costs are non-existent.
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The S&P 500 is down 2.56 percent in the first quarter, while the Dow Jones Industrial Average is 3.5 percent lower - set for their worst quarterly performances in more than two years.
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The United States, which sought to challenge a similar scheme in Australia during trade negotiations, argues that lower set prices are unfair on its pharmaceutical companies and leave U.S. consumers footing the bill.
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Dogs Trust Brigend has an adorable 7-year-old Lhasa Apso named Milo in its care, and the little guy has become quite popular across the internet for his protruding lower set of fangs.
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That's the crux of New York's case: The state claims Exxon kept one set of public numbers to account for the future costs of greenhouse gas regulations and another, much lower set, to make business decisions.
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He stood out here, with his slightly formal clothes, his feathered hair, though in the States he would have been generic enough, an East Coast aspirant prep school kid, maybe not quite the real thing, especially if he smiled too broadly (as he was careful almost never to do) and revealed a lower set of teeth in un-American disarray.
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A subset Q of a partially ordered set P is said to be cofinal if for every x \in P there exists some y \in Q such that x \le y. Every cofinal subset of a partially ordered set with maximal elements must contain all maximal elements. A subset L of a partially ordered set P is said to be a lower set of P if it is downward closed: if y \in L and x \le y then x \in L. Every lower set L of a finite ordered set P is equal to the smallest lower set containing all maximal elements of L.
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Birkhoff's theorem states that any finite distributive lattice can be constructed in this way. :Theorem. Any finite distributive lattice L is isomorphic to the lattice of lower sets of the partial order of the join- irreducible elements of L. That is, there is a one-to-one order-preserving correspondence between elements of L and lower sets of the partial order. The lower set corresponding to an element x of L is simply the set of join- irreducible elements of L that are less than or equal to x, and the element of L corresponding to a lower set S of join-irreducible elements is the join of S. For any lower set S of join-irreducible elements, let x be the join of S, and let T be the lower set of the join-irreducible elements less than or equal to x. Then S = T. For, every element of S clearly belongs to T, and any join- irreducible element less than or equal to x must (by join-primality) be less than or equal to one of the members of S, and therefore must (by the assumption that S is a lower set) belong to S itself.
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By the correspondence between stable matchings and lower sets of rotations, the total weight of any matching is then equal to the total weight of its corresponding lower set, plus the weight of the bottom element of the lattice of matchings. The problem of finding the minimum or maximum weight stable matching becomes in this way equivalent to the problem of finding the minimum or maximum weight lower set in a partially ordered set of polynomial size, the partially ordered set of rotations. This optimal lower set problem is equivalent to an instance of the closure problem, a problem on vertex-weighted directed graphs in which the goal is to find a subset of vertices of optimal weight with no outgoing edges. The optimal lower set is an optimal closure of a directed acyclic graph that has the elements of the partial order as its vertices, with an edge from \alpha to \beta whenever \alpha\le\beta in the partial order.
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Cone-head lathes usually had a countershaft (layshaft) on the back side of the cone which could be engaged to provide a lower set of speeds than was obtainable by direct belt drive. These gears were called back gears. Larger lathes sometimes had two-speed back gears which could be shifted to provide a still lower set of speeds. When electric motors started to become common in the early 20th century, many cone-head lathes were converted to electric power.
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Distributive example lattice, with join-irreducible elements a,...,g (shadowed nodes). The lower set a node corresponds to by Birkhoff's isomorphism is shown in blue. In any partial order, the lower sets form a lattice in which the lattice's partial ordering is given by set inclusion, the join operation corresponds to set union, and the meet operation corresponds to set intersection, because unions and intersections preserve the property of being a lower set. Because set unions and intersections obey the distributive law, this is a distributive lattice.
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There is a small, centrally-positioned, skillion-roofed extension in the rear elevation. This also is clad in fibrous- cement sheeting, but is lower set. In each side elevation there are four pairs of tri-paned stained glass casement windows.
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These bracket sets are nearly 2.5 meters high – 70% the height of the columns. Inter-columnar brackets that occur between every two pillars are of the 5th degree. The hall has no ceiling, and the upper and lower set of rafters are exposed.Steinhardt (1997), 79.
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The revised Regency DF304 labelled Mark II was announced in October 1954. Left-hand-drive cars used the DF305 designation. The new more flowing body was slightly longer with a much longer boot and mudguards and was lower-set. It could now be purchased with a 3½-litre or 4½-litre engine.
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The English Cocker Spaniel is similar to the English Springer Spaniel and at first glance the only major difference is the larger size of the Springer. However English Cockers also tend to have longer, and lower-set ears than English Springers. In addition Springers also tend to have a longer muzzle, their eyes are not as prominent and the coat is less abundant.
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The size of the engine gave the car a centre of gravity that was not just rearward but higher than other cars, due to the height of the upper crankshaft above the ground and the need to have the entire engine raised slightly to make room for the lower set of exhausts which left the engine from underneath the car.
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The breed's gaits are agile and elevated, but generally comfortable to ride. The Lusitano differs from the Andalusian through having a more sloped croup, a lower-set tail, and a more convex head profile. The mane and tail are extremely thick in both breeds. Lusitano in a bullfight The ancestors of the Lusitano were originally used for classical dressage, driving and bullfighting on horseback.
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A Scott-continuous function is always monotonic. A subset of a partially ordered set is closed with respect to the Scott topology induced by the partial order if and only if it is a lower set and closed under suprema of directed subsets. A directed complete partial order (dcpo) with the Scott topology is always a Kolmogorov space (i.e., it satisfies the T0 separation axiom).
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Amongst these there are three types of polyps. The club- like feeding polyps grow up to thirteen millimetres in length, and have two rows of eight tentacles, the lower set being shorter than the upper ones. There are also male and female reproductive polyps (gonozoids) that have a few short terminal tentacles. Scattered among these are specialized defensive stinging polyps (dactylozooids) that are long, coiled threads.
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The first prototype Balbuzard flew on 9 July 1995, powered by a 60 kW (80 hp) Rotax 912. Like the next three prototypes, this aircraft had a glass fibre structure. The second prototype had an 88 kW (118 hp) Textron Lycoming O-235 engine, driving a three-blade, fixed pitch propeller, and a longer span and lower set wing fitted with winglets. The undercarriage height was also increased.
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The baryton is a bowed string instrument of the viol family played in Europe during the 17th and 18th centuries. It has six or seven strings of gut, arranged over a fretted fingerboard, plus a lower set of wire strings. When the gut strings are bowed, the wire strings vibrate sympathetically, enriching the tone. The wire strings may also be plucked by the performer's left thumb, creating a contrasting tonal quality.
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St Michael's church is in Farnley park near the stately home of Farnley Hall.There is another Farnley Hall in North Yorkshire. Shops in the original village of Farnley now include a hair salon, a newsagent, and a mini-mart. Farnley has a lower set of shops (in what was originally Bawn village) consisting of a pizza takeaway, a newsagent, a mini- mart, a butcher and Cow Close Community Corner.
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In 1849, he moved to the Oregon Territory and the next year settled on the north side of the Columbia River. Before moving he married Elizabeth Ann Findley in Oregon City on March 27, 1850, and they had eight children. Chenoweth and family settled at the new community of Cascade, located at the lower set of rapids on the river. There he operated a business portaging cargo and passengers around the set of rapids.
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A new species of the genus Helix from south-western Georgia. Journal of Conchology 39: 483-485 Most land snails bear one or two pairs of tentacles on their heads. In most land snails the eyes are carried on the first (upper) set of tentacles (called ommatophores or more informally 'eye stalks') which are usually roughly 75% of the width of the eyes. The second (lower) set of tentacles act as olfactory organs.
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The normal range of sizes is between tall at the withers, with a weight around . The Parson Russell has a relatively square outline, with a body about as long as the dog is tall. Compared to the Jack Russell Terrier, the Parson Russell has a longer head and a larger chest along with overall a slightly larger body size. The Parson retains the flat skull but not the elongated shape of the Fox Terrier, and with lower set ears.
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The earliest settlement of this city, in the site called CR-44, atop Cerro Palenque itself, is Late Classic (500-850 AD). As a new city center was built to the north, this part of the site was abandoned. The new center was on top of a lower set of hills north of Cerro Palenque in the Terminal Classic (850-1100 AD). This new center includes a 300 meter long plaza and a large ball-court.
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This was coupled to a 4-speed manual gearbox from the Rover P3 saloon. This unit was coupled to a Willys/Ford 2-speed transfer gearbox taken from a Jeep. This not only allowed the selection of a lower set of 'crawler' gears but controlled the selection of drive to the front axle as well. The production 1948 Land Rover used the P3 gearbox, but an entirely different transfer box, designed and built by Rover, was fitted.
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The breathing gas mixture in a diving rebreather loop is usually measured using oxygen cells, and the output of the cells is used by either the diver or an electronic control system to control addition of oxygen to increase partial pressure when it is below the chosen lower set-point, or to flush with diluent gas when it is above the upper set-point. When the partial pressure is between the upper and lower set- points, it is suitable for breathing at that depth and is left until it changes as a result of consumption by the diver, or a change in ambient pressure as a result of a depth change. Accuracy and reliability of measurement is important in this application for two basic reasons. Firstly, if the oxygen content is too low, the diver will lose consciousness due to hypoxia and probably die, or if the oxygen content is too high, the risk of central nervous system oxygen toxicity causing convulsions and loss of consciousness, with a high risk of drowning becomes unacceptable.
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Therefore, the set of cuts, partially ordered by inclusion on the lower set of the cut (or the reverse of the inclusion relation on the upper set), gives an equivalent definition of the Dedekind–MacNeille completion. With the alternative definition, both the join and the meet operations of the complete lattice have symmetric descriptions: if are the cuts in any family of cuts, then the meet of these cuts is the cut where , and the join is the cut where .
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As motivational tools, goals have been shown to improve performance in a wide variety of settings. For example, one study looked at the effects of high goals versus low goals on performance. To investigate this effect, students were given goals for a brainstorming activity; those with higher goals were able to brainstorm more ideas than those with lower goals. Therefore, the investigator concluded that goal setting not only increases performance, but more ambitious goals evoke better performance than lower-set goals.
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Illustrations on show that there are two sets of jaws affixed to the planks. The lower set are level with the top of the planks and are circular when closed to firmly grip the head of the broom. Metal plates rising from the planks carry the upper set which are flat and force the broom corn flat. The jaws are closed by a toggle mechanism operating on horizontal links from the fixed jaw and vertical hanger links from the floor.
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The ground-floor shop windows are all flanked by pilasters and topped with moulding detail including a keystone-like feature that reaches the string course. The mullioned and transomed first-floor windows have horizontal heads with brick keystone detailing. The two attic storeys each have a row of circular dormer windows in the steep roof, the lower set being decorated below with festoons of fruit and flowers, which differ in detail from window to window. The drainpipe heads are all inscribed with 1911 in a lozenge pattern.
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And in an acyclic orientation, every face must have at least one sink. Therefore, an acyclic orientation is a unique sink orientation if and only if there is no other acyclic orientation with a smaller sum. Additionally, a k-regular subgraph of the given graph forms a face of the polytope if and only if its vertices form a lower set for at least one acyclic unique sink orientation. In this way, the face lattice of the polytope is uniquely determined from the graph .
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The upper canine teeth can grow to long and have a wide elliptical cross section, being about deep and wide. A tusk will curve 90° or more from the root, and will not lie flat on a table, as it curves somewhat backwards as it grows. The tusks are not used for digging, but are used for combat with other hogs, and in defense against predators – the lower set can inflict severe wounds. Common warthog ivory is taken from the constantly growing canine teeth.
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The pay by plate system services multiple vehicles by making the driver input the license plate information into a machine. This system results in lower set up costs, maintenance, and prevents drivers from taking advantage of parking meters that have time remaining. In many cities, pay by plate has replaced the road-side parking meter and the pay and display machines. The advantage to the city could be: increased revenue, increased compliance, less disputed tickets, increased parking space utilization and/or reduction in staff [see Results section].
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The Excalibur Queen Air can be recognized by the noticeably smaller engine cowlings and lower-set engines. This STC was originally designed and produced by Ed Swearingen who was well known for his work on the Twin Bonanza, Queen Air, and later Swearingen aircraft (Merlin and Metro). The ownership of this STC has changed hands many times over the years. The current owner is Bemidji Aviation which operates a fleet of Excalibur Queen Airs as well as other aircraft in the charter and freight role in the upper mid-west of the United States.
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The Teddy Roosevelt Terrier is a small to medium-sized American hunting terrier. It is lower-set, with shorter legs, and is more muscular with heavier bone density than the related American Rat Terrier. Much diversity exists in the history of the Teddy Roosevelt Terrier breed, and it shares a common early history with the American Rat Terrier, Fox Paulistinha, and Tenterfield Terrier. The Rat Terrier's background is said to stem from the terriers or other dogs that were brought over by early English and other working-class immigrants.
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A machine in Canada operated by the Toronto Parking Authority Pay and display systems differ from road-side parking meters in that one machine can service multiple vehicle spaces, resulting in lower set up costs. In addition, this system theoretically prevents drivers from taking advantage of parking meters that have time remaining; this factor alone has doubled parking revenues in cities that have switched to pay and display.Toronto reaps big profit in parking - www.preciseparklink.com A driver may occasionally take advantage of remaining time should a departing parker give away a ticket with remaining time.
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Sometimes a small bus runs. The village stretches along the main road, Fieschi Road, and the houses have one side facing this road and the other facing the sea. Corniglia is characterised by narrow roads and a terrace in the rock from which all other four Cinque Terre's villages, two on one side and two on the other, can be seen. The town planning structure presents original characteristics compared to those of the other villages: the houses are lower set, and only more recently higher, similar to those of the villages of the hinterland.
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Two figures sit apart from the people on the endless staircase: one in a secluded courtyard, the other on a lower set of stairs. While most two-dimensional artists use relative proportions to create an illusion of depth, Escher here and elsewhere uses conflicting proportions to create the visual paradox. Ascending and Descending was influenced by, and is an artistic implementation of, the Penrose stairs, an impossible object; Lionel Penrose had first published his concept in the February 1958 issue of the British Journal of Psychology. Escher developed the theme further in his print Waterfall, which appeared in 1961.
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The multiplane idea was taken a step further by the quadruplane. No examples were successful, and as biplane design advanced, it became clear that the disadvantages of the triplane and quadruplane outweighed their advantages. In a practical landplane design, the lower set of wings are typically set approximately level with the underside of the aircraft's fuselage, the middle set level with the top of the fuselage, and the top set supported above the fuselage on cabane struts. In a practical flying boat, even the lowest wing must be placed well above the waterline of the hull, creating a tall structure overall.
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The club has attracted a significantly lower set of attendance figures than the Manchester Storm did. During the team's first season the average attendance for all home league fixtures was given as 2,267, in a 17,245 seat arena (although only the lower 4,500 seats were made available for public use during games). When the move to Altrincham was completed, the attendance averaged 800, climbing to 1,027 in the 09–10 season. This makes the club the third best attended club in the EPIHL, behind the Guildford Flames and Milton Keynes Lightning, and the ninth overall in Great Britain.
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Designed by Fairchild (Canada) in the hope of attracting orders from the Royal Canadian Air Force and Canadian Airways,the 45-80 was an ambitious project, being the largest design yet attempted.Milberry 1979, p. 110. The Sekani was a large sesquiplane of conventional configuration, with the sets of wings joined to the top and bottom of the fuselage and braced by N-struts. The lower set of wings were little more than stubs; their bracing to the upper wings passed through the engine nacelles (mounted on the upper wings), and they carried the pontoon undercarriage beneath them.
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The extended real number line (real numbers together with +∞ and −∞) is a completion in this sense of the rational numbers: the set of rational numbers {3, 3.1, 3.14, 3.141, 3.1415, 3.14159, ...} does not have a rational least upper bound, but in the real numbers it has the least upper bound . A given partially ordered set may have several different completions. For instance, one completion of any partially ordered set is the set of its downwardly closed subsets ordered by inclusion. is embedded in this (complete) lattice by mapping each element to the lower set of elements that are less than or equal to .
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If a locomotive is unable to automatically retrieve temporary speed restriction information, permanent speed restrictions will continue to be enforced. In the event of a total failure of the on-board ACSES system the engineer may revert to the use of the cab signal system without civil speed enforcement. Both situations require permission to be obtained from the train dispatcher and are accompanied by additional maximum speed restrictions. In addition the ACSES system installed on Acela Express trainsets checks the status of the on-board tilting mechanism and if the tilt is not functioning will revert to a lower set of track speeds.
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Banking agents help financial institutions to divert existing customers from crowded branches providing a “complementary”, often more convenient channel. Other financial institutions, especially in developing markets, use agents to reach an “additional” client segment or geography. Reaching poor clients in rural areas is often prohibitively expensive for financial institutions since transaction numbers and volumes do not cover the cost of a branch. In such environments banking agents that piggy back on existing retail infrastructure – and lower set up and running cost - can play a vital role in offering many low-income people their first-time access to a range of financial services.
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Lexus introduced a new design language known as "L-finesse" in the mid-2000s with its LF series concepts and the 2006 Lexus GS. L-finesse is represented by three Japanese kanji characters which translate as "Intriguing Elegance, Incisive Simplicity, and Seamless Anticipation". Design characteristics, including a fastback profile, lower-set grille, and the use of both convex and concave surfaces, are derived from Japanese cultural motifs (e.g. the phrase kirikaeshi in arrowhead shapes). While earlier Lexus models were criticized for reserved and derivative styling, and often mistaken for understated domestic market cars, automotive design analyses described L-finesse as adding a distinctive nature and embrace of Japanese design identity.
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While the unions preached the ideology of equal pay for equal work, they also had a "wage scale" which posed a reality of a set pay for men and a separate lower set pay for women. She goes on to state that with more women in the work force it is "simple justice", social justice, to give men and women equal pay for equal work."Statement of Miss Mary Anderson, 18 may 1950" (League of Women Voters) Mary Anderson was the first "'up from the ranks" labor woman to head an executive department of the federal government. She served under five U.S. presidents during her tenure at the Women's Bureau.
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He has a limited ability to change his physical appearance, as he can retract his lower set of arms, his claws, his antennae and the three spines on his back into his body. Sanders's initial design concepts for Stitch, as seen in early concepts of the film's story, differs from the final version. Stitch was originally going to have a greener fur coloration, which was changed to the now-familiar blue in early development. His black eyes were slightly smaller compared to his final version, his ears flared at their bases instead of close to their tips, and some early drawings placed his nose below the eye line instead of above.
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Cochran's rectorship (1928–1943) is hung just above the lower set of windows. A pair of double red doors are located in the center of the tower, hung in 1952 as part of the church's centennial celebration. The central tower was not completed immediately after the laying of the cornerstone in 1852 but rather over the course of several years, only reaching the same height as the roof of the nave during the rectorship of George Carroll Harris (1859–1862). 1880 etching showing the originally planned spire The narthex of the church is located at the base of the tower, and there is a large bell tower chamfered into the southwest corner of the tower.
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Like a number of other central area stations, Tottenham Court Road underwent improvements during the 1920s to replace the original sets of lifts with escalators. Works commenced in 1923; a new subsurface ticket hall, under St Giles Circus, was constructed and the escalators came into service on 28 September 1926 (upper set) and 1 February 1926 (lower set).Railways Through The Clay; Croome & Jackson; London; 1993; p169 A shaft for three escalators was driven from the ticket hall under the junction down to the east end of the Central line platforms ending at an intermediate circulation space. A further pair of escalators descend from this level to the north end of the Northern line platforms.
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Illustration of the skull of Microgomphodon oligocynus, based on specimen AMNH FARB 5517, originally described as Sesamodon browni Illustration of the skull of Bauria cynops, based on specimen AMNH FARB 5622 Microgomphodon has a short snout and large eye sockets that are roughly equal in size to the temporal openings behind them (these openings are typically much larger in therocephalians). Its incisors are large and pointed, with the lower set splaying forward from the lower jaw. A pair of enlarged canines in the upper jaw separates the incisors in the front from the postcanines in the back. The postcanine teeth are widened and bear cusps that interlock with the postcanines of the lower jaw.
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Like other typical gomphotheres, Amebelodon possessed two sets of tusks, one upper set, (much like those found on modern elephants), and one lower set that extended from the very front of the lower jaws. However, as mentioned above, the lower tusks of the Amebelodon were distinctive in that they were relatively long, slender, and flattened. Because of the resemblance of these lower tusks to shovels, Amebelodon is commonly referred to as a "shovel-tusked" gomphothere (another shovel-tusked gomphothere that may or may not be closely related to Amebelodon is Platybelodon). There has long been an assumption that these lower tusks were actually used as shovels by the animal during feeding, presumably to dig up water plants.
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Tools of Kunda Culture Early Holocene coastal settlements and palaeoenvironment on the shore of the Baltic Sea at Pärnu, southwestern Estonia. Studies were conducted on 16 sections of buried organic matter (pre-Ancylus Lake and pre-Littorina Sea) and associated Stone Age cultural layers in the Pärnu area of southwestern Estonia. Buried organic beds are each part of a sedimentary sequence that is repeated, forming two overlying sets of an orderly succession of five layers. The organic sedimentation of the lower set (set 1) occurred about 10,800–10,200 years BP, and that of the upper set (set 2) about 9450–7800 years BP. Associated with set 1 is the Early Mesolithic settlement of Pulli and with set 2 are the Stone Age cultural layers at Sindi-Lodja.
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Externally, the Lexus LS received the styling cues of Lexus' new design direction, called L-finesse. First shown on the LF-Sh concept, the vehicle gained body forms running the length of the car, wheel arches, arrow- shaped chrome trim, a lower-set grille, and crystalline adaptive headlamps. Fourth-generation, 2006–2009 LS 460 cabin (USF40) The LS 460 interior gained a push-button start, thin-film transistor instrument display, and numerous luxury options, ranging from a hard disk drive-based GPS navigation system and song library to a heated steering wheel and XM NavTraffic. Standard equipment included power 16-way driver and 12-way front passenger seats with lumbar adjustment and seat heaters, leather upholstery, premium sound system, power moonroof, and trunk pass-through.
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The 'B' roll had a lower set of financial and educational qualifications; voters had to be 18 years of age and possess an annual income of 264 pounds or property worth 495 pounds (reduced to 132/275 if the person completed two years of secondary education, 198/385 if the person was 30 years or older, or 132/275 if the person was over 30 years of age and had completed primary education). Ministers of religion as well as Kraal chiefs with a following of at least 20 heads of families automatically gained access to the B roll. The vast majority eligible for the B roll were African, although a few were European. African nationalists rejected the constitution and successfully persuaded most eligible African voters not to register.
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Therefore, the time to compute the completion of a given partial order is . As observe, the problem of listing all cuts in a partially ordered set can be formulated as a special case of a simpler problem, of listing all maximal antichains in a different partially ordered set. If is any partially ordered set, let be a partial order whose elements contain two copies of : for each element of , contains two elements and , with if and only if and . Then the cuts in correspond one-for-one with the maximal antichains in : the elements in the lower set of a cut correspond to the elements with subscript 0 in an antichain, and the elements in the upper set of a cut correspond to the elements with subscript 1 in an antichain.
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The flight engineer, blinded by the firing of the upper deceleration rockets, thought the aircraft was on the runway and fired the lower set early, while the descent-braking rockets did not fire at all. Later unofficial disclaimers alleged to have been made by some members of the Lockheed test crew asserted that the lower rockets fired themselves through an undetermined computer or electrical malfunction, which at the same time failed to fire the descent-braking rockets. As a result, the aircraft's forward flight vector was reduced to near zero, dropping it to the north-south runway and tearing off the starboard wing between the third and fourth engines. During rollout the trailing wing ignited a fire, but crash response teams extinguished the fire within eight seconds of the aircraft stopping, enabling the crew to exit the aircraft without injury.
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A set-point or set point is a factory set or user programmable value for the desired partial pressure of oxygen in a rebreather loop. The feedback of actual oxygen partial pressure measured by the oxygen sensors is compared with the set-points, and if it deviates outside of the limits of upper and lower set-points, the control system will activate a solenoid valve to add oxygen or diluent gas to the loop to correct the oxygen content until it is within the set-point limits. Usually the user can override the gas addition by manual activation of injection valves. Some control systems allow depth activated switching of set-points, so that one pair of set-points can be selected for the main part of the dive, and another, usually richer, for accelerated decompression above the limiting depth.
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The transitive reduction or covering graph of the Dedekind–MacNeille completion describes the order relation between its elements in a concise way: each neighbor of a cut must remove an element of the original partial order from either the upper or lower set of the cut, so each vertex has at most neighbors. Thus, the covering graph has vertices and at most neighbors, a number that may be much smaller than the entries in a matrix that specifies all pairwise comparisons between elements. show how to compute this covering graph efficiently; more generally, if is any family of sets, they show how to compute the covering graph of the lattice of unions of subsets of . In the case of the Dedekind–MacNeille lattice, may be taken as the family of complement sets of principal ideals, and the unions of subsets of are complements of the lower sets of cuts.
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Swiftly sold on by this standardisation-minded operator 165EMJ went to Crawford of Neilston and then Silver Fox Coaches of Glasgow who withdrew it in 1980. Luton 177 (177HTM) was the last of this unloved cohort to survive, being withdrawn by Avro Coaches of Romford Essex in August 1982. East Midland, on the other hand, chose manual Lowlanders (having previously bought lowbridge Atlanteans) because the engine-braking available suited some of their hillier routes in the Peak District, notably route 4 (Chesterfield-Doncaster) and route 17 (Chesterfield-Matlock) and the only modifications over a full service life of around 15 years were the removal of illuminated advertising displays from the first batch and the panelling over of the lower set of apertures in the radiator grille, as the engine was originally over-cooled in the upland climate in which their examples operated. After the fleet merged with Mansfield District, one was transferred there but was not popular because of its lack of cab headroom and heavy controls.
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A BRM P109 similar to the P115 on display at Expo 67 The P115 was a significant refinement of the P83 it replaced, with the most obvious differences being a squarer appearance and the external cooling pipes seen on the P83 being moved within the chassis for better aerodynamics. Magnesium alloy was used to reduce weight over the Duralumin P83, but the car and engine combination was still horrendously overweight compared to its F1 contemporaries, weighing over 620 kg compared to cars like the Lotus 49 and Brabham BT24 which weighed not much more than 500 kg. Added to this the weight distribution was not only significantly rearward but also quite high up due to the higher of the engine's two crankshafts being so high up in the car, as well as the need to raise the engine slightly to accommodate the exhausts from the lower set of cylinders. All this led to less than ideal handling characteristics for the car.
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The 16 sets that are associated with divisors of 120 are the lower sets of this smaller partial order, subsets of elements such that if x ≤ y and y belongs to the subset, then x must also belong to the subset. From any lower set L, one can recover the associated divisor by computing the least common multiple of the prime powers in L. Thus, the partial order on the five prime powers 2, 3, 4, 5, and 8 carries enough information to recover the entire original 16-element divisibility lattice. Birkhoff's theorem states that this relation between the operations ∧ and ∨ of the lattice of divisors and the operations ∩ and ∪ of the associated sets of prime powers is not coincidental, and not dependent on the specific properties of prime numbers and divisibility: the elements of any finite distributive lattice may be associated with lower sets of a partial order in the same way. As another example, the application of Birkhoff's theorem to the family of subsets of an n-element set, partially ordered by inclusion, produces the free distributive lattice with n generators.
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The set of rotations associated with any given stable matching can be obtained by changing the given matching by rotations downward in the partial ordering, choosing arbitrarily which rotation to perform at each step, until reaching the bottom element, and listing the rotations used in this sequence of changes. The stable matching associated with any lower set of rotations can be obtained by applying the rotations to the bottom element of the lattice of stable matchings, choosing arbitrarily which rotation to apply when more than one can apply. Every pair (x,y) of elements of a given stable matching instance belongs to at most two rotations: one rotation that, when applied to the lower of two matchings, removes other assignments to x and y and instead assigns them to each other, and a second rotation that, when applied to the lower of two matchings, removes pair (x,y) from the matching and finds other assignments for those two elements. Because there are n^2 pairs of elements, there are O(n^2) rotations.
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