Synsets for "superabundant"

Synset: superabundant.s.01

Synonyms: superabundant


Definition: most excessively abundant


Lemmas: superabundant





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Superabundant number In mathematics, a superabundant number (sometimes abbreviated as SA) is a certain kind of natural number. A natural number "n" is called superabundant precisely when, for all "m" < "n"
Superabundant number for all "n" greater than the largest known exception, the superabundant number 5040. If this inequality has a larger counterexample, proving the Riemann hypothesis to be false, the smallest such counterexample must be a superabundant number .
Superabundant number proved that if "n" is superabundant, then there exist a "k" and "a", "a", ..., "a" such that
Superabundant number Alaoglu and Erdős observed that all superabundant numbers are highly abundant.
Highly abundant number Alaoglu and Erdős noted that all superabundant numbers are highly abundant, and asked whether there are infinitely many highly abundant numbers that are not superabundant. This question was answered affirmatively by .
Superabundant number That is, they proved that if "n" is superabundant, the prime decomposition of "n" has non-increasing exponents (the exponent of a larger prime is never more than that a smaller prime) and that all primes up to formula_4 are factors of "n". Then in particular any superabundant number is an even integer, and it is a multiple of the "k"-th primorial formula_5
Superabundant number Superabundant numbers were defined by . Unknown to Alaoglu and Erdős, about 30 pages of Ramanujan's 1915 paper "Highly Composite Numbers" were suppressed. Those pages were finally published in The Ramanujan Journal 1 (1997), 119–153. In section 59 of that paper, Ramanujan defines generalized highly composite numbers, which include the superabundant numbers.
Superabundant number where "σ" denotes the sum-of-divisors function (i.e., the sum of all positive divisors of "n", including "n" itself). The first few superabundant numbers are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ... . For example, the number 5 is not a superabundant number because for 1, 2, 3, 4, and 5, the sigma is 1, 3, 4, 7, 6, and 7/4 > 6/5.
Superabundant number Not all superabundant numbers are Harshad numbers. The first exception is the 105th SA number, 149602080797769600. The digit sum is 81, but 81 does not divide evenly into this SA number.
Who breaks a butterfly upon a wheel? It alludes to "breaking on the wheel", a form of torture in which victims had their long bones broken by an iron bar while tied to a Catherine wheel. The quotation is used to suggest someone is "[employing] superabundant effort in the accomplishment of a small matter".
Riemann–Roch theorem for surfaces Comparing this inequality with the sheaf-theoretic version of the Riemann–Roch theorem shows that the superabundance of "D" is given by "s" = dim "H"(O("D")). The divisor "D" was called regular if "i" = "s" = 0 (or in other words if all higher cohomology groups of O("D") vanish) and superabundant if "s" > 0.
Michael Oakeshott In his essay "On Being Conservative" (1956), Oakeshott explained what he regarded as the conservative disposition: "To be conservative ... is to prefer the familiar to the unknown, to prefer the tried to the untried, fact to mystery, the actual to the possible, the limited to the unbounded, the near to the distant, the sufficient to the superabundant, the convenient to the perfect, present laughter to utopian bliss."
Seraph Secondly, the active force which is "heat," which is not found in fire simply, but exists with a certain sharpness, as being of most penetrating action, and reaching even to the smallest things, and as it were, with superabundant fervor; whereby is signified the action of these angels, exercised powerfully upon those who are subject to them, rousing them to a like fervor, and cleansing them wholly by their heat.
Jehol Biota The Jehol Biota has produced fossils of plant macro- and microfossils, including the earliest angiosperms, charophytes and dinocysts, snails (gastropods), clams (bivalves), superabundant aquatic arthropods called conchostracans, ostracods, shrimps, insects, spiders, fish, frogs and salamanders (amphibians), turtles, choristoderes, lizards (squamates), pterosaurs, and dinosaurs including feathered dinosaurs, the largest mammals known from the Mesozoic, and a great diversity of birds including the earliest advanced birds, and the smallest and largest birds known from the Mesozoic.
Burrowing owl Rodent prey is usually dominated by locally superabundant species, like the delicate vesper mouse ("Calomys tener") in southern Brazil. Among squamates and amphibians, small lizards like the tropical house gecko ("Hemidactylus mabouia"), and frogs and toads predominate. Generally, most vertebrate prey is in the weight class of several grams per individual. The largest prey are usually birds, such as eared doves ("Zenaida auriculata") which may weigh almost as much as a burrowing owl.
Dialogues of the Carmelites The chaplain announces that he has been forbidden to preach (presumably for being a non-juror under the Civil Constitution of the Clergy). The nuns remark on how fear rules the country, and no one has the courage to stand up for the priests. Sister Constance asks, "Are there no men left to come to the aid of the country?" "When priests are lacking, martyrs are superabundant," replies the new Mother Superior. Mother Marie says that the Carmelites can save France by giving their lives, but the Mother Superior corrects her: it is not permitted to choose to become a martyr; God decides who will be martyred.
Summa Theologica This is the first course of thought. Then follows a second complex of thoughts, which has the idea of satisfaction as its center. To be sure, God as the highest being could forgive sins without satisfaction; but because his justice and mercy could be best revealed through satisfaction, he chose this way. As little, however, as satisfaction is necessary in itself, so little does it offer an equivalent, in a correct sense, for guilt; it is rather a "superabundant satisfaction", since on account of the divine subject in Christ in a certain sense his suffering and activity are infinite.
General position For points in the plane or on an algebraic curve, the notion of general position is made algebraically precise by the notion of a regular divisor, and is measured by the vanishing of the higher sheaf cohomology groups of the associated line bundle (formally, invertible sheaf). As the terminology reflects, this is significantly more technical than the intuitive geometric picture, similar to how a formal definition of intersection number requires sophisticated algebra. This definition generalizes in higher dimensions to hypersurfaces (codimension 1 subvarieties), rather than to sets of points, and regular divisors are contrasted with superabundant divisors, as discussed in the Riemann–Roch theorem for surfaces.
Letter-winged kite The letter-winged kite is the only fully nocturnal member of its family. Its principal prey is the Long-haired Rat, "Rattus villosissimus". When population numbers of this rodent build up, following good rainfall, the kites are able to breed continuously and colonially so that their numbers increase in parallel. When the rodent populations decline, the now superabundant kites may disperse and appear in coastal areas far from their normal range in which, though they may occasionally breed, they do not persist and eventually disappear. One central Australian study over two and a half years found the kites had relocated to an area within six months of a rodent outbreak starting.
Paranja To send forth a young lady in her eighteenth or twentieth year, in all the superabundant energy of youth, supported upon a stick, and thus muffled up, in the sole view that the assumption of the characteristics of advanced life may spare her certain glances, may be justly deemed the ne plus ultra of tyranny and hypocrisy. These erroneous notions of morality are to be met with, more or less, everywhere in the East; but nowhere does one find such striking examples of Oriental exaggeration as in that seat of ancient Islamite civilization, Bokhara."