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In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms.Dedicated to the discrete logarithm in (/) where is a prime, index calculus leads to a family of algorithms adapted to finite fields and to some families of elliptic curves.
For compactness and convenience, the Ricci calculus incorporates Einstein notation, which implies summation over indices repeated within a term and universal quantification over free indices. Expressions in the notation of the Ricci calculus may generally be interpreted as a set of simultaneous equations relating the components as functions ...
We are free to choose components as infinitesimally small as we wish as long as they remain nonzero. Since the outer product of these terms can be interpreted as a k {\displaystyle k} -volume, a natural way to define a measure is
The calculus of variations began with the work of Isaac Newton, such as with Newton's minimal resistance problem, which he formulated and solved in 1685, and later published in his Principia in 1687, [2] which was the first problem in the field to be formulated and correctly solved, [2] and was also one of the most difficult problems tackled by variational methods prior to the twentieth century.
In mathematics education, calculus is an abbreviation of both infinitesimal calculus and integral calculus, which denotes courses of elementary mathematical analysis.. In Latin, the word calculus means “small pebble”, (the diminutive of calx, meaning "stone"), a meaning which still persists in medicine.
Kūshyār Daylami's main work was probably done about the beginning of the 11th century, and seems to have taken an important part in the elaboration of trigonometry.He continued the investigations of the 10th century mathematician and astronomer Abul Wáfa, and devoted much space to this in his zīj (book of astronomical tables) az-Zīj al-Jamī wal-Baligh ("The Comprehensive and Mature ...
Soal moved to a more statistical and controlled approach, firstly by conducting an experiment in which up to a few hundred persons participated at one time. [5] This involved Soal and a small group of agents enacting a scenario, playing with a certain object, reciting a poem, and so on, which the participants, situated across Great Britain and other countries, were required, at the same time ...
whitlockite, Ca 9 (Mg,Fe)(PO 4) 6 (PO 3 OH) hydroxyapatite, Ca 5 (PO 4) 3 OH; octacalcium phosphate, Ca 8 H 2 (PO 4) 6 · 5 H 2 O; and brushite, CaHPO 4 · 2 H 2 O; The organic component is approximately 85% cellular and 15% extracellular matrix. [5] Cell density within dental plaque and calculus is very high, consisting of an estimated ...