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Division (mathematics)

About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.


Papers
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Journal Article
TL;DR: In this paper, the U.S. Dept. of Energy has provided a grant for the development of an energy-efficient energy harvesting system for the Materials Sciences and Engineering (MSME) program.
Abstract: United States. Dept. of Energy. Office of Basic Energy Science. Division of Materials Sciences and Engineering (Grant DE-SC0010526)

47 citations

Book ChapterDOI
01 Jan 1972
TL;DR: In the first part of this paper the complexity (with respect to multiplication and division) of a general continued fraction and of arbitrary quadratic forms is determined with the help of Pan’s method.
Abstract: In the first part of this paper the complexity (with respect to multiplication and division) of a general continued fraction and of arbitrary quadratic forms is determined with the help of Pan’s method. In the second part some results on avoiding division and on the multiplication of matrices from an algebraic group are reported.

47 citations

Journal ArticleDOI
TL;DR: In this paper, a soap-solution problem is solved in foam, and the solution is interestingly seen in the multitude of film-enclosed cells obtained by blowing air through a tube into the middle of a soap solution.
Abstract: This problem is solved in foam, and the solution is interestingly seen in the multitude of film-enclosed cells obtained by blowing air through a tube into the middle of a soap-solution in a large o...

46 citations

Patent
16 Jul 1971
TL;DR: An extension of the branch of mathematics known as numerical analysis, and specifically of the division of that branch known as approximation, is the add-shift algorithm as mentioned in this paper, which finds solutions to the terms of the polynomial expression by reiterated interpolation.
Abstract: A method of solving a function for values of a variable when values of an independent variable are given, the method being especially valuable for use in or with a computer, an advantage being minimization of storage requirements. The method is an extension of the branch of mathematics known as numerical analysis, and specifically of the division of that branch known as approximation. An expression is developed for a locus of points which approach points on the given function, i.e., a polynomial expression having a high degree of convergence. The method includes finding solutions to the terms of the polynomial expression by reiterated interpolation. Only a relatively small number of factors need be stored. The method can be employed to calculate values to predetermined accuracy, and is suitable for many functions although it is especially well suited for many transcendental functions. Embodiments of apparatus suitable for performing the method are also disclosed. The apparatus includes elements of electronic data processing such as shift registers, adders, and the like to perform the interpolation involving addition, subtraction and division by 2. The algorithm developed as a manifestation of this method is describable as an add-shift algorithm.

46 citations

Patent
06 Jun 1985
TL;DR: The arithmetic pipeline processor (APP) as discussed by the authors is a group of boards capable of solving an equation of the form A.sup.m B.supn +C.supr +D.supm C.supp +E.q F.sups H.
Abstract: The arithmetic pipeline processor (which is used for computer graphics such as a flight simulator) is a group of boards capable of solving an equation of the form A.sup.m B.sup.n +C.sup.o D.sup.P +E.sup.q F.sup.r +G.sup.s H.sup.t where A, B, C, D, E, F, G, H are 32-bit implied one floating point numbers, and m, n, o, p, q, r, s, t can take on the values 1/4, 1/2, 1, 2 and 0. It includes a digital logarithmic calculator using shifters and stored tables to perform arithmetic functions such as multiplication, division, squares, square roots, and fourth roots. It comprises two input ports each capable of receiving digital data N bits wide. Included are a log transform unit, a log sum or difference unit and an antilog unit. Following these is an M-bit Aritmetic Logic Unit (ALU) and circuitry for converting between fixed point and floating point numbers. It uses piece wise linear approximation in conjunction with stored slope information in tables to do the transform calculation of logarithms and antilogarithms. The M-bit arithmetic unit performs accumulation of up to K terms. In a specific emodiment, N=32, M=36, and K=128. Note that a pipeline processor has no central processing unit or software in itself, but it may interface with a computer for inputs and outputs including control information.

46 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20242
2023739
20221,583
2021239
2020416
2019465