Topic
Division (mathematics)
About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.
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TL;DR: Results are strongly suggestive of the operation of a cell size requirement for entry into nuclear division, confirmed by a nutritional shift-down, where nuclear division and cell division are stimulated after the shift.
422 citations
TL;DR: It is shown that the IEEE standard's specification of operations involving the signed infinities, signed zeros, and the exact/inexact flag are such as to make a correct and optimal implementation more efficient.
Abstract: We start with a mathematical definition of a real interval as a closed, connected set of reals. Interval arithmetic operations (addition, subtraction, multiplication, and division) are likewise defined mathematically and we provide algorithms for computing these operations assuming exact real arithmetic. Next, we define interval arithmetic operations on intervals with IEEE 754 floating point endpoints to be sound and optimal approximations of the real interval operations and we show that the IEEE standard's specification of operations involving the signed infinities, signed zeros, and the exact/inexact flag are such as to make a correct and optimal implementation more efficient. From the resulting theorems, we derive data that are sufficiently detailed to convert directly to a program for efficiently implementing the interval operations. Finally, we extend these results to the case of general intervals, which are defined as connected sets of reals that are not necessarily closed.
363 citations
358 citations
TL;DR: In this article, an ordered group in a division ring is embedded in an ordered set of columns and columns, and the columns are ordered by the order in which the columns form the columns.
Abstract: Part I. Embedding an ordered group in a division ring.
331 citations
TL;DR: In this paper, Plateau's theory of extraneous pressure is used to explain the velocity of propagation dependent on the line of vibration. But this theory is not suitable for the case of light traversing a crystal.
Abstract: 1. This problem is solved in fo~m, and the solution is interestingly seen in the multitude of fihn-enclosed cells obtained by blowing air through a tube into the middle of a soap-solution in a large open vessel. I have been led to it by endeavours to understand, and to illustrate, GREE~'S theory of ))extraneous pressure)) whicil gives, for light traversing a crystal, FRESNEL'S wave-surface, with FJ~s~EI,'S supposition (strongly supported as it is by STOXES and RAYLEm~I) of velocity of propagation dependent, not on the distortion-normal, but on the line of vibration. It has been admirably illustrated, and some elements towards its solution beautifully realized in a manner convenient for study and instruction, b y PLATEAU, in the first volume of his Statique des Liquides soumis aux seules Forces Moldculaires.
331 citations