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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01 Jan 1994
TL;DR: This article describes a proof of the functional correctness of a nonrestoring division algorithm and its implementation on an ALU, which is proven by checking several refinements of the algorithm.
Abstract: This article describes a proof of the functional correctness of a nonrestoring division algorithm and its implementation on an ALU. The first part of the proof deals with the correctness of the division algorithm with respect to a specification of division on the integer level. The second part is concerned with the correctness of the actual implementation, which is proven by checking several refinements of the algorithm. All the proofs have been mechanically checked with the Boyer-Moore theorem-proving system, in some cases making use of the interactive proof checker for the system.
25 citations
TL;DR: The comparison between binary and multiple division shows that these different division processes lead to qualitatively different results for the size distribution and the population growth rates.
Abstract: Populations of unicellular organisms that grow under constant environmental conditions are considered theoretically. The size distribution of these cells is calculated analytically, both for the usual process of binary division, in which one mother cell produces always two daughter cells, and for the more complex process of multiple division, in which one mother cell can produce 2n daughter cells with n=1,2,3,… . The latter mode of division is inspired by the unicellular algae Chlamydomonas reinhardtii. The uniform response of the whole population to different environmental conditions is encoded in the individual rates of growth and division of the cells. The analytical treatment of the problem is based on size-dependent rules for cell growth and stochastic transition processes for cell division. The comparison between binary and multiple division shows that these different division processes lead to qualitatively different results for the size distribution and the population growth rates.
25 citations
Patent•
19 Oct 1936
TL;DR: In this article, the shape or configuration of the stream of liquid expelled can be changed from one form to another, depending on the shape of the nozzles used for spraying the liquid.
Abstract: This invention relates to nozzles for spraying liquid, and more particularly to those of the type wherein the shape or configuration of the stream of liquid expelled can be changed from one form to another. This application is a division of my copending application, Serial No. 741,028, filed...
25 citations
Patent•
23 May 1935TL;DR: In this article, the authors present an application related to electric discharge apparatus and has particular relation to apparatus for producing impulses such as are utilized for providing starting currents and starting potentials for vapor discharge devices.
Abstract: My invention relates to electric discharge apparatus and has particular relation to apparatus for producing impulses such as are utilized for providing starting currents and starting potentials for vapor discharge devices. The present application is a division of my copending application Serial...
25 citations
TL;DR: A binary operator on relations which has division like properties is discussed which is relevant to program construction and its mathematical properties are reviewed.
25 citations