Division (mathematics)

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

Steering control mechanism

Abstract: This invention relates to motion picture apparatus and particularly to a motion picture camera truck or dolly wherein the vertical and horizontal adjusting mechanism for the camera may be moved or bodily translated in any direction along straight or curved paths. This application is a division...

Method of making magnetic cores

Abstract: This is a division of my application, Serial Number 722,838, filed January 18, 1947, now Patent 2,456,459 issued December 14, 1948, relating to magnetic cores, more particularly to three phase cores for electric induction apparatus, and to a method of making such cores. An object of the invention...

Uniform Circuits for Division: Consequences and Problems

Abstract: Integer division has been known to lie in P-uniform TC/sup 0/ since the mid-1980s, and recently this was improved to L-uniform TC/sup 0/. At the time that the results in this paper were proved and submitted for conference presentation, it was unknown whether division lay in DLOGTIME-uniform TC/sup 0/ (also known as FOM). We obtain tight bounds on the uniformity required for division, by showing that division is complete for the complexity class FOM+POW obtained by augmenting FOM with a predicate for powering modulo small primes. We also show that, under a well-known number-theoretic conjecture (that there are many \"smooth\" primes), POW (and hence division) lies in FOM. Building on this work, Hesse has shown recently that division is in FOM [17]. The essential idea in the fast parallel computation of division and related problems is that of Chinese remainder representation (CRR)-storing a number in the form of its residues modulo many small primes. The fact that CRR operations can be carried out in log space has interesting implications for small space classes. We define two versions of s(n) space for s(n)=o(log n): dspace(s(n)) as the traditional version where the worktape begins blank, and DSPACE(s(n)) where the space bound is established by endmarkers before the computation starts. We present a new translational lemma, and derive as a consequence that (for example), if one can improve the result of Hartmanis and Berman (1976) that {0/sup n/: n is prime} /spl notin/ dspace (log log n) to show that {0/sup n/: n is prime} /spl notin/ DSPACE (log log n), it would follow that L/spl ne/NP.

Comparison of CD(C) ROADM architectures for space division multiplexed networks

Abstract: We compare different architectures of CD and CDC ROADMs supporting spatial superchannel routing in terms of required components, revealing the most cost-effective designs.