rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Random Number Generators on Computers
  name:
    name part: Nakazawa, Naoya
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Nakazawa, Hiroshi
    role:
      role term: author.
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: si
    date issued: 2025
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (x, 110 pages).
  abstract: This monograph proves that any finite random number sequence is represented by the multiplicative congruential (MC) way. It also shows that an MC random number generator (d, z) formed by the modulus d and the multiplier z should be selected by new regular simplex criteria to give random numbers an excellent disguise of independence. The new criteria prove further that excellent subgenerators (d1,z1) and (d2,z2) with coprime odd submoduli d1 and d2 form an excellent combined generator (d = d1d2,z) with high probability by Sunzi's theorem of the 5th-6th centuries (China), contrasting the fact that such combinations could never be found with MC subgenerators selected in the 20th-century criteria. Further, a combined MC generator (d = d1d2,z) of new criteria readily realizes periods of 252 or larger, requiring only fast double-precision arithmetic by powerful Sunzi's theorem. We also obtain MC random numbers distributed on spatial lattices, say two-dimensional 4000 by 4000 lattices which may be tori, with little pair correlations of random numbers across the nearest neighbors. Thus, we evade the problems raised by Ferrenberg, Landau, and Wong.
  table of contents: 1. Basic Concepts and Tools2. Group Structures3. Designs of MC Generators4. Lattice Structures5. Regular Simplexes and Regular Lattices6. Extended Second-Degree Tests7. MC Generators with Excellent Statistics8. MC Random Numbers on Spatial Lattices9. Random Vector Fields and Random Walks10. Two Addenda and Closing Comments
  target audience: general
  note: Naoya Nakazawa, Hiroshi Nakazawa.
  note: Naoya Nakazawa obtained his DSci (applied number theory) at Osaka Prefectural University, Japan. He is now the representative (theory and computing) of Hirakata Ransu Factory (HRF). Hiroshi Nakazawa obtained his DSci (statistical physics) at Kyoto University, Japan. As a professor at Takuma National College of Technology, Japan, he enjoyed teaching students applied mathematics. He is now the representative (theory and general affairs) of HRF.
  subject:
    topic: Random number generators
  subject:
    topic: Random number generators
    topic: Computer programs
  subject:
    topic: SCIENCE / Mathematical Physics
  subject:
    topic: COMPUTERS / Mathematical & Statistical Software
  classification: QA276.5
  classification: 519/.93
  identifier: 9781003410607
  identifier: 100341060X
  identifier: 9789814968492
  identifier: 9781000908268
  identifier: 1000908267
  identifier: 9781000908312
  identifier: 1000908313
  identifier: 9781003410607 Taylor & Francis
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: TYFRS
    record creation date: 241029
    record change date: 20250103162119.0
    record identifier: in00005611475
    language of cataloging:
      language term: eng