American Journal of Modern Physics

Special Issue

Issue I: Foundations of Hadronic Mathematics

  • Submission Deadline: Jul. 30, 2015
  • Status: Submission Closed
  • Lead Guest Editor: Richard Anderson
About This Special Issue
20th century mathematics underlying mainstream physical and chemical theories is local-differential, thus solely permitting the representation of point-like masses. The Italian-American scientist R. M. Santilli accepted such a mathematics for the representation of particles when the masses are at large mutual distances, thus allowing point-like approximations, as it is the case for the atomic structure. Santilli then identified clear limitation of 20th century mathematics for the representation of extended charge distributions or wavepackets in conditions of partial or total mutual penetration, as it is the case for the synthesis of the neutron from a proton and an electron in the core of a star; for the structure of nuclei, stars and black holes; for the molecular bond of two identical valence electrons in singlet coupling; and other composite systems.

When at the Department of Mathematics of Harvard University in the late 1970s, Santilli developed a series of new mathematics for the representation of extended charge distributions or wavepackets when in condition of partial or total mutual penetration, resulting in:

1. The novel, single valued- isomathematics for the representation of composite matter-systems reversible over time of with extended constituents at short mutual distances;
2. The novel, single valued genomathematics for the representation of composite matter-systems or reactions irreversible over time with extended constituents at short mutual distance;
3. The novel multi-valued hypermathematics for the representation of biological matter-systems.

Additionally, Santilli constructed their anti-Hermitean isodual images for the representation of corresponding antimatter-systems in conditions of increasing complexity. These varieties of new mathematics are today collectively addressed by the name of hadronic mathematics, in view of their applications. The special issue of AJMP on the Foundations of Hadronic Mathematics shall review the above novel mathematics and present new advances for the use in subsequent special issues devoted to its applications.
Lead Guest Editor
  • Richard Anderson

    Board of Trustees, The R. M. Santilli Foundation, Palm Harbor, United States

Published Articles
  • Comments on the Regular and Irregular IsoRepresentations of the Lie-Santilli IsoAlgebras

    Richard Anderson

    Issue: Volume 4, Issue 5-1, October 2015
    Pages: 76-82
    Received: Jul. 27, 2015
    Accepted: Jul. 28, 2015
    Published: Aug. 21, 2015
    DOI: 10.11648/j.ajmp.s.2015040501.19
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    Abstract: As it is well known, 20th century applied mathematics with related physical and chemical theories, are solely applicable to point-like particles moving in vacuum under Hamiltonian interactions (exterior dynamical problems). In this note, we study the covering of 20th century mathematics discovered by R. M. Santilli, today known as Santilli isomathe... Show More
  • Rudiments of IsoGravitation for Matter and its IsoDual for AntiMatter

    Ruggero Maria Santilli

    Issue: Volume 4, Issue 5-1, October 2015
    Pages: 59-75
    Received: Jun. 02, 2015
    Accepted: Jun. 02, 2015
    Published: Aug. 11, 2015
    DOI: 10.11648/j.ajmp.s.2015040501.18
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    Abstract: In this paper, we hope to initiate due scientific process on some of the historical criticisms of Einstein gravitation expressed by Einstein himself as well as by others. These criticisms have remained widely ignored for one century and deal with issues such as: the apparent lack of actual, physical curvature of space due to the refraction of star-... Show More
  • Hyper-Representations by Non Square Matrices Helix-Hopes

    T. Vougiouklis , S. Vougiouklis

    Issue: Volume 4, Issue 5-1, October 2015
    Pages: 52-58
    Received: Jun. 02, 2015
    Accepted: Jun. 02, 2015
    Published: Aug. 11, 2015
    DOI: 10.11648/j.ajmp.s.2015040501.17
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    Abstract: Hyperstructure theory can overcome restrictions which ordinary algebraic structures have. A hyperproduct on non-square ordinary matrices can be defined by using the so called helix-hyperoperations. We define and study the helix-hyperstructures on the representations and we extend our study up to Lie-Santilli theory by using ordinary fields. Therefo... Show More
  • Santilli Autotopisms of Partial Groups

    Raúl M. Falcón , Juan Núñez

    Issue: Volume 4, Issue 5-1, October 2015
    Pages: 47-51
    Received: Jun. 08, 2015
    Accepted: Jun. 15, 2015
    Published: Aug. 11, 2015
    DOI: 10.11648/j.ajmp.s.2015040501.16
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    Abstract: This paper deals with those partial groups that contain a given Santilli isotopism in their autotopism group. A classification of these autotopisms is explicitly determined for partial groups of order n ≤ 4.
  • Hypermathematics, Hv-Structures, Hypernumbers, Hypermatrices and Lie-Santilli Addmissibility

    Thomas Vougiouklis

    Issue: Volume 4, Issue 5-1, October 2015
    Pages: 38-46
    Received: Jun. 02, 2015
    Accepted: Jun. 02, 2015
    Published: Aug. 11, 2015
    DOI: 10.11648/j.ajmp.s.2015040501.15
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    Abstract: We present the largest class of hyperstructures called Hv-structures. In Hv-groups and Hv-rings, the fundamental relations are defined and they connect the algebraic hyperstructure theory with the classical one. Using the fundamental relations, the Hv-fields are defined and their elements are called hypernumbers or Hv-numbers. Hv-matrices are defin... Show More
  • Santilli Isomathematics for Generalizing Modern Mathematics

    Chun-Xuan Jiang

    Issue: Volume 4, Issue 5-1, October 2015
    Pages: 35-37
    Received: Jun. 02, 2015
    Accepted: Jun. 02, 2015
    Published: Aug. 11, 2015
    DOI: 10.11648/j.ajmp.s.2015040501.14
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    Abstract: The establishment of isomathematics, as proposed by R. M. Santilli thirty years ago in the USA, and contributed to by Jiang Chun-Xuan in China during the past 12 years, is significant and has changed modern mathematics. At present, the primary teaching of mathematics is based on the simple operations of addition, subtraction, multiplication and div... Show More
  • Measurable Iso-Functions

    Svetlin G. Georgiev

    Issue: Volume 4, Issue 5-1, October 2015
    Pages: 24-34
    Received: Jun. 02, 2015
    Accepted: Jun. 15, 2015
    Published: Aug. 11, 2015
    DOI: 10.11648/j.ajmp.s.2015040501.13
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    Abstract: In this article are given definitions definition for measurable is-functions of the first, second, third, fourth and fifth kind. They are given examples when the original function is not measurable and the corresponding iso-function is measurable and the inverse. They are given conditions for the isotopic element under which the corresponding is-fu... Show More
  • Santilli’s Isoprime Theory

    Chun-Xuan Jiang

    Issue: Volume 4, Issue 5-1, October 2015
    Pages: 17-23
    Received: Jun. 02, 2015
    Accepted: Jun. 02, 2015
    Published: Aug. 11, 2015
    DOI: 10.11648/j.ajmp.s.2015040501.12
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    Abstract: We study Santilli’s isomathematics for the generalization of modern mathematics via the isomultiplication a× ̂a=abT ̂ and isodivision a÷ ̂b=a/b I ̂, where the new multiplicative unit I ̂≠1 is called Santilli isounit, T ̂I ̂=1, and T ̂ is the inverse of the isounit, while keeping unchanged addition and subtraction, , In this paper, we introduce the ... Show More
  • Outline of Hadronic Mathematics, Mechanics and Chemistry as Conceived by R. M. Santilli

    Richard Anderson

    Issue: Volume 4, Issue 5-1, October 2015
    Pages: 1-16
    Received: Jun. 19, 2015
    Accepted: Jun. 20, 2015
    Published: Aug. 11, 2015
    DOI: 10.11648/j.ajmp.s.2015040501.11
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    Abstract: In this paper, we outline the various branches of hadronic mathematics and their applications to corresponding branches of hadronic mechanics and chemistry as conceived by the Italian-American scientist Ruggero Maria Santilli. According to said conception, hadronic mathematics comprises the following branches for the treatment of matter in conditio... Show More