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Comments on the Regular and Irregular IsoRepresentations of the Lie-Santilli IsoAlgebras
Issue: Volume 4, Issue 5-1, October 2015
Pages: 76-82
Received: 27 July 2015
Accepted: 28 July 2015
Published: 21 August 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 isomathematics, representing particles as being extended, non-spherical and deformable while moving within a physical medium under Hamiltonian and non-Hamiltonian interactions (interior dynamical problems). In particular, we focus the attention on a central part of isomathematics given by the isorepresentations of the Lie-Santilli isoalgebras that have been classified into regular (irregular) isorepresentations depending on whether the structure quantities of the isocommutation rules are constants (functions of local variables). The importance of the study of the isorepresentation theory for a number of physical and chemical applications is pointed out
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...
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Rudiments of IsoGravitation for Matter and its IsoDual for AntiMatter
Issue: Volume 4, Issue 5-1, October 2015
Pages: 59-75
Received: 2 June 2015
Accepted: 2 June 2015
Published: 11 August 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-light within the Sun chromosphere; the absence of a source in the field equations due to the electromagnetic origin (rather than the charge) of gravitational masses; the lack of clear compatibility of general relativity with special relativity, interior gravitational problems, electrodynamics, quantum mechanics and grand unifications; the lack of preservation over time of numerical predictions inherent in the notion of covariance; and other basic issues. We show that a resolution of these historical doubts can be apparently achieved via the use of the novel isomathematics and related iso-Minkowskian geometry based on the embedding of gravitation in generalized isounits, with isodual images for antimatter. Thanks to half a century of prior research, we then show that the resulting new theory of gravitation, known as isogravitation, preserves indeed Einstein's historical field equations although formulated on the iso-Minkowskian geometry over isofields whose primary feature is to have null isocurvature. We then show that isogravitation allows: Einstein field equations to achieve a unified treatment of generally inhomogeneous and anisotropic, exterior and interior gravitational problems; the achievement of a clear compatibility with 20th century sciences; the achievement of time invariant numerical predictions thanks to the strict invariance (rather than covariance) of gravitation under the Lorentz-Santilli isosymmetry; the apparent achievement of a consistent representation of the gravitational field of antimatter thanks ti the isodual iso-Minkowskian geometry; the apparent achievement of a grand unification inclusive of electroweak and gravitational interactions for matter and antimatter without known causality or structural inconsistencies; and other advances. We then present, apparently for the first time, the isogravitational isoaxioms characterized by the infinite family of isotopies of special relativity axioms as uniquely characterized by the Lorentz-Santilli isosymmetry which are applicable to both exterior and interior isogravitational problems of matter with their isodual for antimatter. We finally show, also for the first time, the apparent compatibility of isogravitation with current knowledge on the equivalence principle, matter black holes and other gravitational data.
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-...
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Hyper-Representations by Non Square Matrices Helix-Hopes
T. Vougiouklis
,
S. Vougiouklis
Issue: Volume 4, Issue 5-1, October 2015
Pages: 52-58
Received: 2 June 2015
Accepted: 2 June 2015
Published: 11 August 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. Therefore the related theory can be faced by defining the hyperproduct on the extended set of non square matrices. The obtained hyperstructure is an Hv-algebra or an Hv-Lie-alebra
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...
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Santilli Autotopisms of Partial Groups
Raúl M. Falcón
,
Juan Núñez
Issue: Volume 4, Issue 5-1, October 2015
Pages: 47-51
Received: 8 June 2015
Accepted: 15 June 2015
Published: 11 August 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.
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Hypermathematics, Hv-Structures, Hypernumbers, Hypermatrices and Lie-Santilli Addmissibility
Issue: Volume 4, Issue 5-1, October 2015
Pages: 38-46
Received: 2 June 2015
Accepted: 2 June 2015
Published: 11 August 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 defined to be matrices with entries from an Hv-field. We present the related theory and results on hypermatrices and on the Lie-Santilli admissibility
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...
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Santilli Isomathematics for Generalizing Modern Mathematics
Issue: Volume 4, Issue 5-1, October 2015
Pages: 35-37
Received: 2 June 2015
Accepted: 2 June 2015
Published: 11 August 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 division; a middle level teaching ofmathematics takes these four operations to a higher level, while the university teaching of mathematics extends them to an even higher level. These four arithmetic operations form the foundation of modern mathematics. Santilli isomathematics is a generalisation of these four fundamental operations and heralds a great revolution in mathematics. HIn this paper, we study the four generalized arithmetic operations of isoaddition, isosubtraction, isomultiplication and isodivision at the primary level of isomathematics. The material introduced here should be readily understandable by middle school pupils and university students.Santilli’s isomathematics [1] ßßis based on a generalisation of modern mathematics. Isomultiplication is defined by a× ̂a=abT ̂, isodivision by a÷ ̂b=a/b I ̂, where I ̂≠1 is called an isounit; T ̂I ̂=1, where T ̂ is the inverse of the isounit. If addition and subtraction remain unchanged, (+ ̂,- ̂,× ̂,÷ ̂)are the four arithmetic operations in Santilli’s isomathematics[1-5]. Isoaddition a+ ̂b=a+b+0 ̂ and isosubtraction a+ ̂b=a+b+0 ̂, where 0 ̂≠0 is called the isozero, together with the operations of isomultiplication and isodivision introduced above, form the four arithmetic operations(+ ̂,- ̂,× ̂,÷ ̂) in Santilli-Jiang isomathematics[6]. Santilli [1] suggests isomathematics based on a generalisation of multiplication ×, division ÷, and the multiplicative unit 1 of modern mathematics. It is an epoch making suggestion. From modern mathematics, the foundations of Santilli’s isomathematics will be established
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...
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Measurable Iso-Functions
Issue: Volume 4, Issue 5-1, October 2015
Pages: 24-34
Received: 2 June 2015
Accepted: 15 June 2015
Published: 11 August 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-functions are measurable. It is introduced a definition for equivalent iso-functions. They are given examples when the iso-functions are equivalent and the corresponding real functions are not equivalent. They are deducted some criterions for measurability of the iso-functions of the first, second, third, fourth and fifth kind. They are investigated for measurability the addition, multiplication of two iso-functions, multiplication of iso-function with an iso-number and the powers of measurable iso-functions. They are given definitions for step iso-functions, iso-step iso-functions, characteristic iso-functions, iso-characteristic iso-functions. It is investigate for measurability the limit function of sequence of measurable iso-functions. As application they are formulated the iso-Lebesgue’s theorems for iso-functions of the first, second, third, fourth and fifth kind. These iso-Lebesgue’s theorems give some information for the structure of the iso-functions of the first, second, third, fourth and fifth kind
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...
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Santilli’s Isoprime Theory
Issue: Volume 4, Issue 5-1, October 2015
Pages: 17-23
Received: 2 June 2015
Accepted: 2 June 2015
Published: 11 August 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 isoaddition a+ ̂b=a+b+0 ̂ and the isosubtraction a- ̂b=a-b-0 ̂ where the additive unit 0 ̂≠0 is called isozero, and we study Santilli isomathem,atics formulated with the four isooperations (+ ̂,- ̂,× ̂,÷ ̂). We introduce, apparently for the first time, Santilli’s isoprime theory of the first kind and Santilli’s isoprime theory of the second kind. We also provide an example to illustrate the novel isoprime isonumbers
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 ...
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Outline of Hadronic Mathematics, Mechanics and Chemistry as Conceived by R. M. Santilli
Issue: Volume 4, Issue 5-1, October 2015
Pages: 1-16
Received: 19 June 2015
Accepted: 20 June 2015
Published: 11 August 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 conditions of increasing complexity: 1) 20th century mathematics based on Lie’s theory; 2) IsoMathematics based on Santilli’s isotopies of Lie’s theory; 3) GenoMathematics based on Santilli’s formulation of Albert’s Lie-admissibility; 4) HyperMathematics based on a multi-valued realization of genomathematics with classical operations; and 5) HyperMathematics based on Vougiouklis Hv hyperstructures expressed in terms of hyperoperations. Additionally, hadronic mathematics comprises the anti-Hermitean images (called isoduals) of the five preceding mathematics for the description of antimatter also in conditions of increasing complexity. The outline presented in this paper includes the identification of represented physical or chemical systems, the main mathematical structure, and the main dynamical equations per each branch. We also show the axiomatic consistency of various branches of hadronic mathematics as sequential coverings of 20th century mathematics; and indicate a number of open mathematical problems. Novel physical and chemical applications permitted by hadronic mathematics are presented in subsequent collections.
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...
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