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S-shaped growth curves in fermentations and golden ratio

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International Journal of Biomathematics 2020年第3期13卷 107-136页

作者： Sergey P.Klykov Fermentation Expert Poste RestanteObolensk Serpukhov DistrictMoscow RegionRussia142279

A model of the growth curve of microorganisms was proposed,which reveals a relation-ship with the number of a‘golden section’,1.618…,for main parameters of the growth *** treatment mainly concerns the ratio of the maximum asymptotic value of biomass in the phase of slow growth to the real value of biomass accumulation at the end of exponential growth,which is equal to thc square of the'golden section',i.e.,*** are a few relevant theorems to explain these ***,yet simpler,methods were considered for deterrmining the model parameters based on hyperbolic functions.A comparison was made with one of the alternative models to demonstrate the advantage of the proposed *** proposed model should be useful to apply at various stages of fermentation in scientific and industrial ***,the model could give a new impetus to the development of new mathematical knowledge regarding the algebra of the‘golden section'as a whole,as well as in connection with the introduction of a new equation at decomposing of any roots with any degrees for differences between constants and/or variables.

关键词： golden section golden ratio modeling fermentation S-shaped curves oxy-gen restriction cells numbers theory

The golden ratio Theorem: A Framework for Interchangeability and Self-Similarity in Complex Systems

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Advances in Pure Mathematics 2023年第9期13卷 559-596页

作者： Alessandro Rizzo Brescia Italy

The golden ratio Theorem, deeply rooted in fractal mathematics, presents a pioneering perspective on deciphering complex systems. It draws a profound connection between the principles of interchangeability, self-similarity, and the mathematical elegance of the golden ratio. This research unravels a unique methodological paradigm, emphasizing the omnipresence of the golden ratio in shaping system dynamics. The novelty of this study stems from its detailed exposition of self-similarity and interchangeability, transforming them from mere abstract notions into actionable, concrete insights. By highlighting the fractal nature of the golden ratio, the implications of these revelations become far-reaching, heralding new avenues for both theoretical advancements and pragmatic applications across a spectrum of scientific disciplines.

关键词： Conservation Law Self-Similarity Interchangeability golden ratio Complex Systems Dynamic Exchange Structural Stability Mathematical Modeling Theoretical Framework P vs NP Millennium Problem

Tao and golden ratio: A Scientific View of Contemporary Acupunctural Principles through Geometry

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Chinese Medicine 2023年第3期14卷 95-154页

作者： Adrián Ángel Inchauspe Erica Arakaki Institute of Traditional Chinese Medicine National Academy of Medical Sciences Beijing China Department of Traditional Chinese Medicine Medical University of Hainan Haikou China Scientific Research Department Argentina Acupuncture Society Buenos Aires Argentina N/A Argentina Resuscitation Council (CAR) Buenos Aires Argentina Surgery Department School of Medical Science National University of La Plata (UNLP) La Plata Argentina Specialist in Internal and Geriatric Medicine Buenos Aires Argentina Pain Assessment and Treatment Hospital Italiano Buenos Aires Argentina Clinical Medicine Service “Dr. Cesar Milstein” Assistance Unit Buenos Aires Argentina General On-Duty Service—“Por Mas Salud” “Dr. Cesar Milstein” Assistance Unit Buenos Aires Argentina

It is universally accepted that the philosophy of the Tao is the essence that animates the Chinese Cosmogony. Therefore, in last decades I have tried to consolidate its scientific background, looking for solid explanations through Exact Sciences (“Between Heaven and Earth” Scientific Basis of the Action of Shao Yin: Lightning’s Physical-Mathematical Analysis”;“Is Traditional Chinese Medicine Definitely an Exact Science?”;“Euclidean Geometry and Traditional Chinese Medicine: Diving into the Real Origin of the Five Elements”;“Solitons: A Cutting-Edge Scientific Proposal Explaining the Mechanisms of Acupuntural Action”) Currently, research on Chinese medicine leads us—with Dr. Erica Arakaki, collaborator and assistant—to verify through a profound bibliographic review the application of Fibonacci’s golden ratio in the constitution of T’ai Ji Tu, adding yet more substance to the hypothesis of Acupuncture and demonstrating how said Chinese Ancient Science is not only an empirical knowledge but a wisdom derived from the most ancient exact science: Geometry.

关键词： Five Elements Soliton golden ratio Tao Diagram

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The golden ratio

Journal of Modern Physics 2016年第14期7卷 1944-1948页

作者： Csizmadia Jozsef Inovator plus Ltd. Kanjiza Kanjiza Serbia

The Lorentz transformation (if x = ct) is the same the golden ratio: .

关键词： Lorentz Transformation Relativity golden ratio

Walking on Plane and Matrix Square

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Advances in Pure Mathematics 2021年第4期11卷 296-316页

作者： Balasubramani Prema Rangasamy Former Student of Ramanujan Institute for Advanced Study in Mathematics University of Madras Chennai India

We know Pascal’s triangle and planer graphs. They are mutually connected with each other. For any positive integer n, φ(n) is an even number. But it is not true for all even number, we could find some numbers which would not be the value of any φ(n). The Sum of two odd numbers is one even number. Gold Bach stated “Every even integer greater than 2 can be written as the sum of two primes”. Other than two, all prime numbers are odd numbers. So we can write, every even integer greater than 2 as the sum of two primes. German mathematician Simon Jacob (d. 1564) noted that consecutive Fibonacci numbers converge to the golden ratio. We could find the series which is generated by one and inverse the golden ratio. Also we can note consecutive golden ratio numbers converge to the golden ratio. Lothar Collatz stated integers converge to one. It is also known as 3k + 1 problem. Tao redefined Collatz conjecture as 3k − 1 problem. We could not prove it directly but one parallel proof will prove this conjecture.

关键词： Pascal Triangle Euler Twin Prime Conjecture Goldbach Conjecture golden ratio Matrix Square and Collatz Conjecture

Nuclear Fusion Research and Development Need New Relativistic Mass and Energy Corrections Given by the Information Relativity Theory

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Journal of Applied Mathematics and Physics 2022年第5期10卷 1813-1836页

作者： Hans Hermann Otto Materials Science and Crystallography Clausthal University of Technology Clausthal-Zellerfeld Germany

Hundred years after the conjecture of the British astronomer Eddington that the sun is powered by nuclear fusion of hydrogen, new physics theory may help make energy harvesting by nuclear fusion soon a reality. Researchers as well as investors funding fusion megaprojects are asked to deal with new relativistic corrections for mass and energy proposed by Suleiman in his Information Relativity Theory (IRT). These corrections were calculated in this contribution. It will help to decide whether a venture will be successful and to save big investments when in doubt. The assumed optimal kinetic energy for controlled nuclear fusion must be corrected to a somewhat higher level. At very high kinetic energy in the upper GeV range, it remains not enough baryonic mass to be transformed in energy. The fusion probability faded out to zero already at the golden limit of the recession speed of between target nucleon and projectile nucleon. Cold nuclear fusion, if ever possible, is recommended for protons rather than deuterons at highest experimental possible temperatures around 1000 (K) and needs fine-tuned kinetic nucleon energy. It would be also of interest whether a golden ratio based nuclear fuel confinement chamber could be beneficial. In this connection, also cold nuclear fusion setups should be discussed. Nature is governed by the golden ratio and criticality of physical systems influenced by it, and nuclear physics is not an exception. Computer simulations of the underlying controlled nuclear fusion processes should gain profit from IRT corrected starting information and may tackle anew possible low energy nuclear transmutations considering the wave-like dark components of matter and energy.

关键词： Controlled Thermonuclear Fusion IRT Theory Relativistic Mass Correction Low Energy Nuclear Reaction golden ratio golden Limit of Nuclear Fusion

Simple Formulas of πin Terms of Φ

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Journal of Applied Mathematics and Physics 2024年第5期12卷 1904-1918页

作者： Angelo Pignatelli Independent Researcher Roma Italy

The paper presents a novel exploration of π through a re-calculation of formulas using Archimedes’ algorithm, resulting in the identification of a general family equation and three new formulas involving the golden ratio Φ, in the form of infinite nested square roots. Some related geometrical properties are shown, enhancing the link between the circle and the golden ratio. Applying the same criteria, a fourth formula is given, that brings to the known Dixon’s squaring the circle approximation, thus an easier approach to this problem is suggested, by a rectangle with both sides proportional to the golden ratio Φ.

关键词： π Φ golden ratio Squaring the Circle

Non Degeneration of Fibonacci Series, Pascal’s Elements and Hex Series

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Advances in Pure Mathematics 2020年第7期10卷 393-404页

作者： Balasubramani Prema Rangasamy Ramanujan Institute for Advanced Study in Mathematics University of Madras Chennai India

Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.

关键词： Fibonacci Series Lucas Series golden ratio Various Type of Fibonacci Series Generated by Matrices Matrix Operations on Pascal’s Elements and Hex Numbers

Research on Rough Set Model Based on Criteria

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Research on Rough Set Model Based on Criteria