Branched chain chemical reactions represent a special class of chemical transformation reactions of matter, for the discovery and experimental-theoretical development of which Semenov N. N. and Hinshelwood C. N. were awarded the Nobel Prize in 1956. In nature, such processes are widespread. Objective. To investigate the nature of various numerical sequences of the Fibonacci type and to find out under what conditions they can reflect (express) the patterns of development of branched chain processes. In this work, the state is formulated that branched chain chemical reactions are a particular case of branched chain processes of any nature in different spheres, including biological. It is shown that many branched chain processes can generate numerical sequences of Fibonacci, Lucas, Shannon and others of the same type, which reflect the dynamics of their development. For all the indicated numerical sequences, it is typical that their formation is determined by a general recurrent law, which has been the subject of research for many well-known mathematicians. For each of the indicated numerical sequences they established other laws alternative to the recurrent one, however, they were all of a private nature. They were in accordance with the recurrent law only in the case of one specific sequence. Comparative analysis of many numerical sequences allowed us to find a universal law that is common for all types of sequences and terminologically define it as the law of "doubling with subtraction." For all numerical series the formation of which follows a recurrent law, the law "doubling with subtraction" is equally valid. The opposite is not true since there are numerical sequences that obey only the law of "doubling with subtraction," and the recurrent law is not valid for them. It means that the new law is more fundamental and, in fact, is the primary law and the recurrent law is secondary. Significant differences also exist in the consequences of these two laws. For example, the increments of sequences formed according to the recurrent law and the law of "doubling with subtraction" have fundamental differences in their mathematical expression, although they lead in different ways to the same result, namely, to Ф = 1,618... with the serial numbers of the sequence terms tending to infinity. In the work for each of these laws, a branched chain biological process that was unique to it was found and put in correspondence. In the case of the law of "doubling with subtraction", the process was followed by the termination of chains with characteristic parameters: the chain length is three links, the branching factor is -2. In the case of a recurrent law, the process was without chain termination, with an infinite length and with a branching factor of -2, and with some delay limiting the branching. It seems interesting that such different branched chain processes of different character are described by the same Fibonacci sequence. The processes of branched chain character corresponding to the sequences of Lucas, Shannon, and others are discussed. Conclusions. According to our work, it follows that all formal mathematics, that is, all the mathematical features and patterns related to the Fibonacci sequence is just a description of those features and patterns that are inherent in the branched chain processes that actually produce these and other sequences.
| Published in | Science Journal of Chemistry (Volume 6, Issue 4) |
| DOI | 10.11648/j.sjc.20180604.11 |
| Page(s) | 30-42 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2018. Published by Science Publishing Group |
Branched Chain Processes, Numerical Sequences, Fibonacci Sequences, Lucas Numbers, Recurrent Formula
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APA Style
Yurii Petrenko. (2018). On Branched Chain Processes, the Laws of Development of Which Are Expressed by Numerical Sequences Like Fibonacci Numbers, a New Look at Their Nature. Science Journal of Chemistry, 6(4), 30-42. https://doi.org/10.11648/j.sjc.20180604.11
ACS Style
Yurii Petrenko. On Branched Chain Processes, the Laws of Development of Which Are Expressed by Numerical Sequences Like Fibonacci Numbers, a New Look at Their Nature. Sci. J. Chem. 2018, 6(4), 30-42. doi: 10.11648/j.sjc.20180604.11
AMA Style
Yurii Petrenko. On Branched Chain Processes, the Laws of Development of Which Are Expressed by Numerical Sequences Like Fibonacci Numbers, a New Look at Their Nature. Sci J Chem. 2018;6(4):30-42. doi: 10.11648/j.sjc.20180604.11
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Download@article{10.11648/j.sjc.20180604.11,
author = {Yurii Petrenko},
title = {On Branched Chain Processes, the Laws of Development of Which Are Expressed by Numerical Sequences Like Fibonacci Numbers, a New Look at Their Nature},
journal = {Science Journal of Chemistry},
volume = {6},
number = {4},
pages = {30-42},
doi = {10.11648/j.sjc.20180604.11},
url = {https://doi.org/10.11648/j.sjc.20180604.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjc.20180604.11},
abstract = {Branched chain chemical reactions represent a special class of chemical transformation reactions of matter, for the discovery and experimental-theoretical development of which Semenov N. N. and Hinshelwood C. N. were awarded the Nobel Prize in 1956. In nature, such processes are widespread. Objective. To investigate the nature of various numerical sequences of the Fibonacci type and to find out under what conditions they can reflect (express) the patterns of development of branched chain processes. In this work, the state is formulated that branched chain chemical reactions are a particular case of branched chain processes of any nature in different spheres, including biological. It is shown that many branched chain processes can generate numerical sequences of Fibonacci, Lucas, Shannon and others of the same type, which reflect the dynamics of their development. For all the indicated numerical sequences, it is typical that their formation is determined by a general recurrent law, which has been the subject of research for many well-known mathematicians. For each of the indicated numerical sequences they established other laws alternative to the recurrent one, however, they were all of a private nature. They were in accordance with the recurrent law only in the case of one specific sequence. Comparative analysis of many numerical sequences allowed us to find a universal law that is common for all types of sequences and terminologically define it as the law of "doubling with subtraction." For all numerical series the formation of which follows a recurrent law, the law "doubling with subtraction" is equally valid. The opposite is not true since there are numerical sequences that obey only the law of "doubling with subtraction," and the recurrent law is not valid for them. It means that the new law is more fundamental and, in fact, is the primary law and the recurrent law is secondary. Significant differences also exist in the consequences of these two laws. For example, the increments of sequences formed according to the recurrent law and the law of "doubling with subtraction" have fundamental differences in their mathematical expression, although they lead in different ways to the same result, namely, to Ф = 1,618... with the serial numbers of the sequence terms tending to infinity. In the work for each of these laws, a branched chain biological process that was unique to it was found and put in correspondence. In the case of the law of "doubling with subtraction", the process was followed by the termination of chains with characteristic parameters: the chain length is three links, the branching factor is -2. In the case of a recurrent law, the process was without chain termination, with an infinite length and with a branching factor of -2, and with some delay limiting the branching. It seems interesting that such different branched chain processes of different character are described by the same Fibonacci sequence. The processes of branched chain character corresponding to the sequences of Lucas, Shannon, and others are discussed. Conclusions. According to our work, it follows that all formal mathematics, that is, all the mathematical features and patterns related to the Fibonacci sequence is just a description of those features and patterns that are inherent in the branched chain processes that actually produce these and other sequences.},
year = {2018}
}
TY - JOUR T1 - On Branched Chain Processes, the Laws of Development of Which Are Expressed by Numerical Sequences Like Fibonacci Numbers, a New Look at Their Nature AU - Yurii Petrenko Y1 - 2018/10/11 PY - 2018 N1 - https://doi.org/10.11648/j.sjc.20180604.11 DO - 10.11648/j.sjc.20180604.11 T2 - Science Journal of Chemistry JF - Science Journal of Chemistry JO - Science Journal of Chemistry SP - 30 EP - 42 PB - Science Publishing Group SN - 2330-099X UR - https://doi.org/10.11648/j.sjc.20180604.11 AB - Branched chain chemical reactions represent a special class of chemical transformation reactions of matter, for the discovery and experimental-theoretical development of which Semenov N. N. and Hinshelwood C. N. were awarded the Nobel Prize in 1956. In nature, such processes are widespread. Objective. To investigate the nature of various numerical sequences of the Fibonacci type and to find out under what conditions they can reflect (express) the patterns of development of branched chain processes. In this work, the state is formulated that branched chain chemical reactions are a particular case of branched chain processes of any nature in different spheres, including biological. It is shown that many branched chain processes can generate numerical sequences of Fibonacci, Lucas, Shannon and others of the same type, which reflect the dynamics of their development. For all the indicated numerical sequences, it is typical that their formation is determined by a general recurrent law, which has been the subject of research for many well-known mathematicians. For each of the indicated numerical sequences they established other laws alternative to the recurrent one, however, they were all of a private nature. They were in accordance with the recurrent law only in the case of one specific sequence. Comparative analysis of many numerical sequences allowed us to find a universal law that is common for all types of sequences and terminologically define it as the law of "doubling with subtraction." For all numerical series the formation of which follows a recurrent law, the law "doubling with subtraction" is equally valid. The opposite is not true since there are numerical sequences that obey only the law of "doubling with subtraction," and the recurrent law is not valid for them. It means that the new law is more fundamental and, in fact, is the primary law and the recurrent law is secondary. Significant differences also exist in the consequences of these two laws. For example, the increments of sequences formed according to the recurrent law and the law of "doubling with subtraction" have fundamental differences in their mathematical expression, although they lead in different ways to the same result, namely, to Ф = 1,618... with the serial numbers of the sequence terms tending to infinity. In the work for each of these laws, a branched chain biological process that was unique to it was found and put in correspondence. In the case of the law of "doubling with subtraction", the process was followed by the termination of chains with characteristic parameters: the chain length is three links, the branching factor is -2. In the case of a recurrent law, the process was without chain termination, with an infinite length and with a branching factor of -2, and with some delay limiting the branching. It seems interesting that such different branched chain processes of different character are described by the same Fibonacci sequence. The processes of branched chain character corresponding to the sequences of Lucas, Shannon, and others are discussed. Conclusions. According to our work, it follows that all formal mathematics, that is, all the mathematical features and patterns related to the Fibonacci sequence is just a description of those features and patterns that are inherent in the branched chain processes that actually produce these and other sequences. VL - 6 IS - 4 ER -
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