Genetic System, Fibonacci Numbers, and Phyllotaxis Laws

2010 ◽  
pp. 207-221
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Mathematical Biology ◽  
Genetic Code ◽  
Golden Section ◽  
Fibonacci Numbers ◽  
Biological Evolution ◽  
Genetic System ◽  
Huge Number ◽  
Matrix Methods ◽  
Long Time

This chapter describes data suggesting a connection between matrix genetics and one of the most famous branches of mathematical biology: phyllotaxis laws of morphogenesis. Thousands of scientific works are devoted to this morphogenetic phenomenon, which relates with Fibonacci numbers, the golden section, and beautiful symmetrical patterns. These typical patterns are realized by nature in a huge number of biological bodies on various branches and levels of biological evolution. Some matrix methods are known for a long time to simulate in mathematical forms these phyllotaxis phenomena. This chapter describes connections of the famous Fibonacci (2x2)-matrices with genetic matrices. Some generalizations of the Fibonacci matrices for cases of (2nx2n)-matrices are proposed. Special geometrical invariants, which are connected with the golden section and Fibonacci numbers and which characterize some proportions of human and animal bodies, are described. All these data are related to matrices of the genetic code in some aspects.

Taufiqul Hakim “Amtsilati” dan Pengajaran Nahwu-sharaf

1970 ◽  
Vol 11 (3) ◽  
pp. 389-407
Author(s):  
M Misbah
Keyword(s):  
Reading Skill ◽  
Huge Number ◽  
Time Efficiency ◽  
Study Materials ◽  
Long Time

One of skill becoming goals in study Arabic Ianguage reading skill. Someone wish to reach it must mastering various interconnected knowledge, among others Nahwu –Sharaf. This knowledge becomes burden to one whom studying it especially for beginner. This because the huge number of items exist in Nahwu-Sharaf, so that need very long time to mastering it. This Items effectiveness and time efficiency represent the problem in Nahwu-Sharaf learning. These matters become Taufiqul Hakim’s study materials and concern. Finally he found one new format of efficient and effective method and items in learning Nahwu-Sharaf. The Items compiled in his books entitled “Buku Amtsilati” and his method knows as Amtsilati Method. The application of Amtsilati Method in Nahwu – Sharaf learning emphasize the student activeness, with rather few theory but much practice and also delivering items start from easy then gradually reaching difficult ones.

scholarly journals RISKS, DANGERS, THREATS OF “CONTINUOUS” E-EDUCATION

2020 ◽  
pp. 58-62
Author(s):  
T. Yu. Krotenko
Keyword(s):  
Information And Communication Technologies ◽  
Communication Technologies ◽  
Educational Process ◽  
Digital Learning ◽  
Educational Materials ◽  
Huge Number ◽  
Significant Events ◽  
Educational Structures ◽  
Long Time ◽  
Information And Communication

The term “digitalization” for a long time settled in the agenda of significant events dedicated to education. The education system, fulfilling the adopted program, should prepare a huge number of schoolchildren, students and workers for life with the indispensable use of information and communication technologies. However, often the actual digitalization is reduced either to the digitization of educational materials and documents in educational structures, or to unhindered access to the Internet. If the request for digitalization is addressed to education, then, being in the pedagogical space, it would be reasonable to first determine what and how to teach. The problem of the lack of a reasonable psychological and pedagogical concept of digital learning, which could be used by the subjects of the educational process as a basic one, is raised in the article.

scholarly journals On Insolvability of the 4-th Hilbert Problem for Hyperbolic Geometries

2019 ◽  
pp. 1-21
Author(s):  
Alexey Stakhov ◽  
Samuil Aranson
Keyword(s):  
Diophantine Equations ◽  
Hilbert Problem ◽  
Golden Section ◽  
Fibonacci Numbers ◽  
Fundamental Result ◽  
Minkowski Geometry ◽  
Russian Mathematician ◽  
Mathematical Result ◽  
Non Euclidean Geometry ◽  
Elliptic Geometry

The article proves the insolvability of the 4-th Hilbert Problem for hyperbolic geometries. It has been hypothesized that this fundamental mathematical result (the insolvability of the 4-th Hilbert Problem) holds for other types of non-Euclidean geometry (geometry of Riemann (elliptic geometry), non-Archimedean geometry, and Minkowski geometry). The ancient Golden Section, described in Euclid’s Elements (Proposition II.11) and the following from it Mathematics of Harmony, as a new direction in geometry, are the main mathematical apparatus for this fundamental result. By the way, this solution is reminiscent of the insolvability of the 10-th Hilbert Problem for Diophantine equations in integers. This outstanding mathematical result was obtained by the talented Russian mathematician Yuri Matiyasevich in 1970, by using Fibonacci numbers, introduced in 1202 by the famous Italian mathematician Leonardo from Pisa (by the nickname Fibonacci), and the new theorems in Fibonacci numbers theory, proved by the outstanding Russian mathematician Nikolay Vorobyev and described by him in the third edition of his book “Fibonacci numbers”.

scholarly journals A New Method Encryption and Decryption

Webology ◽  
2021 ◽  
Vol 18 (1) ◽  
pp. 20-31
Author(s):  
Ali Abdulwahhab Mohammed ◽  
Haitham A. Anwer
Keyword(s):  
New Method ◽  
Huge Number ◽  
Private Key ◽  
Encryption And Decryption ◽  
Long Time ◽  
Security Guarantees

In all times manual investigation and decryption of enciphered archives is a repetitive and mistake inclined work. Regularly considerably in the wake of investing a lot of energy in a specific figure, no decipherment can be found. Computerizing the unscrambling of different kinds of figures makes it conceivable to filter through the huge number of encoded messages found in libraries and files. We propose in this paper new algorithm has been made to encrypt the information; this algorithm works to shield information from robbery and can't be decrypted in the text. It is taken care of precisely to very accurately to avoid any penetration to arrive at the first text. It tends to be used in companies or some other system; however, it takes a long time to encrypt it. To the first text when encryption to ensure the assurance of information in full and security. Encrypted text contains a unique key, even when stolen. The private key can't be decrypted by the specialist and licensed by the maker of the code in order to protect the data in an excellent manner. While demonstrating in addition much stronger security guarantees with regards to Differential/ direct assaults. Specifically, we are can to provide new Method Encryption and Decryption with strong bounds for all versions.

PARAMETER OPTIMIZATION OF SINGLE EXPONENTIAL SMOOTHING USING GOLDEN SECTION METHOD FOR GROCERIES FORECASTING

2019 ◽  
Vol 4 (2) ◽  
Author(s):  
Vivi Aida Fitria
Keyword(s):  
Golden Section ◽  
Exponential Smoothing ◽  
Food Prices ◽  
Percentage Error ◽  
Boundary Area ◽  
Section Method ◽  
Golden Section Method ◽  
Long Time ◽  
Exponential Smoothing Method ◽  
Single Exponential

Department of Agriculture and Food Security Malang City, especially in the Field of Food Supply Availability and Distribution requires a reference forecasting of food prices in Malang. The method used in the forecasting calculation is Single Exponential Smoothing. In the process of calculating the Single Exponential Smoothing method, it takes alpha parameters between 0 and 1. The problem is when to estimate the alpha value between 0 to 1 with trial error with the aim of producing minimal forecasting results. Therefore, this study aims to determine the optimal alpha value. The method used in this research is the Golden Section Method. The principle of Golden Section method in this study is to reduce the boundary area so as to produce a minimum MAPE (Mean Absolute Percentage Error) value The data used in this study is the price of 9 commodities of Groceries in Malang since January 1, 2016 until December 31, 2017. The results showed that the Golden Section method found that the optimal alpha value was 0.999 with MAPE average of 9 commodities is 0.79%. So with this golden section method researchers do not need a long time to determine alpha by trial error

Exploratory Calibration of a Retail Location Model Using Search by Golden Section

1971 ◽  
Vol 3 (4) ◽  
pp. 411-432 ◽  
Author(s):  
M Batty
Keyword(s):  
Goodness Of Fit ◽  
Spatial Interaction ◽  
Golden Section ◽  
Fibonacci Numbers ◽  
Location Model ◽  
Fundamental Result ◽  
Calibration Methods ◽  
Retail Location ◽  
Two Parameters ◽  
Parameter Values

This paper presents some experiments in calibrating a retail location model designed for the Kristiansand region in southern Norway. The form and behaviour of the model under extremes of its parameter values is first investigated, and then some calibration methods proposed by Hyman are tested. The need for a more general method is evident and a search procedure based on the Fibonacci numbers is outlined. A generalisation of this method, based on the golden section number, is derived and this method is used to explore the sensitivity of the model's goodness-of-fit to changes in parameter values. A fundamental result of these explorations shows that there is no unique fit for retail models with two parameters, and this result is likely to hold for other models of spatial interaction.

Numeric Genomatrices of Hydrogen Bonds, the Golden Section, Musical Harmony, and Aesthetic Feelings

2010 ◽  
pp. 65-90
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Hydrogen Bonds ◽  
Genetic Code ◽  
System Analysis ◽  
Golden Section ◽  
Mathematical Objects ◽  
Symmetric Methods ◽  
Musical Harmony ◽  
New Knowledge ◽  
Hidden Regularities

This chapter is devoted to a consideration of the Kronecker family of the genetic matrices, but in the new numerical form of their presentation. This numeric presentation gives opportunities to investigate ensembles of parameters of the genetic code by means of system analysis including matrix and symmetric methods. In this way, new knowledge is obtained about hidden regularities of element ensembles of the genetic code and about connections of these ensembles with famous mathematical objects and theories from other branches of science. First of all, this chapter demonstrates the connection of moleculargenetic system with the golden section and principles of musical harmony.

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