Abstract
In this paper we investigate that most of plants have the symmetric property. In addition, the human body is also symmetric and contains the DNA symmetric base complementarity. We can see the logarithm helices in Fibonacci series and helices of plants. The sunflower has a shape of circle. A circle is circular symmetric because the shapes are same when it is shifted on the center. Einstein’s spatial relativity is the relation of time and space conversion by the symmetrically generalization of time and space conversion over the spacial. The left and right helices of plants are the symmetric and have element-wise inverse relationships each other. The weight of center weight Hadamard matrix is 2 and is same as the base 2 of natural logarithm. The helix matrices are symmetric and have element-wise inverses matrics base on the finite group theory A B = B A = \( I_{N} \). Also, we present human a DNA-RNA genetic code with symmetric base complements A = T = U = 30%, C = G = 20% and C + U = G + A. E. Chargaff discovered yeast and octopus DNA base complement [C T; A G] of four componentry A = T = U = 33% and C = G = 17% of the experimental results. This strongly hinted towards the base pair makeup of DNA, although Chargaff did not explicitly state this connection himself. However, it has not been proved in a mathematical analysis view yet. In this paper, we have a simple proof of this problem based on information theory as the doubly stochastic matrix.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Conway, J.H., Guy, R.K.: The Book of Numbers, Springer, New York (1996)
Lee, M.H.: The Arithmetic Code of Animal-plant, Youngil (2004)
Schneider, M.S.: A Beginners Guide to Constructing the Universe the Mathematical Archetypes of Nature, Art, and Science, Kyeongmunsa (2002)
Chargaff, E., Zamenhof, S., Green, C.: Composition of human desoxypentose nucleic acid. Nature 165(4202), 756–777 (1950). https://en.wikipedia.org/wiki/Erwin_Chargaff
Lee, M.H., Hai, H., Lee, S.K.: A mathematical design of Nirenberg RNA standard genetic code and analysis based on the block circulant jacket matrix. Applied to USA patent No. 62/610, 496, 28 December 2017
Papoulis, A., Unnikrishna Pillai, S.: Probability, Random Variables and Stochastic Process. International Education (2002)
Shannon, C.E.,: A mathematical theory of communication. Bell Syst. Techn. J. 27, 31–423 and 623–656 (1948)
Matthew, H., Petoukhov, S.: Mathematics of Bioinformatics. Wiley, New York (2011)
Lee, M.H., Lee, S.K.: A life ecosystem management with base complementary DNA. In: AIMEE 2018, Moscow, 6–8 October 2018 (2018)
Wani, A.A., Badshah, V.H.: On the relations between Lucas sequence and fibonacci-like sequence by matrix methods. International Journal of Mathematical Sciences and Computing (IJMSC) 3(4), 20–36 (2017)
Bellamkonda, S., Gopalan, N.P.: A facial expression recognition model using support vector machines. Int. J. Math. Sci. Comput. (IJMSC) 4(4), 42–55 (2018)
Hamd, M.H., Ahmed, S.K.: Biometric system design for iris recognition using intelligent algorithms. Int. J. Mod. Educ. Comput. Sci. (IJMECS) 10(3), 9–16 (2018)
Patil, A., Kruthi, R., Gornale, S.: Analysis of multi-modal biometrics system for gender classification using face, iris and fingerprint images. Int. J. Image Graph. Signal Process. (IJIGSP) 11(5), 34–43 (2019)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendix
Appendix
Finite group property
-
1.
The transformation of individuals constituting a group is called an element of a group, and each group includes an identical transformation E.
-
2.
The elements of the group can be multiplied with each other. The multiplication of the elements of the group means successive symmetric transformations. A new element made up of the multiplication of elements is also an element of that group.
-
3.
The multiplication of elements satisfies the associative rule and exists in the same group with the inverse of the element of the given group. The symmetric matrix A is \( AB = BA = I_{N} \) in the complex or finite field, and \( B = \frac{1}{n}(a_{ij}^{ - 1} )^{T} \), and satisfies the property of the Jacket matrix.
Rights and permissions
Copyright information
© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Lee, M.H., Kim, J.S. (2020). A Beautiful Question: Why Symmetric?. In: Hu, Z., Petoukhov, S., He, M. (eds) Advances in Artificial Systems for Medicine and Education III. AIMEE 2019. Advances in Intelligent Systems and Computing, vol 1126. Springer, Cham. https://doi.org/10.1007/978-3-030-39162-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-39162-1_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-39161-4
Online ISBN: 978-3-030-39162-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)